The VI-Ts diagram determined by the remotely sensed vegetation index (VI) and land surface temperature (Ts) has been widely applied to estimate land surface moisture status, air temperature, and the partitioning of available surface energy. Defining an ideal VI-Ts diagram requires a large sampling window. However, while estimating air temperature and land surface moisture index (LSMI) using the VI-Ts method, the air temperature should be homogenous over the sampling window, which means that the size of the sampling window cannot be unlimited. Presently, there is no quantitative approach to evaluate the VI-Ts method and the effects of the sampling window size on the VI-Ts method. In this study, we propose the use of the Shannon diversity index (SDI) and the semivariogram method to evaluate the VI-Ts method for the estimations of LSMI and air temperature using ASTER and MODIS datasets in views of space, time, and sensors. The result obtained using the semivariogram method and spatial air temperature collected from 83 meteorological stations in the North China Plain showed that air temperature was homogenous within a sampling window with a width of 66 km on DOY120, 46 km on DOY129, 68.2 km on DOY264, and 83.6 km on DOY360 of 2003. In our case study, the estimated LSMI using ASTER datasets with 90 m resolution is reliable when SDIs are greater than 2.89 for Ts, 2.39 for VI, and 4.87 for VI-Ts, respectively. When SDIs are greater than 2.62 for Ts, 2.61 for VI, and 4.09 for VI-Ts respectively, the air temperature estimation is reliable for all the ASTER datasets. For MODIS datasets, we found that the estimation of air temperature is mainly dependent on the SDI of VI. When it is greater than 2.30 and SDIs are greater than 1.61 for Ts and 3.72 for VI-Ts, at least one LSMI isoline is constructed perfectly, and air temperature can be estimated with high accuracy using MODIS datasets. Our proposed approaches and thresholds can be used for reference in other studies related to LSMI and air temperature estimations with the VI-Ts method, although they need more validation and supplementation by future studies.
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