The capability of some global solar radiation empirical models as the input of the other hydro-climatic processes

The extent of the energy received from the sun to the earth is one of the main and important input parameters in the agricultural, ecological, hydrological, climatological, and environmental models. It has also a key role in most processes related to the soil-plant-atmosphere system such as net radiation, reference evapotranspiration, soil temperature, moisture, and snow melt. In this research, the efficiency of three categories of the global radiation empirical models including sunshine-based, air temperature-based, and cloudiness-based models was evaluated during the 1997-2021 period for the Sanandaj synoptic station and after these model’s calibration procedure, the better models were recognized. By adopting the estimated global radiation by better models as the input of modeling some processes including net radiation, reference evapotranspiration, soil temperature, and moisture and snow melt, the model outputs were compared with the case that the measured global radiation had been adopted as these models input. After the calibration of global radiation models and optimizing the empirical parameters of them, which were performed based on minimizing the RMSE index between the left and right sides of these equations, finally, three models including Angstrom–Prescott model, the Bristow-Campbell model, and the Black model were selected as the representative of each of the three mentioned categories. In the next step, cross validation was applied to these three models based on the MAE، MBE، R2 and Reff indices. The results showed a reasonable agreement between the measured and estimated global radiation based on all of these three selected models. The MAE index for Angstrom–Prescott, Bristow-Campbell, and Black models was 138.5, 227.14, and 251.3 kj.m-2.day-1, respectively which can be considered as the acceptable extent. The MBE index led to obtaining good results with no considerable bias for Angstrom–Prescott model (-3.9 kj.m-2.day-1) and the Bristow-Campbell model (+11.9 kj.m-2.day-1) but a positive overestimating bias using the Black model (+159 kj.m-2.day-1). For all three models, the R2 and Reff were respectively greater than 0.83 and 0.78 values. The best values of these two indices were obtained for the Angstrom–Prescott model. Regarding comparison of the outcome of estimated and measured global radiation when applying as the input of some models, the histogram of the errors (the difference between outputs of some of the processes models based on the estimated and measured global radiation inputs) for net radiation calculation showed the error range mostly from -50 to +50 kj.m-2.day-1 for all of the three global radiation model inputs, which as seemed to be a narrow difference between these two cases. For reference evapotranspiration calculation, the histogram of errors was mainly between very low values of -0.2 to 0.1 mm.day-1 for all of the three global radiation models. Regarding l temperature modeling, the Angstrom–Prescott model (with error range between -0.5 to 0.2 C) showed a better performance than the Bristow-Campbell and Black models (with error range between -1 to 1 C). For soil moisture modeling, the Angstrom–Prescott model showed very suitable performance with the most error values close to zero and the Bristow-Campbell and Black models showed relatively suitable and similar performance. The snow modeling performed based on some few snowy days, the Angstrom–Prescott model with focusing the histogram error between -2 to 0.5 cm can be considered as the best model and the Bristow-Campbell and Black models showed similar but not as good performance. On the whole, the results indicated that the appropriate outcomes were obtained when applying the global radiation estimated by Angstrom–Prescott model as the input of all of the processes models. Regarding Bristow-Campbell and Black methods, which led to obtaining relatively similar results, applying them as the inputs of different models led to a diversity of results including very appropriate (for reference evapotranspiration), appropriate (for net radiation), relatively appropriate (soil temperature and moisture) and not-appropriate (for snow).