Effects of sequential or simultaneous assimilation of observations and localization methods on the performance of the ensemble Kalman filter

Abstract

The various implementations of the ensemble Kalman filter (EnKF) differ from each other in several ways. The effects of these differences are not yet well and completely explored and they include the use of sequential or simultaneous assimilation of observations and the application of localization to the observation error covariance matrix (R-localization) or the background error covariance matrix (B-localization). This study seeks to examine and better understand the effects of these differences, both individually and in combination. To that end, a B-localized sequential scheme, a B-localized simultaneous scheme, an R-localized sequential scheme and an Rlocalized simultaneous scheme are compared using a primitive equation two-layer model with simulated observations and an imperfect model assumption. The comparisons in initial assimilation experiments show that the use of sequential or simultaneous assimilation and R-/B-localization impacts the accuracy of the EnKF analyses and forecasts. Diagnostic experiments show that the schemes generate different amounts of imbalance in the analysis as a result of systematic differences among the schemes in height gradient and wind increments. These disparities in analysis balance translate into accuracy differences during the subsequent forecast and analysis steps. Additional simplified experiments suggest that the differences caused by the sequential or simultaneous assimilation and the R-/B-localization are a function of the characteristic shape of the background error covariances in the model system. Several elements of the forecast-assimilation system including the use of digital filter initialization, the number and type of observations, the ensemble size and the ratio of forecast error to observation error are identified that can significantly increase or decrease the magnitude of the observed differences caused by sequential or simultaneous assimilation and the R-/B-localization.

GSI 3DVar-Based Ensemble–Variational Hybrid Data Assimilation for NCEP Global Forecast System: Single-Resolution Experiments

“…2) EnKF assimilated observations sequentially whereas 3DEnsVar1way assimilated all observations simultaneously. A recent study by Holland and Wang (2013) suggested that the simultaneous/sequential assimilation in combination with different covariance localization methods could lead to performance differences in the ensemble-based data assimilation. 3) The ensemble smoother version of EnKF was adopted where effectively the fourdimensional ensemble covariance was utilized during the 6-h assimilation window.…”

“…The background ensemble covariance could also become more balanced due to the 6-h spinup during the forecast steps of the data assimilation cycling. On the other hand, the covariance localization applied to the ensemble covariance could degrade the balance (e.g., Lorenc 2003;Kepert 2009;Holland and Wang 2013). The impact of the TLNMC on the ensemble increment was therefore investigated.…”

On Serial Observation Processing in Localized Ensemble Kalman Filters

“…Whitaker et al (2008) also compared the assimilation performance of the EnSRF with the LETKF when applied with a global atmospheric model and found only small differences. Similarly, Holland and Wang (2013) compared the LETKF with the EnSRF without particular observation ordering for the assimilation with a simplified atmospheric model. They found only small differences in the state estimates with slightly smaller errors in the LETKF estimates.…”

Optimal Localization for Ensemble Kalman Filter Systems

“…Additional efforts include the successive covariance localization (Zhang et al 2009) and the multi-scale localization approach Kondo et al 2013). More information about comparing simultaneous and sequential assimilation can be found in (Holland et al 2013). …”