SOLAR RADIATION is an essential factor in irrigation scheduling, hydrological cycle, crop growth simulation MODELS and estimation of reference evapotranspiration. The aim of the present research was to investigate the accuracy of SOLAR RADIATION estimation MODELS and their effects on reference evapotranspiration. For this purpose, the meteorological data of 4 synoptic stations including Urmia, Takab, Salmas and Mahabad in West of Urmia lake catchment in daily scale were used. SOLAR RADIATION was estimated using seven MODELS including, Hargreaves- Samani, Allen, Self-Calibrating, Samani, Annandale, Bristow-Campbell and Angstrom- Prescott. Then, the obtained values were used in FAO- Penman- Monteith equation to estimate the reference evapotranspiration. In order to evaluate the MODELS' accuracy, the statistical indicators including root mean square error, mean bias error and determination coefficient were used. The evaluation results of the MODELS showed that the Angstrom- Prescott model had the best performance, and the Samani method was the weakest method in the studied stations. The average values of the root mean square error for the Angstrom- Prescott and Samani methods in the studied region were obtained 0.48 and 1.43 mm/day, respectively.

Evapotranspiration is one of the most important processes in water and radiative transfer in hydrological cycle, and the required energy for this process is provided by SOLAR RADIATION. Therefore, the accuracy of evapotranspiration estimation is strongly depends on the accuracy of SOLAR RADIATION estimation. This study was conducted to evaluate the different surface SOLAR RADIATION MODELS such as empirical MODELS (Angstrom and Hargreaves-Samani), physically-based MODELS (NCEP and GLDAS) and a satellite observation model (CM-SAF). The results showed that the calibrated Angstrom model with R2=0. 9 and SEE=2. 58 was the most efficient model. However, the accuracy of this model is strongly depends on the calibration procedure and the existence of sunshine data. The GLDAS model with R2= 0. 87 and SEE=3. 5 was the second most efficient model after calibrated Angstrom model. The GLDAS model, in spite of 10. 2% overestimation of surface SOLAR RADIATION, can be the most efficient model in areas with the lack of meteorological data.

In addition to use in climate MODELS, SOLAR RADIATION plays a decisive role in development of SOLAR systems programs in different areas. With significant advances in telecommunication and communication sector, the use of satellite imageries for land-based observations has found a wider role than traditional observations. Moderate Resolution Imaging Spectroradiometer (MODIS) satellite products are available to the public free of charge and have a reasonable resolution of 1km × 1km. In this research, it was tried to calculate the amount of total SOLAR RADIATION in 4 stations in Iran, using the Earth's surface and atmospheric MODIS data as an input of the parametric and the Angströ m-Prescott (AP) MODELS and to compare the results with ground-level observations. The AP model output obtained from the MODIS data (APRS) was compared with the AP model output obtained from ground level observation data (APGS). By comparing the results, it was found that the APRS model is more accuracy than the APGS model on cloudy days. So that the amount of RMSE and MBE indices for the APRS model on cloudy days were 41. 74 W/m 2 and 19. 70 W/m 2, respectively, and for APGS model were 43. 6 W/m 2 and 34. 25 W/m 2, respectively. However, the accuracy of the APGS model on sunny days was higher than that of the APRS model. Although the limitations of ground data (point observations) could be an effective factor in choosing one of both MODELS. Results also indicate a high accuracy of the parametric model (RMSE = 16. 56 W/m 2 and R 2 =0. 93), especially on cloudy days. On the other hand, despite of high accuracy of the parametric model, the application of APRS model is easy. However, long period sunshine hour’ s data are needed for calibration of AP coefficients in different regions.

