Calibration and evaluation of R-K evapotranspiration model for winter wheat in North China Plain

Abstract: Understanding of evapotranspiration (ET) of crops is very important for the research on the balance of water, such as hydrology, agronomy and environmental science. The Penman-Monteith equation (PM equation) has been widely used for predicting the actual ET, but the direct application of the PM equation is very difficult because of the determination of canopy resistance. Two operational models are developed to determine the actual ET based on the PM equation: FAO-PM model (FAO is the abbreviation of Food and Agriculture Organization) and Rana and Katerji model (R-K model). To analyze the applicability and stability of these 2 models on predicting the ET from winter wheat field in the North China Plain, the dynamic variations of ET from winter wheat field in 2013-2014 and 2014-2015 were studied on the basis of the data obtained with eddy covariance system (EC) and microclimate observations. The applicability of the R-K model was also analyzed in the experimental field. The R-K model was calibrated and validated with the data obtained in winter wheat growing seasons during 2013-2014 and 2014-2015. The daily ET predicted by the R-K model and the FAO-PM model was compared to the observed ET with the EC method. The application of the R-K model in predicting the ET in different growing stages of winter wheat was further studied. Results indicated that the ET of winter wheat showed obvious seasonal variation, and the minimum daily ET occurred in late January (the value was nearly zero). With the advent of the returning green stage, the winter wheat entered the development stage, and the ET started to increase slowly, reaching the maximum that was 7.37 mm in May for 2013-2014 and 5.72 mm in April for 2014-2015. The minimum monthly ET occurred in January, which was 10.7 and 8.6 mm in 2013-2014 and 2014-2015, respectively; and the maximum monthly ET was 142.8 and 102.5 mm in May for 2013-2014 and 2014-2015, respectively. The total ET of whole growing season was 436.3 and 334.8 mm respectively for these 2 growing seasons. The coefficients a and b in the R-K model were calibrated by using 3 data sets (data in 2013-2014, data in 2014-2015, and data in both years). There was small difference between the 3 data sets, and the stability of the R-K model was good. The calibrated coefficients a and b by using the data in 2013-2014 were 1.277 and 0.540 respectively (R2=0.741 and RMSE=2.034×10-5) and taken as the calibrated coefficients suitable for the experiment field. The data in 2014-2015 were used to validate the performance of the model. In the FAO-PM model, the slope of the linear regression between the observed and predicted values (1.01) was slightly greater than 1.0, the coefficient of determination was higher than 0.85, the index of agreement was 0.90, and the relative error was 16.2%. In the revised R-K model, the slope of linear regression (0.89) was less than 1.0, the coefficient of determination was higher than 0.85, the index of agreement was 0.91 and the relative error was 6.95%. These statistical parameters indicated that predicting daily ET with the revised R-K model performed slightly better than the FAO-PM model. To guide the management of the field irrigation, the ET during different growing stages was predicted with the R-K model. The performance of the model was much better in late-season stage with the relative error less than 0.5%, followed by the development stage with the relative error of about 19%, and then the mid-season stage with the relative error of about 21%, and poor for the initial stage and the overwintering stage with the relative error value of about 48% and 92%, respectively. The sensitivity analysis indicated the R-K model had good stability because it was only slightly sensitive to the aerodynamic resistance and the critical resistance. Overall, the R-K model is a promising model to predict the actual ET, and the calibration and validation of the model need further study at hourly, daily, monthly and annual time scales in different locations.