BIBECHANA 19 (1-2) (2022) 150-159 

 150 

 

 

Estimation of Global Solar Radiation (GSR) From the 

Sunshine Hour of Guranshe, Surkhet, Nepal 
 

Homchandra Adhikari and Nurapati Pantha* 

 

Central Department of Physics, Tribhuvan University, Kirtipur,Kathmandu, Nepal  

*Email: mrnurapati@gmail.com
 
 

Article Information: 
Received: April 17, 2021 

Accepted: October 30, 2021 

 

Keywords:  

Solar Energy  

Meteorological Parameter  

Global-Solar                          

 Radiation  

Sunshine hour  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ABSTRACT 

 

The variation in Global Solar Radiation (GSR) was studied by using 

experimental data via an automatic weather station (CMP3 

pyranometer) located at Guranshe (Surkhet), a hilly area with elevation 

2194m from the sea level. Also, the estimated sunshine hour data of the 

area were used to calculate the GSR for the purpose of comparison with 

the measurements. Our study finds a good agreement between the 

measured (15.65 MJ/m2/day) and estimated/calculated (19.18 

MJ/m2/day) values of annual average GSR. The estimated GSR uses 

Angstrom-Prescott type model for calculating sunshine hours, and the 

coefficients (a=0.28) and (b=0.57) were obtained using the Sangeetas 

and Tiwari model. The annual average estimated sunshine hours was 

found to be 6.86hr which is suitable for GSR based applications. The 

measured data were used to study the seasonal, monthly and diurnal 

variations of GSR. The maximum and minimum values of GSR were 

found during the spring and summer seasons respectively. The 

minimum GSR in summer is because of heavy rainfall, high relative 

humidity, and cloud formation in the sky during the time. The 

coefficient of regression(R) and the coefficient of determination (R2) 

were obtained as R=0.881 and R2=0.776 respectively. Here the high 

value of R (88.1%) indicates that of dependent variable (GSR) is nicely 

predicted by the independent variables. Also the coefficient of 

determination (R2) tells us the strength of the relationship between two 

variables. 

 
DOI: https://doi.org/10.3126/bibechana.v19i1-2.46408 
 

 

This work is licensed under the Creative Commons CC  BY-NC License. https://creativecommons.org/licenses/by-

nc/4.0/ 

 

BIBECHANA 
ISSN 2091-0762 (Print), 2382-5340 (Online) 

Journal homepage: http://nepjol.info/index.php/BIBECHANA 
Publisher: Department of Physics, Mahendra Morang A.M. Campus, TU, Biratnagar, Nepal 

https://doi.org/10.3126/bibechana.v19i1-2.46408
https://creativecommons.org/licenses/by-nc/4.0/
https://creativecommons.org/licenses/by-nc/4.0/


Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

  

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1. Introduction 

 

 

Energy is one of the basic needs for all living 

creatures on earth surfaces without which our 

universe would be no more than a frozen rock. 

The radiation received by the earth from the 

sun in the form of electromagnetic radiation, 

that is radiant energy, is the main source of 

energy on the earth’s surface. Renewable, non-

renewable, and ultimate sources of energy 

obtained on the earth's surface, among with all 

the energy sources, are directly or indirectly 

controlled by the solar energy [1]. Photovoltaic 

and solar thermal capture is the main 

techniques to exploit the solar energy which 

are among the cheapest and fastest-growing 

sources of power in worldwide. 

 

According to the Nepal Electricity Authority 

(NEA) report of the fiscal year 2019/2020, the 

total population accessing electricity reached 

to 86% of the total households. The power 

stations generated a total of 3021 GWh of 

electricity which is 18.57% higher than the 

fiscal year (FY) 2018/2019 [2]. Biomass, 

hydroelectricity, petroleum products, natural 

gas, and coal are the major energy resources in 

Nepal, where 78% of people have access to 

grid-connected energy, 82% use solid fuels 

such as dung, coal, and wood as cooking 

energy. Ninety five percent (95%) of biomass, 

which is casing harmful impact in 

environment, is predominantly used for 

household purposes. Petroleum, an imported 

and non-renewable type of energy, is the 

second largest energy fuel in Nepal [3]. Hence 

the solar energy can be considered as one of 

the best, easily accessible, and renewable type 

of energy sources for Nepal. 

