Estimation of turbulent heat fluxes via variational data assimilation (VDA) approaches has been the subject of several studies. The VDA approaches need an adjoint model that is difficult to derive. In this study, remotely sensed land surface temperature (LST) data from the Moderate Resolution Imaging Spectroradiometer (MODIS) are assimilated into the heat diffusion equation within an ensemble Kalman smoother (EnKS) approach to estimate turbulent heat fluxes. The EnKS approach is tested in the Heihe River Basin (HRB) in northwest China. The results show that the EnKS approach can estimate turbulent heat fluxes by assimilating low temporal resolution LST data from MODIS. The findings indicate that the EnKS approach performs fairly well in various hydrological and vegetative conditions. The estimated sensible (H) and latent (LE) heat fluxes are compared with the corresponding observations from large aperture scintillometer systems at three sites (namely, Arou, Daman, and Sidaoqiao) in the HRB. The turbulent heat flux estimates from EnKS agree reasonably well with the observations, and are comparable to those of the VDA approach. The EnKS approach also provides statistical information on the H and LE estimates. It is found that the uncertainties of H and LE estimates are higher over wet and/or densely vegetated areas (grassland and forest) compared to the dry and/or slightly vegetated areas (cropland, shrubland, and barren land)
