Daily estimation of solar radiation in some climatic samples of Iran using meteorological data

Introduction
Global solar radiation (GSR) is an important parameter for designing and developing different solar energy systems (Tris et al., 1997). The concept of solar radiation means that during a certain period of time, how much solar energy is absorbed by a horizontal surface in an area (Almoroux and Hontoria, 2004; Wang et al., 2011). Iran is a sunny country, and, the optimal utilization of solar energy can be necessary for furure enenrgy development (Jafarkazemi and Mardi, 2019).
 
Methodology
In the present study, solar radiation was investigated in five climates. In this way, the two stations of Ramsar and Rasht represent the very humid cool warm climate, the three stations of Kermanshah, Mashhad and Shiraz represent the very hot semi-arid climate, the three stations of Tabriz, Zanjan and Urmia represent the semi-arid climate. Cold-warm, Birjand, Kerman and Isfahan stations were investigated as representatives of warm dry climate and Ahvaz, Booshehr and Bandar Abbas stations as representatives of warm dry temperate climate.
Daily measured data of wind speed (U), maximum temperature (Tmax), minimum temperature (Tmin), average air temperature (Tave), average relative humidity (RH), sunshine hour (N) and precipitation (R) As independent variables and the amount of solar radiation (RS) as a dependent variable, for each of the mentioned stations, it was prepared from the National Meteorological Organization during the years 1986 to 2010.
After preparing the data and their quality control, solar radiation was estimated using multivariate linear regression fitting under SPSS software. Empirical relationships were calculated for each climate separately.
For this purpose, by applying the ranges, restrictions and characteristics of radiation, regression analysis was performed in the Solver environment of Excel software.
In order to evaluate the research, the results were measured based on the error measurement indices of the mean squared normal error (nRMSE) and mean bias (MBE).
 
Results and discussion
According to Table (2), the meteorological parameters of maximum, minimum and average temperatures, hours of sunshine and wind have a positive correlation with solar radiation, that is, with the increase of each parameter, the amount of radiation also has an increasing trend, except precipitation and relative humidity, which have a negative correlation with radiation. It shows the reverse relationship between these two parameters with solar radiation. The highest correlation between relative humidity and solar radiation (-0.485) and the lowest correlation between precipitation and radiation with a value of -0.048 is in the hot dry climate. The best regression equations obtained from meteorological parameters using SPSS software for different climates are given in Table (3). in which the amount of error between the available parameters has been calculated for each of the stations.
The relationships presented for five climates show that the maximum amount of error based on nRMSE and MBE index in hot dry climate is 11% and -1.15 megajoules per square centimeter per day, respectively. On the other hand, the lowest amount of error based on the two mentioned indicators is in the hot and cold semi-arid climate, which is 8.5% and 0.50 megajoules per square centimeter per day, respectively. To estimate the regression equation in hot and cold semi-arid climates, as the results show, the variables included in the best regression equation in hot and cold semi-arid climates were: maximum temperature, precipitation, minimum temperature, sunshine hour, wind speed and average temperature In hot dry cool climate, the maximum, minimum and average temperature, relative humidity, sunshine hour and wind speed were used. Precipitation, minimum temperature, wind speed and solar hour are used in very hot semi-arid climate, in hot dry climate, maximum and minimum and average temperature, relative humidity, wind speed and solar hour are used, finally in moderately hot dry climate. Precipitation, maximum and average temperature along with wind speed, sunshine hour and relative humidity were used. In very humid, cool, hot, semi-dry, very hot, and dry, moderately hot climates, it is observed that the accuracy of radiation estimation between meteorological parameters is almost within the same interval of change (about 9%). From the MBE index provided between the meteorological parameters, we find that the minimum overestimation value is 0.02 megajoules per square centimeter per day in very humid, cool, hot climates, and the maximum value is (0.50) in the semi-arid, cold, hot climates. be Figure (3) shows the time series graphs of the investigated stations during the relevant statistical period. In general, the estimation of solar radiation using regression equations based on the investigated error measurement indices, which has the least amount of error and, conversely, the highest amount of accuracy, is in the semi-arid, cold, hot climate, because the accuracy is 8.5% based on the nRMSE index. The high accuracy of the equation is used to estimate the radiation, and its MBE value is 0.50, which proves the overestimation of the presented equation.
Meteorological parameters were examined on a daily basis to obtain the regression equation in the years 1986 to 2010 in a very humid cool hot climate as mentioned in Table (4), and in the time series graph, the observed radiation values are more than Radiation values are estimates from regression relationships. The very hot semi-arid climate shows that the estimated radiation values have almost a constant range of changes and its maximum value is approximately 2000 megajoules per square centimeter per day, but the observed radiation value is more than this value. According to the diagram and table (4), the semi-arid, cold and hot climate has MBE value of -0.501 MJ/cm2/day among the parameters, and the estimated amount of radiation has not exceeded 2000 MJ/cm2. In some statistical years, the observed value is more than the estimated value. The time series of the hot and cold semi-arid climate is the same as the rest of the climates and it is higher than the mentioned value, and in the cool and hot dry climate, which has MBE with a value of -1.15 MJ/cm2/day, it is among the meteorological parameters. It is also mentioned in Table (4), and in some of the investigated periods, the amount of observations is more than the estimate, and there is a large fluctuation between the amount of radiation estimated and observations, and the estimated amount is up to about 4000 megajoules per square centimeter per day. is Finally, the hot temperate dry climate with MBE, -0.558 megajoules per square centimeter per day indicates the underestimation of solar radiation in this climate.
 
Conclusions
It is necessary to investigate the energy of solar radiation as it is important and influential parameter on the processes on earth, including water resources. In this research, using the equations obtained from the regression model, the amount of solar radiation reaching the earth's surface was estimated in five different climates in the country, which includes 14 meteorological stations. It was seen that the amount of observed radiation in three climates, semi-arid, very hot, dry, cool, hot, and dry, moderately hot, is lower than the observed amount, and in two climates, very humid, cool, hot, and semi-arid, cold, hot, it is higher than the estimated amount of radiation. According to the regression equations, the amount of error obtained in the hot and cold semi-arid climate has the lowest amount of error and the warm and dry climate has the highest amount of error. The changes in the error percentage of the solar radiation estimation of the other three climates are not large and are about 9%. The meteorological parameters used in the semi-arid, cold, hot climate were temperature, precipitation, sunshine hours, and wind speed. Considering the limitation of measuring solar radiation in the country, the importance of estimating this meteorological parameter is essential in order to use it in the management of water resources by managers.