Polynomial chaos expansion and response surface method for nonlinear modelling of reference evapotranspiration

The feasibility of polynomial chaos expansion (PCE) and response surface method (RSM) models is investigated for modelling reference evapotranspiration (ET0). The modelling results of the proposed models are validated against the M5 model tree and multi-layer perceptron neural network (MLPNN) methods. Two meteorological stations, Isparta and Antalya, in the Mediterranean region of Turkey, are inspected. Various input combinations of daily air temperature, solar radiation, wind speed and relative humidity are constructed as input attributes for the ET0. Generally, the modelling accuracy is increased by increasing the number of inputs. Including wind speed in the model inputs considerably increases their accuracy in modelling ET0. Mean absolute error (MAE), root mean square error (RMSE), agreement index (d) and Nash-Sutcliffe efficiency (NSE) are used as comparison criteria. The PCE is the most accurate model in estimating daily ET0, giving the lowest MAE (0.036 and 0.037 mm) and RMSE (0.047 and 0.050 mm) and the highest d (0.9998 and 0.9999) and NSE (0.9992 and 0.9996) with the four-input PCE models for Isparta and Antalya, respectively.