Mesoscale ensemble-based data assimilation and parameter estimation

The performance of the ensemble Kalman filter (EnKF) in forced, dissipativeflow under imperfect model conditions is investigated through simultaneous state andparameter estimation where the source of model error is the uncertainty in the modelparameters. Two numerical models with increasing complexity are used with simulatedobservations.For lower complexity, a two-dimensional, nonlinear, hydrostatic, non-rotating,and incompressible sea breeze model is developed with buoyancy and vorticity as theprognostic variables. Model resolution is 4 km horizontally and 50 m vertically. Theensemble size is set at 40. Forcing is maintained through an explicit heating functionwith additive stochastic noise. Simulated buoyancy observations on land surface with40-km spacing are assimilated every 3 hours. Up to six model parameters aresuccessfully subjected to estimation attempts in various experiments. The overall EnKFperformance 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) withan average error reduction in buoyancy and vorticity of 40% and 46%, respectively, forthe simultaneous estimation of six parameters.The model chosen to represent the complexity of operational weather forecastingis the Pennsylvania State University-National Center for Atmospheric Research MM5model with a 36-km horizontal resolution and 43 vertical layers. The ensemble size forall experiments is chosen as 40 and a 41st member is generated as the truth with thesame ensemble statistics. Assimilations are performed with a 12-hour interval withsimulated sounding and surface observations of horizontal winds and temperature. Onlysingle-parameter experiments are performed focusing on a constant inserted into thecode as the multiplier of the vertical eddy mixing coefficient. Estimation experimentsproduce very encouraging results and the mean estimated parameter value nicelyconverges to the true value exhibiting a satisfactory level of variability.