Mesoscale ensemble-based data assimilation 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. Two numerical models with increasing complexity are used with simulated observations. For lower complexity, a two-dimensional, nonlinear, hydrostatic, non-rotating, and incompressible sea breeze model is developed with buoyancy and vorticity as the prognostic variables. Model resolution is 4 km horizontally and 50 m vertically. The ensemble size is set at 40. Forcing is maintained through an explicit heating function with additive stochastic noise. Simulated buoyancy observations on land surface with 40-km spacing are assimilated every 3 hours. Up to six model parameters are successfully subjected to estimation attempts in various experiments. The overall EnKF performance in terms of the error statistics is found to be superior to the worst-case scenario (when there is parameter error but no parameter estimation is performed) with an average error reduction in buoyancy and vorticity of 40% and 46%, respectively, for the simultaneous estimation of six parameters. The model chosen to represent the complexity of operational weather forecasting is the Pennsylvania State University-National Center for Atmospheric Research MM5 model with a 36-km horizontal resolution and 43 vertical layers. The ensemble size for all experiments is chosen as 40 and a 41st member is generated as the truth with the same ensemble statistics. Assimilations are performed with a 12-hour interval with simulated sounding and surface observations of horizontal winds and temperature. Only single-parameter experiments are performed focusing on a constant inserted into the code as the multiplier of the vertical eddy mixing coefficient. Estimation experiments produce very encouraging results and the mean estimated parameter value nicely converges to the true value exhibiting a satisfactory level of variability.