Artificial neural networks (ANNs) was used to estimate daily global SOLAR RADIATION at a weather station lacking any measured Rs values based on the measured Rs values at another station with similar climate. The accuracy of ANNs was compared with that of six other MODELS developed for estimating Rs including FAO-56, Hargreaves-Samani, Mahmood-Hubard, Bahel, Annandale, and Bristow-Campbell MODELS. The weather data was selected from Karaj and Shiraz weather stations having arid and semi-arid climates, respectively. The weather data of Karaj station, where daily global SOLAR RADIATION was measured, was used to train ANNs and Shiraz data was used for validation. ANNs generated daily global SOLAR RADIATION estimates with higher degree of accuracy as compared with all the other MODELS used with the input parameters of maximum possible sunshine hours and daily extraterrestrial SOLAR RADIATION, which both depend on latitude and day of the year, and actual sunshine hours with root mean square error (RMSE) of 2.34 Mj m-2 day-1 and correlation coefficient (R) of 0.94 (at 1 percent significant level). In case actual sunshine hours was not available, Annandel and Hargreaves-Samani MODELS with locally calibrated empirical parameters and ANNs with minimum and maximum air temperatures and extraterrestrial RADIATION as input parameters gave the best results.

The concern of the present research was to do a comparative study between the GEP, ANN and ANFIS MODELS to estimate monthly global SOLAR RADIATION. For this purpose, long-term (24-years) monthly data of global SOLAR RADIATION (RS, MJ m − 2 ), sunshine hours and air temperature (° C), from Tabriz synoptic station were used. To perform the artificial intelligence MODELS, a new combination of inputs including monthly mean clearness index (KT), monthly temperature range (Δ T), relative sunshine hours (n/N) and extraterrestrial global SOLAR RADIATION (Ra) were employed. Since the lowest values of MBE and RMSE (0. 13 and 1. 97 MJ m − 2 respectively) and the highest value of R 2 (0. 92) were obtained for ANN model, and therefore, the ANN model was selected as the best model to estimate the monthly global SOLAR RADIATION. Using quarter-quarter (Q-Q) plots revealed that although the ANN model generally presents the best fit for monthly global SOLAR RADIATION data, this model is found to be not successful in estimating the higher values of monthly global SOLAR RADIATION data. Therefore, the application of ANN model is recommended for regions with lower SOLAR RADIATION values. The performance of the ANFIS model was better than other MODELS in covering the highest and lowest values (the first and fourth quarter). Therefore, it can be concluded that the ANFIS model gives more accurate results in the areas with the higher values of SOLAR RADIATION. The findings also show that unlike previous researches which were carried out in daily scale, the performance of GEP technique for modeling monthly global SOLAR RADIATION is satisfactory especially in the ranges of 250 to 800 MJ m − 2. Thus, it can be inferred that GEP can be more powerful in modeling the phenomena which have low fluctuations or a limited range.

