Abstract
Ensemble data assimilation systems generally suffer from underestimated background error covariance that leads to a filter divergence problem—the analysis diverges from the natural state by ignoring the observation influence due to the diminished estimation of model uncertainty. To alleviate this problem, we have developed and implemented the stochastically perturbed hybrid physical–dynamical tendencies to the local ensemble transform Kalman filter in a global numerical weather prediction model—the Korean Integrated Model (KIM). This approach accounts for the model errors associated with computational representations of underlying partial differential equations and the imperfect physical parameterizations. The new stochastic perturbation hybrid tendencies scheme generally improved the background error covariances in regions where the ensemble spread was not sufficiently expressed by the control experiment that used an additive inflation and the relaxation to prior spread method.
Highlights
Numerical weather prediction (NWP) includes inevitable forecast errors due to uncertainties in both initial conditions and models
Large ensemble mean error (EME) are found in the lower atmosphere over the Arctic and Antarctica regions and in the overall stratosphere (Figure 1a); for specific humidity, the tropics and mid-latitudes have larger EMEs than the other regions, especially below 700 hPa (Figure 1c); for zonal wind, large EMEs are found in the tropics from the middle troposphere to the lower stratosphere, Antarctica, and most of the stratosphere except the Northern Hemisphere (NH) (Figure 1e)
These model errors should be correspondingly represented in the ensemble spread (ES) (Figure 1b,d,f); the ESs were relatively underestimated compared to the EMEs
Summary
Numerical weather prediction (NWP) includes inevitable forecast errors due to uncertainties in both initial conditions and models. The ensemble data assimilation (EDA) system is beneficial to represent the initial uncertainties and flow-dependent background error covariance (BEC), improving the assimilation of observations [4]. If the ensemble perturbation includes the true observation and the model error, the unperturbed analysis will represent the analysis error [5]. The EDA usually suffers from the underestimation of BEC due to the limited ensemble size, sampling errors, and model error [6]. This underestimation leads to a filter divergence problem: the analysis diverges from the natural state by ignoring the observation influence due to a small forecast uncertainty. With an over-dispersive ensemble, the analysis ignores the model errors due to a large forecast uncertainty
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