Menu

CHAPTER ONE INTRODUCTION Background The sun is the ultimate source of energy

CHAPTER ONE

INTRODUCTION
Background
The sun is the ultimate source of energy. All of the living beings in this world receives energy from the sun directly or indirectly. Solar radiation is the best choice and economic energy resource of the globe 1. Solar radiation is the form of energy emitted by the Sun in perpetual amount utilized by human beings with use of several sorts of technologies from the very beginning of the human existence in this world. There are basically two types of solar radiation: first one is the direct radiation received from the sun without being scattered by the atmosphere; second one is the diffused radiation received from the sun with its direction altered due to scattering by the atmosphere. Global solar radiation is regarded as the sum of the direct and diffused radiation on the earth surface. Global solar radiation is crucial parameter employed in most of the ecological models and work as input for several photovoltaic conversion system; therefore, it is significant and economic way of renewable energy development of the nation. The provision to estimate the solar energy potential of a place using global solar radiation that can be transformed into electrical energy to withstand energy demand of that place should be done in prior to generation of electrical energy for any specific location 2. Optimal mobilization of solar resources, as in photovoltaic or thermal concentrators power stations requires the adequate knowledge of solar resource behaviour accurately in those places where the installation of power stations is required 3.
Nepal is a land-locked mountainous country, surrounded from three sides by India and one side by China; having a small area of beautiful landscape situated between latitudes from 26°22′ to 30°27′ North and longitudes from 80°40′ to 80°12′ East within a span of 200 km from south to north and about 800 km from east to west. Within this small and beautiful setting, it possesses diversity in biosphere, climate (arctic/alpine to tropical) and landscape (lowland 72 m to highest peak 8848 m high above the sea level). The total area of the country is 1,47,181 square kilometres and is divided into five physiographic regions: High Himal, High Mountain, Middle Mountain, Siwalik ( Chure Range) and the Terai. It does not have its own coal and petroleum resources so far and has no access to the sea/ocean. For the last six years till now fossil fuel prices have raised an all time-high and the world is driven into its deepest recession since the Great Depression. Geopolitical events are driving prices steadily higher. The short?term risks to political stability and economic activity posed by the world’s dependence on fossil fuels are again as manifest as its long?term threat to environmental sustainability. To break this dependency, all the countries in the world need a clean energy revolution. Such a revolution would enhance global energy security, promote long-term economic growth and tackle environmental challenges such as anthropogenic climate change. Available literature tells that consumption of petroleum products in Nepal is increasing wonderfully at the rate of about 10 % per year. Solar radiation occurs abundantly on every corner of the country. Surface incident solar radiation governs/drives the atmospheric circulations, Earth’s climate and Earth’s biosphere naturally. It is also the originator of all other sources of energy that exists on the face of this earth. The main source of energy even today is the fossil fuels. Solar PV generates electricity as one of the best clean and alternative energies. The average global solar radiation in Nepal varies from 3.6-6.2 kWh/m2/day, sun shines for about 300 days a year, the number of sunshine hours amounts almost 2100 hours per year and average insolation intensity about 4.7 kWhm-2day-1(=16.92 MJ/m2/day) it is greater than 4.23kWh/m2/day (15.23 MJ/m2/day) measured by for Lao PDR. Thus, Nepal lies in a favourable insolation zone in the world even though the data in Nepal was based on one year and few sites but that of Lao PDR was based on few years and throughout the country. So, a long term and many sites solar energy data are required to authenticate this statement4.
The installed capacity of power plants connected to the national grid is 1073 MW in which contribution from Hydropower, Diesel cum multi-fuel and solar energy are 1016 MW, 54 MW and 2.68 MW respectively. Nepal Electricity Authority contributes 562 MW while private sectors contributes rest of 511 MW of electricity. Though the present demand is about 1444 MW, there is deficit in the energy due to increasing population and low rate of electricity generation development 5.
Easily available and inextinguishable nature of solar energy resource resides in one of the imperative places among the various possible alternative energy sources. An accurate data base of solar radiation at particular places and selected sites are required for the development, simulations and designing of many solar energy devices/applications and establishment of solar plants as well .
Under this circumstance and knowing the fact that 52 % of the Nepalese households have no access to electricity, flourishing of solar irradiance data are essential for the development of national rural energy programs in general and for the establishment of solar energy technology in particular. For an extensive investment in these technologies from government and private sectors is not only desirable but it is the ultimate options where there is no viable alternative to the solar electricity 6.
For each second of the solar nuclear fusion process, 700 million tons of hydrogen is transformed into the heavier and helium. The sun has used up about half of the hydrogen found in its core since its formation 4.5 billions years ago. Process also generates heat that leads atoms to discharge photons 7. Temperature at the core is about 15 million degrees Kelvin (15 million degrees C or 27 million degrees F). Each photon that produced travels about one micrometer before being absorbed by an adjacent gar molecule. This absorption then causes the heating of the adjacent atom and it re-emits next photon which traverses a short distance before being absorbed by another atom. This process repeats many times before the photon are emitted to outer space at the sun’s surface. The energy transported more by convection than by radiation for last 20 % of the journey to surface requires approximately 100,000 years or about 1025 absorptions and re-emissions to make the journey from the core to the sun’s surface. The time taken by light to travel from the sun’s surface to the Earth is about 8 minute 20 seconds 7.

Conventional energy sources such as fire-wood, cow dung, coal and fossil fuels (petroleum products) release more CO2 into the atmosphere, causing environmental pollution problems that are directly related to the survival of human beings 8.
Excessive release of greenhouse gases (CO2, CH4, NO2, HFCS) into the atmosphere are causing environmental pollutions. Mean while the terrestrial heat trapped is adversely changing the global air temperature. The main existing problem have forced researcher to develop. The renewable energy resources are the best an option to the fossil fuel 8. Continuous and long term radiation are not available in our nation. But only short term monitoring and mobilization of solar radiation has been performed by then the RONAST in collaboration of JICA Japan 9.
Energy
Energy is defined as the strength to do work. There are several forms of energy. On the basis of long term usage and availability of energy resources, there are two types of energy resources. They are renewable and non-renewable energy resources.
Renewable energy is the energy obtained from the continuing or repetitive currents of energy existing in the natural environment. Obvious examples are solar energy, wind energy, tidal energy, geothermal energy, hydropower etc 8.Solar energy is radiant light and heat from the Sun harnessed using a range of technology such as photovoltaic, thermal, heating etc. Wind energy production is based on instantaneous wind speed fluctuation 10.
The main source of energy arises from oil and coals which is the non-renewable form of energy which means that it will perish some day. Also due to these forms of energy the nature is also being degraded as it contributes to the global warming causing to melting of ice caps and disrupting nature 11. Similarly, natural gas, heating oil, propane are some of the examples of non-renewable energy 12.
Energy Scenario of Nepal
Energy is crucial to all sort of development targeted at human welfare including agriculture, household, transport, industrial, commercial and educational sectors which really helps to improve the quality of life. The rate of energy consumption per capita is considered as note worthy indicators of civilization. The energy consumption is also directly connected with socioeconomic activities as well as round development of Nepal 13.
Nepal’s economic and social development is being disturbed by its insufficient energy supply. The country is not independent on its reserves of gas, coal or oil. Though its most significant energy source is water, nearly less than one percent of potential 83,000 megawatts of hydropower is currently being generated. Firewood is the predominant energy carrier, counting for more than 70 percent of consumption .However its use is inadequate and poses a threat to the country’s forests. Meanwhile, the indoor pollution produced by open hearths in homes presents a hazard to health. Mains electricity is generally only available in urban areas and some 30 percent of the population does not have access to it 14.
In comparision with other nations, Nepal has high energy consumption in relation to its gross domestic product (GDP). It does not yet have a strategy for sustainable, efficient energy use for the electricity sector or its main primary energy source, biomass. The power supply is particularly critical during the dry season, during which it is cut off for several hours a day, which has a negative impact on business and private households. Private households, the public sector as well as commerce and industry sector are largely unaware of the economic and ecological advantages of efficient energy use. There are no standards for energy saving domestic appliances lighting or products and processes in industrial use.The persistence of weather events and the effect this has on the availability of solar radiation energy can influence various solar energy applications. Particularly, the persistence of the solar energy can affect energy storage requirements and the need for backup energy sources15.
Table 1.1. Share of Energy consumption in Nepal by fuel type (Year 2073/74) 16
(Total consumption =499.839 million GJ)
S. No. Fuel Type Consumption Percentage
1 Agricultural residue 3.3
2 Animal dung 3.5
3 Hydro Power 4.1
4 Coal 4.0
5 Petroleum 13.8
6 Renewable 3.5
7 Fuel wood 70.47

Nepal have been fulfilled, partly from hydropower, bio-gas, fossil fuels and traditional energy sources such as firewood, cow dung and coal. The use of renewable energy is negligible. Conventional energy sources such as fire wood, cow dung, coal and fossil fuels release more CO2 into the atmosphere, causing environmental pollution problems.
Power crisis in Nepal has been miserable for years. Development of renewable energy such as solar energy and its considerable use in Nepal can significantly support energy demand and contribute to lower air pollution 8.The rapid depletion of energy resources, increasing energy demand and degeneration of ecological values requires an urgent solution in this age. Solar energy as the most important energy resource has become part of the solution to the world’s energy challenges.
Energy utilization is the most important input parameter for economic growth and social development of the countries. Fossil fuels are still major primary energy resource even though their environmental demerits and limited lifetime. Due to awareness of the people on the disadvantage of fossil fuel usage has been increasing day by day and it strikes people’s mind to think about renewable energy resources. Solar radiation which arrives to the earth surface every year is nearly 160 times greater than all known fossil fuel reserves discovered till now 17.
Solar and Wind Energy Resources Assessment (SWERA) reported an annual average of 4.7 kWh/m2/day solar energy is available in Nepal. This indicates that Nepal is rich in solar energy 18.
There is no more solar energy fluctuation in Pokhara in a whole month. It reflects that the local weather condition remains stable as compared to other stations. In this site the solar energy varies from 6.95 MJ/m2/day to 16.22 MJ/m2/day. The overall average energy is about 14.32 MJ/m2/day 19.
Overall energy supply situation has remained encouraging in the fiscal year 2016/2017. Of the total energy consumption of 8,257 Tons of Oil Equivalent (TOE) in the first eight months of the fiscal year 2016/2017, the contribution of traditional , commercial and renewable energy stood at 74.5 percent, 22.0 percent and 3.5 percent respectively. During the same period , electricity generation has increased by 12.3 percent (105.3 Megawatts) reaching a total of 961.2 Megawatts. Electricity leakage has decreased by 2.8 percentage points. As a result, Kathmandu and Pokhara have been made load shedding free zones while load shedding hours have been reduced in other areas as well 20.
Short term monitoring and utilization of solar radiation has been done by the then RONAST in collaboration of JICA, Japan. They installed the 4 KW prototype and 40 kW solar photovoltaic panels at Sunderighat, Kirtipur and Bode, Bhaktapur for the purpose of water pumping in 1992 and 1995 respectively 21.
1.4 Solar energy
Solar energy is a form of energy representing a safe, economic, environmental and renewable energy form is regarded as the alternative energy to improve the energy structure of Nepal22. Solar photovoltaic systems, Solar Photovoltaic water pumping systems, Solar thermal water heaters are some of the solar technologies that have been used in the country. Also solar thermal space heating and illumination in buildings are already in practice. The contribution to the national grid by solar energy is 2.68 MW. However accounting the sum with utilization of Photovoltaic panel in 7,94,276 homes to generate electricity at household purpose is more than this value 23. Also, solar thermal technologies such as solar water heating systems, solar dryer, solar cookers are being utilizing in different parts of our nation. An estimated 17,265 households, 270 commercial establishments and 26 public institutions are now using solar water heaters (SWH) 9.
Solar Radiation
Solar radiation is an electromagnetic wave emitted from the Sun’s surface that originates in the bulk of the Sun where fusion reactions convert Hydrogen atoms into Helium. 3.89×1026 J of nuclear energy is released by the Sun’s core every second. This nuclear energy flux is rapidly transformed into thermal energy and transported toward the surface of the star where it is released in the form of electromagnetic radiation. The power density emitted by the sun is of the magnitude of 64 MW/m2 of which approx. 1370 W/m2 enter the top of the Earth’s atmosphere with no significant absorption in the space 22.
Solar radiation is widely appreciated because of its effect on living matter and the possibility of its application for the useful purposes. It is a perpetual source of natural energy in addition with the other forms of renewable energy has a great potential for a wide variety of applications. The solar radiation characteristics at ground level depends on the altitude, local weather condition. Therefore, while designing solar energy conversion systems, both the quality and the quantity of solar radiation at that location should be considered.
The solar radiation going through the atmosphere is partially reflected back to space and partially absorbed by its constituents, partially diffused, with the remaining reaching the ground absorption and diffusion of solar radiation by the usual constituents of the atmosphere, aerosol particles and water also absorb and cause diffusion and re-emission of solar radiation quite significantly. The annual average GSR in Pokhara is 4.87 kWh/m2/day 13.
Global Solar Radiation
The quantity of solar radiation received by earth’s surface without any change in the direction of straight line without regards to the sun is known as direct solar radiation. Direct solar irradiance is a measure of the rate of solar energy arriving at the Earth’s surface from the Sun’s direct beam, on a plane perpendicular to the beam, and is usually measured by a Pyrheliometer mounted on a solar tracker 13.
Diffuse solar energy is the result of the atmosphere reducing the magnitude of the sun’s beam. Some of the energy removed from the beam is scattered towards the ground at the rate at which this energy falls on a horizontal surface per second is called the diffuse solar irradiance 19. Diffuse solar irradiance is measured by a Pyranometer, with its glass shaded from the sun’s beam. The diffuse irradiance is given by
I_d?=I_dr?+I_da?+I_dm? (1.1)
The sum of direct and diffuse solar radiations on a horizontal surface is called global solar radiation. It depends on geographical and atmospheric parameters. The global spectral irradiation flux G? is given by
G_?=I_n? sin???_z ?+I_d? (1.2)
Where, I_d? is diffused solar radiation andI_n? is direct solar radiation.
The total global solar radiation on the horizontal surface is given by
G=?_0^???G_(? ) d?? (1.3)
Factors affecting Solar Radiation
The solar energy availability depends upon time. The variation in availability occurs daily because of the day night cycle, seasonally due to the rotation of earth around the sun and also eleven year solar cycle. There are basically two types of affecting factors of GSR on earth. One of them is geophysical parameters which are tentatively constant over and over a year because of fixed parameters. However other factor directly or indirectly influence GSR due to the interaction with atmospheric constituents and local environment as well.
In short, the solar radiation depends on the following factors:
The geometry of the Earth (declination, latitude, solar hour angle)
The terrain characteristics (elevation, albedo, surface inclination and orientation, shadows)
The atmospheric attenuation (scattering, absorption) caused by gases, particles and clouds 24.
Solar irradiance is attenuated spectrally when passing through the atmosphere and it is strongly dependent on sky under cloudless conditions. The prevailing winds, which may carry moisture or aerosol particles from distant sources, play a major role in the seasonal variation of solar radiation. Solar radiation availability on the earth’s surface is the main fundamental renewable energy source in nature 25.
Earth’s atmosphere
In order to know about the interaction of the earth’s atmosphere with solar radiation, the study of the composition and the structure of the atmosphere is of high importance. Due to the gravity of the earth , it holds the atmosphere comprising of layers of gases surrounding the earth surface. If the gravity is to be subjected is high and the temperature of the atmosphere is low then an atmosphere is likely to be retained. The advantage of the atmosphere is to protect life on the earth by absorbing the ultraviolet radiations through its successive layers and is to warm the surface through heat retention. Also it reduces the temperature extremes between day and night 26.

Composition of Atmosphere
The Earth’s atmosphere has its major composition of Nitrogen, Oxygen and Argon. The rest of the gases are considered as trace gases including greenhouse gases viz. Carbon dioxide, Methane, Nitrous oxide and ozone. Filtered air comprises of trace amount of many other chemical compounds. Many substances of natural origin may be present in locally and seasonally variable small amounts as aerosols in an unfiltered air sample, including dust of mineral and organic composition, pollen and spores, sea spray, and volcanic ash. Different industrial pollutants also may be present as gases or aerosols, such as Chlorine, Fluorine compounds and elemental mercury vapour. Sulphur compounds such as Hydrogen sulphide and sulphur dioxide may be derived from natural sources or from industrial air pollution 27.

.

Table 1.2 Composition of Atmosphere 26
S. No. Constituents gases Content(% by volume)
1 Nitrogen (N2) 78.084
2 Oxygen (O2) 20.948
3 Argon (Ar) 0.934
4 Carbon dioxide (CO2) 0.033
5 Neon (Ne) 0.018
6 Helium (He) 0.000114
7 Krypton (Kr) 0.0000089
8 Xenon (Xe) 0.00005
9 Hydrogen (H2) 0.00015
10 Methane (CH4 0.000027
11 Nitrous oxide (NO) 0.000019
12 Carbon monoxide (CO) 0.000524
13 Water vapour 0-0.04
14 Ozone (O3) 0-0.0012
15 Sulphur dioxide (SO2) 0-0.0000001
16 Nitrogen dioxide (NO2) 0-0.0000001
17 Ammonia (NH3) 0-0.0000004
18 Nitric oxide (NO) 0-0.00000005
19 Hydrogen Sulphide (H2S) 0-0.000000005
20 Nitric acid vapour (HNO3) Trace

Dry Atmospheric Air
It comprises basically of four gases viz.O2,N2,Ar,CO2 called permanent gases. Depending on the latitude, wind, urban site and season, concentration of these components varies. Ozone is a particular element to be considered in the phenomenon of absorption of solar radiation which absorb almost ultraviolet radiation thereby protecting the earth and its living creatures from high-energy radiations. The amount of Ozone depends on latitude and season which is significant in the area between 15 and 30 km. In the upper atmosphere, Ozone is created by UV radiation from the Sun28 .
Atmospheric Water
The water in the atmosphere is mainly localized in the lower 10 km of the atmosphere. It comes from the evaporation of water from the surface of the earth, the oceans and seas. Its concentration varies so widely. Water is found as gas molecules, a liquid and solid forms in the clouds. For ozone, its effect on solar radiation is important and should determine its atmospheric content. The total optical thickness of the water vapour at the site studied is to say on the total weight of water vapour. The height of the perceptible water depends on the ability of the air to contain water vapour and therefore its relative humidity and temperature which varies from 0.1 to 1 cm in the poles and in the desert where the air is dry , 2 to 5 cm in temperate climates and greater than 5 cm in tropical climates28.
Aerosols
One of the prominent factor affecting the amount of solar radiation reaching the earth’s surface under cloudless sky condition is the presence of aerosol particles in the atmosphere. Its number or mass concentration is a key parameters in the studies of atmospheric radiative effects. They are present in both troposphere ; stratosphere and mostly throughout the atmospheric boundary layer at number concentration depending upon factors such as location, atmospheric conditions, annual and diurnal cycles and presence of local resources29.
Aerosols are the suspensions of liquid and solid particles in the atmosphere, excluding clouds and precipitation. The aerosol particle sizes ranges from 10-4 to 10 mm, falling under the following broad categories: sulphates, black carbon, organic carbon, dust, and sea salt. Aerosol concentrations and composition vary considerably with time and location. The visual range can vary from a few meters to 200 km, depending on the proximity to sources, the strength of the sources, and atmospheric conditions.
Aerosol particles in the atmosphere are produced both in nature and by people. A global aerosol optical depth of about 0.12 is suggested. The aerosol increase the reflected solar radiation at the top of the atmosphere by about 3 Wm-2 globally.At present the absorption and scattering of solar radiation by aerosols have been recognized as important parameters for climate change. A way of probing the atmosphere from the ground is to measure the effect of atmosphere to sunlight transmitted to the earth’s surface30.
It influences the earth’s climate by modifying its energy balance through the direct, indirect and semi-direct effects31. This is because the aerosol physical, chemical and optical properties are highly variable in space and time, because of the short atmospheric lifetime of aerosols and of their inhomogeneous emission. The estimation of aerosol optical properties for very clean atmospheric conditions with low content of aerosol particles, is highly uncertain, especially in regard to the Angstrom wavelength exponent 32.
Clouds
The study of characteristics and location of clouds are key point to understand climate change. Low, thick clouds reflects solar radiation and cool the surface of the earth. High , thin clouds primarily transmit incoming solar radiation ; meanwhile, they trap some of the outgoing infrared radiation emitted by the earth and radiate it back downward, thereby warming the surface of the earth. Whether a given cloud will heat or cool the surface depends on several factors, including the cloud’s altitude, its size and the make-up of the particles that form the cloud. The balance between the cooling and warming actions of clouds is very close although, overall, averaging the effects of all the clouds around the globe, cooling predominates 32.
The attenuation of GSR by cloud depends on wavelength. It is necessary to know that the GSR amount changes nonlinearly with cloud amount. However, for non-obscured sun, there can be an enhancement up to 25 % under broken cloud condition, where scattering from sides of the cloud becomes equally important 33. Clouds affect UV level on the ground and can be estimated by comparing measured data with clear sky modelled data. The daily dose variability caused by clouds assuming constant aerosol concentration can be found in the range of 5-25% 34. The influence of cloud and aerosol on UV can be found from the differences of ground measured daily dose and calculated clear sky dose.

Structure of Atmosphere
The Earth’s atmosphere consists various layers that can be defined according to air temperature. (Figure 1.4) shows these layers in an average atmosphere. Based on the temperature, the atmosphere contains four different layers.

Figure 1.1 Schematic representation of Atmospheric Condition 35.
Troposphere
It extends from depth 8 to 16 kilometres. Greatest depths exist at the tropics where a warm temperature leads to vertical expansion of the lower atmosphere. From the tropics to the Earths polar Regions the troposphere thickness decreases gradually .The depth of this layer at the poles is nearly half thick compared to the tropics . Average depth of the troposphere is approximately 11 kilometres as shown in Fig. 1.4. About 80% of the total mass of the atmosphere lies in troposphere .It is also the layer where the most of the weather occurs. Near the Earth’s surface maximum air temperature occurs in this lays . Air temperature drops uniformly with altitude at a rate of approximately 6.50 Celsius per 1000 meters with increase in height. This phenomenon is commonly known the Environmental Lapse Rate. At the top of the troposphere the average temperature is -56.50C. A narrow transition zone called as the tropopause is located at the upper edge of the troposphere 6.

Stratosphere
Just above the troposphere , stratosphere begins which is the second-lowest layer of Earth’s atmosphere and is separated from troposphere by the tropopause. This layer extends from the top of the troposphere at roughly 12 km above Earth’s surface to the stratopause at the height of about 50 to 55 km.
At the top of the stratosphere the atmospheric pressure is roughly 1/1000 times the pressure at sea level. It contains the ozone layer, which is the part of Earth’s atmosphere that contains relatively high concentrations of that gas. The strastosphere is a layer in which temperature rise with increasing altitude. The elevation in temperature is caused by the absorption of ultraviolet radiation (UV) radiation from the sun by the ozone layer. Although the temperature may be -600C at the tropopause, the top of the stratosphere is much warmer, and may be near 0oC.The stratospheric temperature profile creates very stables atmospheric conditions, so the stratosphere lacks the weather-producing air turbulence that is so prevalent in the troposphere. Consequently the stratosphere is almost completely free of clouds and other forms of weather . However, polar stratospheric or nacreous clouds are occasionally observed in the lower part of this layer of the atmosphere where the air is coldest. The stratosphere is the highest layer that can be accessed by jet-powered aircraft 1.
Mesosphere
The layer of the earth’s atmosphere that is directly above the stratosphere is the mesosphere this layer temperature decreases as the altitude increases. Mesosphere is the third layer of atmosphere and located between stratosphere and thermosphere which extends from the altitude of 50 km to 80 km above the earth’s surface. The streaks of hot gases released from meteors can be seen in this layer. The temperature of this layer decreases with increases in altitude that is from -20C to -1900C. therefore it is the coldest place on the earth and has an average temperature about -850C water vapor is frozen due to the cold temperature of the mesosphere then formed ice clouds. The main fas found in this layer is nitric oxide (NO). strong wind blows from the west to the east during winter and from east to west during spring season in this layer 27.

Thermosphere
It is the second-highest layer of Earth’s atmosphere which extends from the mesopause at an altitude of about 80 km up to the thermopause at an altitude range of 500-1000 km. the height of the thermopause varies considerably due to changes in solar activity. As the thermopause lies at the lower boundary of the exosphere, it is also referred to as theexoobase. The lower part of the thermosphere, from 80 to 550 kilometres above Earth’s surface, contains the ionosphere.
The temperature of the thermosphere gradually increases with height. Unlike the stratosphere beneath it, wherein a temperature inversion is due to the absorption of radiation by ozone, the inversion in the thermosphere occurs due to the extremely low density of its molecules. The temperature of this layer can rise as high as 15000C, though the gas molecules are so far distant that its temperature in the usual sense is not very meaningful. The air is so rarefied that an individual molecule travels an average of 1 kilometre between collisions with other molecules. Although the thermosphere has a high proportion of molecules with high energy, it would not feel hot to a human in direct contact, because its density is too low to conduct a significant amount of energy to or from the skin 1.
Exosphere
It is the fifth and outermost layer of the atmosphere which extends beyond the thermosphere. The temperature of this layer is very high about 1200 to 6000 degrees Centrigrade. The density of air is very low but wind blows at high speed. This layer mainly comprises of very lighter gases like hydrogen and helium, the particles are much more far apart so that they can traverse hundreds of kilometre of distance without any collision with each other and hence, particles rarely collide. The atmosphere no longer behaves like a fluids, these freely moving particles follow ballistic paths and may travel into and out of the magnetosphere or the solar wind. This layer is very far from the earth’s surface so there is no effect of gravity so that air particles may escape from atmosphere 27.

