عنوان مقاله [English]
The extended Abstract
The extent of the energy received from 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 the most of processes related to the soil-plant-atmosphere system such as net radiation, reference evapotranspiration, soil temperature and 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 models calibration procedure, the better models were recognized and by adopting the estimated global radiation by the 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 performed on the basis of the minimizing the RMSE index between the left and right sides of these equations, finally three models including Ångström–Prescott model, Bristow-Campbell model and Black model were selected as the representative of each of the three mentioned categories.
In the next step, the cross validation was applied on 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 Ångström–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 extents. The MBE index led to obtaining good results with no considerable-bias for Ångström–Prescott model (-3.9 kj.m-2.day-1) and 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 of the three models, the R2 and Reff were respectively greater than 0.83 and 0.78 values. The best values of these two indices obtained for the Ångström–Prescott model.
Regarding to comparing 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 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 seems 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-1for all of the three global radiation models. Regarding to soil temperature modeling, the Ångström–Prescott model (the most of the error range between -0.5 to 0.2 ˚C) showed a better performance than the Bristow-Campbell and Black models (the most of the error range between -1 to 1 ˚C). For soil moisture modeling, the Ångström–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 which performed on the basis of some few snowy days, the Ångström–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 good performance.
In overall, the results indicated that the appropriate outcomes were obtained when applying the global radiation estimated by Ångström–Prescott model as the input of all of the processes models. Regarding to 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