Prediction of annual reference evapotranspiration using climatic data

It is important to determine how well ET_o can be estimated from easily observed E_pan (free water evaporation measured by a pan) measurements and the other climatic data. Our objectives are to predict annual ET_o with E_pan data (with a calibrated k_p (=ET_o/E_pan)) and with a 4-variable regression function method. The significance of the trends of E_pan, ET_o and k_p series were detected. The whole data series (ET_o, E_pan, mean temperature, sunlight hours, relative humidity and wind speed) were divided into the early (L-5) years for calibrating k_p and coefficients of a 4-variable function and the last 5 years for predicting ET_o. From the results, significance of series trends decreased when using the modified Mann-Kendall (MMK) test compared to the Mann-Kendall (MK) method. For ET_o, five out of six sites showed significant trends according to the MK statistic Z, and two sites were significant in trend combining with the MMK statistic Z*(j). For E_pan, two sites were significant in trends according to Z, and zero sites were significant in trends combining with Z*(j). For k_p, two sites were significant in trends according to Z, and no sites were significant in trends combining with Z*(j). Thus the calibrated k_p can be treated as a constant when using the E_pan method. The predicted annual ET_o using the E_pan and the multi-variable methods showed generally good agreements with the estimated annual ET_o (based on monthly PM equation) with low relative errors (RE). Mean ET_o values were well predicted by both methods. When using E_pan method, RE ranged from −14.7 to −3.3% for Urumqi, from 17.6 to 21.7% for Xning, from 1.8 to 10.7% for Lanzhou, from 4.7 to 17.0% for Huhehaote, from −7.4 to 9.1% for Beijing, and from −8.6 to 2.3% for Changchun. RE of predicting annual ET_o with 4-variable regression function were even lower compared to E_pan method. The main error source of the predictions came from the deviation between calibrated k_p and the actual k_p of the predicted years when using E_pan method and from random fluctuations of climatic data when using the 4-varible regression function. In conclusion, the MMK test was a robust method for trend detection because it considered serial time dependence. Insignificant trend of the k_p series supports the choice of a mean value as the calibrated k_p and for ET_o predictions. The E_pan method is recommended for prediction of annual ET_o.