Ensemble-based data assimilation for thermally forced circulations

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. Model resolution is 4 km horizontally and 50 m vertically. 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, simulated buoyancy observations (with assumed error of 10^-3 ms^-2) on land surface with 40-km spacing are assimilated every 3 hours. 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. Subsequent analyses continue to remove error at a progressively slower rate and the error ultimately stabilizes within about 24 hours for both variables. 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.