Quick estimation of parameters for the land surface data assimilation system and its influence based on the extended Kalman filter and automatic differentiation

Soil moisture plays a crucial role in drought monitoring, flood forecasting, and water resource management. Data assimilation methods can integrate the strengths of land surface models (LSM) and remote sensing data to generate high-precision and spatio-temporally continuous soil moisture products. However, one of the challenges of the land data assimilation system (LDAS) is how to accurately estimate model and observation errors. To address this, we had previously proposed a dual-cycle assimilation algorithm that can simultaneously estimate the model and observation errors, LSM parameters, and observation operator parameters. However, this algorithm requires a large ensemble size to guarantee stable parameter estimates, resulting in low efficiency and limiting its large-scale applications. To address this limitation, the authors employed the following approaches: (1) using automatic differentiation to compute the Jacobian matrix of LSM instead of constructing a tangent linear model of LSM; and (2) replacing the ensemble Kalman filter framework with the extended Kalman filter (EKF) framework to improve the efficiency of parameter optimization for the dual-cycle algorithm. The EKF-based dual-cycle algorithm accelerated the parameter estimation efficiency near 60 times during a 90-day time period with a model integration time step of 1 h. To evaluate the dual-cycle LDAS at the regional-scale, it was applied to assimilate the SMAP soil moisture over the Tibetan Plateau, and soil moisture estimates were validated using in situ observations from four different climatic areas. The results showed that the EKF-based dual-cycle LDAS corrected biases in both the model and observations and produced more accurate estimates of soil moisture, land surface temperature, and evapotranspiration than did the open loop with default parameters. Furthermore, the spatial distribution of soil parameters (sand content, clay content, and porosity) obtained from the LDAS was more reasonable than those of default values. The EKF-based dual-cycle algorithm developed in this study is expected to improve the assimilation skills of land surface, ecological, and hydrological studies.