Discussion on method of nonlinear fitting dry and wet edges of LST/ NDVI feature space better than traditional linear fitting method

Abstract: Land surface temperature / vegetation index feature space has important applications in quantitative retrieval of water content in soil and crop evapotranspiration. However, at present, the research on the fitting of the dry and wet edges of the land surface temperature/vegetation index feature space was relatively lacking. In the tradition, for dry edge of the model, a simple linear negative correlation was adopted to fit the parameters, and wet edge was considered as a simplified treatment parallel to the coordinate axis. Whether it is appropriate is the focus of this paper that needs to be discussed. The study area was located in Oklahoma, the United States. Based on Landsat TM5 image data, land surface temperature (LST) and normalized difference vegetation index (NDVI) were calculated, and LST was calculated by radiation equation model and NDVI by pixel dichotomy model. And the fitting of dry edges and wet edges of LST/NDVI feature space was carried out with different functions, which included linear function, exponential function, logarithm function, power function and polynomial function. All of them were used to fit dry edges and wet edges respectively, and the results were evaluated by the measured data of water content in soil. The results showed that for the fitting of 5 different functions, r2 value as a whole was between 0.4 and 0.7, and there were some differences in the fitting precision between different fitting methods. For the fitting of dry edges, r2 value of exponential function fitting was 0.64, r2 value of linear function fitting was 0.60, r2 value of logarithm function fitting was 0.41, r2 value of power function fitting was 0.43, and r2 value of polynomial function fitting was 0.67 which was the best fitting way for dry edges. For the fitting of wet edges, r2 value of exponential function fitting was 0.59, r2 value of linear function fitting was 0.63, r2 value of logarithm function fitting was 0.67, r2 value of power function fitting was 0.69, and r2 value of polynomial function fitting was 0.70 which was the best fitting way for wet edges. For the fitting of dry edges and wet edges, polynomial function was the best method. And the results of 5 kinds of function fitting were compared with those from the soil moisture stations in the study area. Root mean square error (RMSE) and mean absolute error (MAE) were calculated, and 5, 25 and 60 cm depth were selected. In the 3 different depths, RMSE and MAE of polynomial function were the smallest. RMSE at 5 cm depth was 0.29, RMSE at 25 cm depth was 0.27, and RMSE at 60 cm depth was 0.28; MAE at 5 cm depth was 0.26, MAE at 25 cm depth was 0.23, and MAE at 60 cm depth was 0.25. The results indicated that the LST/NDVI feature space inversion based on dry edges and wet edges fitting with the polynomial function was the most accurate for the soil surface water content in this study area, and it was most sensitive to water content at 25 cm depth in soil. For an optimal fitting, it must be an optimal solution between fitting accuracy and fitting efficiency. In the process of this study, only small amount of data were involved, so the main consideration was the accuracy of dry edges and wet edges fitting, not taking into account the time cost of computer computing process. But for the large amount of data operations in the actual application process, the time efficiency still needs to be considered.