Local Ensemble Transform Kalman Filter with Cross Validation

Abstract

Many ensemble data assimilation (DA) approaches suffer from the so-called inbreeding problem. As a consequence, there is an excessive reduction in ensemble spread by the DA procedure, causing the analysis ensemble spread to systematically underestimate the uncertainty of the ensemble mean analysis. The stochastic EnKF used for operational NWP in Canada largely avoids this problem by applying cross validation, that is, using an independent subset of ensemble members for updating each member. The goal of the present study is to evaluate two new variations of the local ensemble transform Kalman filter (LETKF) that also incorporate cross validation. In idealized numerical experiments with Gaussian-distributed background ensembles, the two new LETKF approaches are shown to produce reliable analysis ensembles such that the ensemble spread closely matches the uncertainty of the ensemble mean, without any ensemble inflation. In ensemble DA experiments with highly nonlinear idealized forecast models, the deterministic version of the LETKF with cross validation quickly diverges, but the stochastic version produces better results, nearly identical to the stochastic EnKF with cross validation. In the context of a regional NWP system, ensemble DA experiments are performed with the two new LETKF-based approaches with cross validation, the standard LETKF, and the stochastic EnKF. All approaches with cross validation produce similar ensemble spread at the first analysis time, though the amplitude of the changes to the individual members is larger with the stochastic approaches. Over the 10-day period of the experiments, the fit of the ensemble mean background state to radiosonde observations is statistically indistinguishable for all approaches evaluated.

Why does EnKF suffer from analysis overconfidence? An insight into exploiting the ever‐increasing volume of observations

“…Along with localization, covariance inflation is an indispensable component of practical EnKF implementation, unless some special measure like the cross‐validation technique (Houtekamer and Mitchell, 1998; Houtekamer et al ., 2009; Buehner, 2020) is employed. Despite its importance, covariance inflation is often performed in an ad hoc manner.…”

“…Cross‐validation cannot be applied straightforwardly to square‐root filters like the ETKF‐based family of EnKFs and its application has been limited to stochastic EnKF, in which each member is updated independently by assimilating perturbed observations. A recent study by Buehner (2020) showed, however, that cross‐validation can be combined with LETKF by using the gain‐form representation of ETKF (Bishop et al ., 2017) and that cross‐validation does mostly alleviate analysis underdispersion using both idealized experiments and a realistic regional NWP system. Throughout the current article, we have limited our scope to analyzing ETKF and its variants, and the framework developed here cannot deal with the cross‐validation approach.…”

“…Throughout the current article, we have limited our scope to analyzing ETKF and its variants, and the framework developed here cannot deal with the cross‐validation approach. An interesting future direction from this work would thus be to extend the theoretical framework to encompass the LETKF with cross‐validation formulated in Buehner (2020).…”

“…11 For example, the cross‐validation technique, developed at Environment and Climate Change Canada (Houtekamer and Mitchell, 1998; Houtekamer et al ., 2009; Buehner, 2020), is known to eliminate analysis underdispersion in the context of perfect model experiments, whereby making covariance inflation unnecessary.…”

A Method for Imaging Energetic Particle Precipitation With Subionospheric VLF Signals

“…This may have been the result of the filter estimate becoming statistically overconfident relative to the magnitude of the measurement residuals, or one of the ensemble ionospheres may not have been suitable for LWPC. Underestimation of the state covariance by EnKFs is an active research area, but may be improved in future work by implementing additive covariance inflation between iterations or cross validation of the ensemble members in the LETKF measurement update (Buehner, 2020; Houtekamer & Zhang, 2016). If LWPC is the problem, it could be replaced with LMP as the LETKF forward model because LMP is more robust to atypical ionosphere profiles.…”