 

Fossil fuels directly affect the environment and 

human health. Also they are expensive. Large 

hydropower projects have several problems 

such as landslides, sedimentation, and damage 

to aquatic life, ecosystem, and vegetation. 

There are some social challenges such as 

rehabilitation and cultural issues. Hence the 

solar power which is environmentally friendly, 

readily available, and cheap, and can be 

installed at any location can be a good 

alternative source of energy [4]. However, an 

accurate knowledge of the meteorological 

parameters and location of the site should be 

well known before installing solar devices. 

Atmospheric energy balance studies, 

photovoltaic and agricultural studies, thermal 

load analysis on buildings, and meteorological 

forecasting should be reliable and readily 

available for the optimization design and 

performance evaluation of solar technologies 

[5]. 

Energy transfer from the sun to the earth's 

surface in the form of electromagnetic waves 

is called solar radiation. Different atmospheric 

particles like air molecules, ozone, clouds, and 

water vapor deplete the incoming radiation 

through reflection, scattering, and absorption 

[1]. There are other metrological/geological 

factors that affect the energy density of the 

incoming solar radiation (extraterrestrial solar 

radiation). They include rainfall, relative 

humidity, air pressure, air temperature, solar 

zenith angle, precipitation, latitude, sunshine 

duration, solar declination, and earth 

atmosphere [6]. Here the GSR is defined as the 

sum of the direct, diffused, and reflected 

radiation.  

 

Different models can be used to calculate GSR, 

however, the availability and the relevancy of 

meteorological parameters determine the 

model to use in particular territory. In the 

context of Nepal, limited number of studies 

have been carried out on the estimation of GSR 

due to rare meteorological stations and lack of 

complete data of climatic factors. Adhikari et 

al. (2013) estimated the GSR for Biratnagar, 

Kathmandu, Pokhara, and Jumla which are at 



Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

  

 152 

72m, 1350m, 800m, and 2850m above the sea 

level using the Angstrom-Prescott model. They 

observed excellent agreement between the 

measured and estimated values of GSR where 

the maximum and the minimum solar radiation 

(SR) were found in Jumla and Biratnagar 

respectively [3]. Temperature and Relative 

Humidity (RH) based models have been used 

by Adhikari et al. (2014) to estimate the GSR. 

They observed that temperature and GSR have 

a direct relationship whereas RH and GSR have 

an inverse relationship. They also observed a 

strong correlation between the observed and 

estimated values [7]. The GSR was estimated 

and studied on a horizontal surface of 

Nepalgunj (low altitude) by using RadEst 3.00 

software with four models [8]. The CMP6 

pyranometer was used to measure GSR at 

Simara airport, Bara Nepal for the years 2009 

and 2010. Two models, Angstrom-Prescott[9], 

and Sangeetas and Tiwari models [10], were 

used to estimate the GSR and observed that 

GSR were maximum in March, April and May 

due to the sunny and clear weather and the 

minimum was found in summer. Elom and 

Nnamdi (2012) used a regression model and 

estimated the GSR and average temperature 

during the period of 11 years (1996-2006) at 

Onitsha, Nigeria, and found that model 

equations give excellent results and show a 

strong correlation between solar radiation (SR) 

and air temperature. They also observed 87.1% 

of the variation in the monthly mean daily SR 

on a horizontal surface [6]. Kumar et al. (2013) 

developed a new model based on the 

Angstrom-Prescott model in North India, 

Himanchal Pradesh, and observed that by using 

a new model they determine the regression 

constant with only latitude and longitude. 

Previous model used to use other parameters, 

in addition to latitude and longitude, as well 

and found that the new model is far better [5]. 

