Scale-dependent background-error covariance localisation

This paper presents the formulation and preliminary results of a 3D ensemble‐variational data assimilation algorithm (3DEnVar) for the AROME‐France model at 3.8 km horizontal resolution. This algorithm is a deterministic, variational data assimilation scheme that uses background‐error covariances sampled from an ensemble. Our ensemble is an ensemble of data assimilation (EDA) at convective scale, based on the same system with the same spatial resolutions. In ensemble schemes, localization of the covariances is necessary to filter sampling noise. Two different localization schemes have been implemented, one in spectral space and one in grid‐point space. We also evaluate hybrid formulations, where the background‐error covariances are a weighted linear combination of the sampled covariances with the climatological ones. Cycled experiments are performed over a five‐week time period with 3 h updates. The 3DEnVar scheme largely outperforms standard 3D‐Var in terms of forecast scores. The best experiment is the one with the grid‐point localization scheme. A diagnostic of objective localization can provide guidance about the horizontal and vertical localization lengths that give best performance. The hybrid configuration with 80% of ensemble covariances and 20% of climatological ones performs also significantly better than the 3D‐Var, but to a lesser extent than the best 3DEnVar configuration, although it has better balanced initial fields.

Section: Discussionmentioning

confidence: 99%

A 3D ensemble variational data assimilation scheme for the limited‐area AROME model: Formulation and preliminary results

Montmerle

Michel

Arbogast

et al. 2018

“…This method effectively increases the potential rank of the background‐error covariances by a factor of J , which results in the need for fewer ensemble members for similar noise level (Buehner, ). This method is extended in (Buehner and Shlyaeva, ).…”

Section: Sampling Noise and Localizationmentioning

confidence: 99%

A review of operational methods of variational and ensemble‐variational data assimilation

Bannister

2017

322

246

Variational and ensemble methods have been developed separately by various research and development groups and each brings its own benefits to data assimilation. In the last decade or so, various ways have been developed to combine these methods, especially with the aims of improving the background-error covariance matrices and of improving efficiency. The field has become confusing, even to many specialists, and so there is now a need to summarize the methods in order to show how they work, how they are related, what benefits they bring, why they have been developed, how they perform, and what improvements are pending. This article starts with a reminder of basic variational and ensemble techniques and shows how they can be combined to give the emerging ensemble-variational (EnVar) and hybrid methods. A key part of the article includes details of how localization is commonly represented.There has been a particular push to develop four-dimensional methods that are free of linearized forecast models. This article attempts to provide derivations of the formulations of most popular schemes. These are otherwise scattered throughout the literature or absent. It builds on the nomenclature used to distinguish between methods, and discusses further possible developments to the methods, including the representation of model error.Key Words: variational data assimilation; ensemble data assimilation; hybrid data assimilation; flow-dependent background-error covariances; localization; model error; nomenclature Data assimilation and uncertaintyDealing with uncertainty is at the heart of data assimilation (DA). Forecast models (here those used in numerical weather prediction, NWP) use initial conditions that are imperfect, and are based upon imperfect representations of physical processes. It is well known that a free-running model will accumulate errors until its forecast is no longer useful (Tribbia and Baumhefner, 2004). The only way to restore usefulness is to allow the model to be influenced by observations (Leith, 1993). DA (Daley, 1991;Kalnay, 2002;Rabier, 2005) is the procedure of maintaining the link between evolving models and reality by updating the model with fresh observations. Researchers are working towards formal and robust mathematical methods that work in ways that are consistent with the model, the data, and their degree of uncertainty. DA is related to approaches used in other fields and which go by different names, e.g. state estimation (Wunsch, 2012); optimization (Biegler, 1997); history matching (Emerick, 2012); retrieval production (Rodgers, 2000); inverse modelling (Tarantola, 2005)), and there are additionally many ways of solving a DA problem. Most known DA methods are based on probabilistic theories (most, if not all, exploit Bayes' Theorem (Lorenc, 1986)) and each is made practical by making approximations.Traditionally there are three Bayesian-based strategies that allow the DA problem to be solved in approximate (hence suboptimal) ways. These may be categorized as the following. (i) Variation...

“…Since the unbalanced noise of the analysis updates is related to the covariance localization, it could be worth investigating the influence of adaptive localization or more sophisticated methods like the empirical localization functions developed by Anderson and Lei (2013) and Lei et al (2015). Scale-dependent localization, as proposed by Buehner and Shlyaeva (2015), may account for the different dynamical scales that are associated with the convection itself and the surrounding environment. An increase in ensemble size will help to reduce sampling noise on all scales, or a spectral truncation could be applied to the background-error covariance matrix as a first step.…”

Section: Summary and Discussionmentioning

confidence: 99%

Characterizing noise and spurious convection in convective data assimilation

Lange¹,

Craig²,

Janjić³

2017

The occurrence of noise and spurious convective cells in analyses of convective‐scale data assimilation (DA) is a problem that is not quantified sufficiently to develop reliable set‐ups for the DA of radar observations in an ensemble Kalman filter. This article presents two approaches to quantifying these phenomena using a local ensemble transform Kalman filter testbed, where simulated radar observations are assimilated with varying spatial and temporal DA parameters. Firstly, the dynamical coupling of cold pools and emerging cells of organized deep convection is quantified in terms of spatio‐temporal correlations, so that spurious perturbations can be identified. Secondly, the abundance of gravity‐wave noise is characterized by the variance of the vertical velocity field during DA cycling and the ensemble forecasts. This evaluation is performed separately for subsets of model points inside observed storms, in their vicinity and in the surrounding clear‐air regions. Varying horizontal localization lengths, observation averaging scales and the length of the assimilation cycling interval are compared, with respect to the two diagnostic approaches. It is concluded that the cold‐pool coupling method and the partitioned variance of vertical velocity fields are viable measures to quantify the influence of DA parameters and algorithms on the balance of analysis states that are used to initiate forecasts of convection.