## 1 Introduction
However, middle- or coarse-resolution satellite cannot provide accurate subpixel LST estimates. Furthermore, in order to drive a model with remote sensing data, the zero plane displacement height and the roughness length are often calculated using a vegetation index [12]. The vegetation index is directly related to the dynamic parameters. Hence, it is a promising scientific theme, both theoretically and practically, to model and monitor heat fluxes using high temporal resolution LST estimates derived from middle- or coarse-resolution data (e.g., MODIS) and high spatial resolution vegetation index values derived from middle- or high-resolution data (e.g., that obtained by the, Chinese HJ-1A/HJ-1B satellites). It is also significant in expanding the scope of application of satellite data and improving the utilization of the data. Within the last two decades, an alternative technique, called LST downscaling, has been developed to derive high-resolution LST data using the high-resolution visible/NIR bands that are available from either the same or different satellite systems [7; 13]. The most widely used LST downscalingapproaches are the disaggregation procedure for radiometric surface temperature (the DisTrad algorithm) [1] and its descendant, the algorithm for sharpening thermal imagery (the TsHARP model) [14]. These two approaches are classified as statistical models, and they are based on the assumption that the relationship between the normalized difference vegetation index (NDVI) and LST is scale invariant. The performance of these algorithms has been evaluated over different land cover types, including agricultural areas [15], urban areas [16], and other areas, some of which display high heterogeneity [17; 18]. Recently, many improvements have been made to DisTrad and TsHARP so that they include a greater number of independent variables (e.g., the normalized difference built-up index (NDBI), the surface albedo, and the surface reflectance) [19; 20; 21]. Moreover, many studies have questioned the hypothesis that the relationship between LST and NDVI is stationary in space [19; 22; 23]. In fact, the relationship between LST and other land surface parameters is geographically variable. Geographically weighted regression (GWR) is an extension of traditional standard regression techniques that permits local rather than global parameter estimation. It can be used to investigate nonstationary relationships between the dependent variable and the independent variables using geographically varying regression coefficients. [PERSON] et al. [23] proposed a GWR-based LST downscaling algorithm that is based on the assumption that the relationship between LST and other land surface parameters and the digital elevation model (DEM) is geographically variable. They also find that the GWR-based algorithm outperforms the TsHARP algorithm, and the newly added parameters can effectively describe the variation in LST. The DisTrad model, which is based on NDVI segmentation, is generally considered to be more accurate [24], but the effectiveness of the GWR-based algorithm and the DisTrad model have not been compared. The purpose of this work is to investigate the reliability of downscaling algorithms for use with MODIS LST and the estimation of subpixel LE based on downscaled LST values for use in watershed studies. We downscale the MODIS LST products by using the GWR-based algorithm and the DisTrad model, and the performance of the two models is compared with ground-based observations of surface temperature. In addition, a remote sensing-based energy balance model is used to study the effect of the disaggregation of LSTs on the estimation of LE. Moreover, the relative ability of the two downscaling methods to describe the spatial heterogeneity of mixed pixels is assessed by comparing the turbulent heat fluxes estimated from the MODIS LST to the turbulent heat fluxes estimated from the disaggregated temperatures. The differences in the heat flux estimates obtained using the two downscaling methods are analyzed and discussed.