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This paper describes the three-dimensional variational (3D-Var) data assimilation (DA) system for the Model for Prediction Across Scales – Atmosphere with the Joint Effort for Data assimilation Integration (JEDI-MPAS). Its core element is a multivariate background error covariance implemented through multiple linear variable changes, including a wind variable change from stream function and velocity potential to zonal- and meridional-wind components, a vertical linear regression representing wind–mass balance, and multiplication by a diagonal matrix of error standard deviations. The univariate spatial correlations for the "unbalanced" variables utilize the Background error on Unstructured Mesh Package (BUMP), which is one of the generic components in the JEDI framework. The variable changes and univariate correlations are modeled directly on the native MPAS unstructured mesh. BUMP provides utilities to diagnose parameters of the covariance model, such as correlation lengths, from an ensemble of forecast differences, though some manual adjustment of the parameters is necessary because of mismatches between the univariate correlation function assumed by BUMP and the correlation structure in the sample of forecast differences. The resulting multivariate covariances, as revealed by single-observation tests, are qualitatively similar to those found in previous global 3D-Var systems. Month-long cycling DA experiments using a global quasi-uniform 60 km mesh demonstrate that 3D-Var, as expected, performs somewhat worse than a pure ensemble-based covariance, while a hybrid covariance, which combines that used in 3D-Var with the ensemble covariance, significantly outperforms both 3D-Var and the pure ensemble covariance. Due to its simple workflow and minimal computational requirements, the JEDI-MPAS 3D-Var system can be useful for the research community. [ABSTRACT FROM AUTHOR]

An ensemble of 3D ensemble-variational (En-3DEnVar) data assimilations is demonstrated with the Joint Effort for Data assimilation Integration (JEDI) with the Model for Prediction Across Scales – Atmosphere (MPAS-A) (i.e., JEDI-MPAS). Basic software building blocks are reused from previously presented deterministic 3DEnVar functionality and combined with a formal experimental workflow manager in MPAS-Workflow. En-3DEnVar is used to produce an 80-member ensemble of analyses, which are cycled with ensemble forecasts in a 1-month experiment. The ensemble forecasts approximate a purely flow-dependent background error covariance (BEC) at each analysis time. The En-3DEnVar BECs and prior ensemble-mean forecast errors are compared to those produced by a similar experiment that uses the Data Assimilation Research Testbed (DART) ensemble adjustment Kalman filter (EAKF). The experiment using En-3DEnVar produces a similar ensemble spread to and slightly smaller errors than the EAKF. The ensemble forecasts initialized from En-3DEnVar and EAKF analyses are used as BECs in deterministic cycling 3DEnVar experiments, which are compared to a control experiment that uses 20-member MPAS-A forecasts initialized from Global Ensemble Forecast System (GEFS) initial conditions. The experimental ensembles achieve mostly equivalent or better performance than the off-the-shelf ensemble system in this deterministic cycling setting, although there are many obvious differences in configuration between GEFS and the two MPAS ensemble systems. An additional experiment that uses hybrid 3DEnVar, which combines the En-3DEnVar ensemble BEC with a climatological BEC, increases tropospheric forecast quality compared to the corresponding pure 3DEnVar experiment. The JEDI-MPAS En-3DEnVar is technically working and useful for future research studies. Tuning of observation errors and spread is needed to improve performance, and several algorithmic advancements are needed to improve computational efficiency for larger-scale applications. [ABSTRACT FROM AUTHOR]

This paper describes the three-dimensional variational (3DVar) data assimilation (DA) system for the Model for Prediction Across Scales-Atmosphere with the Joint Effort for data Assimilation Integration (JEDI-MPAS). Its core element is a multivariate background error covariance implemented through multiple linear variable changes, including a wind variable change from stream function and velocity potential to zonal and meridional wind components, a vertical linear regression representing wind-mass balance, and multiplication by a diagonal matrix of error standard deviations. The univariate spatial correlations for the "unbalanced" variables utilize the Background error on an Unstructured Mesh Package (BUMP), which is one of generic components in the JEDI framework. The variable changes and univariate correlations are modeled directly on the native MPAS unstructured mesh. BUMP provides utilities to diagnose parameters of the covariance model, such as correlation lengths, from an ensemble of forecast differences, though some manual adjustment of the parameters is necessary because of mismatches between the univariate correlation function assumed by BUMP and the correlation structure in the sample of forecast differences. The resulting multivariate covariances, as revealed by single-observation tests, are qualitatively similar to those found in previous global 3DVar systems. Month-long cycling DA experiments using a global quasi-uniform 60 km mesh demonstrate that 3DVar, as expected, performs somewhat worse than a pure ensemble-based covariance, while a hybrid covariance that combines that used in 3DVar with the ensemble covariance, significantly outperforms both 3DVar and the pure ensemble covariance. Due to its simple workflow and minimal computational requirements, the JEDI-MPAS 3DVar can be useful for the research community. [ABSTRACT FROM AUTHOR]

