## 3 Results
### Model Parameter Optimization DA
Second, 4D-Var is extremely sensitive to the selection of initial conditions, and improper initial values may cause the algorithm to fall into local optimization or face difficulties when trying to converge, so it is necessary to carefully evaluate the effectiveness of initial values and seek more robust optimization algorithms. Although some scholars consider using Jacobian matrix to optimize the initial conditions and parameters of the model, it controls the gradient information, determines the search direction and step size, and then considers the model continuity [136]. However, for large-scale, high-resolution models, the calculation of the Jacobian matrix often requires significant computing resources and memory, and the effect is not always as expected. Sparsity and parallel computing technology can alleviate this problem to some extent, but for extremely large-scale problems, the computing cost is still high. At the same time, although the finite difference method is often used in gradient approximation, it may have adaptability problems in high-dimensional cases [137; 138]. Therefore, the dimensions and characteristics of the data should be fully considered when selecting and applying the gradient approximation method [139]. As the selection of assimilation parameters also has an impact on the results, the selection of parameterization schemes and physical processes will also bring uncertainty to the data analysis results [140]. Based on this, we extract the following possible solutions:  
* Explore the advantages of optimization algorithms such as conjugate gradient method and quasi-Newton method in solving gradient problems. Global optimization techniques such as multiple startup, simulated annealing, and genetic algorithm were used to improve the initialization and optimization strategy of the algorithm and improve the convergence and stability of the algorithm [113]. Try to calibrate the sensitivity error of the initial conditions based on the model. Figure 7: Strategy Framework of assimilation Model based on 4D-Var method. The left figure illustrates the process of simulating Grassland Aboveground Biomass (BM) and Leaf Area Index (LAI) with the ModVegeg grassland model. The right figure displays the distribution of BM and LAI after assimilation [135]. * Search for nonlinear framework: To solve nonlinear uncertainty, explore and develop nonlinear variational assimilation frameworks, such as manifold embedding variational method (ME-Var), four-dimensional variational filtering (4D-VARF), etc. For example, the anisotropic background error and time-window four-dimensional variation algorithm constructed by [PERSON] et al. provides us with valuable reference experience [141]. * Focusing on uncertainty characterization and quantification. Introducing set members to model uncertainty: set Kalman filtering idea, and developing assimilation methods such as set four-dimensional variational (En-4D-Var) [142]. In terms of physical and chemical parameters, we need to pay attention to the quantification of the uncertainty, reduce the uncertainty through the integration of assimilation methods, and improve the adaptability and scalability of assimilation algorithms. * Using ML and AI to improve DA efficiency: Using advanced technologies such as GPU acceleration and distributed parallel computing to develop low-rank or reduced-order models to improve computing efficiency and reduce computing costs [143; 144; 145; 146].