The estimation of background error covariance matrices is a critical component of jcsda data assimilation systems. Most advanced estimation algorithms are based on ensemble perturbed forecasts.…

The National Center for Atmospheric Research (NCAR), which is managed by the University Corporation for Atmospheric Research (UCAR), was awarded a $245,604.01 grant from the National Aeronautics and Space Administration (NASA) to conduct research on linear filtering techniques for ensemble data assimilation. The grant is focused on improving methods for estimating background error covariance matrices, which are a critical component of data assimilation systems used in weather and climate modeling. The work will explore adaptive approaches to localization that can better capture the time-varying nature of model error correlations. This research supports NASA's broader efforts to enhance numerical weather prediction and climate simulation capabilities.

The estimation of background error covariance matrices is a critical component of jcsda data assimilation systems. Most advanced estimation algorithms are based on ensemble perturbed forecasts. Because of computational limitations, those ensembles are limited in size, and filtering of the random sampling noise is necessary. This treatment is usually performed through schur filtering, which consists of an element-by-element product of the sampling covariance with a specified correlation (localization) matrix (hamill ET AL. 2001). The effect of the localization is to zero out many of the spurious long-distance correlations that are artificially created by the sampling noise. This suppression of spurious ensemble correlations has the double benefit to render the ensemble-based forecast error covariance sparse while increasing its rank (bishop and hodyss 2007). In practice, localization makes the implementation of ensemble based 4-dimensional data assimilation systems computationally tractable. In jcsda s GSI data assimilation system the localization matrix is separable, i.e. can be applied separately in the vertical and horizontal directions, but homogeneous and isotropic in each direction. The same localization matrix is furthermore applied to all 3- dimensional variables at all times (wang and LEI 2014). There is no time localization and the GSI 3D and 4DENVAR implementation relies on only two adjustable parameters: a horizontal and a vertical correlation length scale. Separability, independence from the variables and absence of time localization, have been the key assumptions to an efficient implementation of current 4DENVAR operational systems (bishop ET AL. 2011). In its current implementation, the GSI localization parameters do not vary in time. This could be a limitation when the true model error correlations are displaced during the assimilation time window over a distance comparable to the localization length scale, or when the lengths of the true model error correlation is highly dependent on the flow. For instance, the characteristics of the model error can vary greatly over a 6HR time period in the presence of short and repetitive convection episodes. Assuming constant localization length scales is also mathematically incorrect (bocquet 2016). Methods to adaptively adjust the localization length scales have been proposed (bishop and hodyss 2007, anderson 2012, m n trier ET AL. 2015). Those methods have the ability to estimate at a given time the localization length scales that best correspond to the state of the model at that time. The term best refers to some kind of optimality criterion, specific to the method. Menetrier and auligne (2015) showed that localization and hybridization can be jointly considered. This is important, because the authors also showed that a hybrid data assimilation system is more accurate than its ensemble and its variational component taken separately. The approach is based on the theory of linear filtering and was proposed in a 3-dimensional context. This is, at present, the only method successfully demonstrated with a full NWP model on realistic ensemble sizes (25 to 100). The method has furthermore been implemented in the regional GSI at ncar. Its extension in time is not immediate, but the various diagnostics that have been developed at the same time provide the tools to attack the problem. Localization in time has only been recently addressed (lorenc ET AL. 2015, bocquet 2016, desroziers ET AL. 2016). Lagrangian advection of the localization length scales has been proposed as surrogate of a hyperbolic model, for which covariance and localization functions can be evolved along the characteristics curves.