Evaluation of data assimilation methods suitable for frontal structures

Frontal structures, frequently observed in the vicinity of westerly jets and western boundary currents, are characterized by sharp gradients in both horizontal and vertical directions. Forecast errors associated with these fronts often exhibit non-Gaussian distributions due to biases in frontal location or magnitude stemming from sparse observation networks or misrepresented model physics. Such non-Gaussianity poses significant challenges for conventional data assimilation (DA) schemes that rely on Gaussian assumptions.
In this study, we investigate the performance of various ensemble DA methods in representing fronts using idealized simulations with a frontogenesis model (Keyser et al., 1988). The compared methods include the stochastic Ensemble Kalman Filter (EnKF), the Ensemble Adjustment Kalman Filter (EAKF), and the Nonlinear Ensemble Transform Filter (NETF). Furthermore, we propose a novel nonlinear DA approach termed the Kernelized EAKF (KEAKF). By integrating kernel ridge regression into the EAKF framework, KEAKF effectively accounts for nonlinear relationships between state variables.
To simulate realistic forecast biases, the first-guess ensembles are initialized with systematic errors in both frontal magnitude and location. DA performance is rigorously evaluated using three metrics: root mean squared error (RMSE) of temperature (state error), RMSE of the temperature gradient (magnitude error), and the modified Hausdorff distance of frontal locations (displacement error). Our results demonstrate that KEAKF outperforms all other methods across all evaluation metrics. While the EnKF shows relatively stable performance in state estimation, the EAKF is superior in capturing frontal magnitude and location. The NETF, despite its non-Gaussian formulation, shows limited performance due to particle degeneracy in this setting. Finally, we discuss the implications of these findings for maintaining dynamical balances and improving the predictability of frontal systems in more complex dynamical models.