Accurate estimation of surface turbulent heat fluxes is important in numerous hydrological, meteorological, and agricultural applications. Recently, several studies have focused on estimating these fluxes via assimilation of land surface temperature (LST) observations into a surface energy balance model following the variational data assimilation (VDA) scheme. However, current VDAs suffer from the following issues: (1) they do not consider the inherent coupling between water and energy in the soil-plant-atmosphere continuum, (2) they tend to be ill-posed, and (3) they do not explicitly compute the uncertainty of estimates. The goal of this study is to enhance the current VDAs in two major ways: (i) coupling water and energy balance equations, assimilating soil moisture (SM) data in addition to LST, and constraining the VDA estimates by the moisture diffusion equation in addition to the heat diffusion equation; and (ii) analyzing the second-order information that guides toward a well-posed estimation problem and provides uncertainty of parameters. The performance of the proposed VDA is examined through a set of experiments based on a synthetic data set. The results show that simultaneous assimilation of SM and LST improves the estimation of heat fluxes and reduces the sensitivity of VDA to the initial guess of parameters. Furthermore, by adding moisture diffusion equation as an additional constraint, the correlation between the estimated parameters is reduced and the VDA scheme is oriented toward well posedness. The feasibility of extending the proposed VDA in estimating large-scale turbulent fluxes using spaceborne SM and LST data is examined, and promising results are obtained.

Estimation of turbulent heat fluxes by assimilating sequences of land surface temperature (LST) observations into a variational data assimilation (VDA) framework has been the subject of numerous studies. The VDA approaches are focused on the estimation of two key parameters that regulate the partitioning of available energy between sensible and latent heat fluxes. These parameters are neutral bulk heat transfer coefficient CHN and evaporative fraction (EF). The CHN mainly depends on the roughness of the surface and varies on the time scale of changing vegetation phenology. The existing VDA methods assumed that the variations in vegetation phenology over the period of one month are negligible and took CHN as a monthly constant parameter. However, during the growing season, bare soil may turn into a fully vegetated surface within a few weeks. Thus, assuming a constant CHN may result in a significant error in the estimation of surface fluxes, especially in regions with a high temporal variation in vegetation cover. In this study the VDA approach is advanced by taking CHN as a function of leaf area index (LAI). This allows the characterization of the dynamic effect of vegetation phenology on CHN. The performance of the new VDA model is tested over three sites in the United States and one site in China. The results show that the new model outperforms the previous one and reduces the root-mean-square error (and bias) in sensible and latent heat flux estimates across the four sites on average by 31% (61%) and 21% (37%), respectively.

Variational data assimilation (VDA) is an effective technique for the estimation of land surface heat fluxes. In this method, sequences of remotely sensed land surface temperature measurements are assimilated into a dynamic surface energy balance model to estimate the key unknown parameters of the turbulent heat fluxes. Despite the advantages of the VDA technique in the retrieval of land surface heat fluxes, it suffers from a key limitation, which is its tendency to be ill posed. Moreover, unlike ensemble-based schemes, the VDA method itself does not provide estimates of the predictive uncertainty of estimated parameters and, thus, retrieved fluxes. This research addresses these shortcomings by proposing an uncertainty quantification (UQ) framework for the VDA technique. The proposed framework utilizes uncertainty analysis and analysis of error covariance approximation as a tool to quantify the uncertainty of estimated parameters and to guide the formulation of a well-posed estimation problem. It provides a calibration-free tool to assess the performance of the VDA technique in retrieving land surface heat fluxes over a range of land surfaces and climatic conditions. The UQ framework suggests that the VDA approach performs poorly over wet and highly vegetated land surface regions and when the difference between land surface and air temperature is low. Moreover, it reveals that characterizing the effect of vegetation dynamics on the bulk heat transfer coefficient reduces the correlation between unknown parameters and, hence, leads to a more robust estimation of parameters.Index Terms-Land surface hydrology, uncertainty analysis, variational data assimilation (VDA).

Land surface heat and evaporative fluxes exchanged between the land and atmosphere play a crucial role in the terrestrial water and energy balance. Regional mapping of these fluxes is hampered by the lack of in situ measurements (with the required coverage and duration) and the high spatial heterogeneity. In this paper, we propose a Land Integrated Data Assimilation framework (LIDA) based on the variational data assimilation technique to estimate the key parameters of surface heat and evaporative fluxes by jointly assimilating Soil Moisture Active Passive (SMAP) data and Geostationary Operational Environmental Satellite (GOES) surface temperature data into a coupled parsimonious land water and energy balance model. The method is implemented over an area of 31,500 km2 in the U.S. Southern Great Plains, and its performance is evaluated through consistency tests, comparison tests, and uncertainty analyses. The maps of retrieved heat and evaporative fluxes are used to analyze a range of feedback mechanisms in land‐atmosphere interaction, such as the dependence of evapotranspiration on vegetation and water availability.

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