A two-stage inflation method in parameter estimation to compensate for constant parameter evolution in Community Earth System Model

Parameter estimation is defined as the process to adjust or optimize the model parameter using observations. A long-term problem in ensemble-based parameter estimation methods is that the parameters are assumed to be constant during model integration. This assumption will cause underestimation of parameter ensemble spread, such that the parameter ensemble tends to collapse before an optimal solution is found. In this work, a two-stage inflation method is developed for parameter estimation, which can address the collapse of parameter ensemble due to the constant evolution of parameters. In the first stage, adaptive inflation is applied to the augmented states, in which the global scalar parameter is transformed to fields with spatial dependence. In the second stage, extra multiplicative inflation is used to inflate the scalar parameter ensemble to compensate for constant parameter evolution, where the inflation factor is determined according to the spread growth ratio of model states. The observation system simulation experiment with Community Earth System Model (CESM) shows that the second stage of the inflation scheme plays a crucial role in successful parameter estimation. With proper multiplicative inflation factors, the parameter estimation can effectively reduce the parameter biases, providing more accurate analyses.