关键词: Penman-Monteith, Priestley-Taylor, Turc, Hargreaves, Makkink, Blaney-Criddle, FAO24 radiation

Abstract: Accurate estimation of reference crop evapotranspiration (ET0) is essential due to its critical role in determining crop water use and regional assessment of water supply and demand. Though numerous models have been developed, their rigorous test with measured data is lacking. In this paper daily estimates of 16 ET0 models, including five combination-, six radiation- and five temperature-based ones, were evaluated with measurements from April through October in 2012 at a semiarid site of Xiaotangshan, Beijing, China. Daily ET0 was measured by two weighing lysimeters （length×width×depth =1.3m×1.3m×2.3m） located in a fescue grass （Festuca arundinacea Schreb） plot surrounded by a 167ha crop. On basis of root mean square error （RMSE） we found the performance ranking: FAO79 Penman =1963 Peman＞1996 Kimberly Penman＞FAO24 Penman＞FAO56 Penman-Monteith（PM）＞Turc＞FAO24 Blaney-Criddle（BC）＞DeBruin-Keijman＞Jensen-Haise>Priestley-Taylor （PT）＞FAO24 Radiation＞Hargreaves＞Makkink＞Hamon＞Mcloud＞Blaney-Criddle（BC）. Overall, the combination models performed best with RMSE of 1.33-1.47mm?d-1, followed by the radiation models with RMSE of 1.48-1.77mm?d-1 and the temperature models with RMSE of 1.50-2.68mm?d-1. The best FAO79 Penman and 1963 Penman were respectively 10% and 13% more accurate than the best radiation （Turc） and temperature （FAO24 Blaney-Criddle） models. Better performance of the combination and radiation models was due to that they explicitly contain dominant factors（radiation or vapor pressure deficit（VPD））influencing ET0. All models tended to overestimate at low evaporative rate while underestimate at high rate the measured values, exhibiting threshold feature, but on average the combination and radiation methods respectively underestimated by 0.14mm?d-1 and 0.33mm?d-1, whereas the temperature method overestimated by 0.52mm?d-1. The former two had relatively lower threshold ET0 than the latter, and they were thus more applicable to low evaporative condition, and vice versa for the latter. All combination and radiation models, and the Hargreaves and FAO24 BC in temperature method captured measurement trend and showed robust structure. To improve them future efforts should be on local calibration, but for temperature models not capturing measurement trend future focus should be on structure optimization. VPD and maximum humidity RHx were two main factors affecting deviation of combination and radiation methods. The former affected models with underestimation in a positive manner, and the latter affected those with overestimation （1963 Penman、FAO79 Penman） in a negative manner. The calibrated coefficients of the PT （1.38）, Makkink （0.83）, Turc （0.014） and Hamon （1.248） were higher while those of the Hargreaves （0.0019） and BC （0.192） were lower than the original ones. Coefficients of PT and Hamon can also be best estimated with minimum humidity, and those of Turc and Makkink with VPD, and Hargreaves and BC with radiation or sunshine hours. The degree of climate dryness of the study site and the lower relative weight to the aerodynamic component were responsible for poor behavior （RMSE=1.47mm?d-1） of the FAO56 PM. Later modifications to wind function of original Penman appeared fruitless, and therefore we suggest continued use of the older Penman equations in climate similar to our site in China. Meanwhile, more tests of the FAO56 PM against measurements would be valuable to answer questions like “Is the FAO56 PM really superior to the older Penman equations solely in terms of accuracy”, “in what climate it performs better” and “Is it common that it underestimates in high evaporative condition”.

Key words: Penman-Monteith, Priestley-Taylor, Turc, Hargreaves, Makkink, Blaney-Criddle, FAO24 radiation