Modification and Application of Simple Regression Models to Predict Annual Precipitation in Shahrekord and Yazd Weather Stations

Interduction: Spatial and temporal improper distribution of precipitation is one of the major problems in the water district. Increasing population and reduction per capita fresh water has made freshwater resources as a renewable to a semi-renewable source (1).
Rainfall is one of the climatic variables that influence the ground water resources. The existence of models for predicting the annual precipitation and subsequent management of water resources in arid, semi-arid and also humid regions is useful . In this study, the simple regression models that relate the annual precipitation to the duration of 42.5 and 47.5 mm of precipitation from the beginning of autumn (t42.5 and t47.5, respectively) and mean annual precipitation (Pm), in Khuzestan (2), Kerman (3) and southern and western provinces of Iran (4) were evaluated using long-term daily precipitation data of Shahrekord and Yazd Weather stations and, if necessary, modified equations.
In this study, long-term daily precipitation data of Shahrekord and Yazd Weather stations (1360-1392) from Meteorological Administration of Chaharmahal and Bakhtiari and Yazd were prepared, completed and used for analysis. At each station the duration of 42.5 and 47.5 mm of precipitation from the beginning of autumn (t42.5 and t47.5, respectively) for each year, annual precipitation and mean annual precipitation for subsequent calculations were extracted. Then, the homogeneity and adequacy of data were checked using RUN Test. Equations of 1 to 8 were used for predicting the annual precipitation using 70% of the data. The relationship between observed and predicted annual precipitation were evaluated. Then the coefficients of equations were corrected by 70% of the data set using SPSS Software in Shahrekord and Yazd Weather Stations. The remaining 30% of data were used to validate the modified models. Index of agreement (d) and normalized root mean square error (NRMSE), were used to evaluate the models. The NRMSE values close to zero and d values close to 1 indicate proper operation of the model.
Results showed that the models with straight and reverse relationships between t42.5 or t47.5 and Pm were not suitable to estimate the annual precipitation in Shahrekord. However, these models were relatively acceptable for Yazd. While the simple regression model using t42.5, t47.5 and the long-term Pm as independent inputs could be able to predict the annual precipitation of Shahrekord and Yazd stations with acceptable accuracy.
Using the relationship between t42.5, t47.5 and Pa (equations of 1, 3, 4 and 7) for estimating the annual precipitation in Shahrekord and Yazd stations, NRMSE values obtained greater than 0.3 and d index less than 0.7 (Fig. 3 and 4). Furthermore , the models included t42.5, t47.5 and Pm versus Pa (equations of 2, 5, 6 and 8), had not acceptable results (Fig. 5 and 6). By modifying the above mentioned equations (models of 10 to 14 for Shahrekord and 15 to 19 for Yazd) and comparison of measured and predicted annual precipitation by the modified models, the results showed that the linear and inverse relationship between t42.5, t47.5 and annual precipitation could not be an appropriate model for Shahrekord Station (Fig. 7-A and 7-B and 7-C) and results of the evaluation of these relationships for estimating of the average annual precipitation of Yazd were relatively acceptable (Fig. 8-A and 8-B and 8-C results in Yazd station). While the simple linear model including the relationship between those time periods (t42.5, t47.5 ) and the long-term average annual precipitation with corrected coefficients could accurately estimate the annual rainfall in the Shahrekord and Yazd stations (Fig. 7-d and 7-H for Shahrekord and 8-D, 8-H for Yazd station). In order to validate the above results, the models were evaluated with the remaining 30% of the data . Results showed in Figs. 9 and 10. The NRMSE values in Figs. 10-A, 10-B and 10-C, confirm the validity of the relationship between t42.5, t47.5 and annual precipitation.