The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

A new three-dimensional cloud resolving model (CRM) has been developed to study the statistical properties of cumulus convection. The model was applied to simulate a 28-day evolution of clouds over the Atmospheric Radiation Measurement Program (ARM) Southern Great Plains site during the summer 1997 Intensive Observation Period. The model was forced by the large-scale advective tendencies and surface fluxes derived from the observations. The sensitivity of the results to the domain dimensionality and size, horizontal grid resolution, and parameterization of microphysics has been tested. In addition, the sensitivity to perturbed initial conditions has also been tested using a 20-member ensemble of runs. The model captures rather well the observed temporal evolution of the precipitable water and precipitation rate, although it severely underestimates the shaded cloud fraction possibly because of an inability to account for the lateral advection of clouds over the ARM site. The ensemble runs reveal t...

Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities

After six years of scientific, technical developments and meteorological validation, the Application of Research to Operations at Mesoscale (AROME-France) convective-scale model became operational at Meteo-France at the end of 2008. This paper presents the main characteristics of this new numerical weather prediction system: the nonhydrostatic dynamical model core, detailed moist physics, and the as- sociated three-dimensional variational data assimilation (3D-Var) scheme. Dynamics options settings and variables are explained. The physical parameterizations are depicted as well as their mutual interactions. The scale-specific features of the 3D-Var scheme are shown. The performance of the forecast model is evaluated using objective scores and case studies that highlight its benefits and weaknesses.

/pdf/the-arome-france-convective-scale-operational-model-43tn89mjkn.pdf

The AROME-France Convective-Scale Operational Model

The spatial resolution appropriate for the simulation of deep moist convection is addressed from a turbulence perspective. To provide a clear theoretical framework for the problem, techniques for simulating turbulent flows are reviewed, and the source of the subgrid terms in the Navier‐Stokes equation is clarified. For decades, cloud-resolving models have used large-eddy simulation (LES) techniques to parameterize the subgrid terms. A literature review suggests that the appropriateness of using traditional LES closures for this purpose has never been established. Furthermore, examination of the assumptions inherent in these closures suggests that grid spacing on the order of 100 m may be required for the performance of cloud models to be consistent with their design. Based on these arguments, numerical simulations of squall lines were conducted with grid spacings between 1 km and 125 m. The results reveal that simulations with 1-km grid spacing do not produce equivalent squallline structure and evolution as compared to the higher-resolution simulations. Details of the simulated squall lines that change as resolution is increased include precipitation amount, system phase speed, cloud depth, static stability values, the size of thunderstorm cells, and the organizational mode of convective overturning (e.g., upright towers versus sloped plumes). It is argued that the ability of the higher-resolution runs to become turbulent leads directly to the differences in evolution. There appear to be no systematic trends in specific fields as resolution is increased. For example, mean vertical velocity and rainwater values increase in magnitude with increasing resolution in some environments, but decrease with increasing resolution in other environments. The statistical properties of the simulated squall lines are still not converged between the 250- and 125-m runs. Several possible explanations for the lack of convergence are offered. Nevertheless, it is clear that simulations with O(1 km) grid spacing should not be used as benchmark or control solutions for resolution sensitivity studies. The simulations also support the contention that a minimum grid spacing of O(100 m) is required for traditional LES closures to perform appropriately for their design. Specifically, only simulations with 250- and 125-m grid spacing resolve an inertial subrange. In contrast, the 1-km simulations do not even reproduce the correct magnitude or scale of the spectral kinetic energy maximum. Furthermore, the 1-km simulations contain an unacceptably large amount of subgrid turbulence kinetic energy, and do not adequately resolve turbulent fluxes of total water. A guide to resolution requirements for the operational and research communities is proposed. The proposal is based primarily on the intended use of the model output. Even though simulations with O(1 km) grid spacing display behavior that is unacceptable for the model design, it is argued that these simulations can still provide valuable information to operational forecasters. For the research community, O(100 m) grid spacing is recommended for most applications, because a modeling system that is well founded should be desired for most purposes.

https://opensky.ucar.edu/islandora/object/articles%3A17616/datastream/PDF/view

Resolution Requirements for the Simulation of Deep Moist Convection

. SURFEX is a new externalized land and ocean surface platform that describes the surface fluxes and the evolution of four types of surfaces: nature, town, inland water and ocean. It is mostly based on pre-existing, well-validated scientific models that are continuously improved. The motivation for the building of SURFEX is to use strictly identical scientific models in a high range of applications in order to mutualise the research and development efforts. SURFEX can be run in offline mode (0-D or 2-D runs) or in coupled mode (from mesoscale models to numerical weather prediction and climate models). An assimilation mode is included for numerical weather prediction and monitoring. In addition to momentum, heat and water fluxes, SURFEX is able to simulate fluxes of carbon dioxide, chemical species, continental aerosols, sea salt and snow particles. The main principles of the organisation of the surface are described first. Then, a survey is made of the scientific module (including the coupling strategy). Finally, the main applications of the code are summarised. The validation work undertaken shows that replacing the pre-existing surface models by SURFEX in these applications is usually associated with improved skill, as the numerous scientific developments contained in this community code are used to good advantage.

/pdf/the-surfexv7-2-land-and-ocean-surface-platform-for-coupled-261aoq10jv.pdf

The SURFEXv7.2 land and ocean surface platform for coupled or offline simulation of earth surface variables and fluxes

In 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...

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

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.

https://opensky.ucar.edu:/islandora/object/articles%3A11640/datastream/PDF/view

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

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

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