Elekalachi et al. (2016) used an Angstrom-type 

regression equation to estimate GSR on 

horizontal surfaces for Awaka, Enugu, and 

Owerri with the data from archives of the 

National Aeronautics and Space 

Administration (NASA) for a period of 11 

years (2000-2010) [10]. 

Here we use the empirical model to estimate 

the global solar radiation by estimating the 

sunshine hour data. In addition to the GSR and 

the sunshine hour, we study the impact of 

meteorological parameters on global solar 

radiation in Guranshe, Surkhet Nepal. Finally, 

we analyze the month and season wise GSR 

values and suggest the possibility of harvesting 

solar energy in near future. 

 

2. THEORY AND METHOD 

Description of the site 

The automatic weather station is located at 

Guanshe which lies in the Surkhet district and 

border between Surkhet and Dailakh. It is about 

600 km west of the national capital Kathmandu 

and is situated at latitude 28o39'22''N and 

longitude 81o37'45''E in the inner terai valley of 

Nepal. It elevates 2194 m above from the sea 

level. It has a moderate climate, which contains 

the mountainous region and outer terai region. 

Average temperature range from 37.1oC 

maximum to  4.5oC minimum [11]. The 

location of the weather station is shown in 

Figure 1.  

 
 
 
 
 
 
 
 
 

Fig.1: Automatic weather station at Guranshe, 

Surkhet (Provided by the Department of 

Hydrology and Meteorology, Government of 

Nepal) [12]. 

The daily solar radiation on a horizontal 

surface for Guranshe, Surkhet was collected 

from archives of the Department of Hydrology 



Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

  

 153 

and Meteorology, Government of Nepal 

(DHM/GoN) for the year of 2018. Daily data 

of average air temperature, air pressure, 

relative humidity, rainfall for the site were 

obtained from DHM/GoN. CMP3 pyranometer 

(Figure 2) was used to measure global solar 

radiation on a horizontal surface.  

 
 
2.2 Collection of plant materials 
The plant materials (plant & rhizomes) (Figure 

1) were collected in August 2018 from the 

Salyan district (Tharkot hill, altitude: 2,400 m 

above sea level), Karnali province, Nepal. The 

herbarium of the plant was identified and 

authenticated as Bergenia pacumbis (Buch.-

Ham. Ex D. Don) C. Y. Wu & J. T. Pan by 

Taxonomists in National Herbarium and Plant 

Laboratories, Lalitpur, Nepal. The rhizomes 

were washed with tap water followed by 

sterilized distilled water to remove the adhered 

dust, dirt, and other foreign materials and dried 

in shade at room temperature. The dried 

rhizomes were powdered and then stored in an 

airtight polyethylene bag in a cool,  

dry location for ongoing studies. 

 
  
 

 
 
 

 

 
 

Fig.2: CMP3 Pyranometer [13]. 
 
Theoretical detail 

 

The Angstrom-Prescott, and Tiwari and 

Sangeeta model [7] are used to calculate the 

GSR theoretically on a horizontal surface with 

the help of estimated sunshine hour of the year 

2018 for Guranshe, Surkhet. The model is 

given by: 

 
𝐻

𝐻𝑜
= 𝑎 + 𝑏 (

𝑛

𝑁
) … (1) 

Where H is the Monthly average daily GSR on 

the horizontal surface, Ho is the Monthly 

average daily extraterrestrial radiation, n is the 

monthly average daily number of hours of 

bright sunshine, N is the average daily number 

of possible sunshine, a and b are the regression 

constant. 

M. Adb. Elwashed and R.L Syder [14] in their 

paper have presented a regression equation 

which is based on the monthly daily 

temperature. We use equation (2) to estimate 

the sunshine hour data of Guranshe, Surkhet. 

 

                   𝑛 = 4.352 + 0.232𝑇… (2) 

 

Where n is the sunshine hour and T is the 

average daily mean temperature. 

