Impact of the time scale of model sensitivity response on coupled model parameter estimation

That a model has sensitivity responses to parameter uncertainties is a key concept in implementing model parameter estimation using filtering theory and methodology. Depending on the nature of associated physics and characteristic variability of the fluid in a coupled system, the response time scales of a model to parameters can be different, from hourly to decadal. Unlike state estimation, where the update frequency is usually linked with observational frequency, the update frequency for parameter estimation must be associated with the time scale of the model sensitivity response to the parameter being estimated. Here, with a simple coupled model, the impact of model sensitivity response time scales on coupled model parameter estimation is studied. The model includes characteristic synoptic to decadal scales by coupling a long-term varying deep ocean with a slow-varying upper ocean forced by a chaotic atmosphere. Results show that, using the update frequency determined by the model sensitivity response time scale, both the reliability and quality of parameter estimation can be improved significantly, and thus the estimated parameters make the model more consistent with the observation. These simple model results provide a guideline for when real observations are used to optimize the parameters in a coupled general circulation model for improving climate analysis and prediction initialization.