Figure 1.2 Variation of temperature with altitude www.wikipedia.org
Air mass
Air mass defines the direct and optical path length through the earth’s atmosphere; it represents how much atmosphere solar radiation has to pass through before reaching earth surface . Air mass coefficient can be used to help characterize solar spectrum after solar radiation has travelled through the atmosphere. Air mass (AM) equals 1.0 when the Sun is directly overhead at sea level. “AM 1.5” is almost universal when characterizing terrestrial power-generating panels.
The attenuation caused by atmospheric constituents through the relationship between global, direct and diffuse solar radiation with respect to optical air mass can be studied. The optical air mass change has spatial and temporal dependence and influences the radiations flux incident, causing changes in the Global, diffuse and direct solar irradiances 36. The decrease of solar radiation with increase of optical air mass is justified by the increase in the probability of the collision of solar rays with atmospheric constituents 37.

Solar Zenith Angle
Solar zenith angle (SZA) is the angle between the zenith and the sun which is useful in determining whether the sun is rising or setting and also in predicting solar effects on radio communications. Smaller is the solar zenith angle, the higher is the sun is in the sky. As the sun rises, The angle gradually decreases until mid-day. As SZA increases, radiation falling on a horizontal surface on the earth decreases. The value of the Solar Zenith Angle is dependent on the position on the Earth and the local date and time. The incident radiation is directly proportional to the cosine of angle between the beam radiations and normal to the surface leading to cosine effect 36.
Precipitation
Precipitation is defined as liquid or solid condensation of water vapour falling from clouds or deposited from air into the ground. Precipitation is measured as the amount of water that reaches horizontal ground or the horizontal ground projection plane of the earth’s surface, and is expressed as a vertical depth of water or water equivalent of solid precipitation. The unit of precipitation in Nepal is milimeter. Instruments for measuring precipitation is rain gauge precipitation in the form of ice takes, such as show, is called solid precipitation , and that in the form of water drops is sometimes called as liquid precipitation.
The annual precipitation in Nepal varies from place to place ranging from less than 250 mm in mustang area to more than 5000 mm at Lumle near south west of Pokhara 80% of rainfall is found in monsoon season i.e. from June to mid of September. The sky is partially or fully covered with clouds in the summer season thus there is less solar radiation in rainy and cloudy day which might be due to the absorption and reflection of radiation by clouds, aerosols and rain droplets in the atmosphere 13.

Relative Humidity
The relative humidity is a major effecting factors of GSR. It is the ratio of the partial pressure of water vapour to the equilibrium vapour pressure of water at a particular temperature . Relative humidity depends on temperature and the pressure of the system under study. It needs less water vapour to get high relative humidity at low temperatures; more water vapour is essential to attain high relative humidity in warm or hot air. It is known that higher rainfall location have higher value of humidity and relative humidity absorbs the radiation in the atmosphere. Thus values of GSR are found to be lower at a location of higher relative humidity. Hence the relative humidity and GSR is inversely proportional to each other 13.
Altitude
Altitude is one of the major factor influencing the GSR. The GSR increases in altitude mainly due to decreasing amounts of air molecules, ozone, aerosols and clouds in the atmosphere as well as due to show covered surface. Thus, there is not only the single source depending factor. Ignoring those effects , at higher altitude there is dependence of GSR on SZA and wavelength changes. A significant part of global population resides at altitude of up to a few kilometers above the sea level. Simply, the increases in solar radiation flux with respect to height is called the altitude effect 38.
Solar radiation increases at higher altitudes as the atmospheric has less chance to absorb the incoming UV. It has been found that UV increases by up to 4% for every 300m increases in altitude.
Sunshine duration
Sunshine duration is now a days taken as factor for the important determination of global solar radiation data. It is also the parameter with the correlation with global solar radiation, air temperature relative humidity and other climate factor. Sunshine duration during a given period (e.g. within one day) is considered as the sum of the time for which the direct solar irradiance exceeds 120 W/m2. For precise measurement , the sunshine recorder must be accurately adjusted for planar labelling, meridian direction and latitude 39. Sunshine duration is used to measure the percentage ratio of recorded bright sunshine duration and daylight duration for the estimation of GSR in empirical models. Due to financial constraints , there is not adequate numbers of sunshine recorders installed in our country Nepal. The average daily sunshine duration for Nepal has been reported to be 6.8 hours per day from various measurements.

Attenuation of Solar Radiation
The phenomena in which process of coming the radiation on our eye through scattering and re-direction from the atmosphere constituent is known as atmospheric attenuation. Solar radiation is partially depleted and attenuated when it travels through the layers of atmosphere, preventing a substantial portion of it from reaching on the earth’s surface. This phenomena is given by the Bouger’s law or Beer’s law 33 .
Consider I0n? is normally incident monochromatic extraterrestrial irradiance at mean sun-earth distance (r0) and ? is the flux emerged on traversing a distance ‘m’ then according to Beer’s law.
I_0n?=I_on? exp?(-k_? m) (1.4)
Where k_? is the monochromatic extinction or attenuation coefficient.
‘m’ is the optical path length and
k_? m is the monochromatic extinction optical thickness.

Absorption
When the molecules absorb the photon , it increases the energy of the molecules. Oxygen and nitrogen which together constitute 99% of the atmosphere volume, absorbs strongly fraction of the solar radiation having the wavelength shorter than about 0.3 ?m. The very short wavelengths ionize the gas molecules. Other wavelength in the ultraviolet are absorbs by ozone in the layer between 20 and 50 km above of the earth. Different molecules absorbs the different wavelengths of radiation. For examples, O2 and O3 almost wavelengths shorter than 300 nm 39.
The gases that comprises our atmosphere are selective absorbers of radiation because each gas absorbs only particular wavelengths of light. The atmosphere absorbs far better in the long wave end of the electromagnetic spectrum which is the region of maximum emission (10 ?m) for the earth.

Atmospheric Scattering
As sunlight penetrates the atmosphere it may be absorbed, scattered, reflected or refracted before reaching the surface. Scattering is a result of the interaction between the electromagnetic field of the incoming light with the electric field of the atmospheric molecules and aerosols. This interaction is synchronized and as a result the scattered light has the same frequency and wavelength as the incoming light. Scattering differs with particle size and varies with wavelength. For this reason , the spectral composition of the scattered light differs from that of the incoming light. The attenuation of light in the atmosphere is caused by absorption and scattering , and can be divided into effects that remove and add light to a given viewing ray. The amount of scattered energy depends strongly on the ratio of particle size to the wavelength of the incident wave 13.
x= 2?r/? (1.5)
where ? is the wavelength of incoming radiation and r is the radius of scattering particles. Depending upon the size of particles, scattering can be categorized as given below:
Rayleigh scattering
Mie scattering
Non selective scattering

Rayleigh Scattering
If the size of scattering particles is small compared to the wavelength of incident radiation (r ? ?/10), the scattered intensity on both forward and backward direction is same. This type of scattering is referred to as Rayleigh scattering. This type of scattering is therefore wavelength dependent. As the wavelength decreases, the amount of scattering increases. Because of Rayleigh scattering, the sky appears blue. This is because blue light is scattered around four times as much as red light, and UV light is scattered about 16 times as much as red light. This solution is given by at the end of century by Lord Rayleigh and simply called as Rayleigh’s theory 40.
?=(8?^3 (?n-1)?^2)/(3N??^2 ) (1.6)
where, ? is the refractive index of the particle
?=1.29 kg/m3 is the density
N=2.28×?10?^25/kg is the number of molecules
? is the wavelength of light
n=1.008735?^(-4.08)
where ? is being in micrometer unit. Rayleigh scattering is the consequence of why sky appears blue. From Rayleigh relation , blue coloured light is scattered more than red , orange , green and yellow 41.
Mie Scattering
In Mie scattering the light is scattered forward and is highly anisotropic 41. The Rayleigh theory is not applicable when the particle dimension is comparable to the wavelength of incident radiation. In such case wave equation needed to solve wave equation so at the beginning of the 20th century Gustav Mie and in his honour the theory is named as Mie’s theory. Both reflected and scattered intensity in Mie scattering is greater than in Rayleigh scattering.
Angstrom gave the Angstrom’s turbidity coefficient. And ? is being wavelength coefficient with wavelength ?. For larger particles if (r ??/10), the angular distribution of scattered intensity becomes more complex with more energy scattered in the forward direction. This type of scattering is described by Mie scattering theory 27.
1.13.5 Non Selective Scattering
It is the third type of scattering which occurs in the lower portion of the atmosphere when the particles are much larger than the incident radiation. This type of scattering does not depend upon wavelength and is the primary cause of haze 39.
Reflection
When the change of the propagation environment, a part of the electromagnetic wave reflected again towards the original environment. Each body which receives an amount of EMR may reflect a part. Reflected radiation is mainly reflected from the terrain and is , therefore, more important in mountainous region. The fraction of the intensity of solar radiation that is reflected is called the albedo of the surface. Reflection is a process where sunlight is redirected by 1800 after it strikes on atmospheric particles. The reflection of solar radiation depends on the nature of the reflecting surface. For solar radiation, albedo is dependent of clouds and ground surface 31.
Albedo
The albedo of a surface is the part of the incident sunlight that the surface reflects. Radiation that is not reflected is absorbed by the surface. The absorbed energy increases the surface temperature, evaporates water, melts and sublimates snow and ice , and energizes the turbulent heat exchange between the surface and the lowest layer of the atmosphere. The surface albedo is a key ingredient in the remote sensing of surface and atmospheric properties from space. The spectral and angular dependence of reflected sunlight is used to inter surface properties such as the extent and nature of vegetation cover. It must also be allowed for when determining atmospheric composition such as the amount, size, and optical properties of haze particles. Over continents, the largest component of the reflected sunlight under cloud-free conditions is due to reflection by the surface. As a consequence the determination of atmospheric composition from reflected sunlight needs proper knowledge of the contribution made by the reflecting surface 1.
Different surfaces have different albedo. Oceans , lakes, and forests reflect relatively small fractions of the incident sunlight and have low albedos while snow, sea, ice, and deserts reflect relatively large function of the incident sunlight and have large albedos. It should be noticed that an albedo is not an intrinsic property of a surface. Instead for any surface, the albedo depends on the spectral and angular distributions of the incident light, which in turn are governed by atmospheric composition and the direction of the beam of light from the sun 42.

Table 1.4 Albedo of surface with sun over our head 42
S. No. Surface Albedo
1 Vegetation 0.2
2 Light color soil 0.3
3 Dark color soil 0.1
4 Water 0.1
5 Clouds/snow 0.5-0.9

Review of Literature
Solar radiation is a renewable energy sources that has been used throughout the history of human beings. Passive solar technologies were already used by ancient civilizations especially for warming and heating. Concentration of solar radiation was extensively studied and in the 19th century the first solar-based mechanical engines were built. Now-a-days, there exist an extremely large variety of solar technologies that are applied around the world. Many paper have been published regarding the global solar radiation in Nepal. The more radiation more energy is produced. In Nepal the study of solar radiation is not old.
But there are some report found to measurement of solar wind energy resources assessment reported the annual average of 4.7 kWh/m2/day and 4.23 kWh/m2/day solar energy available in Nepal. The present of energy demand of Nepal have been fulfilled partly from hydropower, biogas, fossil fuel and traditional energy sources such as fire, wood and coal 13,43. The use of renewable energy is negligible. Renewable energy is the energy obtained from the continuing of repetitive currents of energy occurring in natural environments. Obvious example of renewable of energy is solar energy. Continuous and long term radiation are not available in Nepal. But short term and monitoring and utilization of solar radiation has been done by royal Nepal academy of science and technology (RONAST) in collaboration of Japan 9.
Alternative energy promotion centre (AEPC) under the government of Nepal has conducted a project solar and wind energy resources assessment (SWERA) under united nations environment program (UNEP)/Global environment fund (GEF) from march 2003 to 2006. The study recommended the annual average solar insolation of about 4.7kWh/m2/day in Nepal. SWERA report showed that there is lower solar radiation potential at low altitude plain region than at high altitude mountains and north western part of the country 43. The solar resource map developed by DLR Germany satellite estimates 3.5-4 kWh/m2/day of energy at the central mid hill region and higher energy of 5-5.5 kWh/m2/day is found in the north western region. Similarly, the solar map report of national renewable energy laboratory (NREL) USA shows that there is almost equal amount 4.5 to 5 kWh/m2/day of solar radiation found throughout the country. But in north-western region of Nepal the solar insolation is found to be 6-6.5 kWh/m2/day based on the results of the measurements carried out by SWERA. These solar resources satellite derived DLR and NREL solar resource maps are compared with the ground level measured data of 4 sites. The relative bias-ness of the model data with respect to the ground level measured data is analyzed considering point to point as well as region monthly and annual variation. It shows that within a particular point of location, DLR satellite data has higher relative biasness in comparison to NREL data 44.
In India also various researchers developed and investigated correlations in monthly mean global solar radiation and relative duration of sunshine (Modi ; Sukhatme, 1979; Garg ; Garg, 1985). Due to high solar potential and large number of clear sky days, Rajasthan is suitable region for installation of solar energy devices. Intensity of global solar radiation in ranging between 66.4 kWh/m2/day in about half of Rajasthan, but literature survey reveals that very few studies have been done about solar radiation correlations for this region except for Jodhpur (26.30? N, 73.02? E) which is situated in west region of Rajasthan (Modi ; Sukhatne 1979). Jaipur(26.92?N, 75.87?E) is the capital city of Rajasthan and having annual average of mean daily global solar radiation (19.42 MJ/m2/day). which is comparable to annual average of mean daily global solar radiation at Jodhpur (19.97 MJ/m2/day) 28.
Nepal is located in favourable latitudes receives ample solar radiation throughout the country. The average global solar radiation varies 3.6-6.2 kWh/m2/day and sunshine about 300 days in year. The national average sunshine hour and solar energy 6.8 kWh/m2/day and 4.7 kWh/m2/day respectively 45. It is greater than the 15.8 MJ/m2/day measured by Solar Energy Research Laboratory, Department of Physics, Silpakorn University, Thailand for Lao PDR. Choice of solar energy, in country like Nepal, is the best and ultimate option among the different energy including alternative energy sources. If we think of complete solution of rural electrification in Nepal, we have to plan to link up micro-hydro/pico-hydro with solar energy exploitation. Thus , an accurate knowledge and database of solar radiation at a particular place and selected sites are important for the development of many solar devices, the establishment of solar plant at the proposed site and for estimation of their performance 46. The radiation reaching the earth surface is modified significantly by clouds, water vapour, ice, aerosols, and atmospheric constituents in its intensity and the sun-shine duration. The beam radiation (radiation coming directly from the solar disk) is attenuated by the presence of cloud in its path,as well as by various atmospheric elements. The depletion of the direct beam by the cloud depends on the type of clouds, their thickness, and the number of layers. The radiation scattered by the atmospheric constituents is called diffused radiation where a portion of this radiation goes back by about 6% of the incident radiation to space, and a portion , about 20% of the incident radiation , reaches the earth surface46.
The global solar radiation was estimated using sunshine duration in Himalayan region of Kathmandu using relative sunshine hours. In this paper, the empirical constants are found to be 0.21 and 0.25 respectively. The performance of the model is tested by Root mean square Error, Mean Bias Error, Mean Percentage Error and Coefficient of Determination whose values are 0.071, 0.055, 0.047 and 0.71 respectively 47.
Kafle 48 studied the global solar radiation at Biratnagar. He found that the observed global solar radiation shows diurnal variation with maximum at noon time, there is a day by day and month to month variation of solar radiation. A maximum 1209.08 W/m2 on 5th May 12:00 NST and minimum 51.11 W/m2 on 13th Jan 17:00 NST.
Tiwari 49 studied the different empirical models for correlation of monthly average daily global solar radiation with hour of sunshine on a horizontal surface at Tribhuvan International Airport, Kathmandu, Nepal and found out a set of constants for Angstrom-type correlation of first and second order to estimate monthly average daily global solar radiation . He obtained H1=0.471n+13.206, R2=0.559 (T.I.A. data from 1975 to 1985) the constants employing sunshine hours data recorded Kathmandu latitude 27?42′ N, longitude 85?22′ E. Least square regression was performed to derive these constants.

1.15 Objectives of the Study
The main aim of this study is to estimate the Global Solar Radiation using meteorological parameters in empirical model.Some of the objectives are:
To study and analyze the seasonal, daily and monthly variation of global solar radiation at Pokhara.
To estimate the global solar radiation based on meteorological parameters and to test modified angstrom relation.
To compare the measured global solar radiation with the predicted global solar radiation at Pokhara.
1.16 Limitation of the Study
Energy research has its own limitation to meet its research objective in a perfect manner . Here are some as the constraints imposed on this study:-
Secondary data is used from the department of the hydrology and meteorology where huge amount of longterm meteorological data are not available.
It is difficult to handle the analysis of the data regarding. Global solar radiation due to insufficient and in exhaustive data provided by the hydrology and meteorology department of Nepal.
There is limitation over time and money.

CHAPTER TWO
THE PHYSICS OF SUN
2.1 General Consideration
The sun is located near the outward tip of the Sagittarius arm of the Milkyway galaxy. The Sun is at the centre of the Solar system to which all the planets and their satellites revolve around continuously. The energy reaching the earth surface in the form of radiation supports almost all life on the earth. The same radiation is responsible for climate and weather in the earth 50.
It is important to know about the Sun before knowing about the distribution of the solar radiation and its effects at different location.
2.2 The Sun
The Sun is the nearest star from our home planet earth and is situated at the average distance of 1.5×108 km away from the earth. Its mass is approximately 1.99×1032 kg , average density 1400kg/m3 and is a gaseous sphere of diameter 1.39×106 km. Its temperature varies from 5770 K at radiation surface to 5×106 K at its Centre. Sun encloses about 99.86% of the total mass of the solar system51.
The Sun has major composition of hydrogen and helium which account for 74.9% and 23.8% of the mass of the Sun in the photosphere respectively. All heavier elements accounts for fewer than 2% of the mass , with Oxygen (roughly 1%), Carbon(0.3%), Neon (0.2%), and Iron(0.2%) being the most abundant 52.
Based on the nuclear fusion reaction, solar energy is generated due to steady conversion of four hydrogen atoms into single helium atom with release of large amount of energy. As the result, the mass of Sun decreases; that reduced mass is converted into energy according to the Einstein’s Mass Energy relation given as
E=mc^2 (2.1)
Where E is the energy released, m is the reduced mass and c is the speed of light.
The structure of the Sun is illustrated in the Figure 2.1 below. The major division of its structure are central core,radiative zone, convection zone, photosphere, chromospheres, and corona.

Figure 2.1 The internal structure of the Sun www.google.com
2.2.1 Core
The core is the innermost part of the Sun and is considered to be extended from centre to about 0.2 to 0.25 of solar radius. Here gravity has squeezed the Sun so much that hydrogen compresses together to form helium and releases energy via nuclear fusion reaction. All the energy that comes away from the Sun and all the reaches the earth started in the core. It is the hottest, densest part of the Sun which is 150 times denser than the water and has a blazing temperature of around 15 million degree Celsius 50.
The core consists of 34% of the Sun’s mass while only 0.8% of the Sun’s volume. The core of the Sun generates 99% of the fusion power of the Sun. The two distinct reactions in which four hydrogen nuclei fuses in one helium nucleus are the proton-proton chain reaction and the CNO cycle 48.
2.2.2 Radiative Zone
This is the layer of the Sun above the super dense core. Density decreases moving away from the core. Light produced by nuclear fusion in the core traverse out in the shell called radiative zone. It is less dense than core but it is still so dense that light from core bounces around taking about 100,000 years to move through the radiative zone 49.
2.2.3 Convection Zone
It is the layer of Sun above the radiative zone. When the density of the radiative zone becomes low enough, energy from the core in the form of light is converted into heat. Much like the bubbles in a pot of boiling, the heat from the edge of of the radiative zone rises until it cools enough that it sinks back down. This pattern of the heated material rising then cooling happens in big bubbles called convection cells 50.
2.2.4 Photosphere
The material that reaches top of the convection zone cools by giving light. The first part of the Sun that is visible to us where the light we see from the sun originates is called as photosphere. Even though the layer is not solid we call this part of the Sun the surface and it is also where the solar atmosphere starts. It is about 500 km thick and the temperature in this layer varies from 8000 K to 4000 K. The photosphere is marked by relatively bright granules about 150 km in diameter. The bright granules are separated by dark regions known as faculae and variable features called sunspots. It looks as a bright disk or by a naked eye but on magnification of this layer, dark circular spots could be seen which are known as sunspots. Sunspot is supposed to be a cool region with a temperature of about 4600 K while the temperature of the photosphere is about 6000 K. This region above the photosphere is called solar atmosphere and corona. This region contains vapour of almost all the familiar elements 49.
2.2.5 Chromosphere
Above photosphere is a layer of atmosphere about 10,000 km deep called chromosphere. The chromospheres is no longer white light like the photosphere but is mostly red in visible region. It can be seen as red flashes during a total solar eclipse. The density of the chromosphere is only 10-4 times that of the photosphere and its density lowers with distance from the centre of the Sun. The temperature decreases from the inner boundary at about 6,000 K to a minimum of approximately 3,800 K 50.
2.2.6 Corona
It is the highest part of the solar atmosphere which starts around 10,000 km above solar photosphere. Unlike the atmosphere of the earth , the atmosphere of the Sun continues to get hotter on moving away from the solar surface. At 20,000 – 25,000 km away from the solar surface, the corona has an average temperature of 1,000,000 to 2,000,000 million degree Celsius. The corona is 10-12 times denser than the photosphere, and so produces about one-millionth as much visible light 53.
2.3 Solar Radiation Geometry
The astronomical relationship between the Sun and the earth is significant for the description of motion of the earth around the Sun which considers the motion of the earth around its polar axis and the angle between the earth’s equator and the plane containing the sun-earth orbital system. Rotation of earth around its axis is responsible for diurnal variation, the position of its axis relative to the Sun causes seasonal variation 36. Thus the parameters like sun-earth distance (r), latitude (?), longitude (L), altitude (?), solar declination (?),zenith angle (?z), azimuthal angle (?), hour angle (?) are frequently employed.
2.3.1 Sun Earth distance (r)
Figure 2.2: Motion of the Earth around the Sun 53.
The earth revolves around the sun in an elliptical path thus there is no fixed distance between the sun and the earth. The amount of solar radiation coming to the earth surface is inversely proportional to the square of the distance between sun and earth 53. Thus it is very important to determine the value of sun-earth distance precisely. The unit used to measure the separation between sun and earth is astronomical unit(AU) and the value is 1 AU.
1 AU=1.496×?10?^6 km (2.2)
The minimum distance between sun and earth is about 0.983 AU and the maximum is approximately 1.017 AU. The earth is at its closest point to the sun (perihelion) on 3rd January and as its farthest point (aphelion) on 4th July. On 4th April and 5th October earth is at its mean distance from the sun 54.

Figure 2.3: Sun and Earth relationship 50

Spencer established the fourier series type of expression for the reciprocal of the square of the sun-earth distance ‘r’, here called eccentricity correction factor of earth’s orbit, denoted by E0 and given by,
E_0=?(r_0/r)?^2=1.00011+0.034221cos??+0.01280sin??+0.000719sin?2?+0.000077sin?2? (2.3)
where ?=(2?(d_n-1))/365 , in radians which is also known as day angle .
And dn is the day number of year ranging from 1 on 1st January to 365 on 31st December. But for leap year the day number will be 366.
2.3.2 Solar Declination (?)
The angle between the rays of the Sun and the plane of the earth’s equator is called as solar declination. The angle between the earth axis and the plane of the earth orbit is nearly constant, it varies with the seasons and its period is one year which is the time required by the earth to complete its revolution around the Sun. Moreover, the equator of the earth is considered to be in the equatorial plane. Solar declination is derived by drawing a line between the center of the earth and the Sun. The angle of declination attains a maximum value of 23?27′ when the projection of the earth axis on the plane of the earth orbit is on the same line linking the earth and the Sun. The angle of declination is slightly decreasing due to the changes in the tilt of the earth’s axis 55.
The declination varies between -23.?45?^0 on June 21. Clearly, the declination has the same numerical value as latitude at which the Sun is directly overhead at solar noon on a given day, where the extremes are the tropics of Cancer (23.45? N) and Capricorn (23.45? S). The angle of declination ,?, is estimated using the formula given by 54
?_s=23.45sin??(360(284+d_n))/365? (2.4)
where dn is the day number during the year with the 1st of January set as dn=1 and dn=365 for 31st December.
2.3.3 Longitude (L) and Latitude (?)
Longitude and latitude are the two geographical co-ordinates considered to locate the any position of earth’s surface with reference to Greenwich meridian, London and to the equator respectively. The angle between the plane defining the considered meridians and plane defining the Greenwich meridian is called as longitude (L) which varies between 0? and ±180?, 180? E and 180? W of Greenwich meridian. The lines of constant longitude (meridian) passes from pole to pole on the globe like segment boundaries on a peeled orange. Every meridian must cross the equator 54.
The latitude (?) of a place is considered as the angle made by the radial line joining location of to the centre of earth to the projection of line on the equatorial line. It varies between 0? to 90? in the northern hemisphere and the negative value for the southern hemisphere.
2.3.4 Apparent position of sun
In order to know about solar radiation reaching on the horizontal surface of earth it is required to be known about relationship between the solar position in the sky and the surface coordinates in the earth. The most commonly used parameters to specify the position of the sun is solar zenith angle (?z), solar altitude (?), azimuth angle (?), hour angle (?) etc. which are explained below:

Figure 2.4 Apparent position of the Sun 56
2.3.4.1 Zenith Angle (?z)
It is the angle between the sun’s rays and the normal line in the horizontal plane. In a three-dimensional coordinate system the zenith is the axis perpendicular to the horizontal plane. Zenith angle is calculated from a local zenith, meaning that it differs based on the location of the person or device making the measurement. It varies from 0? to 90?. It is also called the zenith distance in degrees i.e.0?? ?z ? 90? 56.
2.3.4.2 Azimuth Angle (?)
Azimuth angle is the direction of a celestial object, measured clockwise around the observer’s horizon from north. So an object due north has an azimuth of 0?, one due east 90?, south 180? and west 270?. Azimuth and altitude are frequently used together to give the direction of an object in the topocentric coordinate system 50.

