Jurnal Natural

. Solar energy plays an important role in the temperature distribution on the Earth's surface and essential energy that sustains life for human. In the calculation of solar energy, the limitation of solar radiation data is a major obstacle. Solar radiation data is very limited at some observation stations due to the costly procurement of measuring instruments and complicated techniques. Estimation of global solar radiation using empirical models is one way to overcome the limitations of global solar radiation data at various locations. This study built the Angstrom-Prescott model to estimate global solar radiation based on the sunshine duration’s parameter in Aceh Besar Regency. Two years (2019-2020) global solar radiation and sunshine duration data from Aceh Climatological Station were used to estimate global solar radiation in 2021. Data for 2021 was using to evaluate the equation H/H 0 =0.28+0.22 (n/N), the results showed good model accuracy with an RMSE value of 0.052 and a MAPE of 11% (good forecasting). The model equation has been reliable to calculate solar radiation in four locations in Aceh Besar Regency.


INTRODUCTION
Solar radiation energy has an important role as the driver of global climate change [1].At some condition, it can trigger extreme rainfall and will lead to hydrometeorological disasters such as floods, landslides [2].The combination of the sun's radiation with various volcanic activities impacts the increasing average temperature and also the sea level that makes some mainland sink [3].However, solar radiation energy is essential factor that sustains life for human.There are various processes in life depend on solar energy, such as the process of building agricultural models [4], the environment [5], hydrology [6], and ecology [7].Moreover, solar energy data is important to the solar collector's design [8] and photovoltaic cell [9] measurements.
To calculate the solar radiation intensity, there are three methods: using instrumentations (pyranometers, pyrheliometers, heliographs, etc), satellite images, and various physical and empirical models.Though the use of instrumentations and satellite images is reliable and more accurate, the installation and processing are high costs [10][11][12].Therefore, the empirical method could be the option for estimating solar radiation using available climatological parameters.
One of the most widely applied empirical models is the Angström-Prescott or AP model [13;14].This equation relates the relative daily solar radiation and relative daily sunshine duration in a given location.Several studies modify the AP model equation by adding other meteorological parameters such as air temperature [15][16][17][18][19], atmospheric pressure [20], rainfall [12], and the combination of air humidity and air temperature [21].Meanwhile, the other works were conducted by modifying the structure of the AP model from linear regression equations to the second-degree, thirddegree, exponential, and logarithmic [22;23].However, these modified models require more computational time than simple linear models and often do not provide a significant increase in accuracy, compared to the original model which used only daily sunshine duration [17-19;22;23].Indonesia is located in the equatorial region which allows solar irradiation is relatively evenly distributed [24].Like other regions in Indonesia, Aceh Besar receives abundant solar radiation each year.This abundance of solar energy needs to be utilized in much more immense ways.Therefore, this paper builds an empirical model to estimate daily solar radiation using daily sunshine duration data.1).ASRS is a BMKG instrument consisting of sensor components, each of which has a different performance and produces several data or parameters related to solar radiation, including global radiation (Global Horizontal Irradiance/ GHI), diffuse radiation (Diffuse Horizontal Irradiance/ DHI), and reflective solar radiation or reflective irradiance), UV-A radiation, UV-B radiation, long duration of irradiation, and photosynthetically Active Radiation (PAR) which is useful for plant growth purposes.All solar radiation quantities were measured in 10-minute intervals.The recorded data are an instantaneous value, referred to as solar irradiance, and have units of W/m 2 .The parameter used in this research was solar global radiation (GHI).
Data quality test was performed by checking error data and calculating blank data on daily solar radiation data.Error data on ASRS output is generally recorded with the value "9999" so that data were eliminated.Meanwhile, blank data at intervals of 10 minutes, which amounted to more than one data per hour, were eliminated as well.Elimination of the data was carried out to avoid large fluctuations in data when calculating the average hourly and daily.After the data quality test, the data were converted into daily average (total radiation amount for 24 hours).
Sunshine duration data or LPM (Lama Penyinaran Matahari) was obtained from the Campbell-Stokes, which recorded the duration of sunlight from the burn trace on the recording card.As the sun moves, the sunlight hit the glass sphere and burns the card.The length of the burn trace left on the card represents the sunshine duration on that day.For this study, sunshine duration data were obtained from four locations (Table 1).
The daily solar radiation and daily sunshine duration data for two years (2019-2020) from Aceh Climatological Station were used to estimate daily solar radiation for one year (2021) while the measured daily solar radiation data in 2021 is used to evaluate the model.The model will be used to calculate the average of daily solar radiation in 2021 over Aceh Besar region, using daily sunshine duration data from all three meteorological stations in Aceh Besar regency.These sunshine duration data have different periods depending on data availability.Demplot and Waduk Keuliling Climatological sites have 11 months of data (Jan-Nov) for 2021.