The extraterrestrial solar radiation (Ho) on a 

horizontal surface is given by, Iqbal [5] as 

follows: 

 

𝐻𝑜 =
24

𝜋
∗ 𝐼𝑠𝑐𝐸𝑜[(

𝜋

180
)𝜔𝑠(𝑆𝑖𝑛𝛿𝑆𝑖𝑛∅) +

(𝐶𝑜𝑠∅𝐶𝑜𝑠𝛿𝑆𝑖𝑛𝜔𝑠)]… (3) 

 

Where Isc and Eo are the solar constant and 

eccentricity correction factor which is given as, 

 

𝐼𝑠𝑐 =
1367∗3600

106 MJ/m2/day 

 

𝐸𝑜 = 1 + 0.33𝐶𝑜𝑠
360𝑁𝑑

365
 

 

Where, Nd is the day of the year, Julian days 

(1st January, Nd=1 and 31th December, 

Nd=365). ωs is hour angle, ∅ being latitude of 

site and 𝛿 is the solar declination which can be 

calculated as, 

 

𝜔𝑠 = 𝑎𝑟𝑐𝐶𝑜𝑠(−𝑡𝑎𝑛∅𝑡𝑎𝑛𝛿) 

And 

𝛿 = 23.45[
360(𝑁𝑑 + 284)

365
] 



Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

  

 154 

 

The maximum possible sunshine hours or day 

length can be calculated as, 

 

𝑁 =
2

15
𝑎𝑟𝑐𝐶𝑜𝑠(−𝑡𝑎𝑛∅𝑡𝑎𝑛𝛿)… (4) 

=
2

15
𝜔𝑠 

The regression coefficients a and b are 

calculated by using Sangeeta and Tiwari model 

[10, 15] by, 

 

𝑎 = −0.110 + 0.235𝑐𝑜𝑠∅ + 0.323
𝑛

𝑁
… (5) 

𝑏 = 1.449 − 0.553𝑐𝑜𝑠∅ − 0.694
𝑛

𝑁
… (6) 

Where, ∅ is the latitude of the particular 

location. 

 

To predict the accuracy of the model and also 

to know how the calculated GSR (Hc) varies 

with measured GSR (Hm) following statistical 

test is done 

𝑅𝑀𝑆𝐸 = [∑
(𝐻𝑖𝑐−𝐻𝑖𝑚)2

𝑁

𝑛
𝑖=1 ]

1

2
… (7) 

Where, n is the number of data i.e. several 

months, Him is the ith measured value, Hic is 

the ith calculated value and N is the number of 

observations. Root Mean Square Error 

(RMSE) measures how much error is obtained 

between the calculated and the measured data 

set. Also tells us that how the calculated GSR 

deviates from the measured GSR. 

                                                       𝑀𝐵𝐸 =
∑ (𝐻𝑖𝑐−𝐻𝑖𝑚)𝑛

𝑖=1

𝑁
… (8) 

Mean Bias Error (MBE) is an indication of the 

average deviation of calculated values from the 

measured values. 

𝑀𝑃𝐸 =
∑

(𝐻𝑖𝑚−𝐻𝑖𝑐)

𝐻𝑖𝑚
∗100𝑛

𝑖=1

𝑁
… (9) 

Mean Percentage Error (MPE) is the computed 

average of the percentage of errors by which 

the calculated value of a model differs from the 

measurement values of the quantity being 

predicted. 

𝑀𝐴𝐸 =
∑ |(𝐻𝑖𝑐−𝐻𝑖𝑚)|𝑛

𝑖=1

𝑁
… (10) 

Mean Absolute Error (MAE) measures how far 

calculated values are away from the measured 

values. Hence, another statistical parameter 

like the coefficient of regression (R), 

coefficient of determination (R2) is also 

calculated. 

2. Results and Discussion 

Table 1 shows the climatic data for Guranshe, 

Surkhet, which is based on the above 

theoretical approach. The values of monthly 

mean extraterrestrial solar radiation (Ho), 

monthly mean measured GSR (Hm), the 

monthly mean of calculated GSR (Hc), the 

monthly mean of daily hours of bright sunshine 

(n), the monthly mean of day length (N), the 

monthly mean of measured clearness index 

(Hm/Ho), monthly mean of calculated 

clearness index (Hc/Ho) and the monthly ratio 

of sunshine hours (n/N). 