Figure 2.5 Azimuth Angle Wikipedia.org
2.3.4.3 Solar altitude angle (?)
It is an angle between the horizon and the line to the sun. Solar altitude is measured in degrees. The value of the solar altitude varies based on the time of day, the time of year and the latitude on earth and the complement of zenith angle is ?=90-?_z 57.
2.3.4.4 Hour angle (?)
Hour angle shows how much sidereal time has passed because the object was on the local meridian. It is also the angular between the object and the meridian, measured in hours ( 1 hour= 15 degrees). It varies from 180? to 180? The measuring time is adopted from noon based on the local time, being positive in morning and negative in afternoon. The trigonometric relation between the sun and a horizontal surface with a given geographical position are as follows 57:
cos???_z ?=sin??? sin???+ ? ? cos?? cos?? cos??=sin?? (2.5)
Then , equation (2.5) can be solved for the sunset hour angle ?=?s, ?z=90?
Then, cos??90??=0=sin??? sin???+ ? ? cos?? cos?? cos??
cos??w_s ?=-(sin?? sin??)/(cos?? cos?? )=-tan???tan?? ?
? ??_s=cos^(-1)??(-tan???tan???)? ? ? (2.6)
The sunset hour angle is equal to the sunrise hour angle except for the sign difference.
The total sunshine hours can be written as
N= 2/15 cos^(-1)??(-tan???tan???)? ? ? (2.7)
The number of daylight varies with latitude for different day of year. The total sunshine hour is 12 hours for March and September 21, and is independent of latitude. However, the maximum and minimum total sunshine hour is found in June 21 and December 21 respectively 56.
2.4 Nature of the Sun Light
The origin of the solar radiation obtained on the Earth is the transformation of hydrogen into helium through solar fusion. Helium is constantly being produced from lighter hydrogen as four nuclei merge to form one nucleus of helium with a release of electromagnetic energy 50.
The emitted energy of the sun is 3.8×1026 W and it comes from the thermonuclear fusion of hydrogen into heat temperatures around 1.5×106 K at the core of the Sun. The energy released by the thermonuclear reaction is carried by energetic photons, but because the strong absorption of the peripheral gases, most of these photons do not penetrate the surface. The Sun radiates electromagnetic energy in terms of photons which are light particles. Almost 30% of this incident energy of the Earth is reflected back, but the rest is absorbed and is , eventually, retransmitted to deep space in terms of long-wave infrared radiation. The total power that is incident on the Earth’s surface from the Sun every year is 1.73×1014 KW and it is equivalent to 1.5 ×1018 KWh annually, which is equivalent to 1.9×1014. With comparison to the annual world consumption of almost 1010 Tons, this is a very large and inappreciable amount. This energy is regarded to be spread all over the world’s surface and, thus, the amount that falls on one square meter at noon time is about 1 KW in the tropical regions. The amount of solar power density changes with latitude, elevation, season of the year and the time of a particular day. Most of the developing nations lie within the tropical belt of the world where there are high solar power densities, and so they want to exploit this source in the most beneficial ways. On the other hand, about 80% of the world’s populations live between latitudes 35? N and 35?S. These regions attains the Sun’s radiation for almost 3000-4000 h/year. In terms of solar power densities, this is equivalent to around 2000 KWh/year. Moreover, in these low altitude regions,seasonal sunlight hour changes are not important. This means that these areas receive the Sun’s radiation almost uniformly throughout the year 58.
2.5 Solar Radiation Spectrum
The distribution of electromagnetic radiation emitted by the sun as a function of the wavelength incident on the top of the atmosphere is called solar spectrum. Also, the solar radiation spectrum presents a reference chart showing the amount of solar radiation emitted by the Sun, across the complete spectrum, from the extremely high energy gamma rays, through X-rays, Extreme Ultraviolet (EUV), Ultraviolet (UV), visible wavelengths, infrared (IR), far infrared (FIR), and to radio frequencies. Electromagnetic radiation travels in the form of wave with the speed of light (3×108 m/sec) in vacuum. The sun emits energy at the rate of 6.2×107 W/m2. The visible region lies in the wavelength range between 4000? and 7700?. This band contains seven different colors as Violet, Indigo, Blue, Green, Yellow, Orange, and Red with increasing order of Wavelength. In 1800 Sir Willium Hersel observed invisible radiation beyond the red end and gave the infrared radiation. In 1801, J. W. Ritter found ultraviolet radiation away from the violet edge of the spectrum. The distribution of the energy in the solar spectrum is not uniform. About 50% energy lies in the above visible region, 40% in the visible region and rest 10% in the shorter wavelength region 59.

Figure 2.6: Solar Spectrum 59

The following table shows the distribution of solar radiation according to wavelength.
Table 2.1: Table showing Electromagnetic Spectrum 56
S. No. Name of Region Wavelength (cm) Frequency (cps)
1 Gamma rays 10-9 3×1019
2 X-rays 10-8 3×1018
3 Ultraviolet 3×10-5 1015
4 Visible 4×10-5 to 8×10-5 4.3×1014to 7.5×1014
5 Infrared 10-4 to 10-1 3×1012 to 4.3×1014
6 Microwave 1 3×1010
7 Spacecraft 102 3×108
8 Television and FM 103 3×107
9 Short Wave 104 3×106
10 AM, Radio Wave 105 3×105

2.6 Blackbody Radiation
An object or system which absorbs all radiation incident on it and re-radiates the energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it is referred to as blackbody radiation. A black body is one which absorbs and emits the maximum amount of radiation in which such emitted radiation is theoretically considered as black body radiation 54.
2.7 Blackbody spectrum
The radiation from the Sun may be represented by that of a black body at a temperature of about 6000 K. Measurements of the solar radiation are made at the earth (not at the surface of the Sun ) so are lower intensity than that given by the Planck spectrum by the ratio ( Rs/res)2, where Rs is the Sun’s radius and res is the mean distance between the earth and Sun. Moreover, the Sun’s radiation has to pass through the earth’s atmosphere before reaching the surface which slightly decreases its intensity. The spectrum is plotted in the figure 2.5 reduced by the appropriate geometric factor. Note that absorption in the atmosphere omits certain wavelengths nearly completely. The area enclosed between the curve and the horizontal axis is the total power per unit area at all wavelengths . This is 1350 W/m2 60.

Figure 2.7 Variation of intensity with wavelength 60
The area enclosed by the curve on top, the horizontal axis on the bottom, and the two dashed lines, is the amount of power per unit area in the visible range, 520 W/m2. The amount of radiation in the ultraviolet (below 400nm) and infrared (above 700 nm) ranges are 192 and 640 W/m2 respectively.
2.8 Planck’s Radiation
The emissive power of a black body at any wavelength and temperature called its spectral emissive power is given by Planck’s law61
?_? (T)=(2hc^2)/?^5 1/(e^((hc/(?k_? T)) )-1) (2.5)
where, h= Planck’s constant, c= velocity of light in air, ?= wavelength of radiation, T= Absolute temperature

2.9 Stefan-Boltzmann Equation
The total energy emitted per unit area per unit area per second by a black body is proportional to the fourth power of the absolute temperature. This is called as Stefan-Boltzmann equation 62. Mathematically,
F=?T^4 (2.6)
where, ? is called Stefan’s constant and its value is given by
?=5.67×?10?^(-8) Jm^(-2) S^(-1) K^(-4)
2.10 Wien’s Displacement Law
Wien’s displacement law states that “The product of the wavelength corresponding maximum energy ?m and the absolute temperature ‘T’ is constant.”
i.e. ?_m T=constant (2.7)
The value of ?_m T is found to be 2879.8 ?mK.
Hence, the relation ?_m T=2897.8 ?mK is called Wien’s displacement law. Since the Sun is a black body at 5777K, the wavelength ?_max=2897.8/5777=0.5016 ?m .This wavelength corresponds to green line 1. Hence, we come to the conclusion that the maximum power can be emitted in the case of green region.
2.11 Kirchoff’s Law
Kirchoff”s law states that the emissivity (??) of a given wavelength is equal to the absorptivity (A?) in a medium under thermodynamic equilibrium. i.e. (??)= (A?)..This relation requires the condition of thermodynamic equilibrium, such that uniform temperature and isotropic radiation is received 27.
2.12 Solar Constant
Solar constant is the amount of incoming solar radiation per unit area incident on a plane normal to the rays at a distance of one astronomical unit from the sun.It is not a true constant but seems to vary slightly. The solar constant also can be defined as the average amount of solar radiation received by the Earth’s atmosphere per unit area, when the Earth is at its average distance from the Sun 60.
The solar constant depends upon the Sun-earth distance distance and varies slightly over the year. The mean value of solar constant is 1367 W/m2. The mean value of solar constant as accepted by NASA (National Aeronautics and Space Administration) and WRC (World Radiation Centre) is 1353±21 W/m2 and 1367±1.7 W/m2.

Figure 2.8 Solar Radiation Spectrum 61
Solar constant can be determined by an empirical formula given by;
S=?S_0?^2 ?R_0?^2/S^2
S=S_0 (1.00010+0.034221 cos???_0 ?+0.001280 sin???_o ?+0.000719 cos??2?_0 ?+0.000077 sin??2?_0 ? ) (2.8)
where R0 is the mean sun-earth distance and ?0 is defined in terms of day number of year starting from January.
?_0=(2n(d_n-1))/365 (2.9)
where dn is the day number and is counted from 1 to 365 starting from January 1st .The maximum value of solar constant is 1400 W/m2 around 4th January and minimum value is 1309 W/m2 around 5th July.
2.13 Extraterrestrial Solar Radiation
Solar radiation which is incident outside the earth’s atmosphere is called extraterrestrial radiation. On average the extraterrestrial irradiance is 1367 Watts/meter2 (W/m2). This value changes by ±3% as the earth orbits the sun. The radiation spans a large range of wavelengths from 200 nm to more than 5000 nm with peak around 500 nm. The NASA (1968-1971) standard spectral irradiance at the average sun-earth distance outside the atmosphere is given in figure 1.3. Approximately 47% of the incident extraterrestrial solar radiation is in the visible wavelengths from 380 nm to 780 nm. Furthermore, the infrared portion of the spectrum with wavelengths greater than 780 nm accounts for another 46% of the incident energy and the ultraviolet portion of the spectrum is with wavelengths below 380 nm accounts for 7% of the extraterrestrial solar radiation 62.
2.14 Terrestrial Solar Radiation
The thermal radiation of the earth’s surface, as the surface of the earth has a comparatively low temperature; it radiates electromagnetic waves with wavelengths of 30-80 microns, which fall into the infrared portion of the spectrum, which is not visible to the eye. The surface of the earth cools down due to its intrinsic radiation. The flow of intrinsic radiation of the surface of the earth is directed upward and is absorbed almost fully by the atmosphere, thus heating it. The atmosphere, in turn , sends counter-radiation toward the surface of the earth (atmospheric counter-radiation) at approximately the same wavelengths, which partially compensates for the loss of heat by the surface of the earth as a consequence of its intrinsic radiation. The distinction between the radiation of the surface of the earth and the counter-radiation is called effective radiation. On clear nights the counter-radiation reduces and the effective radiation increases; therefore, the surface of the earth is cooled suddenly and the lower layers of the air are cooled by it. In the process fog or dew may occur, and in the spring and fall, there may be frosts. On cloudy nights , on the other hands , the counter-radiation increases because of the radiation of the clouds, and the effective radiation and cooling of the surface of the earth are decreased. During the day the surface of the earth also receives solar radiation in addition to the counter-radiation. Together they exceed terrestrial radiation for most of the day (during the warm part of the year in moderate latitudes), and the surface of the earth heats up. Terrestrial radiation is one of the most significant factors determining the thermal conditions of the surface of the earth and of the atmosphere 63.
2.15 Empirical Relation
The first and the most widely used correlation for estimating daily global solar radiation was given by 61, who derived a linear relationship between the ratio of average daily global solar radiation to the corresponding value on a completely clear day at a given location and the ratio of average daily sunshine duration to the maximum possible sunshine duration 62. A fundamental difficulty with Angstrom correlation lies in the definition of the term clear sky global radiation 62. 64 and others have changed the method to base it on extraterrestrial radiation (H0) on a horizontal surface rather than on clear day radiation and therefore proposed the relation given by equation 2.7 65.

Figure 2.9 Direct, diffuse and reflected solar radiation

H_g/H_0 =a+bn/N (2.10)
where, a and b are regression constants or correlation coefficients. The ratio H_g/H_0 is clearness parameter or cloudiness index, n/N is fraction of sunshine hours and Ho is the monthly average daily extraterrestrial radiation on the horizontal surface given by 62 as follows:
H_0=24/? I_sc E_0 ?/180 ?_s sin?? sin??+cos?? cos?? sin???_s? (2.11)
where,
? I?_sc=(1367×3600)/1000000 MJ/m^2 h (2.12)
is the solar constant,
? E?_0=1+0.033cos360n/365 (2.13)
is the eccentricity correction, n is the day number of the year. n=1 for January 1st and n=365 for December 31st , ? is the latitude of the site,
?=23.45sin??(360(n+284))/365? (2.14)
is the solar declination,
?_s=cos^(-1)??(-tan???tan???)? ? ? (2.15)
is the hour angle, and
N= 2/15 ?_s (2.16)
is the maximum possible sunshine hours.

CHAPTER-3
METHODS AND MATERIALS

3.1 Introduction
We must be aware about the solar radiation entering the certain place of earth so as to design the different kinds of devices in order to record the amount of solar radiation that the earth’s surface receives. The estimation of GSR in our study includes Pokhara valley. Our aim is to predict daily GSR using CMP6 Pyranometers. For the advancement of solar energy technology, solar radiation data are highly important. Data are available from network of monitoring stations where solar radiation is continually recorded. Since measuring and recording instruments for solar radiation are of high expense, no of stations in the network in a developing country is limited and insufficient to use; hence to get rid of this difficulty, some mathematical models associating with the solar radiation to the meteorological parameters has been proposed66. Moreover, the analysis and estimation of GSR has been done using modified form of appropriate Angstrom – Prescott empirical equation.
3.2 Description of the Study Area
The locations selected consists of Pokhara for measuring the solar radiation. These selected sites includes altitude of 800 m above the sea level. The site is briefly introduced as given below:

Pokhara:
Pokhara (28.22° N, 84° E) is located in the western part of Nepal at the altitude 800 m from the sea level. It is a Metropolitan City that lies in warm and cold moderate climatic zone. And the total precipitation is about 4785 mm per year (Source: DHM/GON) which is the highest in Nepal. The temperature ranges from 25 to 35 °C in summer, and 2 to 15 °C, in winter67.

Figure 3.1 Map of Nepal indicating Pokhara 68
3.3 Description of Instruments
In our work we have studied solar radiation and sunshine hours using the following instruments:
3.3.1 Pyranometer
The word Pyranometer has been derived from the Greek language where ‘pyr’ means fire, ‘ano’ means sky and ‘meter’ means measurement. Thus Pyranometer is a device that measures the radiation coming from the sun.The ground based GSR monitoring was made on CMP6 Pyranometer. A thermopile detectors in the Pyranometer generates voltages which are the function of incident radiation. A potentiometer is essential to detect and record this output. Radiation data usually must be taken over certain period of time, such as an hour or a day.
The two uses of pyranometers are : measurements of solar radiation on horizontal surfaces and measurements of solar radiation on inclined surfaces. The thermocouple thermopile on instruments is rotationally symmetrical which is enclosed inside K5 glass domes. A white screen protects the body of the pyranometer from heating and a drying catridge prevents the condensation inside the sensor. A spirit level and levelling screws are provided 69.

Figure 3.2 CMP6 Pyranometer 70

Table 3.1 : Specifications of CMP6 Pyranometer 71
S. No. Specialities Range of values
1 Spectral range 285-2800 nm
2 Sensitivity 5-20 ?VW?1m2
3 Impedance 20-200 ohm
4 Response time ?18s (95% of final value)
5 Non linearity ?1% (0 to 1000 wm-2)
6 Zero offset ?15 wm2 (200wm-2)
7 ISO-9060 class First class

Measurements of diffused radiation can be done with pyranometer by shading the instrument from beam radiation which is usually done by means of shadow ring. The ring is used to allow continuous recording of diffused radiation without the necessity of continuous positioning of smaller shading devices; adjustments need to be done for changing declination only.
The area under study is situated far from a shadow won’t be cast on it anytime and is selected away from any obstruction over the azimuth range between earliest sunrise and latest sunset should have an elevation not exceeding 5?.This is significant for the precise measurement of the direct solar radiation. The diffused solar radiation is feebly affected by obstructions near the horizon. The pyranometer is located distant from the light colored walls or others objects likely to reflect sunlight onto it 72.
3.3.2 Measurements of Sunshine Duration
Sunshine duration can be regarded as the period of time for which the earth’s surface receives the radiation directly from the sun. In 2003, WMO defined sunshine duration as the period during which direct solar irradiance exceeds a threshold value of 120 watts per square meter (W/m2)50. It is equivalent to the level of solar irradiance shortly after sunrise or shortly before sunset in a cloud free conditions. It was evaluated by comparing the sunshine duration recorded using a Campbell-Stokes sunshine recorder with the real direct solar irradiance.
3.3.2.1 Campbell-Stokes sunshine recorders
They have been employed as a device to measure sunshine instrument to measure sunshine duration and have merits that it lacks moving parts and requires no electric power. Also their demerits are that the characteristics of the recording paper or photosensitized paper used in them influence the preciseness of the measurements, differences between observers may arise in evaluating the occurrence of sunshine, and the recording paper must be substituted after sunset. It focuses sunlight through a glass sphere onto a recording card kept at its focal point. The length of the burn trace left on the card indicates the sunshine duration 52.

Fig. 3.3 Campbell-Stokes Sunshine Recorder 50
The structure of the device is shown in figure 3.3. A homogeneous transparent glass sphere L is supported on an arc XY, and is focused so that an image of the sun is formed on recording paper kept in a metallic bowl FF’ fixed to the arc. The glass sphere is concentric to this bowl, which consists of three partially overlapping grooves into which recording cards for use in the summer, winter or spring and autumn are set . Three separate recording cards are used depending on the season. The focus shifts as the sun moves, and a burn trace is left on the recording card at the focal point. A burn trace at a certain point shows the presence of sunshine at that time, and the recording card is scaled with hour’s marks so that the exact time of sunshine occurrence can be gained. Measuring the overall length of the burn traces reveals the sunshine duration for that day. For accurate measurement, the sunshine recorder must be properly adjusted for planar levelling, meridional direction and latitude. Campbell Stokes and Jordan sunshine recorders mark the occurrence of sunshine on recording paper at a position corresponding to the azimuth of the sun at the site, and the time of sunshine occurrence is expressed in local apparent time 73.
3.4 Empirical Relation to estimate GSR
There are several empirical relations that have been established to predict the amount of GSR on horizontal surface. These empirical relations employ several meteorological parameters such as sunshine duration, humidity, maximum and minimum temperatures, rainfall, wind speed, altitude etc. Most of the literatures suggested that the empirical equation using sunshine duration have best performance than other empirical relations involving remaining parameters. Generally, it is accepted that models for solar radiation prediction are necessary, because in most cases the density and number of solar radiation measuring stations cannot explain the essential variability 74.
Thus, it is realizable that new models and improvements to present modelling techniques are continually proposed which intend to improve estimates of solar radiation values with the use of more readily meteorological parameters 75,76,77.
The monthly average daily solar radiations, sunshine duration, temperature, relative humidity, precipitation, were availed from the Department of Hydrology and Meteorology, Government of Nepal. The obtained data covered a period of three years (2015,2016). The bright sunshine hours are calculated from the measured global solar radiation and diffused solar radiation. The period is regarded as bright sunshine if direct solar radiation is greater than or equal to 120 W/m2 78.
The solar radiation reaching the earth’s surface can be estimated by empirical models when measured data are available. The simplest model commonly used to estimate the average global solar radiation on horizontal surface is the well known Angstrom Prescort equation 79.
In my research work following empirical models are used to calculate the predicted value of Global Solar Radiation.
H_g/H_0 =a+b(n/N) (3.1)
H_g/H_0 =a+b((n )/N)+cT_max (3.2)
H_g/H_0 =a+b(n/N)+c?(n/N)?^2 (3.3)
where a, b, and c are empirical constants and N is the maximum monthly mean daily sunshine hours, Tmax are the monthly mean daily maximum and minimum temperature. The measured data were used in linear and multiple linear regression analysis by writing subroutines for calculating the extraterrestrial radiation values H0 and the day length N sunshine duration the standard procedure 80. H0 and N for the average day of each month were calculated using the equations given in (2.13) and (2.10) respectively. For the next step , the computer programs were used to find out the empirical constants of above equations with the help of measured values of Hg and other meteorological parameters. Values of the empirical constants a, b and c are evaluated. The obtained correlations were then utilized to predict the global radiation Hg for the considered location (Pokhara) for the period (2015, 2016). The calculated values of Hg were compared with the measured data.
3.5 Statistical Methods
To evaluate the performance of the models of solar radiations statistically,there are various statistical test methods to be used. Among these, correlation mean bias errors (MBE), root mean square error (RMSE), mean percentage error (MPE) are the most widely used ones.
3.5.1 Mean Bias Error
The mean bias error (MBE) gives information on the long-term performance of the correlations by providing a comparision of the exact deviation between calculated measured values term by term. The ideal value of MBE is zero. The MBE is given as
MBE=?(H_g(pred) -H_g(obs) ) /N (3.4)
3.5.2 Root Mean Square Error
The root mean square error (RMSE) is a oftenly used measure of the differences between values predicted by a model or an estimator and the values exactly observed from the thing being modelled or predicted. RMSE is a good measure of accuracy; whose value is always positive, representing zero in the ideal case and can be calculated using the formula given as
RMSE={?(??(H_g(pred) -H_(g(obs)))?^2/N) (3.5)
3.5.3 Mean Percentage Error
The mean percentage error (MPE) is the calculated mean of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.
The formula for the mean percentage error is given as
MPE=(H_g(pre) -H_g(obs) )/H_g(obs) ×100/N (3.6)

3.5.4 Coefficient of Determination
The coefficient of determination, denoted by R2 is the proportion of the variance in the dependent variable that is predictable from the independent variable. It is used for the prediction of the future outcomes on the basis of the other related information. It provides a measure of how well the observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model. Its value ranges from 0 to 1.
R^2=1-SS_res/SS_total (3.7)
where,
SS_res=?(H_g(mea) -?average H?_g(mea) )^2= ?e_i^2 (3.8)
is the residual sum of squares
SS_total=?(H_g(pre) -average H_g(mea) )^2 (3.10)
is the total sum of squares
e_i=H_g(mea) -H_(g(pre)) (3.10)
is the residuals 81.

CHAPTER FOUR
RESULTS AND DISSCUSSION
4.1 Introduction
The best model among the models studied was determined in this work with the help of GSR data, sunshine hour and maximum temperature of the year 2015 and 2016. With the use of these data, the regression constants a, b and c were obtained by using regression technique for each model. The global solar radiation data for this work was measured by employing CMP6 Pyranometer at the research site Pokhara. Also the variation of GSR with seasons, months and days were studied. GSR variation with some other meteorological parameters like precipitation, maximum temperature was also studied. Then the empirical equations were employed for the estimation of GSR.
4.2 Seasonal Variation of GSR
Figure 4.1 shows the seasonal variation of global solar radiation of Pokhara while errors in Table 4.1 in 2015. For 2015, the GSR in winter, spring, summer, and autumn were 13.99, 19.71, 18.47 and 12.09 MJ/m2 /day respectively. Clearly, it shows that there was maximum and minimum global solar radiation in Spring and Autumn respectively. The annual average of GSR is 16.06 MJ/m2 /day for 2015.

Figure 4.1 Seasonal Variation of GSR in Pokhara in 2015
Table 4.1 Seasonal errors for Pokhara in 2015
S. No. Seasons Errors
1 Winter 0.69
2 Spring 0.98
3 Summer 0.92
4 Autumn 0.60

Similarly, Figure 4.2 shows the seasonal variation of global solar radiation at Pokhara in 2016 with errors in Table 4.2. For 2016, the GSR for winter, spring, summer, and autumn were 14.52, 18.66, 17.65 and 12.80 MJ/m2/day . The annual average of GSR in 2016 is 15.90 MJ/m2/day.
High value of GSR in spring is attributed due to less solar zenith angle, less cloud and less rainfall whereas lower value of GSR in Autumn is due to large solar zenith angle.

Figure 4.2 Seasonal Variation of GSR in Pokhara in 2016

Table 4.2 Seasonal errors of Pokhara in 2016
S. No. Seasons Errors
1 Winter 0.73
2 Spring 0.93
3 Summer 0.88
4 Autumn 0.64

4.3 Monthly Mean Variation of GSR
Figure 4.3 indicates the monthly mean variation of GSR of Pokhara in 2015. The maximum and minimum value of GSR is 17.87 and 13.88 MJ/m2/day in May and December respectively. The annual average measured value of GSR is (15.22±1.92) MJ/m2/day which is adequate to generate the solar energy. The coefficient of determination and p-values are found as 0.98 and ?0.0032. Hence, it implies that about 98 percent of data is closer to the best line. The p-value is found within the range of permissible limit. Moreover, the trend line of fourth degree polynomial is fitted with the measured data of GSR in Pokhara which is as shown in Figure 4.3.