The Angstrom-Prescott model
To provide the solar radiation data, several models have been suggested to use the daily sunshine duration as input variable.The most widely applied model was proposed by Angström (1924) and later modified by Prescott (1940).The formula Angstrom-Prescott can be written as [25;26]: wherein ( ! ) is the solar radiation at the top of the atmosphere or extraterrestrial radiation, (n) is the daily sunshine duration and (N) is the day length.The ratio of solar radiation (/ ! ) is known as clearness index, which indicates how transparent the skies on a given day.Coefficient "a" can be interpreted as the solar radiation fraction that reaches the Earth's surface on a cloudy day, which depend on the type and thickness of clouds.The other coefficient is "b" which describe the total of solar radiation fraction.The sum (a+b) is given the potential fraction of extraterrestrial radiation available to reach the earth's surface.Coefficients "a" and "b" of the A-P model were determined by the least square method.
! is a function of solar constant (Isc), latitude (ϕ), day of the year (D), solar declination (δ) and solar hour angle (ωs). !can be calculated using the equations (4), whereas solar declination (δ) and solar hour angle (ωs) was calculated using the equations ( 5) and ( 6), respectively [25;26].In this study, the value of the solar constant, was set at 1367 W/m 2 and the latitude (ϕ) was set 5.4 due to the latitude of Aceh Climatological Station.The empirical model will be evaluated using several statistical metrics, which RMSE and MAPE.Let  " and  !denoted the predicted and measured values at data point i, respectively.Then, RMSE and MAPE are defined as: Where n is the number of data points.The closer RMSE is to 0, the more accurate the model is.For the MAPE evaluation, the highly accurate estimation is show by the value less than 10%, good estimation ranging from 10 to 20%, reasonable forecasting ranging from 20% to 50%, and inaccurate estimation is the MAPE value over 50% [27].Besar which is surrounded by three highlands, namely hills in the east, Mount Seulawah in the southeast, and Mount Bukit Barisan.The existence of mountains causes climate differences even though the places are not far apart [28].The local interactions between the sea and the topography of Bukit Barisan have a strong influence on the weather and climate in Aceh, especially on cloud cover which has an impact on the variations of solar radiation.

RESULTS AND DISCUSSION
The diurnal radiation intensity in Figure 1 shows that the solar radiation in Aceh Besar began to be measured at 06.10-07.00WIB to 18.10-19.00WIB.Aceh is an area located in the western part of Indonesia where the sun rises and sets longer than the central and eastern parts of Indonesia so that every day the intensity of solar radiation begins to be measured at 06.00 WIB to 19.00 WIB.The highest intensity occurred at 12.10-13.00WIB (noon), with a median value of 703 W/m 2 of data and a fluctuation range of 527-894 W/m 2 .Variations of topography or altitude affect radiation reception and also surface temperature.That urban area has a high surface temperature, in contrast, vegetation has a low surface temperature [29] The daily solar radiation estimation model The regression results between the LPM variable and the solar radiation variable show a positive linear relationship as shown in Figure 2. The increase of LPM value is followed by an increase in the solar radiation.(n/N) for Nigeria [30], / !=0.22+0.50(n/N) for India [31], / !=0.24+0.51(n/N) for Zambia [32].This similarity of the coefficients implies that the countries in equator area is relatively homogeneous in solar radiation pattern.The value of coefficient of determination (R 2 ) is 0.82, which indicates that the LPM variable can explain 82.52% of the solar radiation.Figure 3 shows the distribution of models' residuals against estimated radiation values.At lower radiation, the spread of residuals is slightly wider, however, the residuals slightly better at higher radiation.Generally, estimates of the model produce well-distributed.The RMSE and MAPE are 0.052 and 11% respectively.MAPE value still in the ranges of the reasonable forecasting category (20% < MAPE< 50%) and can be used in estimation calculations.
The estimated of monthly solar radiation model in 2021 is compared with the measured radiation as shown in Figure 4. Generally, it shows a fairly good similarity pattern, the model radiation can follow the measured radiation pattern, however, in March, July, and November the estimated radiation value is higher than the measured radiation with differences is 232.2W/m 2 , 158.2 W/m 2 and 233 W/m 2 , respectively.For 2021 in Aceh Climatological Station the highest values occurred in February while the lowest occurred in November.This is due to the movement of the sun to the equator March-April and September-October.In contrast, the radiation becomes lower as the sun move to ) and sunshine duration (/).the north and south solstice in December-January and June-July.