Introduction SOLAR RADIATION is the main source of all energies on the Earth and is an important parameter in hydrology studies, water resource management, water balance equations, and plant growth simulation MODELS. The most common instrument for recording global SOLAR RADIATION data (GSR), is using pyranometer; however, because of the high costs of installation and maintenance, it is not possible to establish a RADIATION site for such purposes. In areas where ground measurements are not available, the Global SOLAR RADIATION (GSR) can be estimated by empirical and semi-empirical MODELS, satellite techniques, artificial intelligence MODELS and other geostatistical approaches. In artificial intelligence MODELS such as neural networks, various meteorological parameters like air temperature, relative humidity, sunshine hours, etc. are easily integrated to estimate global SOLAR RADIATION. In most commonly used RADIATION MODELS (e. g. Angstrom-based MODELS) for estimating daily GSR, the sunshine hours and cloud cover are two important input parameters. Unfortunately, those parameters are not measured very accurately in weather site. Moreover, for time scales less than daily (e. g. hourly) using sunshine hour as an input, is not possible for predicting the sub-scale temporal GSR. The main purpose of this study, is comparing Multiple Linear Regression model and three types of artificial intelligence MODELS (MLP, GRNN, ANFIS) against each other to estimate GSR in cold semi-arid climate of Hamedan, in order to present the most accurate model by including the soil data and ignoring the sunshine hours. Materials and Methods Study Area: According to the Extended De-Martonne climate classification model, Hamedan is located in a semi-arid-very cold area and has a mean altitude of 1851 meters above sea level. In this study, GSR and meteorological variables (daily values of maximum air temperature, mean air temperature, minimum air temperature, air pressure, air relative humidity, soil temperature and rainfall) recorded at Bu-Ali Sina University weather site, located at latitude 34’ 48” and longitude 48’ 28” . These data were recorded every 10 minute during 31 Dec. 2016, to 10 Mar. 2018 by using an automated Spanish GEONICA Logger. MODELS: Multiple linear Regression (MR): This model is a simple and linear model that estimates the target variable by assigning a constant optimized coefficient for each input variable. Adaptive Neuro-Fuzzy Inference System (ANFIS): A multi-layered network model that uses advanced neural network learning algorithms and fuzzy logic, to describe the relationships between inputs and outputs. This model uses the neural network’ s Learning ability and fuzzy rules, to define the relationships between input-output variables. Generalized Regression Neural Network (GRNN): Is a three-layered neural network, which the number of neurons in the first and last layers like other neural networks, is respectively equal to the input and output vectors. But, unlike other networks, the number of hidden layers of neurons in GRNN model is equal to the number of observational data. Evaluation criteria: To evaluate the MODELS performances against actual field measurements, the Root Mean Square Error (RMSE) and Coefficient of Determination (R2) have been used. Results and discussion The correlations of MODELS input variables (eight independent variables) versus GSR (dependent variable) were evaluated. Results revealed that maximum air temperature, average air temperature, relative humidity and soil temperature are respectively the most influencing inputs for modeling GSR, if using minimum numbers of meteorological parameters. Among them, maximum air temperature, minimum air temperature, atmospheric relative humidity and soil temperature, were selected as the best inputs, for modeling with least parameters. By using correlation test, as a 2-variables input matrix (relative humidity and soil temperature) 3-variables (mean air temperature, relative humidity and soil temperature) and the whole 4 parameters, were selected as 4-variables input matrix. The percentage of train and test data was 75% and 25% respectively. In this research, the MODELS were run by using two different samples: Random and non-random samples. The results of the evaluations showed that random samples had higher accuracy in GSR estimates. In MR model, the 4-variables input, and in three artificial intelligence MODELS (GRNN, ANFIS, MLP), 3-variables input showed the superior performances. Finally, the MODELS were evaluated by using all of the eight inputs. At this stage, MLP with RMSE=3. 04 Mj. m-2. day-1 and R2=86. 33%, ANFIS with RMSE=3. 26 Mj. m-2. day-1 and R2=84. 43%, GRNN with RMSE=3. 41 Mj. m-2. day-1 and R2=82. 86%, and MR with RMSE=4. 11 Mj. m-2. day-1 and R2=75. 20%, provided the best GSR estimates respectively. Conclusion The results showed that, in all numbers of input variables, random and non-random samples, artificial intelligence MODELS present better performance than linear regression. By availability of the whole eight meteorological variables (daily values of maximum air temperature, mean air temperature, minimum air temperature, air pressure, air relative humidity, soil temperature and rainfall), MLP model can present the best GSR estimates. If all input parameters are not available, employing Generalized Regression Neural Network (GRNN) model and 3-variable inputs of mean air temperature, relative air humidity, and soil temperature is suggested for estimating the Global SOLAR RADIATION (GSR) in cold semi-arid climate of Hamedan. It is noteworthy that in estimating GSR, two important parameters of sunshine hours and cloud cover were not used in our research. Testing the MODELS performances in other climate types is suggested as future works.