Figure 4.3 Monthly mean variation of GSR in Pokhara for year 2015
The maximum and minimum value of measured GSR is found to be 17.74 and 10.63 MJ/m2/day in August and December respectively in year 2016. The annual measured value of GSR (15.18±1.06) MJ/m2/day is also adequate to generate the solar energy. The coefficient of determination and p-values are found as 0.91 and ?0.0086. Hence, it implies that about 91 percent of data is closer to the best line.

Figure 4.4 Monthly Mean Variation of GSR in Pokhara for 2016
With reference to the Figure 4.3 and Figure 4.4, it can be seen that the solar radiation is slightly overestimated in some months while it is under estimated in some other months so that they could nearly be cancelled to each other so as to hold good agreement between the estimated and measured GSR for the site having same meteorological parameters.
Figure 4.3 indicates the trend of global solar radiation at Pokhara, with high value during summer season even though it is monsoon season in Nepal. In these year, due to less rainfall high value of global solar radiation is obtained during the summer. The low value of radiation is obtained during winter season between the months of November– January due to dust, haze, fog that cover the atmosphere at that period of the year.
In the same way, Figure 4.4 indicates the trend of global solar radiation at Pokhara, with high value during the dry season. During rainy season, the minimum radiation is obtained as the rain bearing clouds hide the sky.
There were two maxima and two minima for GSR during the year with major maxima between February – April i.e. dry and pre-monsoon season and minor maxima during August – October. The major minima occur between May – Jly sometimes up to August due to the rain carrying clouds pervading radiation in the sky while the minor minima occurs during winter season especially in January and December mainly due to dust, haze covering the atmosphere at that period of the year. There is strong relationship between sunshine hour and measured GSR meaning that sunshine hour vary season to season due to annual motion of the year. Meanwhile, sunshine hour affects GSR directly.

4.4 Estimation of GSR using Different Parameters
Since the measurement of the global solar radiation is difficult, quite expensive, time consuming and also being costly in maintenance , it’s better to use a solar estimator based on the meteorological parameters. Several empirical models are in practice though modified Angstrom model is the widely used model.
In this study, I have used sunshine hour and maximum temperature as meteorological parameters. The modified Angstrom equation given in equations (3.1) and (3.2) and Ahmad and Ulfat equation (3.3) for Pokhara in 2015 are given below:
H_g/H_0 =0.42+0.22n/N (4.1)
H_g/H_0 =0.45+0.14n/N+0.002T_max (4.2)
H_g/H_o =0.49+0.11n/N-0.05?(n/N)?^2 (4.3)
The errors in the above equations for Kathmandu in the year of 2015 are presented in Table 4.
Table 4.3 : Errors for Pokhara in 2015
Modified Angstrom
Equation given by MBE
(MJ/m2/day) RMSE
(MJ/m2/day) MPE
(%) R2
(4.1) 0.02 0.13 3.66 0.94
(4.2) 0.01 0.15 6.79 0.97
Ahmad and Ulfat Equation given by
(4.3) 0.03 0.16 9.13 0.85

The equations (4.1), (4.2), (4.3) are used to estimate the GSR using sunshine duration of Pokhara. Figure 4.5, 4.6 and 4.7 show the comparison between measured and the predicted values of GSR in Pokhara which are given below:

Figure 4.5 Comparison between the measured and predicted GSR of Pokhara in 2015

Figure 4.6 Comparison between the measured and predicted GSR of Pokhara in 2015

Figure 4.7 Comparison between the measured and predicted GSR of Pokhara in 2015
The graphs above indicate that the measured and estimated values of global solar radiation in Pokhara for year 2015 are very much similar tentatively. But slight variation in these values are due to the weather conditions.
In the same way, the modified Angstrom equations (3.1), (3.2) and Ahmad and Ulfat equation (3.3) for Pokhara in 2016 are given below:
H_g/H_0 =0.43+0.20n/N (4.4 )
H_g/H_0 =0.41+0.23n/N-0.003T_max (4.5)
H_g/H_o =0.43+0.21n/N-0.007?(n/N)?^2 (4.6)
The errors in the above equations for Pokhara in 2016 are presented in Table 4.4.
Table 4.4: Errors for Pokhara in 2016
Modified Angstrom
Equation given by MBE
(MJ/m2/day) RMSE
(MJ/m2/day) MPE
(%) R2
(4.4) 0.06 0.13 15.19 0.92
(4.5) 0.05 0.12 15.53 0.95
(4.6) 0.08 0.14 16.69 0.89

Again these equations (4.4), (4.5) and (4.6) are used to estimate GSR using sunshine duration of Pokhara while Figure 4.8, 4.9 and 4.10 show the comparison between the measured and predicted values of GSR in Pokhara which are shown below:

Figure 4.8 Comparision between the measured and predicted GSR of Pokhara in 2016

Figure 4.9 Comparision between the measured and predicted GSR of Pokhara in 2016

Figure 4.10 Comparison between the measured and predicted GSR of Pokhara in 2016
The graphs above indicate that the measured and estimated values of global solar radiation in Pokhara for year 2016 are very much similar tentatively. But slight variation in these values are due to the weather conditions.

The regression coefficients ‘a’ and ”b’ are called empirical constants which depends upon different factors such as sunshine hour, relative humidity, latitude and maximum temperature of air. Clearly the value of MBE and RMSE using sunshine hour as a meteorological parameters in two years were minimum than for using other parameters. Furthermore, it can be observed that the measured and estimated values of GSR are in close agreement while using sunshine hour as a meteorological parameter.
4.4.1 Estimation of GSR using regression coefficients
Modified Angstrom relation is used to estimate the GSR. The regression coefficients calculated from years 2015 and 2016 of Pokhara are applied to predict the GSR for year 2017. In accordance with the values of statistical tools RMSE, MBE and MPE as in above tables , they indicated that adopted model finely agreed and gives the best value of GSR. Also, the measured GSR against estimated values of Pokhara for 2015 given by empirical equations 4.1, 4.2 and 4.3 are shown in Figure 4.11, 4.12 and 4.13.

Figure 4.11 : Estimated and measured GSR of Pokhara in 2015

Figure 4.12 : Estimated and measured GSR of Pokhara in 2015

Figure 4.13: Estimated and measured GSR of Pokhara 2015
Similarly, the measured GSR against the estimated GSR values of Pokhara for the year 2016 as given by equations 4.4, 4.5 and 4.6 are shown in Figure 4.14, 4.15 and 4.16 below:.

Figure 4.14 : Estimated and measured GSR of Pokhara in 2016

Figure 4.15 Estimated and measured GSR of Pokhara in 2016

Figure 4.16 Estimated and measured GSR of Pokhara in 2016
The linear relationship between GSR and maximum temperature of Pokhara for the year 2015 and 2016 are shown in Figure 4.17 and 4.18 shown below :

Figure 4.17 Monthly mean variation of GSR with maximum temperature of Pokhara in 2015

Figure 4.18 Monthly mean variation of GSR with maximum temperature of Pokhara in 2016
The linear relationship between GSR and sunshine hour of Pokhara for the year 2015 and 2016 are shown in Figure 4.19 and 4.20 shown below :

Figure 4.19: Monthly mean variation of GSR with sunshine hour (n) of Pokhara in 2015

Figure 4.20: Monthly mean variation of GSR with sunshine hour (n) of Pokhara in 2016
Similarily , the linear relationship between GSR and Rainfall of Pokhara for the year 2015 and 2016 are shown in Figure 4.21 and 4.22 below:

Figure 4.21 Monthly mean Variation of Rainfall with GSR of Pokhara in the year 2015

Fig. 4.22 Monthly mean Variation of Rainfall with GSR of Pokhara in the year 2016
The linear relationship between Hg/H0 and n/N of Pokhara in the year 2015 and 2016 are shown in Figure 4.25 and 4.26 below:

Figure 4.25: Monthly mean variation of Hg/H0 with n/N of Pokhara in 2015

Figure 4.26: Monthly mean variation of Hg/H0 with n/N of Pokhara in 2016
The regression coefficients ‘a’ and ‘b’ are calculated for year 2015 and 2016 of Pokhara by applying Modified Angstrom Model with use of sunshine hour, maximum temperature and Ahmad and Ulfat equation are shown in equations from (4.1) to (4.6). These values of regression coefficients can be applied to predict GSR in Pokhara. From the comparision of predicted GSR with measured GSR , it is seen that they are in quite good accordance with the errors viz. MBE, RMSE and MPE. Table 4.3 and 4.4 indicates that MBE, RMSE and MPE are so small. The value of R2 are in the range of 0.90 to 0.99 for year 2015 and 2016. Hence , it can be concluded that Angstrom model provide reasonably high extent of precision in the value of GSR and can be very efficiently employed to generate useful energy for fulfilling the current high energy demand in Pokhara. Moreover, linearity between GSR and other meteorological parameters like maximum temperature, sunshine hour, n/N and also between Hg/H0 and n/N showed the best fit to the observed data in which goal is to get a good relationship among them. These relationships may be used to predict future values of one variable when other is known.

CHAPTER FIVE
CONCLUSION
5.1 Conclusions
It is observed that the global solar radiation varies month to month due to local weather condition , clouds, wind blow and precipitation. Also, the maximum abd minimum value is found on spring and autumn due to presence of fog, dust particles, cloud and position of Sun, etc.
In this study, modified Angstrom empirical relation and Ahmad and Ulfat relation were employed to obtain the value of the regression coefficients for the years 2015 ; 2016. These coefficients ‘a’ and ‘b’ for year 2015 and 2016 were calculated as (0.45,0.16 ) and (0.41 ,0.24 ) respectively by using modified Angstrom technique. By using Ahmad and Ulfat technique , the calculated values of ‘a’ and ‘b’ for year 2015 and 2016 are (0.49 ,0.11 ) and (0.42 ,0.21 ) respectively.In clear perfect sky condition, the transmission of the atmosphere global solar radiation is given as the sum of the regression coefficients a+b, whereas the transmissivity of an overcast atmosphere is interpreted as the intercept (a+b=1). From this finding , the atmosphere transmittivity, under clear sky for Pokhara is obtained as very well comparable values. Moreover, The statistical tests unleash the fact that sunshine based model can be employed with hgher degree of accuracy for the prediction of GSR in Pokhara. The obtained empirical equations can be employed for upcoming years in Pokhara.
The trend line of GSR in Pokhara alongwith some related meteorological parameters was investigated in this work. The trend line of the estimated GSR in Pokhara is ascending order due to comparison of measured GSR so that it would suggest that the obtained result can be utilized to generate a large amount of useful energy from solar energy which will be the significant way to meet the increasing demands of energy in Pokhara.
On the basis of this study, the annual variation of solar radiation during two years, it can be concluded that there is no significant variation of solar radiation. The measured and predicted values of GSR are very close. Average bright sunshine receives in Pokhara is nearly 7.0 hours per day. Because of the availability of solar energy, there is a important concern. The modified Angstrom equation and Ahmad and Ulfat equation are developed for Pokhara by using meteorological parameters such as sunshine hour and temperature. The errors have been calculated and the GSR is estimated. The key finding of this work are :
The monthly and daily mean variation of GSR can be best estimated from the Angstrom type of correlation using meteorological parameters.
The predicted GSR at Pokhara is in well agreement with measured GSR given by modified Angstrom relation of first degree model.
Developed linear regression relations can be used for the similar type geological and climate condition.
5.2 Future Work
The measured data of global solar radiation are compared with the estimated value of GSR. The satellite data of GSR can be compared with the ground measured GSR. The solar energy prediction can be studied to find the application of solar energy in rural areas of Nepal. Similarly, it is useful to develop solar map in the future.

REFERENCES
1 P. N. Nath, Estimation of Global Solar Radiation Using EmpiricModels On Horizontal Surface In Jumla, Nepal, M. Sc. (Physics) Thesis,1,(2017).
2 M. S. Okundamiya and A. N. Nzeako, Empirical model for estimating global solar Radiation on Horizontal Surfaces for selected cities in the six Geopolitical zones in Nigeria, Journal of Control Science and Engineering,9, (2011).
3 G. Salazar, P. Utrillas, A. Esteve, J. M. Lozano, M. Aristizabal, Estimation Of of daily average values of the Anstrom turbidity coefficient ? using a corrected Yang Hybrid Model, Renewable Energy,51, 182-188, (2012).
4 K. R. Adhikari, B. K. Bhattarai, S. Gurung, Estimation of Global Solar Radiation for four selected sites in Nepal using Sunshine Hours, Temperature and Relative Humidity, Journal of Power and Energy Engineering,1, 1-9, (2013).
5 White paper presented by Ministry of Energy, Water Resources and Irrigation ,Government of Nepal (2017).
6 K. R. Adhikari, S. Gurung, B. K. Bhattarai, Energy Potential in Nepal and Global Context, Journal of Institute of Engineering,9,1, 95-106 (2012).
7 P. Michael, Natural Science, Encyclopedia of Earth (2010).
8 S. Adhikari,S. Adhikary, Solar Energy Potential in Kathmandu Valley, Nepal, Journal of Hydrology and Meteorology(2012), 8(1), 77-82, (2012).
9 SWERA, United Nation Environment Program: Global Environment Facility (UNDP/GEF), Solar and Wind Energy Resource Assessment in Nepal (SWERA) project, Government of Nepal, Ministry of Environment, Science and Technology, Nepal (2010).
10 R. Calif, R. Emilion, T. Soubdhan, R. Blonbou, Wind Speed PDF classification using Dirichlect mixtures (2011).
11 S. Chettri, A. Chettri, S. Chettri, Dual Axis Self-tracking Solar Panel, International Journal of Computer Applications,14, 141, (2016).
12 EIA 2016-17 Winter Fuels Outlook, NASEO-EIA 2016-17 Winter Energy Outlook Webinar, (2016).
13 K. N. Poudyal, Estimation Of Global Solar Radiation potential in Nepal, Ph.D. Thesis, 20-30 (2015).
14 CBS, Nepal Living Standards Survey 2010/11, Statistical Report Volume 1, Central Bureau of Statistics, National Planning Commission Secretariat, Government of Nepal (2011).
15 S. Wilcox, National Solar Radiation Database 1991-2010 Update: User’s manual, National Renewable Energy Laboratory (2012).
16 Economic Survey, Ministry of Finance, Government of Nepal for the Fiscal year 2016/2017.
17 A. Teke, H. B. Yildirim, O. Celik, Evaluation and Performance comparision of different models for the estimation of Solar Radiation, Renewable and Sustainable Energy Reviews,50, 1097-1107, (2015).
18 K. N. Poudyal, B. K. Bhattarai, B. K. Sapkota, B. Kjeldstad, Solar Radiation Potential at four sites of Nepal , Journal of the Institute of Engineering, 8(3), 189-197, (2012).
19 M. Despotovic, V. Nedic, D. Despotovic, S. Cvetanovic, Review and Statistical analysis of different Global Solar Radiation Sunshine models, Renewable and Sustainable Energy Reviews, 52, 1869-1880, (2015).
20 Economic survey for Fiscal Year 2016/17, Government of Nepal, Ministry of finance, Singh Durbar, Kathmandu (2016).
21 K. Poudyal, B. K. Bhattarai, B. K. Sapkota, B. Kjeldstad, Solar Radiation Potential at four sites of Nepal, Journal of the Institute of Engineering, 8(3), 189-197 (2012).
22 Y. Liu, Y. Zhou, D. wang, Y. Wang, Y. Li, Y. Zhu, Classification of Solar radiation zones, and general models for estimating the daily global solar radiation on Horizontal Surfaces in China, Energy Conversion and management, 154, 168-179, (2017).
23 White paper, Ministry of Energy, Water Resources and Irrigation, Government of Nepal 2018.
24 A. Kumar, A. K. Dwivedi, solar Power Parameter calculator, International Journal of engineering Invention, 2(5), (2013).
25 K. D. V, S. K. Rao, M. Premalathu, C. Naveen, Method and Strategy for predicting daily Global Solar Radiation using only one and two input variables for Indian Stations, Journal of Renewable and Sustainable Energy,10, (2008).
26 K. N. Liou, Radiation and cloud processes in the atmosphere, Oxford University Press, (1992).
27 H. S. Sedhai, Estimation of Global Solar Radiation using Empirical Model at Kathmandu Valley, Nepal, M. Sc (Physics) Dissertation, T. U. , Nepal (2018).
28 J. A. Prescott, Evaporation from water surface in relation to solar radiation, Transactions of the Royal society of Australia, 46, 114-118, (1940).
29 Y. A. Eltba, M. H. Ruslan, M. A. Alghoul, M. Y. Othman , K. Sopian, T. M. Razykov, Solar attenuation by aerosols : an overview, renewable and sustainable Energy reviews, 16, 4246-4276, (2012).
30 P. K. Mandal, M. I. Mamun, M. Islam, Construction of an inexpensive sun photometer to measure aerosol optical depth and comparisions between the measured data and satellite observations, American Journal of Remote Sension, 2(5),37-43, (2015).
31 C. D. Papadim, N. Hatzianastassiou, C. Matsoutas, M. Kanakidou, Mihalopoulos, and I. Vardavas, The direct effect of aerosols on solar radiation over the broader Meditterranean basin ,12, 7165-7185, (2012).
32 M. Kannel, H. Ohvril, H. Teral, V. Russak, A. Kallis, A simple parametrization of columnar aerosol optical thickness, Proc. Sci. Biol. Ecol. 56 ,1, 57-68, (2007).
33 E. J. McCartney, Optics of the Atmosphere: scattering by molecules and particles, New York, John Wiley and sons, Inc. 421, (1976).
34 B. K. Bhattarai, B. Kjeldstad, T. M. Thorseth, A. Baghen, Erythemal dose in Kathmandu, Nepal based on solar UV measurements from multichannel filter radiometer, its deviation from satellite and radiative transfer simulations, Atmospheric Research, 85, 112-119, (2007).
35 www.staceyirvin.com
36 I. C. Moreno, M. A. Serrano, J. Canada, G. Gurrea, M. P. Utrillas, Effect of the relative optical air mass and the clearness index on solar erythemal UV irradiance, Journal of Photochemistry and Photography B: Biology, 138, 92-98 (2014).
37 A. D. Pai, J. F. Escobedo, D. Martins, E. T. Teramoto, Analysis of hourly, global, direct, and diffuse Solar Radiation Attenuations as a function of optical air mass, Science Direct, 57, 1060-1069 (2007).
38 K. N. Poudyal, P. Daponte, L. D. Vito, B. K. Bhattarai, B. K. Sapkota, Study of variation of Global Solar Radiation at different altitudes at Himalayan Region-A case study in Nepal, 3rd Symposium IMEKO TC 19, (2010).
39 B. Lamichhane, Measurement and Analysis of Solar Radiation on Horizontal Surface at Kirtipur, M.Sc. Thesis, T.U., Kathmandu (2005).
40 M. Mfon D. Umoh, O. Udo and N. Udoakah, Estimation of Global Solar Radiation on Horizontal Surface from Sunshine hours and other Meteorological Parameters for Calabar, Nigeria, Journal of Asian Scientific Research,1083-1089 (2013).
41 WMO, Guide to Meteorological Instruments and Methods of Observation, World Meteorological Organization-No. 8 (2008).
42 J. M. Wallace, and P.V. Hobbs, Atmospheric Science (2006).
43 K. R. Adhikari, B. K. Bhattarai and S. Gurung, Estimation of Global Solar Radiation for Four Selected Sites in Nepal, Journal of Institute of Engineering, 8, 189 – 197 (2013).
44 A. Angstrom, Solar and Terrestrial Radiation, Quart J Roy Met Soc, 50, 121
125 (1924).
45 K. N. Poudyal, B. K. Bhaatarai, and B. Kjeldstad, Study of Estimation of Global Solar Radiation using Pyranometer and NILU-UV irradiance meter at Pokhara Valley in Nepal, Journal of Institute of Engineering, 9, 69-78 (2014).
46 H. O. Menges, C. Ertekin, M. H. Sonmete, Evaluation of Solar Radiation Models for Konya, Turkey, Energy Conversion and Management, 47 (2006).
47 K. N. Poudyal, B. K. Bhattarai, B. Kjeldstad, Estimation of Global Solar Radiation using sunshine Duration in Himalaya Region, J. Chemical Science, 2(11), 20-25 (2012).
48 S. P. Kafle, Study of Global Solar Irradiance at Biratnagar, M. Sc. Physics, Diddertation, Central Department of Physics, Tribhuvan University, Nepal (2010).
49 S. Tiwari, Empirical models for the Estimation of Global Solar Radiation at Tribhuvan International Airport, M. Sc. (Physics) Dissertation, T. U. (2009).
50 J. A. Duffie and W. A. Backman, Design of Photovoltaic Systems, Solar Engineering of Thermal Processes, Fourth Edition, 754-773 (1991).
51 U. Koray, and A. Hepbasli,Solar radiation models, Parts 2: Comparision and developing new models, Energy resources,26(5) ,521-530, (2004).
52 A. L. McAlester, The Earth: An introduction to the geological and geophysical sciences (1983).
53 M. Iqwal, An introduction to Solar radiation ,Academic Press Toronto, Canada Google Scholar (1983).
54 M. Pidwirny, Earth- Sun Geometry, Fundamental of physical Geography, Second Edition (2006).
55 Levine and Joel, The photochemistry of atmospheres, Elsevier, (2012).
56 J. Waewask and C. Chancham, The Clearness Index Model for Estimation of global solar radiation in Thailand, Tharmmasat International Journal of Science and Technology, 15, 54-61 (2010).
57 L. Crovini and L. Galgani, On the accuracy of the experimental proof of Planck’s radiation Law, Lettere al Nuovo Cimento, 39(10), 210-214 (1984).
58 S. Zekai, Solar energy fundamentals and modelling techniques: atmosphere, environment, climate change and renewable energy, Springer Science ; Business Media, (2008).
59 R. W. David, T. H. Vonder Haar, and S. K.Cox, The effect of Solar radiation absorption in the tropical troposphere, Journal of Applied Meteorology, 14(4), 433-444 (1975).
60 E. O. Ogolo, Estimation of Global Solar Radiation in Nigeria using a Modified Angstrom Model and the trend Analysis of the Allied Meteorological Components, Indian Journal of Radio and Space Physics, 43, (2014).
61 E. Louis, AKPABIO and E. ETUK, Relationship between Global Solar Radiation and Sunshine Duration for One, Nigria, Turk J Phys, 27, 161-167 (2003).
62 Goswami, D. Yogi, Kreith, Frank and Kreider, F. Jan, Principles of Solar Engineering, Second Edition,Taylor and Francis, Philadelphia, PA, (2000).
63 H. Suehrcke and P. G. McCormick, The distribution of average instantaneous terrestrial solar radiation over the day, solar Energy,42.4, 303-309, (1989).
64 J. W. Spencer, Fourier series representation of the position of the sun, (1972).
65 K. Scharmer, J. Greif and R. Dogniaux, The European solar radiation Atlas,2, (2000).
66 Mani, Anna, Handbook of Solar Radiation data for India, Allied Publishers,New Delhi, (1980).
67 http://hyperphysics.phy-astr.gsu.edu.
68 www.lonelyplanet.com/map/asia/Pokhara (2016)
69 Kipp ; Zonen, Pyranometer Instruction Manual (2010)
70 B. R. KC, S. Gurwa, Study of Solar Energy Potential using CMP6 Pyranometer at Nepalgunj, Nepal, Journal of Advanced Academic Research,3(1), (2016).
71 F. W. Burari, M. A. Abdul and D. W. Medugu, Comparative studies of Measured and Estimated Values of Global Solar Radiation using a Constructed Reliable Model Pyranometer and Angrostom-Prescott Model at Bauchi, Nigeria, Advances in applied science research, 1(1), 80-88, (2010).
72 A. Aryal, Measurement and Comparison of Global Solar Radiation Using NPN Phototransistor. M.Sc. Dissertation, T.U. (2012).
73 A. Muhammad, T. H. Darma, Estimation of Global Solar Radiation for Kano State Nigeria Based on Meteorological Data, IOSR, Journal of Applied Physics,6,19-23, (2014).
74 B. Lamichhane, Measurement and Analysis of Solar Radiation on Horizontal Surface at Kirtipur, M.Sc. Thesis, T.U., Kathmandu (2005).
75 T. S. Muneer, Younes, and S. Munawwar, Discussion on solar radiation modelling, Renewable and Sustainable Energy Reviews, 11(4) , 551-602, (2007).
76 S. A. Safi, Zeroual and M. Hassani, Prediction of global daily solar radiation using higher order statistics, Renewable Energy, 27.4, (2002).
77 D. Marcello, G. Bellocchi, and F. Fontana, RadEst3.00:software to estimate daily radiation data from commonly available meteorological variables, European Journal of Agronomy, 18,3, 363-367, (2003).
78 F. Ahmad, I. Ulfat, Empirical models for correlation of monthly average daily global solar radiation with hours of sunshine on a horizontal surface at Karachi, Pakisthan, Turk J Phys , 28, 301-307, (2007).
79 R. B. Tiwari, Models for the Correlation of Monthly Average daily Global Solar Radiation with Hours of Sunshine on Horizontal Surface at T.I Airport, Kathmandu M.Sc. (Physics) Dissertation, Central Department of physics, T.U., Nepal (2009).
80 J. Ahmad, G. N. Tiwari, Solar Radiation Models ,International Journal of Energy and Environment, 1, 3, 513-532, (2010).
81 J. D. Nagelkerke, A Note on a General Definition of the Coefficient of Determination ,Biometrika, 78(3), 691-692 (1991).