Estimated solar radiation in Aceh Besar Regency
The model equation is used to calculate monthly solar radiation for a period of 10 years (2010-2021), the monthly solar radiation can be seen in Figure 5.In general, the monthly solar radiation intensity in Aceh Besar Staklim in the 2010-2021 period ranges from 3579.7-5724.9W/m 2 .The strong intensity occurs in March (5308 W/m 2 ).The dry season in Aceh Besar (May-September) exibit very uniform pattern day to day solar radiation.Although the monthly pattern of radiation varying from each city, Aceh Besar has similar pattern with Kupang.Morisson [33] shows that in Kupang, the maximum irradiation occurs in Oktober-November and minimum in May-April.However, there are the cities that have uniform pattern of monthly radiation, due to the influence of local geography which cause a high humidity.The pattern of solar radiation (MJ/m 2 day) in 2010-2021 shows an increase and decrease in line with the pattern of solar declination (Figure 6).The intensity of solar radiation increases in March-April and August-September as the sun approaches the equator, on the contrary in June-July and December-January the intensity of solar radiation decreases as the sun moves away from the equator.There is a uniqueness in this pattern of solar radiation intensity, namely, when the sun's declination is at a minimum position or 0 degrees, the intensity shows a clear pattern of increase in February-March, while in August-September it does not show a significant pattern of increased.
The regression equation of the model has a value of a = 0.2797 and b = 0.2293.These values could written as, / != 0.2797+0.2293(n/N).This model slightly different from the other countries which located in equator area.Some of the models are / !=0.23+0.38

Figure 4 .
Figure 4. Comparison of monthly estimated radiation and measured radiation in 2021.

Figure 6 .
Figure 6.Average monthly solar radiation and sun declination for Aceh Climatological Station.

Figure 7 .
Figure 7. Average monthly solar radiation estimated by model.

Table 1 .
The locations of solar radiation data used in this study Copyright © 2023 Jurnal Natural p-ISSN: 1411-8513; e-ISSN: 2541-4062.Open access under CC-BY license.
[34]estimate of monthly average of solar radiation in four locations in Aceh Besar is show in Figure7.In general, the monthly average radiation in all station shows a uniform pattern throughout 2021, except in June at Waduk Keuliling Climatological Site.This is due to specific condition of humidity occur in June.The average value of daily solar radiation over Aceh Besar region for 2021 ranged from 3204.3 W/m 2 to 5611.8 W/m 2 or 3.2 kWh/m 2 to 5.6 kWh/m 2 .Aceh Besar is located on the western coast Sumatera which has lower solar radiation as the region is known to be dominated by highland.The average of solar radiation in Aceh Besar for 2021 is 4.48 kWh/m 2 .This value is comparable to the values of daily solar radiation over Indonesia region calculated in previous works.Rumbayan[34]found that yearly average of solar radiation value are 4.75 kWh/m 2 for Bengkulu, 4.97 kWh/m 2 for Jakarta, 4.83 kWh/m 2 for Samarinda, 5.98 kWh/m 2 for Manado and 5.67 kWh/m 2 for Ambon.CONCLUSIONThe Angstrom-Prescott regression model which was built based on data on solar radiation intensity/global solar radiation in 2020 in Aceh Besar resulted in an estimation model equation with R 2 of 0.82.Calculation of solar radiation using the model equation produces / != 0.28 + 0.22 (/).The evaluation of the model shows that the resulting model has good accuracy with an RMSE of 0.052, while MAPE is worth 11% indicates the model has good forecasting.Monthly solar radiation at four locations in Aceh Besar was calculated using the model equation, for ten years (2010-2021) at Aceh Climatological Station and one year (2021) SIM Meteorological Station, Demplot and Climatological sites.The average value of daily solar radiation over Aceh Besar Region for 2021 ranged from 3.2 kWh/m 2 to 5.6 kWh/m 2 while highest irradiation occurs in March.