Using Bayesian analysis to compare the performance of three evapotranspiration models for rainfed jujube (Ziziphus jujuba Mill.) plantations in the Loess Plateau

In order to select suitable evapotranspiration (ET) models for rainfed and sparsely cultivated jujube (Ziziphus jujuba Mill.) plantations in the Loess Plateau, this study used Bayesian analysis to compare the performances (accuracies and uncertainties) of the Shuttleworth–Wallace (SW) model, the Penman–Monteith (PM) model and the Penman–Monteith equation with a variable surface canopy resistance (PMv) model in terms of daily and hourly ET. To determine seasonal variations and soil water dependence, probabilistic analyses were independently used to calibrate the SW and PM model parameters at every growth stages and the PMv model parameters for different soil water conditions in the growth season of rainfed jujube plantations in 2013. Finally, data for the growth season in 2012 were used to validate the calibrated models. The results showed that the posterior distributions of the parameters of the three models narrowed down at both daily and hourly scales, suggesting decreasing uncertainties in the parameters. Some model parameters varied with season (increasing for the last two growth seasons) or soil water condition (decreasing with increasing soil moisture). The performances of the ET models also varied with time scale, generally less precise at hourly than at daily time scale. Irrespectively, the three ET models met the evaluation criteria (mean relative error (MAE)<20% and coefficient of determination (R2)>0.8 and Willmott index of agreement (D)>0.8) with acceptable accuracy and uncertainty at the daily time scale in both calibration (with R2, MAE and D values of 0.94, 6.78% and 0.94 for the SW model; 0.94, 7.52% and 0.94 for the PM model; and 0.89, 8.49% and 0.83 for the PMV model, respectively) and validation periods (with R2, MAE and D values of 0.94, 5.77% and 0.92 for the SW model; 0.93, 5.15% and 0.91 for the PM model; and 0.89, 10.26% and 0.86 for the PMV model, respectively). Where only climate data were available, the PMV model was recommended for estimation of daily ET in the study area due to less complexity, low data requirements, and high accuracy. Where sufficient monitoring data were available, the PM model was preferred for estimation of the daily ET in the study area due to less complexity and small differences in performance with the SW model. All three models met the evaluation criteria for calibration period(with R2, MAE and D values of 0.92, 16.04% and 0.92 for the SW model; 0.96, 14.37% and 0.94 for the PM model; and 0.89, 18.56% and 0.91 for the PMV model, respectively) while only the SW model met the evaluation criteria for validation period (with R2, MAE and D values of 0.87, 16.33% and 0.88 for the SW model; 0.85, 20.70% and 0.85 for the PM model; and 0.85, 23.95% and 0.83 for the PMV model, respectively) at the hourly time scale. Based on model accuracy and uncertainty at the hourly time scale, the SW model was recommended for use in estimating ET in jujube plantations in the Loess Plateau.