CHAPTER ONE

INTRODUCTION
Background
The sun is the ultimate source of energy. All of the living beings in this world receives energy from the sun directly or indirectly. Solar radiation is the best choice and economic energy resource of the globe 1. Solar radiation is the form of energy emitted by the Sun in perpetual amount utilized by human beings with use of several sorts of technologies from the very beginning of the human existence in this world. There are basically two types of solar radiation: first one is the direct radiation received from the sun without being scattered by the atmosphere; second one is the diffused radiation received from the sun with its direction altered due to scattering by the atmosphere. Global solar radiation is regarded as the sum of the direct and diffused radiation on the earth surface. Global solar radiation is crucial parameter employed in most of the ecological models and work as input for several photovoltaic conversion system; therefore, it is significant and economic way of renewable energy development of the nation. The provision to estimate the solar energy potential of a place using global solar radiation that can be transformed into electrical energy to withstand energy demand of that place should be done in prior to generation of electrical energy for any specific location 2. Optimal mobilization of solar resources, as in photovoltaic or thermal concentrators power stations requires the adequate knowledge of solar resource behaviour accurately in those places where the installation of power stations is required 3.
Nepal is a land-locked mountainous country, surrounded from three sides by India and one side by China; having a small area of beautiful landscape situated between latitudes from 26°22′ to 30°27′ North and longitudes from 80°40′ to 80°12′ East within a span of 200 km from south to north and about 800 km from east to west. Within this small and beautiful setting, it possesses diversity in biosphere, climate (arctic/alpine to tropical) and landscape (lowland 72 m to highest peak 8848 m high above the sea level). The total area of the country is 1,47,181 square kilometres and is divided into five physiographic regions: High Himal, High Mountain, Middle Mountain, Siwalik ( Chure Range) and the Terai. It does not have its own coal and petroleum resources so far and has no access to the sea/ocean. For the last six years till now fossil fuel prices have raised an all time-high and the world is driven into its deepest recession since the Great Depression. Geopolitical events are driving prices steadily higher. The short?term risks to political stability and economic activity posed by the world’s dependence on fossil fuels are again as manifest as its long?term threat to environmental sustainability. To break this dependency, all the countries in the world need a clean energy revolution. Such a revolution would enhance global energy security, promote long-term economic growth and tackle environmental challenges such as anthropogenic climate change. Available literature tells that consumption of petroleum products in Nepal is increasing wonderfully at the rate of about 10 % per year. Solar radiation occurs abundantly on every corner of the country. Surface incident solar radiation governs/drives the atmospheric circulations, Earth’s climate and Earth’s biosphere naturally. It is also the originator of all other sources of energy that exists on the face of this earth. The main source of energy even today is the fossil fuels. Solar PV generates electricity as one of the best clean and alternative energies. The average global solar radiation in Nepal varies from 3.6-6.2 kWh/m2/day, sun shines for about 300 days a year, the number of sunshine hours amounts almost 2100 hours per year and average insolation intensity about 4.7 kWhm-2day-1(=16.92 MJ/m2/day) it is greater than 4.23kWh/m2/day (15.23 MJ/m2/day) measured by for Lao PDR. Thus, Nepal lies in a favourable insolation zone in the world even though the data in Nepal was based on one year and few sites but that of Lao PDR was based on few years and throughout the country. So, a long term and many sites solar energy data are required to authenticate this statement4.
The installed capacity of power plants connected to the national grid is 1073 MW in which contribution from Hydropower, Diesel cum multi-fuel and solar energy are 1016 MW, 54 MW and 2.68 MW respectively. Nepal Electricity Authority contributes 562 MW while private sectors contributes rest of 511 MW of electricity. Though the present demand is about 1444 MW, there is deficit in the energy due to increasing population and low rate of electricity generation development 5.
Easily available and inextinguishable nature of solar energy resource resides in one of the imperative places among the various possible alternative energy sources. An accurate data base of solar radiation at particular places and selected sites are required for the development, simulations and designing of many solar energy devices/applications and establishment of solar plants as well .
Under this circumstance and knowing the fact that 52 % of the Nepalese households have no access to electricity, flourishing of solar irradiance data are essential for the development of national rural energy programs in general and for the establishment of solar energy technology in particular. For an extensive investment in these technologies from government and private sectors is not only desirable but it is the ultimate options where there is no viable alternative to the solar electricity 6.
For each second of the solar nuclear fusion process, 700 million tons of hydrogen is transformed into the heavier and helium. The sun has used up about half of the hydrogen found in its core since its formation 4.5 billions years ago. Process also generates heat that leads atoms to discharge photons 7. Temperature at the core is about 15 million degrees Kelvin (15 million degrees C or 27 million degrees F). Each photon that produced travels about one micrometer before being absorbed by an adjacent gar molecule. This absorption then causes the heating of the adjacent atom and it re-emits next photon which traverses a short distance before being absorbed by another atom. This process repeats many times before the photon are emitted to outer space at the sun’s surface. The energy transported more by convection than by radiation for last 20 % of the journey to surface requires approximately 100,000 years or about 1025 absorptions and re-emissions to make the journey from the core to the sun’s surface. The time taken by light to travel from the sun’s surface to the Earth is about 8 minute 20 seconds 7.

Conventional energy sources such as fire-wood, cow dung, coal and fossil fuels (petroleum products) release more CO2 into the atmosphere, causing environmental pollution problems that are directly related to the survival of human beings 8.
Excessive release of greenhouse gases (CO2, CH4, NO2, HFCS) into the atmosphere are causing environmental pollutions. Mean while the terrestrial heat trapped is adversely changing the global air temperature. The main existing problem have forced researcher to develop. The renewable energy resources are the best an option to the fossil fuel 8. Continuous and long term radiation are not available in our nation. But only short term monitoring and mobilization of solar radiation has been performed by then the RONAST in collaboration of JICA Japan 9.
Energy
Energy is defined as the strength to do work. There are several forms of energy. On the basis of long term usage and availability of energy resources, there are two types of energy resources. They are renewable and non-renewable energy resources.
Renewable energy is the energy obtained from the continuing or repetitive currents of energy existing in the natural environment. Obvious examples are solar energy, wind energy, tidal energy, geothermal energy, hydropower etc 8.Solar energy is radiant light and heat from the Sun harnessed using a range of technology such as photovoltaic, thermal, heating etc. Wind energy production is based on instantaneous wind speed fluctuation 10.
The main source of energy arises from oil and coals which is the non-renewable form of energy which means that it will perish some day. Also due to these forms of energy the nature is also being degraded as it contributes to the global warming causing to melting of ice caps and disrupting nature 11. Similarly, natural gas, heating oil, propane are some of the examples of non-renewable energy 12.
Energy Scenario of Nepal
Energy is crucial to all sort of development targeted at human welfare including agriculture, household, transport, industrial, commercial and educational sectors which really helps to improve the quality of life. The rate of energy consumption per capita is considered as note worthy indicators of civilization. The energy consumption is also directly connected with socioeconomic activities as well as round development of Nepal 13.
Nepal’s economic and social development is being disturbed by its insufficient energy supply. The country is not independent on its reserves of gas, coal or oil. Though its most significant energy source is water, nearly less than one percent of potential 83,000 megawatts of hydropower is currently being generated. Firewood is the predominant energy carrier, counting for more than 70 percent of consumption .However its use is inadequate and poses a threat to the country’s forests. Meanwhile, the indoor pollution produced by open hearths in homes presents a hazard to health. Mains electricity is generally only available in urban areas and some 30 percent of the population does not have access to it 14.
In comparision with other nations, Nepal has high energy consumption in relation to its gross domestic product (GDP). It does not yet have a strategy for sustainable, efficient energy use for the electricity sector or its main primary energy source, biomass. The power supply is particularly critical during the dry season, during which it is cut off for several hours a day, which has a negative impact on business and private households. Private households, the public sector as well as commerce and industry sector are largely unaware of the economic and ecological advantages of efficient energy use. There are no standards for energy saving domestic appliances lighting or products and processes in industrial use.The persistence of weather events and the effect this has on the availability of solar radiation energy can influence various solar energy applications. Particularly, the persistence of the solar energy can affect energy storage requirements and the need for backup energy sources15.
Table 1.1. Share of Energy consumption in Nepal by fuel type (Year 2073/74) 16
(Total consumption =499.839 million GJ)
S. No. Fuel Type Consumption Percentage
1 Agricultural residue 3.3
2 Animal dung 3.5
3 Hydro Power 4.1
4 Coal 4.0
5 Petroleum 13.8
6 Renewable 3.5
7 Fuel wood 70.47

Nepal have been fulfilled, partly from hydropower, bio-gas, fossil fuels and traditional energy sources such as firewood, cow dung and coal. The use of renewable energy is negligible. Conventional energy sources such as fire wood, cow dung, coal and fossil fuels release more CO2 into the atmosphere, causing environmental pollution problems.
Power crisis in Nepal has been miserable for years. Development of renewable energy such as solar energy and its considerable use in Nepal can significantly support energy demand and contribute to lower air pollution 8.The rapid depletion of energy resources, increasing energy demand and degeneration of ecological values requires an urgent solution in this age. Solar energy as the most important energy resource has become part of the solution to the world’s energy challenges.
Energy utilization is the most important input parameter for economic growth and social development of the countries. Fossil fuels are still major primary energy resource even though their environmental demerits and limited lifetime. Due to awareness of the people on the disadvantage of fossil fuel usage has been increasing day by day and it strikes people’s mind to think about renewable energy resources. Solar radiation which arrives to the earth surface every year is nearly 160 times greater than all known fossil fuel reserves discovered till now 17.
Solar and Wind Energy Resources Assessment (SWERA) reported an annual average of 4.7 kWh/m2/day solar energy is available in Nepal. This indicates that Nepal is rich in solar energy 18.
There is no more solar energy fluctuation in Pokhara in a whole month. It reflects that the local weather condition remains stable as compared to other stations. In this site the solar energy varies from 6.95 MJ/m2/day to 16.22 MJ/m2/day. The overall average energy is about 14.32 MJ/m2/day 19.
Overall energy supply situation has remained encouraging in the fiscal year 2016/2017. Of the total energy consumption of 8,257 Tons of Oil Equivalent (TOE) in the first eight months of the fiscal year 2016/2017, the contribution of traditional , commercial and renewable energy stood at 74.5 percent, 22.0 percent and 3.5 percent respectively. During the same period , electricity generation has increased by 12.3 percent (105.3 Megawatts) reaching a total of 961.2 Megawatts. Electricity leakage has decreased by 2.8 percentage points. As a result, Kathmandu and Pokhara have been made load shedding free zones while load shedding hours have been reduced in other areas as well 20.
Short term monitoring and utilization of solar radiation has been done by the then RONAST in collaboration of JICA, Japan. They installed the 4 KW prototype and 40 kW solar photovoltaic panels at Sunderighat, Kirtipur and Bode, Bhaktapur for the purpose of water pumping in 1992 and 1995 respectively 21.
1.4 Solar energy
Solar energy is a form of energy representing a safe, economic, environmental and renewable energy form is regarded as the alternative energy to improve the energy structure of Nepal22. Solar photovoltaic systems, Solar Photovoltaic water pumping systems, Solar thermal water heaters are some of the solar technologies that have been used in the country. Also solar thermal space heating and illumination in buildings are already in practice. The contribution to the national grid by solar energy is 2.68 MW. However accounting the sum with utilization of Photovoltaic panel in 7,94,276 homes to generate electricity at household purpose is more than this value 23. Also, solar thermal technologies such as solar water heating systems, solar dryer, solar cookers are being utilizing in different parts of our nation. An estimated 17,265 households, 270 commercial establishments and 26 public institutions are now using solar water heaters (SWH) 9.
Solar Radiation
Solar radiation is an electromagnetic wave emitted from the Sun’s surface that originates in the bulk of the Sun where fusion reactions convert Hydrogen atoms into Helium. 3.89×1026 J of nuclear energy is released by the Sun’s core every second. This nuclear energy flux is rapidly transformed into thermal energy and transported toward the surface of the star where it is released in the form of electromagnetic radiation. The power density emitted by the sun is of the magnitude of 64 MW/m2 of which approx. 1370 W/m2 enter the top of the Earth’s atmosphere with no significant absorption in the space 22.
Solar radiation is widely appreciated because of its effect on living matter and the possibility of its application for the useful purposes. It is a perpetual source of natural energy in addition with the other forms of renewable energy has a great potential for a wide variety of applications. The solar radiation characteristics at ground level depends on the altitude, local weather condition. Therefore, while designing solar energy conversion systems, both the quality and the quantity of solar radiation at that location should be considered.
The solar radiation going through the atmosphere is partially reflected back to space and partially absorbed by its constituents, partially diffused, with the remaining reaching the ground absorption and diffusion of solar radiation by the usual constituents of the atmosphere, aerosol particles and water also absorb and cause diffusion and re-emission of solar radiation quite significantly. The annual average GSR in Pokhara is 4.87 kWh/m2/day 13.
Global Solar Radiation
The quantity of solar radiation received by earth’s surface without any change in the direction of straight line without regards to the sun is known as direct solar radiation. Direct solar irradiance is a measure of the rate of solar energy arriving at the Earth’s surface from the Sun’s direct beam, on a plane perpendicular to the beam, and is usually measured by a Pyrheliometer mounted on a solar tracker 13.
Diffuse solar energy is the result of the atmosphere reducing the magnitude of the sun’s beam. Some of the energy removed from the beam is scattered towards the ground at the rate at which this energy falls on a horizontal surface per second is called the diffuse solar irradiance 19. Diffuse solar irradiance is measured by a Pyranometer, with its glass shaded from the sun’s beam. The diffuse irradiance is given by
I_d?=I_dr?+I_da?+I_dm? (1.1)
The sum of direct and diffuse solar radiations on a horizontal surface is called global solar radiation. It depends on geographical and atmospheric parameters. The global spectral irradiation flux G? is given by
G_?=I_n? sin???_z ?+I_d? (1.2)
Where, I_d? is diffused solar radiation andI_n? is direct solar radiation.
The total global solar radiation on the horizontal surface is given by
G=?_0^???G_(? ) d?? (1.3)
Factors affecting Solar Radiation
The solar energy availability depends upon time. The variation in availability occurs daily because of the day night cycle, seasonally due to the rotation of earth around the sun and also eleven year solar cycle. There are basically two types of affecting factors of GSR on earth. One of them is geophysical parameters which are tentatively constant over and over a year because of fixed parameters. However other factor directly or indirectly influence GSR due to the interaction with atmospheric constituents and local environment as well.
In short, the solar radiation depends on the following factors:
The geometry of the Earth (declination, latitude, solar hour angle)
The terrain characteristics (elevation, albedo, surface inclination and orientation, shadows)
The atmospheric attenuation (scattering, absorption) caused by gases, particles and clouds 24.
Solar irradiance is attenuated spectrally when passing through the atmosphere and it is strongly dependent on sky under cloudless conditions. The prevailing winds, which may carry moisture or aerosol particles from distant sources, play a major role in the seasonal variation of solar radiation. Solar radiation availability on the earth’s surface is the main fundamental renewable energy source in nature 25.
Earth’s atmosphere
In order to know about the interaction of the earth’s atmosphere with solar radiation, the study of the composition and the structure of the atmosphere is of high importance. Due to the gravity of the earth , it holds the atmosphere comprising of layers of gases surrounding the earth surface. If the gravity is to be subjected is high and the temperature of the atmosphere is low then an atmosphere is likely to be retained. The advantage of the atmosphere is to protect life on the earth by absorbing the ultraviolet radiations through its successive layers and is to warm the surface through heat retention. Also it reduces the temperature extremes between day and night 26.

Composition of Atmosphere
The Earth’s atmosphere has its major composition of Nitrogen, Oxygen and Argon. The rest of the gases are considered as trace gases including greenhouse gases viz. Carbon dioxide, Methane, Nitrous oxide and ozone. Filtered air comprises of trace amount of many other chemical compounds. Many substances of natural origin may be present in locally and seasonally variable small amounts as aerosols in an unfiltered air sample, including dust of mineral and organic composition, pollen and spores, sea spray, and volcanic ash. Different industrial pollutants also may be present as gases or aerosols, such as Chlorine, Fluorine compounds and elemental mercury vapour. Sulphur compounds such as Hydrogen sulphide and sulphur dioxide may be derived from natural sources or from industrial air pollution 27.

.

Table 1.2 Composition of Atmosphere 26
S. No. Constituents gases Content(% by volume)
1 Nitrogen (N2) 78.084
2 Oxygen (O2) 20.948
3 Argon (Ar) 0.934
4 Carbon dioxide (CO2) 0.033
5 Neon (Ne) 0.018
6 Helium (He) 0.000114
7 Krypton (Kr) 0.0000089
8 Xenon (Xe) 0.00005
9 Hydrogen (H2) 0.00015
10 Methane (CH4 0.000027
11 Nitrous oxide (NO) 0.000019
12 Carbon monoxide (CO) 0.000524
13 Water vapour 0-0.04
14 Ozone (O3) 0-0.0012
15 Sulphur dioxide (SO2) 0-0.0000001
16 Nitrogen dioxide (NO2) 0-0.0000001
17 Ammonia (NH3) 0-0.0000004
18 Nitric oxide (NO) 0-0.00000005
19 Hydrogen Sulphide (H2S) 0-0.000000005
20 Nitric acid vapour (HNO3) Trace

Dry Atmospheric Air
It comprises basically of four gases viz.O2,N2,Ar,CO2 called permanent gases. Depending on the latitude, wind, urban site and season, concentration of these components varies. Ozone is a particular element to be considered in the phenomenon of absorption of solar radiation which absorb almost ultraviolet radiation thereby protecting the earth and its living creatures from high-energy radiations. The amount of Ozone depends on latitude and season which is significant in the area between 15 and 30 km. In the upper atmosphere, Ozone is created by UV radiation from the Sun28 .
Atmospheric Water
The water in the atmosphere is mainly localized in the lower 10 km of the atmosphere. It comes from the evaporation of water from the surface of the earth, the oceans and seas. Its concentration varies so widely. Water is found as gas molecules, a liquid and solid forms in the clouds. For ozone, its effect on solar radiation is important and should determine its atmospheric content. The total optical thickness of the water vapour at the site studied is to say on the total weight of water vapour. The height of the perceptible water depends on the ability of the air to contain water vapour and therefore its relative humidity and temperature which varies from 0.1 to 1 cm in the poles and in the desert where the air is dry , 2 to 5 cm in temperate climates and greater than 5 cm in tropical climates28.
Aerosols
One of the prominent factor affecting the amount of solar radiation reaching the earth’s surface under cloudless sky condition is the presence of aerosol particles in the atmosphere. Its number or mass concentration is a key parameters in the studies of atmospheric radiative effects. They are present in both troposphere & stratosphere and mostly throughout the atmospheric boundary layer at number concentration depending upon factors such as location, atmospheric conditions, annual and diurnal cycles and presence of local resources29.
Aerosols are the suspensions of liquid and solid particles in the atmosphere, excluding clouds and precipitation. The aerosol particle sizes ranges from 10-4 to 10 mm, falling under the following broad categories: sulphates, black carbon, organic carbon, dust, and sea salt. Aerosol concentrations and composition vary considerably with time and location. The visual range can vary from a few meters to 200 km, depending on the proximity to sources, the strength of the sources, and atmospheric conditions.
Aerosol particles in the atmosphere are produced both in nature and by people. A global aerosol optical depth of about 0.12 is suggested. The aerosol increase the reflected solar radiation at the top of the atmosphere by about 3 Wm-2 globally.At present the absorption and scattering of solar radiation by aerosols have been recognized as important parameters for climate change. A way of probing the atmosphere from the ground is to measure the effect of atmosphere to sunlight transmitted to the earth’s surface30.
It influences the earth’s climate by modifying its energy balance through the direct, indirect and semi-direct effects31. This is because the aerosol physical, chemical and optical properties are highly variable in space and time, because of the short atmospheric lifetime of aerosols and of their inhomogeneous emission. The estimation of aerosol optical properties for very clean atmospheric conditions with low content of aerosol particles, is highly uncertain, especially in regard to the Angstrom wavelength exponent 32.
Clouds
The study of characteristics and location of clouds are key point to understand climate change. Low, thick clouds reflects solar radiation and cool the surface of the earth. High , thin clouds primarily transmit incoming solar radiation ; meanwhile, they trap some of the outgoing infrared radiation emitted by the earth and radiate it back downward, thereby warming the surface of the earth. Whether a given cloud will heat or cool the surface depends on several factors, including the cloud’s altitude, its size and the make-up of the particles that form the cloud. The balance between the cooling and warming actions of clouds is very close although, overall, averaging the effects of all the clouds around the globe, cooling predominates 32.
The attenuation of GSR by cloud depends on wavelength. It is necessary to know that the GSR amount changes nonlinearly with cloud amount. However, for non-obscured sun, there can be an enhancement up to 25 % under broken cloud condition, where scattering from sides of the cloud becomes equally important 33. Clouds affect UV level on the ground and can be estimated by comparing measured data with clear sky modelled data. The daily dose variability caused by clouds assuming constant aerosol concentration can be found in the range of 5-25% 34. The influence of cloud and aerosol on UV can be found from the differences of ground measured daily dose and calculated clear sky dose.

Structure of Atmosphere
The Earth’s atmosphere consists various layers that can be defined according to air temperature. (Figure 1.4) shows these layers in an average atmosphere. Based on the temperature, the atmosphere contains four different layers.

Figure 1.1 Schematic representation of Atmospheric Condition 35.
Troposphere
It extends from depth 8 to 16 kilometres. Greatest depths exist at the tropics where a warm temperature leads to vertical expansion of the lower atmosphere. From the tropics to the Earths polar Regions the troposphere thickness decreases gradually .The depth of this layer at the poles is nearly half thick compared to the tropics . Average depth of the troposphere is approximately 11 kilometres as shown in Fig. 1.4. About 80% of the total mass of the atmosphere lies in troposphere .It is also the layer where the most of the weather occurs. Near the Earth’s surface maximum air temperature occurs in this lays . Air temperature drops uniformly with altitude at a rate of approximately 6.50 Celsius per 1000 meters with increase in height. This phenomenon is commonly known the Environmental Lapse Rate. At the top of the troposphere the average temperature is -56.50C. A narrow transition zone called as the tropopause is located at the upper edge of the troposphere 6.

Stratosphere
Just above the troposphere , stratosphere begins which is the second-lowest layer of Earth’s atmosphere and is separated from troposphere by the tropopause. This layer extends from the top of the troposphere at roughly 12 km above Earth’s surface to the stratopause at the height of about 50 to 55 km.
At the top of the stratosphere the atmospheric pressure is roughly 1/1000 times the pressure at sea level. It contains the ozone layer, which is the part of Earth’s atmosphere that contains relatively high concentrations of that gas. The strastosphere is a layer in which temperature rise with increasing altitude. The elevation in temperature is caused by the absorption of ultraviolet radiation (UV) radiation from the sun by the ozone layer. Although the temperature may be -600C at the tropopause, the top of the stratosphere is much warmer, and may be near 0oC.The stratospheric temperature profile creates very stables atmospheric conditions, so the stratosphere lacks the weather-producing air turbulence that is so prevalent in the troposphere. Consequently the stratosphere is almost completely free of clouds and other forms of weather . However, polar stratospheric or nacreous clouds are occasionally observed in the lower part of this layer of the atmosphere where the air is coldest. The stratosphere is the highest layer that can be accessed by jet-powered aircraft 1.
Mesosphere
The layer of the earth’s atmosphere that is directly above the stratosphere is the mesosphere this layer temperature decreases as the altitude increases. Mesosphere is the third layer of atmosphere and located between stratosphere and thermosphere which extends from the altitude of 50 km to 80 km above the earth’s surface. The streaks of hot gases released from meteors can be seen in this layer. The temperature of this layer decreases with increases in altitude that is from -20C to -1900C. therefore it is the coldest place on the earth and has an average temperature about -850C water vapor is frozen due to the cold temperature of the mesosphere then formed ice clouds. The main fas found in this layer is nitric oxide (NO). strong wind blows from the west to the east during winter and from east to west during spring season in this layer 27.

Thermosphere
It is the second-highest layer of Earth’s atmosphere which extends from the mesopause at an altitude of about 80 km up to the thermopause at an altitude range of 500-1000 km. the height of the thermopause varies considerably due to changes in solar activity. As the thermopause lies at the lower boundary of the exosphere, it is also referred to as theexoobase. The lower part of the thermosphere, from 80 to 550 kilometres above Earth’s surface, contains the ionosphere.
The temperature of the thermosphere gradually increases with height. Unlike the stratosphere beneath it, wherein a temperature inversion is due to the absorption of radiation by ozone, the inversion in the thermosphere occurs due to the extremely low density of its molecules. The temperature of this layer can rise as high as 15000C, though the gas molecules are so far distant that its temperature in the usual sense is not very meaningful. The air is so rarefied that an individual molecule travels an average of 1 kilometre between collisions with other molecules. Although the thermosphere has a high proportion of molecules with high energy, it would not feel hot to a human in direct contact, because its density is too low to conduct a significant amount of energy to or from the skin 1.
Exosphere
It is the fifth and outermost layer of the atmosphere which extends beyond the thermosphere. The temperature of this layer is very high about 1200 to 6000 degrees Centrigrade. The density of air is very low but wind blows at high speed. This layer mainly comprises of very lighter gases like hydrogen and helium, the particles are much more far apart so that they can traverse hundreds of kilometre of distance without any collision with each other and hence, particles rarely collide. The atmosphere no longer behaves like a fluids, these freely moving particles follow ballistic paths and may travel into and out of the magnetosphere or the solar wind. This layer is very far from the earth’s surface so there is no effect of gravity so that air particles may escape from atmosphere 27.

