A study of enhancive parameter correction with coupled data assimilation for climate estimation and prediction using a simple coupled model

Uncertainties in physical parameters of coupled models are an important source of model bias and adversely impact initialisation for climate prediction. Data assimilation using error covariances derived from model dynamics to extract observational information provides a promising approach to optimise parameter values so as to reduce such bias. However, effective parameter estimation in a coupled model is usually difficult because the error covariance between a parameter and the model state tends to be noisy due to multiple sources of model uncertainties. Using a simple coupled model consisting of the 3-variable Lorenz model and a slowly varying slab 'ocean', this study first investigated how to enhance the signal-to-noise ratio in covariances between model states and parameters, and then designed a data assimilation scheme for enhancive parameter correction (DAEPC). In DAEPC, parameter estimation is facilitated after state estimation reaches a 'quasi-equilibrium' where the uncertainty of coupled model states is sufficiently constrained by observations so that the covariance between a parameter and the model state is signal dominant. The observation-updated parameters are applied to improving the next cycle of state estimation and the refined covariance of parameter and model state further improves parameter correction. Performing dynamically adaptive state and parameter estimations with speedy convergence, DAEPC provides a systematic way to estimate the whole array of coupled model parameters using observations, and produces more accurate state estimates. Forecast experiments show that the DAEPC initialisation with observation-estimated parameters greatly improves the model predictability - while valid 'atmospheric' forecasts are extended two times longer, the 'oceanic' predictability is almost tripled. The simple model results here provide some insights for improving climate estimation and prediction with a coupled general circulation model.