The mean daily global SOLAR RADIATION flux is influenced by astronomical, climatological, geographical, geometrical, meteorological, and physical parameters. This paper deals with the study of the effects of influencing parameters on the mean daily global SOLAR RADIATION flux, and also with the computation of the SOLAR RADIATION flux at the surface of the earth in locations without SOLAR RADIATION measurements. The reference–real data were borrowed from the Iranian Meteorological Organization. The analysis of data showed that the mean daily SOLAR RADIATION flux on a horizontal surface is related to parameters such as: mean daily extraterrestrial SOLAR RADIATION, average daily ratio of sunshine duration, mean daily relative humidity, mean daily maximum air temperature, mean daily maximum dew point temperature, mean daily atmospheric pressure, and sine of the SOLAR declination angle. Multiple regression and correlation analysis were applied to predict the mean daily global SOLAR RADIATION flux on a horizontal surface. The MODELS were validated when compared with the reference–measured data of global SOLAR RADIATION flux. The results showed that the MODELS estimate the global SOLAR RADIATION flux within a narrow relative error band. The values of mean bias errors and root mean square errors were within acceptable margins. The predicted values of global SOLAR RADIATION flux by this approach can be used for the design and performance estimation in SOLAR applications. The model can be used in areas where meteorological stations do not exist and information on SOLAR RADIATION flux cannot be obtained experimentally.

The more accurate estimate of evaporation in SOLAR Stills is considered as an important step in the planning and design of condensation irrigation system in hot and dry region. Since received RADIATION to evaporation surface is different inside and outside the Still, to initial estimate of evaporation in Stills, can not apply the commonly techniques used in open surface water. The main purpose of this study is modification of Penman model (as a compound and base model to estimate evaporation from open surface) RADIATION component and Priestley – Taylor model (as a recommended RADIATION model for estimating evaporation from closed environments such as greenhouses) to estimate the evaporation rate from the SOLAR Stills. Comparison of measured and estimated values over the one-year period of the study showed that modification the RADIATION component have a positive effect in more accurate estimate of evaporation from SOLAR Stills. The results showed that the modified Penman model is capable of estimate evaporation from Still with R2=0.950, MBE=1.116 (mm/day) and RMSE=1.258 (mm/day).

Precipitation and air temperature data, only, are often recorded at meteorological stations, with RADIATION being measured at very few weather stations, especially in developing countries. Therefore there arises a need for suitable MODELS to estimate SOLAR RADIATION for a completion of data sets. This paper is about an evaluation of eight MODELS for an estimation of daily SOLAR RADIATION (Q) from commonly measured variables in six synoptic stations of Iran, namely: Mashhad, Kerman, Tabriz, Esfehan, Hamedan and Zanjan using daily rainfall and temperature data for a duration of three years of 2000, 2001 and 2002. These stations represent several arid and semiarid sub-climates of Iran as based on extended-De Martonne climatic classification (semiarid-cold: Mashhad and Tabriz, arid-cold: Esfehan, Kerman, semiarid-extracold: Hamedan and Zanjan). The STATISTICA (ver. 6.0) software was employed for non-linear multivariate regression. The results indicated that most of the MODELS overestimated in lower values of SOLAR RADIATION while underestimating in the higher ranges, indicating a systematic error. Performance of the MODELS was evaluated based on the Root Mean Square Errors (RMSE) as well as R2. RMSE ranged from 1.14 to 7.76 Cal cm-2 min-1 for the whole data range and in all the six stations. Among the eight MODELS, the Richardson model rendered the best agreement with the measured data in Kerman and Zanjan stations. In case of Hamedan station, Bristow and Campbell model was the most suitable. As for Tabriz station, De Jong and Stewart model using rainfall and range of daily temperature data led to the best performance. In Mashhad station, McCaskill equation can be recommended. Analysis of the data in Esfehan station showed no significant difference among the MODELS. Due to variation in equations' performances, to come to valid conclusions and to choose the most suitable RADIATION MODELS, further study would be required from other climatic regions the country.