Figure 1.2 Variation of temperature with altitude www.wikipedia.org
Air mass
Air mass defines the direct and optical path length through the earth’s atmosphere; it represents how much atmosphere solar radiation has to pass through before reaching earth surface . Air mass coefficient can be used to help characterize solar spectrum after solar radiation has travelled through the atmosphere. Air mass (AM) equals 1.0 when the Sun is directly overhead at sea level. “AM 1.5” is almost universal when characterizing terrestrial power-generating panels.
The attenuation caused by atmospheric constituents through the relationship between global, direct and diffuse solar radiation with respect to optical air mass can be studied. The optical air mass change has spatial and temporal dependence and influences the radiations flux incident, causing changes in the Global, diffuse and direct solar irradiances 36. The decrease of solar radiation with increase of optical air mass is justified by the increase in the probability of the collision of solar rays with atmospheric constituents 37.

Solar Zenith Angle
Solar zenith angle (SZA) is the angle between the zenith and the sun which is useful in determining whether the sun is rising or setting and also in predicting solar effects on radio communications. Smaller is the solar zenith angle, the higher is the sun is in the sky. As the sun rises, The angle gradually decreases until mid-day. As SZA increases, radiation falling on a horizontal surface on the earth decreases. The value of the Solar Zenith Angle is dependent on the position on the Earth and the local date and time. The incident radiation is directly proportional to the cosine of angle between the beam radiations and normal to the surface leading to cosine effect 36.
Precipitation
Precipitation is defined as liquid or solid condensation of water vapour falling from clouds or deposited from air into the ground. Precipitation is measured as the amount of water that reaches horizontal ground or the horizontal ground projection plane of the earth’s surface, and is expressed as a vertical depth of water or water equivalent of solid precipitation. The unit of precipitation in Nepal is milimeter. Instruments for measuring precipitation is rain gauge precipitation in the form of ice takes, such as show, is called solid precipitation , and that in the form of water drops is sometimes called as liquid precipitation.
The annual precipitation in Nepal varies from place to place ranging from less than 250 mm in mustang area to more than 5000 mm at Lumle near south west of Pokhara 80% of rainfall is found in monsoon season i.e. from June to mid of September. The sky is partially or fully covered with clouds in the summer season thus there is less solar radiation in rainy and cloudy day which might be due to the absorption and reflection of radiation by clouds, aerosols and rain droplets in the atmosphere 13.

Relative Humidity
The relative humidity is a major effecting factors of GSR. It is the ratio of the partial pressure of water vapour to the equilibrium vapour pressure of water at a particular temperature . Relative humidity depends on temperature and the pressure of the system under study. It needs less water vapour to get high relative humidity at low temperatures; more water vapour is essential to attain high relative humidity in warm or hot air. It is known that higher rainfall location have higher value of humidity and relative humidity absorbs the radiation in the atmosphere. Thus values of GSR are found to be lower at a location of higher relative humidity. Hence the relative humidity and GSR is inversely proportional to each other 13.
Altitude
Altitude is one of the major factor influencing the GSR. The GSR increases in altitude mainly due to decreasing amounts of air molecules, ozone, aerosols and clouds in the atmosphere as well as due to show covered surface. Thus, there is not only the single source depending factor. Ignoring those effects , at higher altitude there is dependence of GSR on SZA and wavelength changes. A significant part of global population resides at altitude of up to a few kilometers above the sea level. Simply, the increases in solar radiation flux with respect to height is called the altitude effect 38.
Solar radiation increases at higher altitudes as the atmospheric has less chance to absorb the incoming UV. It has been found that UV increases by up to 4% for every 300m increases in altitude.
Sunshine duration
Sunshine duration is now a days taken as factor for the important determination of global solar radiation data. It is also the parameter with the correlation with global solar radiation, air temperature relative humidity and other climate factor. Sunshine duration during a given period (e.g. within one day) is considered as the sum of the time for which the direct solar irradiance exceeds 120 W/m2. For precise measurement , the sunshine recorder must be accurately adjusted for planar labelling, meridian direction and latitude 39. Sunshine duration is used to measure the percentage ratio of recorded bright sunshine duration and daylight duration for the estimation of GSR in empirical models. Due to financial constraints , there is not adequate numbers of sunshine recorders installed in our country Nepal. The average daily sunshine duration for Nepal has been reported to be 6.8 hours per day from various measurements.

Attenuation of Solar Radiation
The phenomena in which process of coming the radiation on our eye through scattering and re-direction from the atmosphere constituent is known as atmospheric attenuation. Solar radiation is partially depleted and attenuated when it travels through the layers of atmosphere, preventing a substantial portion of it from reaching on the earth’s surface. This phenomena is given by the Bouger’s law or Beer’s law 33 .
Consider I0n? is normally incident monochromatic extraterrestrial irradiance at mean sun-earth distance (r0) and ? is the flux emerged on traversing a distance ‘m’ then according to Beer’s law.
I_0n?=I_on? exp?(-k_? m) (1.4)
Where k_? is the monochromatic extinction or attenuation coefficient.
‘m’ is the optical path length and
k_? m is the monochromatic extinction optical thickness.

Absorption
When the molecules absorb the photon , it increases the energy of the molecules. Oxygen and nitrogen which together constitute 99% of the atmosphere volume, absorbs strongly fraction of the solar radiation having the wavelength shorter than about 0.3 ?m. The very short wavelengths ionize the gas molecules. Other wavelength in the ultraviolet are absorbs by ozone in the layer between 20 and 50 km above of the earth. Different molecules absorbs the different wavelengths of radiation. For examples, O2 and O3 almost wavelengths shorter than 300 nm 39.
The gases that comprises our atmosphere are selective absorbers of radiation because each gas absorbs only particular wavelengths of light. The atmosphere absorbs far better in the long wave end of the electromagnetic spectrum which is the region of maximum emission (10 ?m) for the earth.

Atmospheric Scattering
As sunlight penetrates the atmosphere it may be absorbed, scattered, reflected or refracted before reaching the surface. Scattering is a result of the interaction between the electromagnetic field of the incoming light with the electric field of the atmospheric molecules and aerosols. This interaction is synchronized and as a result the scattered light has the same frequency and wavelength as the incoming light. Scattering differs with particle size and varies with wavelength. For this reason , the spectral composition of the scattered light differs from that of the incoming light. The attenuation of light in the atmosphere is caused by absorption and scattering , and can be divided into effects that remove and add light to a given viewing ray. The amount of scattered energy depends strongly on the ratio of particle size to the wavelength of the incident wave 13.
x= 2?r/? (1.5)
where ? is the wavelength of incoming radiation and r is the radius of scattering particles. Depending upon the size of particles, scattering can be categorized as given below:
Rayleigh scattering
Mie scattering
Non selective scattering

Rayleigh Scattering
If the size of scattering particles is small compared to the wavelength of incident radiation (r ? ?/10), the scattered intensity on both forward and backward direction is same. This type of scattering is referred to as Rayleigh scattering. This type of scattering is therefore wavelength dependent. As the wavelength decreases, the amount of scattering increases. Because of Rayleigh scattering, the sky appears blue. This is because blue light is scattered around four times as much as red light, and UV light is scattered about 16 times as much as red light. This solution is given by at the end of century by Lord Rayleigh and simply called as Rayleigh’s theory 40.
?=(8?^3 (?n-1)?^2)/(3N??^2 ) (1.6)
where, ? is the refractive index of the particle
?=1.29 kg/m3 is the density
N=2.28×?10?^25/kg is the number of molecules
? is the wavelength of light
n=1.008735?^(-4.08)
where ? is being in micrometer unit. Rayleigh scattering is the consequence of why sky appears blue. From Rayleigh relation , blue coloured light is scattered more than red , orange , green and yellow 41.
Mie Scattering
In Mie scattering the light is scattered forward and is highly anisotropic 41. The Rayleigh theory is not applicable when the particle dimension is comparable to the wavelength of incident radiation. In such case wave equation needed to solve wave equation so at the beginning of the 20th century Gustav Mie and in his honour the theory is named as Mie’s theory. Both reflected and scattered intensity in Mie scattering is greater than in Rayleigh scattering.
Angstrom gave the Angstrom’s turbidity coefficient. And ? is being wavelength coefficient with wavelength ?. For larger particles if (r ??/10), the angular distribution of scattered intensity becomes more complex with more energy scattered in the forward direction. This type of scattering is described by Mie scattering theory 27.
1.13.5 Non Selective Scattering
It is the third type of scattering which occurs in the lower portion of the atmosphere when the particles are much larger than the incident radiation. This type of scattering does not depend upon wavelength and is the primary cause of haze 39.
Reflection
When the change of the propagation environment, a part of the electromagnetic wave reflected again towards the original environment. Each body which receives an amount of EMR may reflect a part. Reflected radiation is mainly reflected from the terrain and is , therefore, more important in mountainous region. The fraction of the intensity of solar radiation that is reflected is called the albedo of the surface. Reflection is a process where sunlight is redirected by 1800 after it strikes on atmospheric particles. The reflection of solar radiation depends on the nature of the reflecting surface. For solar radiation, albedo is dependent of clouds and ground surface 31.
Albedo
The albedo of a surface is the part of the incident sunlight that the surface reflects. Radiation that is not reflected is absorbed by the surface. The absorbed energy increases the surface temperature, evaporates water, melts and sublimates snow and ice , and energizes the turbulent heat exchange between the surface and the lowest layer of the atmosphere. The surface albedo is a key ingredient in the remote sensing of surface and atmospheric properties from space. The spectral and angular dependence of reflected sunlight is used to inter surface properties such as the extent and nature of vegetation cover. It must also be allowed for when determining atmospheric composition such as the amount, size, and optical properties of haze particles. Over continents, the largest component of the reflected sunlight under cloud-free conditions is due to reflection by the surface. As a consequence the determination of atmospheric composition from reflected sunlight needs proper knowledge of the contribution made by the reflecting surface 1.
Different surfaces have different albedo. Oceans , lakes, and forests reflect relatively small fractions of the incident sunlight and have low albedos while snow, sea, ice, and deserts reflect relatively large function of the incident sunlight and have large albedos. It should be noticed that an albedo is not an intrinsic property of a surface. Instead for any surface, the albedo depends on the spectral and angular distributions of the incident light, which in turn are governed by atmospheric composition and the direction of the beam of light from the sun 42.

Table 1.4 Albedo of surface with sun over our head 42
S. No. Surface Albedo
1 Vegetation 0.2
2 Light color soil 0.3
3 Dark color soil 0.1
4 Water 0.1
5 Clouds/snow 0.5-0.9

Review of Literature
Solar radiation is a renewable energy sources that has been used throughout the history of human beings. Passive solar technologies were already used by ancient civilizations especially for warming and heating. Concentration of solar radiation was extensively studied and in the 19th century the first solar-based mechanical engines were built. Now-a-days, there exist an extremely large variety of solar technologies that are applied around the world. Many paper have been published regarding the global solar radiation in Nepal. The more radiation more energy is produced. In Nepal the study of solar radiation is not old.
But there are some report found to measurement of solar wind energy resources assessment reported the annual average of 4.7 kWh/m2/day and 4.23 kWh/m2/day solar energy available in Nepal. The present of energy demand of Nepal have been fulfilled partly from hydropower, biogas, fossil fuel and traditional energy sources such as fire, wood and coal 13,43. The use of renewable energy is negligible. Renewable energy is the energy obtained from the continuing of repetitive currents of energy occurring in natural environments. Obvious example of renewable of energy is solar energy. Continuous and long term radiation are not available in Nepal. But short term and monitoring and utilization of solar radiation has been done by royal Nepal academy of science and technology (RONAST) in collaboration of Japan 9.
Alternative energy promotion centre (AEPC) under the government of Nepal has conducted a project solar and wind energy resources assessment (SWERA) under united nations environment program (UNEP)/Global environment fund (GEF) from march 2003 to 2006. The study recommended the annual average solar insolation of about 4.7kWh/m2/day in Nepal. SWERA report showed that there is lower solar radiation potential at low altitude plain region than at high altitude mountains and north western part of the country 43. The solar resource map developed by DLR Germany satellite estimates 3.5-4 kWh/m2/day of energy at the central mid hill region and higher energy of 5-5.5 kWh/m2/day is found in the north western region. Similarly, the solar map report of national renewable energy laboratory (NREL) USA shows that there is almost equal amount 4.5 to 5 kWh/m2/day of solar radiation found throughout the country. But in north-western region of Nepal the solar insolation is found to be 6-6.5 kWh/m2/day based on the results of the measurements carried out by SWERA. These solar resources satellite derived DLR and NREL solar resource maps are compared with the ground level measured data of 4 sites. The relative bias-ness of the model data with respect to the ground level measured data is analyzed considering point to point as well as region monthly and annual variation. It shows that within a particular point of location, DLR satellite data has higher relative biasness in comparison to NREL data 44.
In India also various researchers developed and investigated correlations in monthly mean global solar radiation and relative duration of sunshine (Modi & Sukhatme, 1979; Garg & Garg, 1985). Due to high solar potential and large number of clear sky days, Rajasthan is suitable region for installation of solar energy devices. Intensity of global solar radiation in ranging between 66.4 kWh/m2/day in about half of Rajasthan, but literature survey reveals that very few studies have been done about solar radiation correlations for this region except for Jodhpur (26.30? N, 73.02? E) which is situated in west region of Rajasthan (Modi & Sukhatne 1979). Jaipur(26.92?N, 75.87?E) is the capital city of Rajasthan and having annual average of mean daily global solar radiation (19.42 MJ/m2/day). which is comparable to annual average of mean daily global solar radiation at Jodhpur (19.97 MJ/m2/day) 28.
Nepal is located in favourable latitudes receives ample solar radiation throughout the country. The average global solar radiation varies 3.6-6.2 kWh/m2/day and sunshine about 300 days in year. The national average sunshine hour and solar energy 6.8 kWh/m2/day and 4.7 kWh/m2/day respectively 45. It is greater than the 15.8 MJ/m2/day measured by Solar Energy Research Laboratory, Department of Physics, Silpakorn University, Thailand for Lao PDR. Choice of solar energy, in country like Nepal, is the best and ultimate option among the different energy including alternative energy sources. If we think of complete solution of rural electrification in Nepal, we have to plan to link up micro-hydro/pico-hydro with solar energy exploitation. Thus , an accurate knowledge and database of solar radiation at a particular place and selected sites are important for the development of many solar devices, the establishment of solar plant at the proposed site and for estimation of their performance 46. The radiation reaching the earth surface is modified significantly by clouds, water vapour, ice, aerosols, and atmospheric constituents in its intensity and the sun-shine duration. The beam radiation (radiation coming directly from the solar disk) is attenuated by the presence of cloud in its path,as well as by various atmospheric elements. The depletion of the direct beam by the cloud depends on the type of clouds, their thickness, and the number of layers. The radiation scattered by the atmospheric constituents is called diffused radiation where a portion of this radiation goes back by about 6% of the incident radiation to space, and a portion , about 20% of the incident radiation , reaches the earth surface46.
The global solar radiation was estimated using sunshine duration in Himalayan region of Kathmandu using relative sunshine hours. In this paper, the empirical constants are found to be 0.21 and 0.25 respectively. The performance of the model is tested by Root mean square Error, Mean Bias Error, Mean Percentage Error and Coefficient of Determination whose values are 0.071, 0.055, 0.047 and 0.71 respectively 47.
Kafle 48 studied the global solar radiation at Biratnagar. He found that the observed global solar radiation shows diurnal variation with maximum at noon time, there is a day by day and month to month variation of solar radiation. A maximum 1209.08 W/m2 on 5th May 12:00 NST and minimum 51.11 W/m2 on 13th Jan 17:00 NST.
Tiwari 49 studied the different empirical models for correlation of monthly average daily global solar radiation with hour of sunshine on a horizontal surface at Tribhuvan International Airport, Kathmandu, Nepal and found out a set of constants for Angstrom-type correlation of first and second order to estimate monthly average daily global solar radiation . He obtained H1=0.471n+13.206, R2=0.559 (T.I.A. data from 1975 to 1985) the constants employing sunshine hours data recorded Kathmandu latitude 27?42′ N, longitude 85?22′ E. Least square regression was performed to derive these constants.

1.15 Objectives of the Study
The main aim of this study is to estimate the Global Solar Radiation using meteorological parameters in empirical model.Some of the objectives are:
To study and analyze the seasonal, daily and monthly variation of global solar radiation at Pokhara.
To estimate the global solar radiation based on meteorological parameters and to test modified angstrom relation.
To compare the measured global solar radiation with the predicted global solar radiation at Pokhara.
1.16 Limitation of the Study
Energy research has its own limitation to meet its research objective in a perfect manner . Here are some as the constraints imposed on this study:-
Secondary data is used from the department of the hydrology and meteorology where huge amount of longterm meteorological data are not available.
It is difficult to handle the analysis of the data regarding. Global solar radiation due to insufficient and in exhaustive data provided by the hydrology and meteorology department of Nepal.
There is limitation over time and money.

CHAPTER TWO
THE PHYSICS OF SUN
2.1 General Consideration
The sun is located near the outward tip of the Sagittarius arm of the Milkyway galaxy. The Sun is at the centre of the Solar system to which all the planets and their satellites revolve around continuously. The energy reaching the earth surface in the form of radiation supports almost all life on the earth. The same radiation is responsible for climate and weather in the earth 50.
It is important to know about the Sun before knowing about the distribution of the solar radiation and its effects at different location.
2.2 The Sun
The Sun is the nearest star from our home planet earth and is situated at the average distance of 1.5×108 km away from the earth. Its mass is approximately 1.99×1032 kg , average density 1400kg/m3 and is a gaseous sphere of diameter 1.39×106 km. Its temperature varies from 5770 K at radiation surface to 5×106 K at its Centre. Sun encloses about 99.86% of the total mass of the solar system51.
The Sun has major composition of hydrogen and helium which account for 74.9% and 23.8% of the mass of the Sun in the photosphere respectively. All heavier elements accounts for fewer than 2% of the mass , with Oxygen (roughly 1%), Carbon(0.3%), Neon (0.2%), and Iron(0.2%) being the most abundant 52.
Based on the nuclear fusion reaction, solar energy is generated due to steady conversion of four hydrogen atoms into single helium atom with release of large amount of energy. As the result, the mass of Sun decreases; that reduced mass is converted into energy according to the Einstein’s Mass Energy relation given as
E=mc^2 (2.1)
Where E is the energy released, m is the reduced mass and c is the speed of light.
The structure of the Sun is illustrated in the Figure 2.1 below. The major division of its structure are central core,radiative zone, convection zone, photosphere, chromospheres, and corona.

Figure 2.1 The internal structure of the Sun www.google.com
2.2.1 Core
The core is the innermost part of the Sun and is considered to be extended from centre to about 0.2 to 0.25 of solar radius. Here gravity has squeezed the Sun so much that hydrogen compresses together to form helium and releases energy via nuclear fusion reaction. All the energy that comes away from the Sun and all the reaches the earth started in the core. It is the hottest, densest part of the Sun which is 150 times denser than the water and has a blazing temperature of around 15 million degree Celsius 50.
The core consists of 34% of the Sun’s mass while only 0.8% of the Sun’s volume. The core of the Sun generates 99% of the fusion power of the Sun. The two distinct reactions in which four hydrogen nuclei fuses in one helium nucleus are the proton-proton chain reaction and the CNO cycle 48.
2.2.2 Radiative Zone
This is the layer of the Sun above the super dense core. Density decreases moving away from the core. Light produced by nuclear fusion in the core traverse out in the shell called radiative zone. It is less dense than core but it is still so dense that light from core bounces around taking about 100,000 years to move through the radiative zone 49.
2.2.3 Convection Zone
It is the layer of Sun above the radiative zone. When the density of the radiative zone becomes low enough, energy from the core in the form of light is converted into heat. Much like the bubbles in a pot of boiling, the heat from the edge of of the radiative zone rises until it cools enough that it sinks back down. This pattern of the heated material rising then cooling happens in big bubbles called convection cells 50.
2.2.4 Photosphere
The material that reaches top of the convection zone cools by giving light. The first part of the Sun that is visible to us where the light we see from the sun originates is called as photosphere. Even though the layer is not solid we call this part of the Sun the surface and it is also where the solar atmosphere starts. It is about 500 km thick and the temperature in this layer varies from 8000 K to 4000 K. The photosphere is marked by relatively bright granules about 150 km in diameter. The bright granules are separated by dark regions known as faculae and variable features called sunspots. It looks as a bright disk or by a naked eye but on magnification of this layer, dark circular spots could be seen which are known as sunspots. Sunspot is supposed to be a cool region with a temperature of about 4600 K while the temperature of the photosphere is about 6000 K. This region above the photosphere is called solar atmosphere and corona. This region contains vapour of almost all the familiar elements 49.
2.2.5 Chromosphere
Above photosphere is a layer of atmosphere about 10,000 km deep called chromosphere. The chromospheres is no longer white light like the photosphere but is mostly red in visible region. It can be seen as red flashes during a total solar eclipse. The density of the chromosphere is only 10-4 times that of the photosphere and its density lowers with distance from the centre of the Sun. The temperature decreases from the inner boundary at about 6,000 K to a minimum of approximately 3,800 K 50.
2.2.6 Corona
It is the highest part of the solar atmosphere which starts around 10,000 km above solar photosphere. Unlike the atmosphere of the earth , the atmosphere of the Sun continues to get hotter on moving away from the solar surface. At 20,000 – 25,000 km away from the solar surface, the corona has an average temperature of 1,000,000 to 2,000,000 million degree Celsius. The corona is 10-12 times denser than the photosphere, and so produces about one-millionth as much visible light 53.
2.3 Solar Radiation Geometry
The astronomical relationship between the Sun and the earth is significant for the description of motion of the earth around the Sun which considers the motion of the earth around its polar axis and the angle between the earth’s equator and the plane containing the sun-earth orbital system. Rotation of earth around its axis is responsible for diurnal variation, the position of its axis relative to the Sun causes seasonal variation 36. Thus the parameters like sun-earth distance (r), latitude (?), longitude (L), altitude (?), solar declination (?),zenith angle (?z), azimuthal angle (?), hour angle (?) are frequently employed.
2.3.1 Sun Earth distance (r)
Figure 2.2: Motion of the Earth around the Sun 53.
The earth revolves around the sun in an elliptical path thus there is no fixed distance between the sun and the earth. The amount of solar radiation coming to the earth surface is inversely proportional to the square of the distance between sun and earth 53. Thus it is very important to determine the value of sun-earth distance precisely. The unit used to measure the separation between sun and earth is astronomical unit(AU) and the value is 1 AU.
1 AU=1.496×?10?^6 km (2.2)
The minimum distance between sun and earth is about 0.983 AU and the maximum is approximately 1.017 AU. The earth is at its closest point to the sun (perihelion) on 3rd January and as its farthest point (aphelion) on 4th July. On 4th April and 5th October earth is at its mean distance from the sun 54.

Figure 2.3: Sun and Earth relationship 50

Spencer established the fourier series type of expression for the reciprocal of the square of the sun-earth distance ‘r’, here called eccentricity correction factor of earth’s orbit, denoted by E0 and given by,
E_0=?(r_0/r)?^2=1.00011+0.034221cos??+0.01280sin??+0.000719sin?2?+0.000077sin?2? (2.3)
where ?=(2?(d_n-1))/365 , in radians which is also known as day angle .
And dn is the day number of year ranging from 1 on 1st January to 365 on 31st December. But for leap year the day number will be 366.
2.3.2 Solar Declination (?)
The angle between the rays of the Sun and the plane of the earth’s equator is called as solar declination. The angle between the earth axis and the plane of the earth orbit is nearly constant, it varies with the seasons and its period is one year which is the time required by the earth to complete its revolution around the Sun. Moreover, the equator of the earth is considered to be in the equatorial plane. Solar declination is derived by drawing a line between the center of the earth and the Sun. The angle of declination attains a maximum value of 23?27′ when the projection of the earth axis on the plane of the earth orbit is on the same line linking the earth and the Sun. The angle of declination is slightly decreasing due to the changes in the tilt of the earth’s axis 55.
The declination varies between -23.?45?^0 on June 21. Clearly, the declination has the same numerical value as latitude at which the Sun is directly overhead at solar noon on a given day, where the extremes are the tropics of Cancer (23.45? N) and Capricorn (23.45? S). The angle of declination ,?, is estimated using the formula given by 54
?_s=23.45sin??(360(284+d_n))/365? (2.4)
where dn is the day number during the year with the 1st of January set as dn=1 and dn=365 for 31st December.
2.3.3 Longitude (L) and Latitude (?)
Longitude and latitude are the two geographical co-ordinates considered to locate the any position of earth’s surface with reference to Greenwich meridian, London and to the equator respectively. The angle between the plane defining the considered meridians and plane defining the Greenwich meridian is called as longitude (L) which varies between 0? and ±180?, 180? E and 180? W of Greenwich meridian. The lines of constant longitude (meridian) passes from pole to pole on the globe like segment boundaries on a peeled orange. Every meridian must cross the equator 54.
The latitude (?) of a place is considered as the angle made by the radial line joining location of to the centre of earth to the projection of line on the equatorial line. It varies between 0? to 90? in the northern hemisphere and the negative value for the southern hemisphere.
2.3.4 Apparent position of sun
In order to know about solar radiation reaching on the horizontal surface of earth it is required to be known about relationship between the solar position in the sky and the surface coordinates in the earth. The most commonly used parameters to specify the position of the sun is solar zenith angle (?z), solar altitude (?), azimuth angle (?), hour angle (?) etc. which are explained below:

Figure 2.4 Apparent position of the Sun 56
2.3.4.1 Zenith Angle (?z)
It is the angle between the sun’s rays and the normal line in the horizontal plane. In a three-dimensional coordinate system the zenith is the axis perpendicular to the horizontal plane. Zenith angle is calculated from a local zenith, meaning that it differs based on the location of the person or device making the measurement. It varies from 0? to 90?. It is also called the zenith distance in degrees i.e.0?? ?z ? 90? 56.
2.3.4.2 Azimuth Angle (?)
Azimuth angle is the direction of a celestial object, measured clockwise around the observer’s horizon from north. So an object due north has an azimuth of 0?, one due east 90?, south 180? and west 270?. Azimuth and altitude are frequently used together to give the direction of an object in the topocentric coordinate system 50.

