Evaluation of the Weak Constraint Data Assimilation Approach for Estimating Turbulent Heat Fluxes at Six Sites

A number of studies have estimated turbulent heat fluxes by assimilating sequences of land surface temperature (LST) observations into the strong constraint-variational data assimilation (SC-VDA) approaches. The SC-VDA approaches do not account for the structural model errors and uncertainties in the micrometeorological variables. In contrast to the SC-VDA approaches, the WC-VDA approach (the so-called weak constraint-VDA) accounts for the effects of structural and model errors by adding a model error term. In this study, the WC-VDA approach is tested at six study sites with different climatic and vegetative conditions. Its performance is also compared with that of SC-VDA at the six study sites. The results show that the WC-VDA produces 10.16% and 10.15% lower root mean square errors (RMSEs) for sensible and latent heat flux estimates compared with the SC-VDA approach. The model error term can capture errors in the turbulent heat flux estimates due to errors in LST and micrometeorological measurements, as well as structural model errors, and does not allow those errors to adversely affect the turbulent heat flux estimates. The findings also indicate that the estimated model error term varies reasonably well, so as to capture the misfit between predicted and observed net radiation in different hydrological and vegetative conditions. Finally, synthetically generated positive (negative) noises are added to the hydrological input variables (e.g., LST, air temperature, air humidity, incoming solar radiation, and wind speed) to examine whether the WC-VDA approach can capture those errors. It was found that the WC-VDA approach accounts for the errors in the input data and reduces their effect on the turbulent heat flux estimates.