Table 1: Climatic parameters for Guranshe, 

Surkhet 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
In Table 1, Ho, Hm, and Hc are in the unit of 

MJ/m2/day, n and N are in the unit of hours. 

From table 1, we can say that the value of 

annual extraterrestrial solar radiation (Ho) 

found to be 31.83 MJ/m2/day, measured global 

solar radiation (Hm), calculated global solar 

radiation (Hc) is found to be 15.65 MJ/m2/day 

and 19.18 MJ/m2/day. Annually 6.86 hours of 

the bright sunshine hour was observed which 

indicates that the Guranshe, Surkhet is a place 

Month Ho Hm Hc a b n N Hm/Ho Hc/Ho n/N 

Jan 22.08 16.35 13.73 0.29 0.55 6.26 10.4 0.74 0.62 0.6 

Feb 26.41 16.96 16.46 0.29 0.54 6.65 11.01 0.64 0.62 0.6 

Mar 31.91 22.31 20.68 0.31 0.51 7.67 11.82 0.7 0.65 0.65 

Apr 37 21.23 23.64 0.3 0.53 8.03 12.7 0.57 0.64 0.63 

May 39.95 21.78 25.08 0.29 0.54 8.23 13.43 0.55 0.63 0.61 

Jun 40.95 16.51 25.34 0.29 0.55 8.23 13.8 0.4 0.62 0.6 

Jul 40.34 9.79 21.12 0.23 0.67 5.83 13.63 0.24 0.52 0.43 

Aug 37.95 9.35 19.81 0.23 0.67 5.52 12.99 0.25 0.52 0.42 

Sep 33.62 10.66 18.94 0.26 0.62 6.05 12.15 0.32 0.56 0.5 

Oct 28 17.73 17.92 0.3 0.52 7.15 11.27 0.63 0.64 0.63 

Nov 23 13.37 14.82 0.3 0.52 6.77 10.55 0.58 0.64 0.64 

Dec 20.69 11.73 12.66 0.28 0.56 5.96 10.2 0.57 0.61 0.58 

Average 31.83 15.65 19.18 0.28 0.57 6.86     

 



Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

  

 155 

where a high possibility of GSR can be 

obtained which can be the favorite place for 

solar farming. The value of regression 

constants a and b in the Angstrom-Prescott 

model, calculated by using Tiwari and 

Sangeeta model, are found to be a=0.28 and 

b=0.57. 

Based on the above calculations in Table1, 

statistical error arises between the calculated 

and measured value. Table2 shows the analysis 

between the calculated value and the measured 

value of the Guranshe, Surkhet of the year 

2018.                                                  

Table 2: Statistical tools. 

 

RMSE 

MJ/m2/day 

MBE 

MJ/m2/day 

MAE 

MJ/m2/day 

MPE 

% 

5.01 3.69 3.82 -6.94 

 

From Table 2, RMSE is found to be 5.01 

MJ/m2/day, which measures how much error is 

found between the calculated value and the 

measured value. Similarly, MBE, MAE, and 

MPE are found to be 3.69 MJ/m2/day, 3.82 

MJ/m2/day, and -6.94%, negative value 

indicates that our estimated data is 

underestimated. The values in Table 2 show 

good agreement between the calculated and the 

measured values of global solar radiation for 

the year of 2018.  

The Seasonal, Monthly, and daily variation of 

Global Solar Radiation of Guranshe, Surkhet of 

the year 2018 is shown in Figure 3, Figure 4, 

and Figure 5: 

 

 
 

 

 

 

 

 

 

 

 

Fig.3: Seasonal variation of GSR. 

 

 

 

 

 

 

 

 

 

 

         

 

 

 

Fig.4: Monthly variation of GSR. 

