Parameter estimation for a simple two-source evapotranspiration model using Bayesian inference and its application to remotely sensed estimations of latent heat flux at the regional scale

Abstract

A simple two-source evapotranspiration (ET) model was applied to the Yingke and Daman irrigation districts of the Zhangye Oasis, which is located in the middle reaches of the Heihe River, China. The ET model was composed of two parts, including an evaporation (E) sub-model and a transpiration (T) sub-model. A separated parameter estimation scheme was conducted using Bayesian inference. First, an empirical multiplier was estimated for an E sub-model using observations that were collected after crop harvests. The empirical multiplier was then assigned to the most-likely value in the simple two-source ET model. Second, a global sensitivity analysis was performed to identify the key parameters that were responsible for most of the variability in the λET results within the T sub-model. To avoid equifinality or over-parameterization, Bayesian inference was applied to estimate the key parameters that induced the most variability in the first set. A second set of Bayesian inference was then performed by fixing the most-likely values of these parameters, and the other parameters were defined one-by-one as Bayesian parameters. These parameters were estimated for seven sites. The coefficient of determination for the modeled λET and the observed values exceeded 0.9. Next, a cluster analysis was conducted using the canopy height, leaf area index (LAI) and soil moisture content to classify the fields with the highest similarities and then to distribute the same parameter values to similar fields. Finally, λET was estimated using the most-likely values of the parameters at the regional scale. The root-mean-square error of the remotely sensed estimates was less than 20Wm−2, the mean absolute percent error did not exceed 4%, and the correlation coefficient was greater than 0.97. The validation was conducted for both the modeled λET at the point scale and for the remotely sensed λET at the satellite pixel scale. The results demonstrate that the separated parameter estimation scheme using Bayesian inference yields reasonable parameter values; using cluster analysis, the most-likely values of the parameters can be effectively applied to estimate remotely sensed λET.