Estimating land surface evapotranspiration based on trapezoidal relationship between land surface temperature and vegetation index

Abstract: Land surface evapotranspiration (ET) is an important link in the process of regional water cycle. Many methods have been proposed for estimating ET utilizing information from different types of remotely sensed data, often in combination with ancillary surface and atmospheric observations. In particular, Ts-VI (surface temperature/vegetation index) triangle method using optical and thermal infrared satellite data is common for the retrieval of ET. However, Ts-VI triangle method has several major limitations, including the subjectivity of determining the dry and wet edges and the difficulty in defining the ET at the joint of dry edge and wet edge. By modifying the concept of the vegetation index-temperature (VIT) trapezoid proposed by Moran et al. (1994), Wang et al. (2011) developed a method of constructing the trapezoidal relationship between land surface temperature (Ts) and enhanced vegetation index (EVI) using ground-based meteorological observations and satellite remotely sensed surface temperature and vegetation index data jointly based on the energy balance equation. On the basis of that, a land surface actual ET estimating method was developed in the present study by estimating Priestley-Taylor coefficient, and then ET was calculated using the Priestley-Taylor equation for each pixel. The method is composed of three major steps: 1) establish Ts-VI trapezoidal space under extreme conditions, i.e., full vegetation cover and bare soil with extreme dryness and wetness, for each pixel, based on the principle of land-surface energy balance; 2) calculate the Priestley-Taylor coefficient for each pixel according to the position of the observed Ts-VI point in the trapezoid space; 3) finally use the Priestley-Taylor equation to estimate actual ET of the pixel. Compared with the method of VIT trapezoid, the Ts-VI trapezoid method has the advantage of taking into account the interaction of different variables and parameters (such as the net radiation Rn, aerodynamic resistance ra, sensible heat flux density H, stability correction for heat ψh, stability correction for momentum ψm) in the process of calculating the Ts at four extreme conditions, which better describes the relationship between those parameters. In addition, another major differences between the Ts-VI trapezoid method and the Ts-VI triangle method as well as the VIT trapezoid method is that, we did not assume zero ET at dry edge (except at the dry point at bare soil condition).The method was validated using MODIS data and ground observation data for the semi-arid Walnut Gulch watershed at Arizona, USA. The result of ET estimation was satisfied with mean absolute error of about 35.5%.