                                                           
 

 

 

 

 

 

 

 

 

 

 

Fig.5: Daily variation of GSR. 

 
The maximum and minimum seasonal global 

solar radiation are found in the spring and 

summer season respectively. In the spring 

season GSR is found to be 21.77 MJ/m2/day 

and in the summer season GSR is found to be 

11.88 MJ/m2/day for the year of 2018. The 

variation in local weather condition is the main 

reason for such differences. Minimum GSR in 

the summer season is due to cloudy sky of rainy 

circumstances (average 9.67 mm per day). The 

high value of GSR in the spring season, on the 

other hand, is due to the less cloud, less rainfall, 

and less solar zenith angle. In the winter 

season, the more fog, large solar zenith cause 

lower value of GSR. From the monthly 

variation of GSR as shown in Figure 4, it is 

found that the low values of global solar 



Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

  

 156 

radiation are found in July, August and 

September (9.79 MJ/m2/day, 9.35 MJ/m2/day, 

and 10.7 MJ/m2/day). The high values,  

on the other hand, are found in March, April 

and May (22.3 MJ/m2/day, 21.2 MJ/m2/day and 

21.8 MJ/m2/day respectively).  The daily 

variation of GSR is shown in Figure 5, and 

reveals that the value of GSR is continuously 

increasing and found a maximum (of value 

22.3 MJ/m2/day) in March. After attending the 

peck value, the GSR starts decreasing and is 

found to be a minimum (of 9.35 MJ/m2/day) in 

August. It is due to the rainy season where there 

is high rainfall and relative humidity. The 

annual average GSR of the year 2018 is found 

to be 15.65 MJ/m2/day. The maximum value of 

global solar radiation suggests that there is a 

high potential of solar energy in that place. 
 
 
 
 
 
 
 

 
 
 
 

Fig.6: Monthly variation of sunshine hour (red 
line with stars) and GSR (blue line with 

circles). 
Sunshine hour indicates the sun in the clear sky 

seen during a certain period usually expressed 

in an hour. The monthly variation of the 

estimated sunshine hour of Guranshe, Surkhet 

is shown in Figure 6, from the above graph we 

can say that the estimated sunshine hour (n) 

continuously increases from January to June. It 

means that the sun shining hour increases and 

becomes maximum hours (hr.) in April, May, 

and June i.e. on average 8 hours in a day. After 

reaching 8hr (with some fluctuations) it starts 

decreasing which indicates that the sunshine 

hour changes every day/month due to the solar 

declination, zenith angle, and other 

climatological factors. The estimated sunshine 

hour data indicates that it annually averages to 

6.86 hours in a day at Guranshe, Surkhet.  

The variation of the measured value of GSR 

with the estimated sunshine hour is shown in 

Figure 6. The trend of the GSR and sunshine 

hour (SSH) is similar, which indicates that the 

GSR has a direct relation with the SSH. In the 

starting month, January, sunshine hour and 

GSR start increasing which is consistent with 

the theory. After the month of June the trend of 

GSR and SSH both decrease which is due to the 

heavy rainfall and high relative humidity. After 

August they resume increasing and reach to the 

maximum values in the October. Beyond 

October the values of SSH and GSR again 

decrease as per direct relationship between 

them. The more sunshine hour means the more 

radiation to the ground, which is generally 

found in the spring (shown in the graph). 

Physical phenomenon like scattering and 

absorption of incoming radiation are also low 

in a clear sky of the season. The variation of 

global solar radiation (GSR) with 

meteorological parameters like air temperature, 

air pressure, relative humidity, and rainfall is 

shown in Figure 7, Figure 8 and Figure 9.  

 

 

 

 

 

 

 

 

 

 

Fig.7: Daily variation of GSR with Average 

Air Temperature for the year 2018. 

 

 

 
 

 
 
 



Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

  

 157 

 
Fig.8: Daily variation of GSR with Air 

Pressure for the year 2018. 

 

 

 

 

 

 

 

Fig.9: Monthly variation of GSR with 

Relative Humidity for the year 2018. 

