Ensemble–based simultaneous state and parameter estimation for an idealized nonlinear sea breeze model

The effectiveness of the ensemble Kalman filter (EnKF) for thermally-forced circulations is investigated with simulated observations. A two-dimensional, nonlinear, hydrostatic, non-rotating, and incompressible sea breeze model is developed for this purpose with buoyancy and vorticity as the prognostic variables. Forcing is maintained through an explicit heating function with additive stochastic noise. Pure forecast experiments reveal that the model exhibits moderate nonlinearity. The strongest nonlinearity occurs along the sea breeze front at the time of peak sea breeze phase. Considerable small-scale error growth occurs at this phase for vorticity, while buoyancy is dominated by large-scale error as the direct result of the initial condition uncertainty.

In the EnKF experiments, as a result of their resolution, the observations naturally sample the larger-scale flow structure. At the first analysis step, the filter is found to remove most of the large-scale error resulting from the initial conditions and the domain-averaged error of buoyancy and vorticity is reduced by about 83% and 42%, respectively. At later model times, while mostly large-scale buoyancy errors due to the stochastic heating uncertainty are effectively removed, the filter also performs well at reducing smaller-scale vorticity errors associated with the sea breeze front. This is an indication that observations also contain useful small-scale information relevant at the scales of frontal convergence.

Up to six model parameters are 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). 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.