Modified Response-Surface Method: New Approach for Modeling Pan Evaporation

Abstract

This paper modifies the response surface method (RSM) by combining the polynomial and exponential basic mathematical functions to improve the accuracies for modeling monthly pan evaporations. The hybrid response surface function (HRSF) is developed based on exponential approximation and second-order polynomial estimation using the normalized input data set that includes temperature, relative humidity, wind speed, and solar radiation to predict pan evaporations of the Siirt and Diyarbakir stations in Turkey. A novel sensitivity analysis is proposed to obtain the effects of input databases on pan evaporation. According to the sensitivity analysis, the temperature and solar radiation are found to be the most effective parameters on pan evaporation. The performance of HRSF is compared with second-order response surface function, adaptive neuro-fuzzy inference system (ANFIS), and M5 model tree (M5Tree) models in three different applications. The optimal predictions are evaluated based on different training and test data sets for each approach. In the first application, monthly pan evaporations of Siirt and Diyarbakir are separately estimated. At Siirt Station, HRSF models are found to be better than the RSM, ANFIS, and M5Tree models in almost all the selected data sets. In Diyarbakir, the HRSF and ANFIS models provide almost the same accuracy and they are found to be slightly better than the RSM for all the calibration cases. In the second application, the most sensitive two climatic input variables (temperature and solar radiation) of Siirt and Diyarbakir stations are separately used for approximate pan evaporation. The HRSF and RSM give better estimates than the ANFIS and M5Tree models in cases of limited climatic inputs. In the third application, Diyarbakir’s monthly pan evaporations are estimated using climatic data from Siirt or both Siirt and Diyarbakir stations. In all applications, the HRSF generally performs superior to the RSF, ANFIS, and M5Tree models, while the worst results are generally obtained from the M5Tree model. The accuracy of the models generally increases by increasing number of training data. The ANFIS and M5Tree are found to be more sensitive to training data length than the RSF and HRSF.