 

Figure 7 shows that there is a strong agreement 

between the measured global solar radiation 

and average air temperature. It the beginning of 

the Figure 7, both air temperature and global 

solar radiation increase to attain maximum and 

then both decrease sharply due to the cloudy 

days, high relative humidity, and high 

frequency of rainfall in July, August, and 

September. The annual average air temperature 

was found to be of 10.82oC in the year 2018.   

The daily variation of global solar radiation 

with air pressure is shown in Figure 8. Air 

pressure is the pressure exerted by the weight 

of air in the atmosphere of earth, which 

depends on the gravitational force. In Figure 8, 

we see that as the air pressure increases global 

solar radiation also increases and vice versa 

which indicates the direct relationship between 

the air pressure and global solar radiation. The 

minimum value of air pressure is found in July 

i.e. 775.747haPa and maximum in October i.e. 

783.45haPa. On average 780.747haPa pressure 

is found in the year of 2018 which is suitable 

for solar farming. 

The monthly variation of GSR with relative 

humidity is shown in Figure 9. A strong inverse 

relation is found between global solar radiation 

and relative humidity. Low relative humidity 

i.e. 38.59% is found in the winter season due to 

dry and the presence of less moisture and high 

relative humidity i.e. 90.50% is found in the 

summer season due to the presence of lots of 

water vapor. Water in the air acts as a 

disturbance of GSR that falls on the ground 

which decreases the amount of GSR on the 

surface. The correct level of humidity and GSR 

are important for professional visitors and 

tourists in the place. Hence the future energy 

harvesting project has to consider the effect of 

vegetation in humidity and vice versa. Rainfall 

and water vapor in the air are the related 

quantities and show the similar effects (inverse 

relation) to GSR. From the beginning of the 

year i.e. from January, there is low rainfall and 

GSR is found to be increasing. The increase in 

rainfall gets accelerated after a certain month 

i.e. in the rainy season where the average of 

9.68 mm of rainfall is found in three months: 

July, August, and September. The inverse 

relation between the GSR and rainfall can be 

understood in terms of cloud; the rainfall 

requires cloud in the sky and the presence of 

clouds blocks GSR. However, the rainfall 

fluctuates within a single month and the 

reciprocate effect can be seen in GSR. It has 

been noted that the maximum rainfall and the 

minimum GSR in August are found as 14.43 

mm and 9.34, MJ/m2/day respectively.  

 

An empirical model: finding coefficient of 

determination and coefficient of regression: 

We have used two models; (i) Angstrom-

Prescott, and (ii) Tiwari and Sangeeta model to 

predict the GSR at that particular place by 

using correlation coefficients a, b, sunshine 

hour (n), extraterrestrial radiation (Ho), and 

day length (N). The value of regression 

coefficient was found by using Tiwari and 

Sangeeta model.   
𝐻

𝐻𝑜
= 𝑎 + 𝑏(

𝑛

𝑁
)… (1) 

The left-hand side of this equation is the 

clearness index ( 
𝐻

𝐻𝑜
). The values of a and b are 

found 0.28 and 0.57 (Table1). The coefficient 

of determination (R2) and coefficient of 

regression (R) are determined from Figure 10 

where we show the graph between measured 

clearness index (
𝐻𝑚

𝐻𝑜
) and calculated clearness 

index ( 
𝐻𝑐

𝐻𝑜
). 



Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

  

 158 

 

 

 

 

 

 

 

 

Fig.10: Measured clearness index (
𝐻𝑚

𝐻𝑜
) versus 

calculated clearness index ( 
𝐻𝑐

𝐻𝑜
) 

Figure 10 finds the coefficient of regression 

(R) as 0.881 and the coefficient of 

determination (R2) as 0.776. The regression 

coefficient says us negative or positive 

correlation between dependent and 

independent variables. We find positive 

correlation coefficient from our calculations. 