Figure 2.5 Azimuth Angle Wikipedia.org
2.3.4.3 Solar altitude angle (?)
It is an angle between the horizon and the line to the sun. Solar altitude is measured in degrees. The value of the solar altitude varies based on the time of day, the time of year and the latitude on earth and the complement of zenith angle is ?=90-?_z 57.
2.3.4.4 Hour angle (?)
Hour angle shows how much sidereal time has passed because the object was on the local meridian. It is also the angular between the object and the meridian, measured in hours ( 1 hour= 15 degrees). It varies from 180? to 180? The measuring time is adopted from noon based on the local time, being positive in morning and negative in afternoon. The trigonometric relation between the sun and a horizontal surface with a given geographical position are as follows 57:
cos???_z ?=sin??? sin???+ ? ? cos?? cos?? cos??=sin?? (2.5)
Then , equation (2.5) can be solved for the sunset hour angle ?=?s, ?z=90?
Then, cos??90??=0=sin??? sin???+ ? ? cos?? cos?? cos??
cos??w_s ?=-(sin?? sin??)/(cos?? cos?? )=-tan???tan?? ?
? ??_s=cos^(-1)??(-tan???tan???)? ? ? (2.6)
The sunset hour angle is equal to the sunrise hour angle except for the sign difference.
The total sunshine hours can be written as
N= 2/15 cos^(-1)??(-tan???tan???)? ? ? (2.7)
The number of daylight varies with latitude for different day of year. The total sunshine hour is 12 hours for March and September 21, and is independent of latitude. However, the maximum and minimum total sunshine hour is found in June 21 and December 21 respectively 56.
2.4 Nature of the Sun Light
The origin of the solar radiation obtained on the Earth is the transformation of hydrogen into helium through solar fusion. Helium is constantly being produced from lighter hydrogen as four nuclei merge to form one nucleus of helium with a release of electromagnetic energy 50.
The emitted energy of the sun is 3.8×1026 W and it comes from the thermonuclear fusion of hydrogen into heat temperatures around 1.5×106 K at the core of the Sun. The energy released by the thermonuclear reaction is carried by energetic photons, but because the strong absorption of the peripheral gases, most of these photons do not penetrate the surface. The Sun radiates electromagnetic energy in terms of photons which are light particles. Almost 30% of this incident energy of the Earth is reflected back, but the rest is absorbed and is , eventually, retransmitted to deep space in terms of long-wave infrared radiation. The total power that is incident on the Earth’s surface from the Sun every year is 1.73×1014 KW and it is equivalent to 1.5 ×1018 KWh annually, which is equivalent to 1.9×1014. With comparison to the annual world consumption of almost 1010 Tons, this is a very large and inappreciable amount. This energy is regarded to be spread all over the world’s surface and, thus, the amount that falls on one square meter at noon time is about 1 KW in the tropical regions. The amount of solar power density changes with latitude, elevation, season of the year and the time of a particular day. Most of the developing nations lie within the tropical belt of the world where there are high solar power densities, and so they want to exploit this source in the most beneficial ways. On the other hand, about 80% of the world’s populations live between latitudes 35? N and 35?S. These regions attains the Sun’s radiation for almost 3000-4000 h/year. In terms of solar power densities, this is equivalent to around 2000 KWh/year. Moreover, in these low altitude regions,seasonal sunlight hour changes are not important. This means that these areas receive the Sun’s radiation almost uniformly throughout the year 58.
2.5 Solar Radiation Spectrum
The distribution of electromagnetic radiation emitted by the sun as a function of the wavelength incident on the top of the atmosphere is called solar spectrum. Also, the solar radiation spectrum presents a reference chart showing the amount of solar radiation emitted by the Sun, across the complete spectrum, from the extremely high energy gamma rays, through X-rays, Extreme Ultraviolet (EUV), Ultraviolet (UV), visible wavelengths, infrared (IR), far infrared (FIR), and to radio frequencies. Electromagnetic radiation travels in the form of wave with the speed of light (3×108 m/sec) in vacuum. The sun emits energy at the rate of 6.2×107 W/m2. The visible region lies in the wavelength range between 4000? and 7700?. This band contains seven different colors as Violet, Indigo, Blue, Green, Yellow, Orange, and Red with increasing order of Wavelength. In 1800 Sir Willium Hersel observed invisible radiation beyond the red end and gave the infrared radiation. In 1801, J. W. Ritter found ultraviolet radiation away from the violet edge of the spectrum. The distribution of the energy in the solar spectrum is not uniform. About 50% energy lies in the above visible region, 40% in the visible region and rest 10% in the shorter wavelength region 59.

Figure 2.6: Solar Spectrum 59

The following table shows the distribution of solar radiation according to wavelength.
Table 2.1: Table showing Electromagnetic Spectrum 56
S. No. Name of Region Wavelength (cm) Frequency (cps)
1 Gamma rays 10-9 3×1019
2 X-rays 10-8 3×1018
3 Ultraviolet 3×10-5 1015
4 Visible 4×10-5 to 8×10-5 4.3×1014to 7.5×1014
5 Infrared 10-4 to 10-1 3×1012 to 4.3×1014
6 Microwave 1 3×1010
7 Spacecraft 102 3×108
8 Television and FM 103 3×107
9 Short Wave 104 3×106
10 AM, Radio Wave 105 3×105

2.6 Blackbody Radiation
An object or system which absorbs all radiation incident on it and re-radiates the energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it is referred to as blackbody radiation. A black body is one which absorbs and emits the maximum amount of radiation in which such emitted radiation is theoretically considered as black body radiation 54.
2.7 Blackbody spectrum
The radiation from the Sun may be represented by that of a black body at a temperature of about 6000 K. Measurements of the solar radiation are made at the earth (not at the surface of the Sun ) so are lower intensity than that given by the Planck spectrum by the ratio ( Rs/res)2, where Rs is the Sun’s radius and res is the mean distance between the earth and Sun. Moreover, the Sun’s radiation has to pass through the earth’s atmosphere before reaching the surface which slightly decreases its intensity. The spectrum is plotted in the figure 2.5 reduced by the appropriate geometric factor. Note that absorption in the atmosphere omits certain wavelengths nearly completely. The area enclosed between the curve and the horizontal axis is the total power per unit area at all wavelengths . This is 1350 W/m2 60.

Figure 2.7 Variation of intensity with wavelength 60
The area enclosed by the curve on top, the horizontal axis on the bottom, and the two dashed lines, is the amount of power per unit area in the visible range, 520 W/m2. The amount of radiation in the ultraviolet (below 400nm) and infrared (above 700 nm) ranges are 192 and 640 W/m2 respectively.
2.8 Planck’s Radiation
The emissive power of a black body at any wavelength and temperature called its spectral emissive power is given by Planck’s law61
?_? (T)=(2hc^2)/?^5 1/(e^((hc/(?k_? T)) )-1) (2.5)
where, h= Planck’s constant, c= velocity of light in air, ?= wavelength of radiation, T= Absolute temperature

2.9 Stefan-Boltzmann Equation
The total energy emitted per unit area per unit area per second by a black body is proportional to the fourth power of the absolute temperature. This is called as Stefan-Boltzmann equation 62. Mathematically,
F=?T^4 (2.6)
where, ? is called Stefan’s constant and its value is given by
?=5.67×?10?^(-8) Jm^(-2) S^(-1) K^(-4)
2.10 Wien’s Displacement Law
Wien’s displacement law states that “The product of the wavelength corresponding maximum energy ?m and the absolute temperature ‘T’ is constant.”
i.e. ?_m T=constant (2.7)
The value of ?_m T is found to be 2879.8 ?mK.
Hence, the relation ?_m T=2897.8 ?mK is called Wien’s displacement law. Since the Sun is a black body at 5777K, the wavelength ?_max=2897.8/5777=0.5016 ?m .This wavelength corresponds to green line 1. Hence, we come to the conclusion that the maximum power can be emitted in the case of green region.
2.11 Kirchoff’s Law
Kirchoff”s law states that the emissivity (??) of a given wavelength is equal to the absorptivity (A?) in a medium under thermodynamic equilibrium. i.e. (??)= (A?)..This relation requires the condition of thermodynamic equilibrium, such that uniform temperature and isotropic radiation is received 27.
2.12 Solar Constant
Solar constant is the amount of incoming solar radiation per unit area incident on a plane normal to the rays at a distance of one astronomical unit from the sun.It is not a true constant but seems to vary slightly. The solar constant also can be defined as the average amount of solar radiation received by the Earth’s atmosphere per unit area, when the Earth is at its average distance from the Sun 60.
The solar constant depends upon the Sun-earth distance distance and varies slightly over the year. The mean value of solar constant is 1367 W/m2. The mean value of solar constant as accepted by NASA (National Aeronautics and Space Administration) and WRC (World Radiation Centre) is 1353±21 W/m2 and 1367±1.7 W/m2.

Figure 2.8 Solar Radiation Spectrum 61
Solar constant can be determined by an empirical formula given by;
S=?S_0?^2 ?R_0?^2/S^2
S=S_0 (1.00010+0.034221 cos???_0 ?+0.001280 sin???_o ?+0.000719 cos??2?_0 ?+0.000077 sin??2?_0 ? ) (2.8)
where R0 is the mean sun-earth distance and ?0 is defined in terms of day number of year starting from January.
?_0=(2n(d_n-1))/365 (2.9)
where dn is the day number and is counted from 1 to 365 starting from January 1st .The maximum value of solar constant is 1400 W/m2 around 4th January and minimum value is 1309 W/m2 around 5th July.
2.13 Extraterrestrial Solar Radiation
Solar radiation which is incident outside the earth’s atmosphere is called extraterrestrial radiation. On average the extraterrestrial irradiance is 1367 Watts/meter2 (W/m2). This value changes by ±3% as the earth orbits the sun. The radiation spans a large range of wavelengths from 200 nm to more than 5000 nm with peak around 500 nm. The NASA (1968-1971) standard spectral irradiance at the average sun-earth distance outside the atmosphere is given in figure 1.3. Approximately 47% of the incident extraterrestrial solar radiation is in the visible wavelengths from 380 nm to 780 nm. Furthermore, the infrared portion of the spectrum with wavelengths greater than 780 nm accounts for another 46% of the incident energy and the ultraviolet portion of the spectrum is with wavelengths below 380 nm accounts for 7% of the extraterrestrial solar radiation 62.
2.14 Terrestrial Solar Radiation
The thermal radiation of the earth’s surface, as the surface of the earth has a comparatively low temperature; it radiates electromagnetic waves with wavelengths of 30-80 microns, which fall into the infrared portion of the spectrum, which is not visible to the eye. The surface of the earth cools down due to its intrinsic radiation. The flow of intrinsic radiation of the surface of the earth is directed upward and is absorbed almost fully by the atmosphere, thus heating it. The atmosphere, in turn , sends counter-radiation toward the surface of the earth (atmospheric counter-radiation) at approximately the same wavelengths, which partially compensates for the loss of heat by the surface of the earth as a consequence of its intrinsic radiation. The distinction between the radiation of the surface of the earth and the counter-radiation is called effective radiation. On clear nights the counter-radiation reduces and the effective radiation increases; therefore, the surface of the earth is cooled suddenly and the lower layers of the air are cooled by it. In the process fog or dew may occur, and in the spring and fall, there may be frosts. On cloudy nights , on the other hands , the counter-radiation increases because of the radiation of the clouds, and the effective radiation and cooling of the surface of the earth are decreased. During the day the surface of the earth also receives solar radiation in addition to the counter-radiation. Together they exceed terrestrial radiation for most of the day (during the warm part of the year in moderate latitudes), and the surface of the earth heats up. Terrestrial radiation is one of the most significant factors determining the thermal conditions of the surface of the earth and of the atmosphere 63.
2.15 Empirical Relation
The first and the most widely used correlation for estimating daily global solar radiation was given by 61, who derived a linear relationship between the ratio of average daily global solar radiation to the corresponding value on a completely clear day at a given location and the ratio of average daily sunshine duration to the maximum possible sunshine duration 62. A fundamental difficulty with Angstrom correlation lies in the definition of the term clear sky global radiation 62. 64 and others have changed the method to base it on extraterrestrial radiation (H0) on a horizontal surface rather than on clear day radiation and therefore proposed the relation given by equation 2.7 65.

Figure 2.9 Direct, diffuse and reflected solar radiation

H_g/H_0 =a+bn/N (2.10)
where, a and b are regression constants or correlation coefficients. The ratio H_g/H_0 is clearness parameter or cloudiness index, n/N is fraction of sunshine hours and Ho is the monthly average daily extraterrestrial radiation on the horizontal surface given by 62 as follows:
H_0=24/? I_sc E_0 ?/180 ?_s sin?? sin??+cos?? cos?? sin???_s? (2.11)
where,
? I?_sc=(1367×3600)/1000000 MJ/m^2 h (2.12)
is the solar constant,
? E?_0=1+0.033cos360n/365 (2.13)
is the eccentricity correction, n is the day number of the year. n=1 for January 1st and n=365 for December 31st , ? is the latitude of the site,
?=23.45sin??(360(n+284))/365? (2.14)
is the solar declination,
?_s=cos^(-1)??(-tan???tan???)? ? ? (2.15)
is the hour angle, and
N= 2/15 ?_s (2.16)
is the maximum possible sunshine hours.

CHAPTER-3
METHODS AND MATERIALS

3.1 Introduction
We must be aware about the solar radiation entering the certain place of earth so as to design the different kinds of devices in order to record the amount of solar radiation that the earth’s surface receives. The estimation of GSR in our study includes Pokhara valley. Our aim is to predict daily GSR using CMP6 Pyranometers. For the advancement of solar energy technology, solar radiation data are highly important. Data are available from network of monitoring stations where solar radiation is continually recorded. Since measuring and recording instruments for solar radiation are of high expense, no of stations in the network in a developing country is limited and insufficient to use; hence to get rid of this difficulty, some mathematical models associating with the solar radiation to the meteorological parameters has been proposed66. Moreover, the analysis and estimation of GSR has been done using modified form of appropriate Angstrom – Prescott empirical equation.
3.2 Description of the Study Area
The locations selected consists of Pokhara for measuring the solar radiation. These selected sites includes altitude of 800 m above the sea level. The site is briefly introduced as given below:

Pokhara:
Pokhara (28.22° N, 84° E) is located in the western part of Nepal at the altitude 800 m from the sea level. It is a Metropolitan City that lies in warm and cold moderate climatic zone. And the total precipitation is about 4785 mm per year (Source: DHM/GON) which is the highest in Nepal. The temperature ranges from 25 to 35 °C in summer, and 2 to 15 °C, in winter67.

Figure 3.1 Map of Nepal indicating Pokhara 68
3.3 Description of Instruments
In our work we have studied solar radiation and sunshine hours using the following instruments:
3.3.1 Pyranometer
The word Pyranometer has been derived from the Greek language where ‘pyr’ means fire, ‘ano’ means sky and ‘meter’ means measurement. Thus Pyranometer is a device that measures the radiation coming from the sun.The ground based GSR monitoring was made on CMP6 Pyranometer. A thermopile detectors in the Pyranometer generates voltages which are the function of incident radiation. A potentiometer is essential to detect and record this output. Radiation data usually must be taken over certain period of time, such as an hour or a day.
The two uses of pyranometers are : measurements of solar radiation on horizontal surfaces and measurements of solar radiation on inclined surfaces. The thermocouple thermopile on instruments is rotationally symmetrical which is enclosed inside K5 glass domes. A white screen protects the body of the pyranometer from heating and a drying catridge prevents the condensation inside the sensor. A spirit level and levelling screws are provided 69.

Figure 3.2 CMP6 Pyranometer 70

Table 3.1 : Specifications of CMP6 Pyranometer 71
S. No. Specialities Range of values
1 Spectral range 285-2800 nm
2 Sensitivity 5-20 ?VW?1m2
3 Impedance 20-200 ohm
4 Response time ?18s (95% of final value)
5 Non linearity ?1% (0 to 1000 wm-2)
6 Zero offset ?15 wm2 (200wm-2)
7 ISO-9060 class First class

Measurements of diffused radiation can be done with pyranometer by shading the instrument from beam radiation which is usually done by means of shadow ring. The ring is used to allow continuous recording of diffused radiation without the necessity of continuous positioning of smaller shading devices; adjustments need to be done for changing declination only.
The area under study is situated far from a shadow won’t be cast on it anytime and is selected away from any obstruction over the azimuth range between earliest sunrise and latest sunset should have an elevation not exceeding 5?.This is significant for the precise measurement of the direct solar radiation. The diffused solar radiation is feebly affected by obstructions near the horizon. The pyranometer is located distant from the light colored walls or others objects likely to reflect sunlight onto it 72.
3.3.2 Measurements of Sunshine Duration
Sunshine duration can be regarded as the period of time for which the earth’s surface receives the radiation directly from the sun. In 2003, WMO defined sunshine duration as the period during which direct solar irradiance exceeds a threshold value of 120 watts per square meter (W/m2)50. It is equivalent to the level of solar irradiance shortly after sunrise or shortly before sunset in a cloud free conditions. It was evaluated by comparing the sunshine duration recorded using a Campbell-Stokes sunshine recorder with the real direct solar irradiance.
3.3.2.1 Campbell-Stokes sunshine recorders
They have been employed as a device to measure sunshine instrument to measure sunshine duration and have merits that it lacks moving parts and requires no electric power. Also their demerits are that the characteristics of the recording paper or photosensitized paper used in them influence the preciseness of the measurements, differences between observers may arise in evaluating the occurrence of sunshine, and the recording paper must be substituted after sunset. It focuses sunlight through a glass sphere onto a recording card kept at its focal point. The length of the burn trace left on the card indicates the sunshine duration 52.

Fig. 3.3 Campbell-Stokes Sunshine Recorder 50
The structure of the device is shown in figure 3.3. A homogeneous transparent glass sphere L is supported on an arc XY, and is focused so that an image of the sun is formed on recording paper kept in a metallic bowl FF’ fixed to the arc. The glass sphere is concentric to this bowl, which consists of three partially overlapping grooves into which recording cards for use in the summer, winter or spring and autumn are set . Three separate recording cards are used depending on the season. The focus shifts as the sun moves, and a burn trace is left on the recording card at the focal point. A burn trace at a certain point shows the presence of sunshine at that time, and the recording card is scaled with hour’s marks so that the exact time of sunshine occurrence can be gained. Measuring the overall length of the burn traces reveals the sunshine duration for that day. For accurate measurement, the sunshine recorder must be properly adjusted for planar levelling, meridional direction and latitude. Campbell Stokes and Jordan sunshine recorders mark the occurrence of sunshine on recording paper at a position corresponding to the azimuth of the sun at the site, and the time of sunshine occurrence is expressed in local apparent time 73.
3.4 Empirical Relation to estimate GSR
There are several empirical relations that have been established to predict the amount of GSR on horizontal surface. These empirical relations employ several meteorological parameters such as sunshine duration, humidity, maximum and minimum temperatures, rainfall, wind speed, altitude etc. Most of the literatures suggested that the empirical equation using sunshine duration have best performance than other empirical relations involving remaining parameters. Generally, it is accepted that models for solar radiation prediction are necessary, because in most cases the density and number of solar radiation measuring stations cannot explain the essential variability 74.
Thus, it is realizable that new models and improvements to present modelling techniques are continually proposed which intend to improve estimates of solar radiation values with the use of more readily meteorological parameters 75,76,77.
The monthly average daily solar radiations, sunshine duration, temperature, relative humidity, precipitation, were availed from the Department of Hydrology and Meteorology, Government of Nepal. The obtained data covered a period of three years (2015,2016). The bright sunshine hours are calculated from the measured global solar radiation and diffused solar radiation. The period is regarded as bright sunshine if direct solar radiation is greater than or equal to 120 W/m2 78.
The solar radiation reaching the earth’s surface can be estimated by empirical models when measured data are available. The simplest model commonly used to estimate the average global solar radiation on horizontal surface is the well known Angstrom Prescort equation 79.
In my research work following empirical models are used to calculate the predicted value of Global Solar Radiation.
H_g/H_0 =a+b(n/N) (3.1)
H_g/H_0 =a+b((n )/N)+cT_max (3.2)
H_g/H_0 =a+b(n/N)+c?(n/N)?^2 (3.3)
where a, b, and c are empirical constants and N is the maximum monthly mean daily sunshine hours, Tmax are the monthly mean daily maximum and minimum temperature. The measured data were used in linear and multiple linear regression analysis by writing subroutines for calculating the extraterrestrial radiation values H0 and the day length N sunshine duration the standard procedure 80. H0 and N for the average day of each month were calculated using the equations given in (2.13) and (2.10) respectively. For the next step , the computer programs were used to find out the empirical constants of above equations with the help of measured values of Hg and other meteorological parameters. Values of the empirical constants a, b and c are evaluated. The obtained correlations were then utilized to predict the global radiation Hg for the considered location (Pokhara) for the period (2015, 2016). The calculated values of Hg were compared with the measured data.
3.5 Statistical Methods
To evaluate the performance of the models of solar radiations statistically,there are various statistical test methods to be used. Among these, correlation mean bias errors (MBE), root mean square error (RMSE), mean percentage error (MPE) are the most widely used ones.
3.5.1 Mean Bias Error
The mean bias error (MBE) gives information on the long-term performance of the correlations by providing a comparision of the exact deviation between calculated measured values term by term. The ideal value of MBE is zero. The MBE is given as
MBE=?(H_g(pred) -H_g(obs) ) /N (3.4)
3.5.2 Root Mean Square Error
The root mean square error (RMSE) is a oftenly used measure of the differences between values predicted by a model or an estimator and the values exactly observed from the thing being modelled or predicted. RMSE is a good measure of accuracy; whose value is always positive, representing zero in the ideal case and can be calculated using the formula given as
RMSE={?(??(H_g(pred) -H_(g(obs)))?^2/N) (3.5)
3.5.3 Mean Percentage Error
The mean percentage error (MPE) is the calculated mean of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.
The formula for the mean percentage error is given as
MPE=(H_g(pre) -H_g(obs) )/H_g(obs) ×100/N (3.6)

3.5.4 Coefficient of Determination
The coefficient of determination, denoted by R2 is the proportion of the variance in the dependent variable that is predictable from the independent variable. It is used for the prediction of the future outcomes on the basis of the other related information. It provides a measure of how well the observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model. Its value ranges from 0 to 1.
R^2=1-SS_res/SS_total (3.7)
where,
SS_res=?(H_g(mea) -?average H?_g(mea) )^2= ?e_i^2 (3.8)
is the residual sum of squares
SS_total=?(H_g(pre) -average H_g(mea) )^2 (3.10)
is the total sum of squares
e_i=H_g(mea) -H_(g(pre)) (3.10)
is the residuals 81.

CHAPTER FOUR
RESULTS AND DISSCUSSION
4.1 Introduction
The best model among the models studied was determined in this work with the help of GSR data, sunshine hour and maximum temperature of the year 2015 and 2016. With the use of these data, the regression constants a, b and c were obtained by using regression technique for each model. The global solar radiation data for this work was measured by employing CMP6 Pyranometer at the research site Pokhara. Also the variation of GSR with seasons, months and days were studied. GSR variation with some other meteorological parameters like precipitation, maximum temperature was also studied. Then the empirical equations were employed for the estimation of GSR.
4.2 Seasonal Variation of GSR
Figure 4.1 shows the seasonal variation of global solar radiation of Pokhara while errors in Table 4.1 in 2015. For 2015, the GSR in winter, spring, summer, and autumn were 13.99, 19.71, 18.47 and 12.09 MJ/m2 /day respectively. Clearly, it shows that there was maximum and minimum global solar radiation in Spring and Autumn respectively. The annual average of GSR is 16.06 MJ/m2 /day for 2015.

Figure 4.1 Seasonal Variation of GSR in Pokhara in 2015
Table 4.1 Seasonal errors for Pokhara in 2015
S. No. Seasons Errors
1 Winter 0.69
2 Spring 0.98
3 Summer 0.92
4 Autumn 0.60

Similarly, Figure 4.2 shows the seasonal variation of global solar radiation at Pokhara in 2016 with errors in Table 4.2. For 2016, the GSR for winter, spring, summer, and autumn were 14.52, 18.66, 17.65 and 12.80 MJ/m2/day . The annual average of GSR in 2016 is 15.90 MJ/m2/day.
High value of GSR in spring is attributed due to less solar zenith angle, less cloud and less rainfall whereas lower value of GSR in Autumn is due to large solar zenith angle.

Figure 4.2 Seasonal Variation of GSR in Pokhara in 2016

Table 4.2 Seasonal errors of Pokhara in 2016
S. No. Seasons Errors
1 Winter 0.73
2 Spring 0.93
3 Summer 0.88
4 Autumn 0.64

4.3 Monthly Mean Variation of GSR
Figure 4.3 indicates the monthly mean variation of GSR of Pokhara in 2015. The maximum and minimum value of GSR is 17.87 and 13.88 MJ/m2/day in May and December respectively. The annual average measured value of GSR is (15.22±1.92) MJ/m2/day which is adequate to generate the solar energy. The coefficient of determination and p-values are found as 0.98 and ?0.0032. Hence, it implies that about 98 percent of data is closer to the best line. The p-value is found within the range of permissible limit. Moreover, the trend line of fourth degree polynomial is fitted with the measured data of GSR in Pokhara which is as shown in Figure 4.3.

