Improvement of a Regional Multiscale NLS-4DVar Assimilation System Based on the CWRF-CoLM Coupled Model

Ensemble perturbations in 4DEnVar-type methods are pulled in two directions at once: estimating a reliable background-error covariance (BEC) calls for perturbations large enough to sample real error structure, while a valid tangent-linear (TL) approximation calls for perturbations small enough to stay near-linear. This study resolves this conflict by introducing a shrinkage factor (w) into a multigrid NLS-4DVar framework, decoupling the perturbation scale used for BEC estimation from that used for TL approximation. An independent finite-difference test verifies this decoupling, showing that TL accuracy is governed by a trade-off between nonlinear truncation error and numerical error. Based on this framework, an improved Regional Multiscale Nonlinear Least Squares (NLS) 4DVar Data Assimilation System was developed based on the CWRF-CoLM coupled model. A one-month cycling assimilation experiment (July 2021) shows that the new scheme (DA2) outperforms the original (DA1): analysis RMSE and bias are reduced for U/V winds, T, and QVAPOR, 3-day forecast RMSE improves broadly, and the 24-h precipitation threat score at moderate-to-heavy rainfall thresholds is notably higher, which is consistent with a preferential benefit for strongly nonlinear moisture and convective processes. Although only atmospheric observations are assimilated, land-surface forecasts (2-m temperature, 2-m humidity, soil moisture) also improve indirectly, driven by a more accurate initial moisture field and better-represented land-atmosphere coupling. Beyond its practical performance, this decoupling strategy completes a previously unverified aspect of the NLS-4DVar formulation and offers a generalizable approach for mitigating nonlinear errors in ensemble-based variational assimilation.