This implies that the increase in dependent 

variable on increasing the independent 

variables. The coefficient of determination, 

which lies in between 0 and 1, is also known 

as the goodness of fit. It tells us how strong 

the relationship between two variables is. The 

regression coefficient 0.881 means 88.1% of 

the dependent variable is predicted from the 

information of independent variables. Hence 

the good (high) value of regression coefficient 

tells us a good prediction of clearness index. 

For a clearer (less cloudy) day there is high 

value of the global solar radiation.  In the 

Figure 10, we see high values of the 

coefficient of regression and coefficient of 

determination which indicates the high to 

clearness index in Guranshe, Surkhet (for the 

year 2018). From the above discussion, we 

see that the annual average of measured and 

the calculated/predicted values of GSR are 

found to be 15.65MJ/m2/day and 19.18 

MJ/m2/day respectively. Also, the correlation 

coefficients are found to be a = 0.28 and b = 

0.57. The GSR values from our calculations 

fall in same order of magnitude comparing to 

the previous studies at different places, like in 

Lukla(14.51MJ/m2/day),Kathmandu(13.753

MJ/m2/day),Pokhara(16.499MJ/m2/day),Jum

la(19.884MJ/m2/day)andSimikot(16.562MJ/

m2/day) [7].The comparison clearly shows 

that our calculation for Guranshe agrees the 

most (within 5.4% of difference) with 

Pokhara. This is due to similar geological and 

metrological situation in both the places. All 

the values (from our calculations and previous 

study) show the good potential of solar energy 

technology in those places. The results also 

inspire the authorities in sub-Himalaya terrain 

(like Surkhet), inner terai, and also other 

similar geographical locations of Nepal to 

promote solar energy harvesting industries 

like Photovoltaic solar panels, solar water 

heater, Dye-sensitized solar cells, Energy 

storage, Rechargeable batteries and other 

possible applications [16].  

 

 
 
 
3. Conclusions 

The measured GSR, calculated GSR and other 

meteorological parameters affecting GSR were 

studied by using the available data. The GSR 

of the year 2018 A.D. at Guranshe, Surkhet 

was measured at the horizontal surface using a 

CMP3 pyranometer. On the other hand, GSR 

and the other empirical constants have been 

estimated by using numerical models like: 

Angstrom-Prescott and Tiwari and Sangeeta  

 

model. The annual average of measured and 

the calculated/predicted values of GSR were 

found to be 15.65MJ/m2/day 

(4.35kWh/m2/day) and 19.18 MJ/m2/day 

(5.33kWh/m2/day) respectively. Also, the 

correlation coefficients were found to be 

a=0.28 and b=0.57. The comparison in 

between the measured and calculated values of 

GSR were performed by using the methods of 



Adhikari and Pantha  / BIBECHANA 19 (1-2) (2022) 150-159 

 

 

 

159 

Root Mean Square Error (RMSE), Mean Bias 

Error (MBE), Mean Absolute Error (MAE), 

and Mean Percentage Error (MPE). Various 

metrological parameters like average air 

temperature, sunshine hour, air pressure, 

relative humidity were found to be affecting 

the values of GSR as per established 

relationship. Our study shows that Gurashe 

(Surkhet) has similar average GSR value 

comparing to the other places of Nepal and 

better agreement is seen with Pokhara due to 

similar geological/metrological parameters.  

Harvesting the solar energy can be helpful for 

solar farming and mitigating the energy crisis 

of the places especially where the other sources 

of energy are hardly accessible. Having high 

potential of tourist destination, the regularity in 

energy supply through alternative source can 

enhance its pace of development in Surkhet 

and similar territories of Nepal. 

Acknowledgment 

The authors acknowledge the Department of 

Hydrology and Meteorology (DHM/GoN), 

Government of Nepal for providing 

meteorological data relevant to the study. 

Special thanks are due to Prof. Dr. K. N. 

Poudyal, faculty member at IOE, Pulchwk 

Campus, Tribhuvan University, and Sanjeep 

Sapkota for useful discussions. 

 

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	3. Conclusions