Treatment of model error through ensemble-based simultaneous state and parameter estimation

The performance of the ensemble Kalman filter (EnKF) in forced, dissipative flow under imperfect model conditions is investigated through simultaneous state and parameter estimation where the source of model error is the uncertainty in the model parameters. A two-dimensional, nonlinear, hydrostatic, non-rotating, and incompressible sea breeze model is used for this purpose with buoyancy and vorticity as the prognostic variables and a square-root filter with covariance localization is employed. Up to six model parameters are subjected to estimation attempts in various experiments. While the estimation of single imperfect parameters results in error of model variables that is indistinguishable from the respective perfect-parameter cases, increasing the number of estimated parameters to six inevitably leads to a decline in the level of improvement achieved by parameter estimation. However, the overall EnKF performance in terms of the error statistics is still superior to the worst-case scenario (when there is parameter error but no parameter estimation is performed). For the simultaneous estimation of six parameters, average error reduction in buoyancy and vorticity compared to the worst case is 40% and 46%, respectively.

Several aspects of the filter configuration (e.g., observation location, ensemble size, radius of influence, and parameter variance limit) are found to considerably influence the identifiability of the parameters. The parameter-dependent response to such factors implies strong nonlinearity between the parameters and the state of the model and suggests that a straightforward spatial covariance localization does not necessarily produce optimality. The current ongoing work involves the extension of the ensemble-based parameter estimation idea to a real sea breeze case using the NCAR/PSU nonhydrostatic MM5 model. To this end, the uncertainty associated with the boundary layer processes is being utilized and parameters such as vertical diffusion coefficients of momentum and heat as well as the bulk Richardson number are being explored in terms of their sensitivity, identifiability, and impact on the analysis quality.