Yann Michel

Heterogeneous Convective-Scale Background Error Covariances with the Inclusion of Hydrometeor Variables

Convective-scale models used in NWP nowadays include detailed realistic parameterization for the representation of cloud and precipitation processes. Yet they still lack advanced data assimilation schemes able to efficiently use observations to initialize hydrometeor fields. This challenging task may benefit from a better understanding of the statistical structure of background errors in precipitating areas for both traditional and hydrometeor variables, which is the goal of this study. A special binning has been devised to compute separate background error covariance matrices for precipitating and nonprecipitating areas. This binning is based on bidimensional geographical masks defined by the vertical averaged rain content of the background error perturbations. The sample for computing the covariances is taken from an ensemble of short range forecasts run at 3-km resolution for the prediction of two specific cases of convective storms over the United States. The covariance matrices and associated diagnostics are built on the control variable transform formulation typical of variational data assimilation. The comparison especially highlights the strong coupling of specific humidity, cloud, and rain content with divergence. Shorter horizontal correlations have been obtained in precipitating areas. Vertical correlations mostly reflect the cloud vertical extension due to the convective processes. The statistics for hydrometeor variables show physically meaningful autocovariances and statistical couplings with other variables. Issues for data assimilation of radar reflectivity or more generally of observations linked to cloud and rain content with this kind of background error matrix formulation are thereon briefly discussed.

Inhomogeneous Background Error Modeling and Estimation over Antarctica

Abstract The structure of the analysis increments in a variational data assimilation scheme is strongly driven by the formulation of the background error covariance matrix, especially in data-sparse areas such as the Antarctic region. The gridpoint background error modeling in this study makes use of regression-based balance operators between variables, empirical orthogonal function decomposition to define the vertical correlations, gridpoint variances, and high-order efficient recursive filters to impose horizontal correlations. A particularity is that the regression operators and the recursive filters have been made spatially inhomogeneous. The computation of the background error statistics is performed with the Weather Research and Forecast (WRF) model from a set of forecast differences. The mesoscale limited-area domains of interest cover Antarctica. Inhomogeneities of background errors are shown to be related to the particular orography and physics of the area. Differences seem particularly pronounce...

Linear Filtering of Sample Covariances for Ensemble-Based Data Assimilation. Part I: Optimality Criteria and Application to Variance Filtering and Covariance Localization

AbstractIn data assimilation (DA) schemes for numerical weather prediction (NWP) systems, the estimation of forecast error covariances is a key point to get some flow dependency. As shown in previous studies, ensemble data assimilation methods are the most accurate for this task. However, their huge computational cost raises a strong limitation to the ensemble size. Consequently, covariances estimated with small ensembles are affected by random sampling errors. The aim of this study is to develop a theory of covariance filtering in order to remove most of the sampling noise while keeping the signal of interest and then to use it in the DA scheme of a real NWP system. This first part of a two-part study presents the theoretical aspects of such criteria for optimal filtering based on the merging of the theories of optimal linear filtering and of sample centered moments estimation. Its strength relies on the use of sample estimated quantities and filter output only. These criteria pave the way for new algori...

Toward a new cloud analysis and prediction system

What: Reviewing current and recent cloud analysis efforts and evaluating the state of the science, synergies, and collaborations in modeling clouds, 40 experts in cloud modeling, observations, and data assimilation met to move decisively toward a realization of cloud analysis systems for operational use. When: 1–3 September 2009 Where: Boulder, Colorado TOWARD A NEW CLOUD ANALYSIS AND PREDICTION SYSTEM

Linear Filtering of Sample Covariances for Ensemble-Based Data Assimilation. Part II: Application to a Convective-Scale NWP Model

AbstractIn Part I of this two-part study, a new theory for optimal linear filtering of covariances sampled from an ensemble of forecasts was detailed. This method, especially designed for data assimilation (DA) schemes in numerical weather prediction (NWP) systems, has the advantage of using optimality criteria that involve sample estimated quantities and filter output only. In this second part, the theory is tested with real background error covariances computed using a large ensemble data assimilation (EDA) at the convective scale coupled with a large EDA at the global scale, based respectively on the Applications of Research to Operations at Mesoscale (AROME) and ARPEGE operational NWP systems. Background error variances estimated with a subset of this ensemble are filtered and evaluated against values obtained with the remaining members, which are considered as an independent reference. Algorithms presented in Part I show relevant results, with the homogeneous filtering being quasi optimal. Heterogene...

Data Assimilation of Tropopause Height Using Dry Intrusion Observations

Abstract This article investigates the problem of initializing upper-level potential vorticity by using the detection of dry intrusions that can be seen in water vapor images. First, a satellite image processing technique has been developed for the identification and tracking of dry intrusions on geostationary satellite images. This technique can also be applied to images derived from model fields through a radiative transfer model. A linking algorithm automatically compares the trajectories of the dry intrusions in the model and in the satellite images. Differences of brightness temperatures are then converted to differences of tropopause height through a simple linear model, which is based on the correlation found in the background. As the scheme is likely to provide observations of the tropopause height, it also suggests that a space-alignment representation of the errors be used. A simple one-dimensional study provides a depiction of the background error covariance in alignment space, which is compare...

Displacing Potential Vorticity Structures by the Assimilation of Pseudo-Observations

Abstract Classic formulations of variational data assimilation in amplitude space are not able to directly handle observations that measure the geographical positions of meteorological features like fronts and vortices. These observations can be derived from satellite images, as is already the case for tropical cyclones. Although some advanced data assimilation algorithms have been specifically designed to tackle the problem, a widespread way of dealing with this information is to use so-called bogussing pseudo-observations: user-specified artificial observations are inserted in a traditional data assimilation scheme. At the midlatitudes, there is a relationship between dry intrusions in water vapor images and upper-level potential vorticity structures. Some prior work has also shown that it was possible to automatically identify dry intrusions with tracking algorithms. The difference of positions between model and image dry intrusions could therefore be used as observations of the misplacement of potenti...

Modelling background error correlations with spatial deformations: a case study

A long-term goal in variational data assimilation is to improve the anisotropy of background error correlations. One way to achieve anisotropic correlations is to introduce spatial deformations. This deformation can be specified a priori for instance by using the geostrophic transform (GT) as introduced by Desroziers (1997). The deformation can also be estimated from a purely statistical point of view (Michel, 2013a). The aim of this study is to evaluate the performance of such spatial deformation techniques for the use of background error modelling. A large ensemble of variational assimilations with perturbed observations is set up on a case study with the global ARPEGE model. An anisotropy index and a length scale diagnostic are defined to compare objectively the effectiveness of the deformations. This effectiveness is measured as the ability of the inverse spatial deformations to make the correlations more isotropic or more homogeneous. The results are shown to depend on the vertical level and on the variable. Generally, the statistical deformation is able to reduce the anisotropy while the GT is giving much smaller improvements that are, in this case study, confined to the frontal area of an extratropical cyclone.