Figure 4.3 Monthly mean variation of GSR in Pokhara for year 2015
The maximum and minimum value of measured GSR is found to be 17.74 and 10.63 MJ/m2/day in August and December respectively in year 2016. The annual measured value of GSR (15.18±1.06) MJ/m2/day is also adequate to generate the solar energy. The coefficient of determination and p-values are found as 0.91 and ?0.0086. Hence, it implies that about 91 percent of data is closer to the best line.

Figure 4.4 Monthly Mean Variation of GSR in Pokhara for 2016
With reference to the Figure 4.3 and Figure 4.4, it can be seen that the solar radiation is slightly overestimated in some months while it is under estimated in some other months so that they could nearly be cancelled to each other so as to hold good agreement between the estimated and measured GSR for the site having same meteorological parameters.
Figure 4.3 indicates the trend of global solar radiation at Pokhara, with high value during summer season even though it is monsoon season in Nepal. In these year, due to less rainfall high value of global solar radiation is obtained during the summer. The low value of radiation is obtained during winter season between the months of November– January due to dust, haze, fog that cover the atmosphere at that period of the year.
In the same way, Figure 4.4 indicates the trend of global solar radiation at Pokhara, with high value during the dry season. During rainy season, the minimum radiation is obtained as the rain bearing clouds hide the sky.
There were two maxima and two minima for GSR during the year with major maxima between February – April i.e. dry and pre-monsoon season and minor maxima during August – October. The major minima occur between May – Jly sometimes up to August due to the rain carrying clouds pervading radiation in the sky while the minor minima occurs during winter season especially in January and December mainly due to dust, haze covering the atmosphere at that period of the year. There is strong relationship between sunshine hour and measured GSR meaning that sunshine hour vary season to season due to annual motion of the year. Meanwhile, sunshine hour affects GSR directly.

4.4 Estimation of GSR using Different Parameters
Since the measurement of the global solar radiation is difficult, quite expensive, time consuming and also being costly in maintenance , it’s better to use a solar estimator based on the meteorological parameters. Several empirical models are in practice though modified Angstrom model is the widely used model.
In this study, I have used sunshine hour and maximum temperature as meteorological parameters. The modified Angstrom equation given in equations (3.1) and (3.2) and Ahmad and Ulfat equation (3.3) for Pokhara in 2015 are given below:
H_g/H_0 =0.42+0.22n/N (4.1)
H_g/H_0 =0.45+0.14n/N+0.002T_max (4.2)
H_g/H_o =0.49+0.11n/N-0.05?(n/N)?^2 (4.3)
The errors in the above equations for Kathmandu in the year of 2015 are presented in Table 4.
Table 4.3 : Errors for Pokhara in 2015
Modified Angstrom
Equation given by MBE
(MJ/m2/day) RMSE
(MJ/m2/day) MPE
(%) R2
(4.1) 0.02 0.13 3.66 0.94
(4.2) 0.01 0.15 6.79 0.97
Ahmad and Ulfat Equation given by
(4.3) 0.03 0.16 9.13 0.85

The equations (4.1), (4.2), (4.3) are used to estimate the GSR using sunshine duration of Pokhara. Figure 4.5, 4.6 and 4.7 show the comparison between measured and the predicted values of GSR in Pokhara which are given below:

Figure 4.5 Comparison between the measured and predicted GSR of Pokhara in 2015

Figure 4.6 Comparison between the measured and predicted GSR of Pokhara in 2015

Figure 4.7 Comparison between the measured and predicted GSR of Pokhara in 2015
The graphs above indicate that the measured and estimated values of global solar radiation in Pokhara for year 2015 are very much similar tentatively. But slight variation in these values are due to the weather conditions.
In the same way, the modified Angstrom equations (3.1), (3.2) and Ahmad and Ulfat equation (3.3) for Pokhara in 2016 are given below:
H_g/H_0 =0.43+0.20n/N (4.4 )
H_g/H_0 =0.41+0.23n/N-0.003T_max (4.5)
H_g/H_o =0.43+0.21n/N-0.007?(n/N)?^2 (4.6)
The errors in the above equations for Pokhara in 2016 are presented in Table 4.4.
Table 4.4: Errors for Pokhara in 2016
Modified Angstrom
Equation given by MBE
(MJ/m2/day) RMSE
(MJ/m2/day) MPE
(%) R2
(4.4) 0.06 0.13 15.19 0.92
(4.5) 0.05 0.12 15.53 0.95
(4.6) 0.08 0.14 16.69 0.89

Again these equations (4.4), (4.5) and (4.6) are used to estimate GSR using sunshine duration of Pokhara while Figure 4.8, 4.9 and 4.10 show the comparison between the measured and predicted values of GSR in Pokhara which are shown below:

Figure 4.8 Comparision between the measured and predicted GSR of Pokhara in 2016

Figure 4.9 Comparision between the measured and predicted GSR of Pokhara in 2016

Figure 4.10 Comparison between the measured and predicted GSR of Pokhara in 2016
The graphs above indicate that the measured and estimated values of global solar radiation in Pokhara for year 2016 are very much similar tentatively. But slight variation in these values are due to the weather conditions.

The regression coefficients ‘a’ and ”b’ are called empirical constants which depends upon different factors such as sunshine hour, relative humidity, latitude and maximum temperature of air. Clearly the value of MBE and RMSE using sunshine hour as a meteorological parameters in two years were minimum than for using other parameters. Furthermore, it can be observed that the measured and estimated values of GSR are in close agreement while using sunshine hour as a meteorological parameter.
4.4.1 Estimation of GSR using regression coefficients
Modified Angstrom relation is used to estimate the GSR. The regression coefficients calculated from years 2015 and 2016 of Pokhara are applied to predict the GSR for year 2017. In accordance with the values of statistical tools RMSE, MBE and MPE as in above tables , they indicated that adopted model finely agreed and gives the best value of GSR. Also, the measured GSR against estimated values of Pokhara for 2015 given by empirical equations 4.1, 4.2 and 4.3 are shown in Figure 4.11, 4.12 and 4.13.

Figure 4.11 : Estimated and measured GSR of Pokhara in 2015

Figure 4.12 : Estimated and measured GSR of Pokhara in 2015

Figure 4.13: Estimated and measured GSR of Pokhara 2015
Similarly, the measured GSR against the estimated GSR values of Pokhara for the year 2016 as given by equations 4.4, 4.5 and 4.6 are shown in Figure 4.14, 4.15 and 4.16 below:.

Figure 4.14 : Estimated and measured GSR of Pokhara in 2016

Figure 4.15 Estimated and measured GSR of Pokhara in 2016

Figure 4.16 Estimated and measured GSR of Pokhara in 2016
The linear relationship between GSR and maximum temperature of Pokhara for the year 2015 and 2016 are shown in Figure 4.17 and 4.18 shown below :

Figure 4.17 Monthly mean variation of GSR with maximum temperature of Pokhara in 2015

Figure 4.18 Monthly mean variation of GSR with maximum temperature of Pokhara in 2016
The linear relationship between GSR and sunshine hour of Pokhara for the year 2015 and 2016 are shown in Figure 4.19 and 4.20 shown below :

Figure 4.19: Monthly mean variation of GSR with sunshine hour (n) of Pokhara in 2015

Figure 4.20: Monthly mean variation of GSR with sunshine hour (n) of Pokhara in 2016
Similarily , the linear relationship between GSR and Rainfall of Pokhara for the year 2015 and 2016 are shown in Figure 4.21 and 4.22 below:

Figure 4.21 Monthly mean Variation of Rainfall with GSR of Pokhara in the year 2015

Fig. 4.22 Monthly mean Variation of Rainfall with GSR of Pokhara in the year 2016
The linear relationship between Hg/H0 and n/N of Pokhara in the year 2015 and 2016 are shown in Figure 4.25 and 4.26 below:

Figure 4.25: Monthly mean variation of Hg/H0 with n/N of Pokhara in 2015

Figure 4.26: Monthly mean variation of Hg/H0 with n/N of Pokhara in 2016
The regression coefficients ‘a’ and ‘b’ are calculated for year 2015 and 2016 of Pokhara by applying Modified Angstrom Model with use of sunshine hour, maximum temperature and Ahmad and Ulfat equation are shown in equations from (4.1) to (4.6). These values of regression coefficients can be applied to predict GSR in Pokhara. From the comparision of predicted GSR with measured GSR , it is seen that they are in quite good accordance with the errors viz. MBE, RMSE and MPE. Table 4.3 and 4.4 indicates that MBE, RMSE and MPE are so small. The value of R2 are in the range of 0.90 to 0.99 for year 2015 and 2016. Hence , it can be concluded that Angstrom model provide reasonably high extent of precision in the value of GSR and can be very efficiently employed to generate useful energy for fulfilling the current high energy demand in Pokhara. Moreover, linearity between GSR and other meteorological parameters like maximum temperature, sunshine hour, n/N and also between Hg/H0 and n/N showed the best fit to the observed data in which goal is to get a good relationship among them. These relationships may be used to predict future values of one variable when other is known.

CHAPTER FIVE
CONCLUSION
5.1 Conclusions
It is observed that the global solar radiation varies month to month due to local weather condition , clouds, wind blow and precipitation. Also, the maximum abd minimum value is found on spring and autumn due to presence of fog, dust particles, cloud and position of Sun, etc.
In this study, modified Angstrom empirical relation and Ahmad and Ulfat relation were employed to obtain the value of the regression coefficients for the years 2015 & 2016. These coefficients ‘a’ and ‘b’ for year 2015 and 2016 were calculated as (0.45,0.16 ) and (0.41 ,0.24 ) respectively by using modified Angstrom technique. By using Ahmad and Ulfat technique , the calculated values of ‘a’ and ‘b’ for year 2015 and 2016 are (0.49 ,0.11 ) and (0.42 ,0.21 ) respectively.In clear perfect sky condition, the transmission of the atmosphere global solar radiation is given as the sum of the regression coefficients a+b, whereas the transmissivity of an overcast atmosphere is interpreted as the intercept (a+b=1). From this finding , the atmosphere transmittivity, under clear sky for Pokhara is obtained as very well comparable values. Moreover, The statistical tests unleash the fact that sunshine based model can be employed with hgher degree of accuracy for the prediction of GSR in Pokhara. The obtained empirical equations can be employed for upcoming years in Pokhara.
The trend line of GSR in Pokhara alongwith some related meteorological parameters was investigated in this work. The trend line of the estimated GSR in Pokhara is ascending order due to comparison of measured GSR so that it would suggest that the obtained result can be utilized to generate a large amount of useful energy from solar energy which will be the significant way to meet the increasing demands of energy in Pokhara.
On the basis of this study, the annual variation of solar radiation during two years, it can be concluded that there is no significant variation of solar radiation. The measured and predicted values of GSR are very close. Average bright sunshine receives in Pokhara is nearly 7.0 hours per day. Because of the availability of solar energy, there is a important concern. The modified Angstrom equation and Ahmad and Ulfat equation are developed for Pokhara by using meteorological parameters such as sunshine hour and temperature. The errors have been calculated and the GSR is estimated. The key finding of this work are :
The monthly and daily mean variation of GSR can be best estimated from the Angstrom type of correlation using meteorological parameters.
The predicted GSR at Pokhara is in well agreement with measured GSR given by modified Angstrom relation of first degree model.
Developed linear regression relations can be used for the similar type geological and climate condition.
5.2 Future Work
The measured data of global solar radiation are compared with the estimated value of GSR. The satellite data of GSR can be compared with the ground measured GSR. The solar energy prediction can be studied to find the application of solar energy in rural areas of Nepal. Similarly, it is useful to develop solar map in the future.

REFERENCES
1 P. N. Nath, Estimation of Global Solar Radiation Using EmpiricModels On Horizontal Surface In Jumla, Nepal, M. Sc. (Physics) Thesis,1,(2017).
2 M. S. Okundamiya and A. N. Nzeako, Empirical model for estimating global solar Radiation on Horizontal Surfaces for selected cities in the six Geopolitical zones in Nigeria, Journal of Control Science and Engineering,9, (2011).
3 G. Salazar, P. Utrillas, A. Esteve, J. M. Lozano, M. Aristizabal, Estimation Of of daily average values of the Anstrom turbidity coefficient ? using a corrected Yang Hybrid Model, Renewable Energy,51, 182-188, (2012).
4 K. R. Adhikari, B. K. Bhattarai, S. Gurung, Estimation of Global Solar Radiation for four selected sites in Nepal using Sunshine Hours, Temperature and Relative Humidity, Journal of Power and Energy Engineering,1, 1-9, (2013).
5 White paper presented by Ministry of Energy, Water Resources and Irrigation ,Government of Nepal (2017).
6 K. R. Adhikari, S. Gurung, B. K. Bhattarai, Energy Potential in Nepal and Global Context, Journal of Institute of Engineering,9,1, 95-106 (2012).
7 P. Michael, Natural Science, Encyclopedia of Earth (2010).
8 S. Adhikari,S. Adhikary, Solar Energy Potential in Kathmandu Valley, Nepal, Journal of Hydrology and Meteorology(2012), 8(1), 77-82, (2012).
9 SWERA, United Nation Environment Program: Global Environment Facility (UNDP/GEF), Solar and Wind Energy Resource Assessment in Nepal (SWERA) project, Government of Nepal, Ministry of Environment, Science and Technology, Nepal (2010).
10 R. Calif, R. Emilion, T. Soubdhan, R. Blonbou, Wind Speed PDF classification using Dirichlect mixtures (2011).
11 S. Chettri, A. Chettri, S. Chettri, Dual Axis Self-tracking Solar Panel, International Journal of Computer Applications,14, 141, (2016).
12 EIA 2016-17 Winter Fuels Outlook, NASEO-EIA 2016-17 Winter Energy Outlook Webinar, (2016).
13 K. N. Poudyal, Estimation Of Global Solar Radiation potential in Nepal, Ph.D. Thesis, 20-30 (2015).
14 CBS, Nepal Living Standards Survey 2010/11, Statistical Report Volume 1, Central Bureau of Statistics, National Planning Commission Secretariat, Government of Nepal (2011).
15 S. Wilcox, National Solar Radiation Database 1991-2010 Update: User’s manual, National Renewable Energy Laboratory (2012).
16 Economic Survey, Ministry of Finance, Government of Nepal for the Fiscal year 2016/2017.
17 A. Teke, H. B. Yildirim, O. Celik, Evaluation and Performance comparision of different models for the estimation of Solar Radiation, Renewable and Sustainable Energy Reviews,50, 1097-1107, (2015).
18 K. N. Poudyal, B. K. Bhattarai, B. K. Sapkota, B. Kjeldstad, Solar Radiation Potential at four sites of Nepal , Journal of the Institute of Engineering, 8(3), 189-197, (2012).
19 M. Despotovic, V. Nedic, D. Despotovic, S. Cvetanovic, Review and Statistical analysis of different Global Solar Radiation Sunshine models, Renewable and Sustainable Energy Reviews, 52, 1869-1880, (2015).
20 Economic survey for Fiscal Year 2016/17, Government of Nepal, Ministry of finance, Singh Durbar, Kathmandu (2016).
21 K. Poudyal, B. K. Bhattarai, B. K. Sapkota, B. Kjeldstad, Solar Radiation Potential at four sites of Nepal, Journal of the Institute of Engineering, 8(3), 189-197 (2012).
22 Y. Liu, Y. Zhou, D. wang, Y. Wang, Y. Li, Y. Zhu, Classification of Solar radiation zones, and general models for estimating the daily global solar radiation on Horizontal Surfaces in China, Energy Conversion and management, 154, 168-179, (2017).
23 White paper, Ministry of Energy, Water Resources and Irrigation, Government of Nepal 2018.
24 A. Kumar, A. K. Dwivedi, solar Power Parameter calculator, International Journal of engineering Invention, 2(5), (2013).
25 K. D. V, S. K. Rao, M. Premalathu, C. Naveen, Method and Strategy for predicting daily Global Solar Radiation using only one and two input variables for Indian Stations, Journal of Renewable and Sustainable Energy,10, (2008).
26 K. N. Liou, Radiation and cloud processes in the atmosphere, Oxford University Press, (1992).
27 H. S. Sedhai, Estimation of Global Solar Radiation using Empirical Model at Kathmandu Valley, Nepal, M. Sc (Physics) Dissertation, T. U. , Nepal (2018).
28 J. A. Prescott, Evaporation from water surface in relation to solar radiation, Transactions of the Royal society of Australia, 46, 114-118, (1940).
29 Y. A. Eltba, M. H. Ruslan, M. A. Alghoul, M. Y. Othman , K. Sopian, T. M. Razykov, Solar attenuation by aerosols : an overview, renewable and sustainable Energy reviews, 16, 4246-4276, (2012).
30 P. K. Mandal, M. I. Mamun, M. Islam, Construction of an inexpensive sun photometer to measure aerosol optical depth and comparisions between the measured data and satellite observations, American Journal of Remote Sension, 2(5),37-43, (2015).
31 C. D. Papadim, N. Hatzianastassiou, C. Matsoutas, M. Kanakidou, Mihalopoulos, and I. Vardavas, The direct effect of aerosols on solar radiation over the broader Meditterranean basin ,12, 7165-7185, (2012).
32 M. Kannel, H. Ohvril, H. Teral, V. Russak, A. Kallis, A simple parametrization of columnar aerosol optical thickness, Proc. Sci. Biol. Ecol. 56 ,1, 57-68, (2007).
33 E. J. McCartney, Optics of the Atmosphere: scattering by molecules and particles, New York, John Wiley and sons, Inc. 421, (1976).
34 B. K. Bhattarai, B. Kjeldstad, T. M. Thorseth, A. Baghen, Erythemal dose in Kathmandu, Nepal based on solar UV measurements from multichannel filter radiometer, its deviation from satellite and radiative transfer simulations, Atmospheric Research, 85, 112-119, (2007).
35 www.staceyirvin.com
36 I. C. Moreno, M. A. Serrano, J. Canada, G. Gurrea, M. P. Utrillas, Effect of the relative optical air mass and the clearness index on solar erythemal UV irradiance, Journal of Photochemistry and Photography B: Biology, 138, 92-98 (2014).
37 A. D. Pai, J. F. Escobedo, D. Martins, E. T. Teramoto, Analysis of hourly, global, direct, and diffuse Solar Radiation Attenuations as a function of optical air mass, Science Direct, 57, 1060-1069 (2007).
38 K. N. Poudyal, P. Daponte, L. D. Vito, B. K. Bhattarai, B. K. Sapkota, Study of variation of Global Solar Radiation at different altitudes at Himalayan Region-A case study in Nepal, 3rd Symposium IMEKO TC 19, (2010).
39 B. Lamichhane, Measurement and Analysis of Solar Radiation on Horizontal Surface at Kirtipur, M.Sc. Thesis, T.U., Kathmandu (2005).
40 M. Mfon D. Umoh, O. Udo and N. Udoakah, Estimation of Global Solar Radiation on Horizontal Surface from Sunshine hours and other Meteorological Parameters for Calabar, Nigeria, Journal of Asian Scientific Research,1083-1089 (2013).
41 WMO, Guide to Meteorological Instruments and Methods of Observation, World Meteorological Organization-No. 8 (2008).
42 J. M. Wallace, and P.V. Hobbs, Atmospheric Science (2006).
43 K. R. Adhikari, B. K. Bhattarai and S. Gurung, Estimation of Global Solar Radiation for Four Selected Sites in Nepal, Journal of Institute of Engineering, 8, 189 – 197 (2013).
44 A. Angstrom, Solar and Terrestrial Radiation, Quart J Roy Met Soc, 50, 121
125 (1924).
45 K. N. Poudyal, B. K. Bhaatarai, and B. Kjeldstad, Study of Estimation of Global Solar Radiation using Pyranometer and NILU-UV irradiance meter at Pokhara Valley in Nepal, Journal of Institute of Engineering, 9, 69-78 (2014).
46 H. O. Menges, C. Ertekin, M. H. Sonmete, Evaluation of Solar Radiation Models for Konya, Turkey, Energy Conversion and Management, 47 (2006).
47 K. N. Poudyal, B. K. Bhattarai, B. Kjeldstad, Estimation of Global Solar Radiation using sunshine Duration in Himalaya Region, J. Chemical Science, 2(11), 20-25 (2012).
48 S. P. Kafle, Study of Global Solar Irradiance at Biratnagar, M. Sc. Physics, Diddertation, Central Department of Physics, Tribhuvan University, Nepal (2010).
49 S. Tiwari, Empirical models for the Estimation of Global Solar Radiation at Tribhuvan International Airport, M. Sc. (Physics) Dissertation, T. U. (2009).
50 J. A. Duffie and W. A. Backman, Design of Photovoltaic Systems, Solar Engineering of Thermal Processes, Fourth Edition, 754-773 (1991).
51 U. Koray, and A. Hepbasli,Solar radiation models, Parts 2: Comparision and developing new models, Energy resources,26(5) ,521-530, (2004).
52 A. L. McAlester, The Earth: An introduction to the geological and geophysical sciences (1983).
53 M. Iqwal, An introduction to Solar radiation ,Academic Press Toronto, Canada Google Scholar (1983).
54 M. Pidwirny, Earth- Sun Geometry, Fundamental of physical Geography, Second Edition (2006).
55 Levine and Joel, The photochemistry of atmospheres, Elsevier, (2012).
56 J. Waewask and C. Chancham, The Clearness Index Model for Estimation of global solar radiation in Thailand, Tharmmasat International Journal of Science and Technology, 15, 54-61 (2010).
57 L. Crovini and L. Galgani, On the accuracy of the experimental proof of Planck’s radiation Law, Lettere al Nuovo Cimento, 39(10), 210-214 (1984).
58 S. Zekai, Solar energy fundamentals and modelling techniques: atmosphere, environment, climate change and renewable energy, Springer Science & Business Media, (2008).
59 R. W. David, T. H. Vonder Haar, and S. K.Cox, The effect of Solar radiation absorption in the tropical troposphere, Journal of Applied Meteorology, 14(4), 433-444 (1975).
60 E. O. Ogolo, Estimation of Global Solar Radiation in Nigeria using a Modified Angstrom Model and the trend Analysis of the Allied Meteorological Components, Indian Journal of Radio and Space Physics, 43, (2014).
61 E. Louis, AKPABIO and E. ETUK, Relationship between Global Solar Radiation and Sunshine Duration for One, Nigria, Turk J Phys, 27, 161-167 (2003).
62 Goswami, D. Yogi, Kreith, Frank and Kreider, F. Jan, Principles of Solar Engineering, Second Edition,Taylor and Francis, Philadelphia, PA, (2000).
63 H. Suehrcke and P. G. McCormick, The distribution of average instantaneous terrestrial solar radiation over the day, solar Energy,42.4, 303-309, (1989).
64 J. W. Spencer, Fourier series representation of the position of the sun, (1972).
65 K. Scharmer, J. Greif and R. Dogniaux, The European solar radiation Atlas,2, (2000).
66 Mani, Anna, Handbook of Solar Radiation data for India, Allied Publishers,New Delhi, (1980).
67 http://hyperphysics.phy-astr.gsu.edu.
68 www.lonelyplanet.com/map/asia/Pokhara (2016)
69 Kipp & Zonen, Pyranometer Instruction Manual (2010)
70 B. R. KC, S. Gurwa, Study of Solar Energy Potential using CMP6 Pyranometer at Nepalgunj, Nepal, Journal of Advanced Academic Research,3(1), (2016).
71 F. W. Burari, M. A. Abdul and D. W. Medugu, Comparative studies of Measured and Estimated Values of Global Solar Radiation using a Constructed Reliable Model Pyranometer and Angrostom-Prescott Model at Bauchi, Nigeria, Advances in applied science research, 1(1), 80-88, (2010).
72 A. Aryal, Measurement and Comparison of Global Solar Radiation Using NPN Phototransistor. M.Sc. Dissertation, T.U. (2012).
73 A. Muhammad, T. H. Darma, Estimation of Global Solar Radiation for Kano State Nigeria Based on Meteorological Data, IOSR, Journal of Applied Physics,6,19-23, (2014).
74 B. Lamichhane, Measurement and Analysis of Solar Radiation on Horizontal Surface at Kirtipur, M.Sc. Thesis, T.U., Kathmandu (2005).
75 T. S. Muneer, Younes, and S. Munawwar, Discussion on solar radiation modelling, Renewable and Sustainable Energy Reviews, 11(4) , 551-602, (2007).
76 S. A. Safi, Zeroual and M. Hassani, Prediction of global daily solar radiation using higher order statistics, Renewable Energy, 27.4, (2002).
77 D. Marcello, G. Bellocchi, and F. Fontana, RadEst3.00:software to estimate daily radiation data from commonly available meteorological variables, European Journal of Agronomy, 18,3, 363-367, (2003).
78 F. Ahmad, I. Ulfat, Empirical models for correlation of monthly average daily global solar radiation with hours of sunshine on a horizontal surface at Karachi, Pakisthan, Turk J Phys , 28, 301-307, (2007).
79 R. B. Tiwari, Models for the Correlation of Monthly Average daily Global Solar Radiation with Hours of Sunshine on Horizontal Surface at T.I Airport, Kathmandu M.Sc. (Physics) Dissertation, Central Department of physics, T.U., Nepal (2009).
80 J. Ahmad, G. N. Tiwari, Solar Radiation Models ,International Journal of Energy and Environment, 1, 3, 513-532, (2010).
81 J. D. Nagelkerke, A Note on a General Definition of the Coefficient of Determination ,Biometrika, 78(3), 691-692 (1991).