On 24th September 2021, JEDI-MPAS 1.0.0, a new data assimilation (DA) system for the Model Prediction Across Scales - Atmosphere (MPAS-A) built on the software framework of the Joint Effort for Data assimilation Integration (JEDI), was publicly released for community use. JEDI-MPAS capabilities include three-dimensional variational (3DVar) and ensemblevariational (EnVar) schemes for deterministic analyses, the ensemble of DAs (EDA) technique to produce ensembles of analyses, and dual resolution, where the analysis increment and the input forecast ensemble are at a lower resolution than that of the background and analysis, thus decreasing computational requirements. Moreover, JEDI-MPAS operates directly on the native MPAS unstructured mesh and can be applied without code modifications to all MPAS meshes, whether uniform, variable resolution, global, or regional. On the observation side, one advanced feature in JEDI-MPAS is the full all-sky approach for satellite radiance DA with the introduction of hydrometeor analysis variables. This paper describes the formulation and implementation of EnVar for JEDI-MPAS. JEDI-MPAS 1.0.0 is evaluated with month-long cycling 3DEnVar experiments with a global 30km-60km dual-resolution configuration. The robustness and credible performance of JEDI-MPAS are demonstrated by establishing a benchmark non-radiance DA experiment, then incrementally adding microwave radiances from three sources: AMSU-A temperature sounding channels in clear-sky scenes, AMSU-A window channels in all-sky scenes, and MHS water vapor channels in clear-sky scenes. JEDI-MPAS 3DEnVar behaves well with substantial and significant positive impact ob15 tained for almost all aspects of forecast verification when progressively adding more microwave radiance data. In particular, the day-5 forecast of the best-performing JEDI-MPAS experiment yields an anomaly correlation coefficient (ACC) of 0.8 for 500 hPa geopotential height, a gap of roughly a half day when compared to cold start forecasts initialized from operational analyses of the National Centers for Environmental Prediction, whose ACC does not drop to 0.8 until a lead time of 5.5 days. This indicates JEDI-MPAS's great potential for both research and operations. Further development of JEDI-MPAS is ongoing, with emphasis on 3DVar, EDA, and cloud analysis from all-sky radiance observations. [ABSTRACT FROM AUTHOR]

This study aims at introducing two conservative thermodynamic variables (moist-air entropy potential temperature and total water content) into a one-dimensional variational data assimilation system (1D-Var) to demonstrate the benefit for future operational assimilation schemes. This system is assessed using microwave brightness temperatures from a ground-based radiometer installed during the field campaign SOFGO3D dedicated to fog forecast improvement. An underlying objective is to ease the specification of background error covariance matrices that are currently highly dependent on weather conditions making difficult the optimal retrievals of cloud and thermodynamic properties during fog conditions. Background error covariance matrices for these new conservative variables have thus been computed by an ensemble approach based on the French convective scale model AROME, for both all-weather and fog conditions. A first result shows that the use of these matrices for the new variables reduces some dependencies to the meteorological conditions (diurnal cycle, presence or not of clouds) compared to usual variables (temperature, specific humidity). Then, two 1D-Var experiments (classical vs. conservative variables) are evaluated over a full diurnal cycle characterized by a stratus-evolving radiative fog situation, using hourly brightness temperatures. Results show, as expected, that analysed brightness temperatures by the 1D-Var are much closer to the observed ones than background values for both variable choices. This is especially the case for channels sensitive to water vapour and liquid water. On the other hand, analysis increments in model space (water vapour, liquid water) show significant differences between the two sets of variables. [ABSTRACT FROM AUTHOR]

Developing effective ways to model and cycle the background‐error covariance matrix is an active area of research in data assimilation. An important aspect of this problem when using a filter to model the background‐error correlations is the computation of normalization factors to ensure that the diagonal elements of the modelled correlation matrix are all equal to one. Updating the parameters of a flow‐dependent correlation model on each assimilation cycle requires updating the normalization factors, which is costly using traditional methods such as randomization. In this article, we discuss the normalization problem within the context of a diffusion filter‐based covariance model used for background‐error modelling in a variational data assimilation system for the global ocean. We evaluate various methods for estimating normalization factors when the diffusion tensor of the correlation model is derived from an ensemble of ocean states. Our results show that estimates produced using inexpensive methods derived from analytical considerations of the diffusion equation can have significant errors, especially near boundaries. Estimates obtained using randomization with a small sample size (∼100) are more accurate in a globally averaged sense but are noisy and can have unacceptably large errors locally. Next, we focus on the specific problem of accounting for flow‐dependent correlation parameters in the vertical component of the diffusion operator only, which is especially important near the surface for the assimilation of sea surface temperature observations. Remarkably accurate estimates are obtained by approximating the normalization matrix as a separable product of two normalization matrices: one computed using randomization with the horizontal diffusion operator only and the other computed using randomization with the vertical diffusion operator only. If the parameters of the horizontal component of the diffusion operator are static, then only the normalization factors of the flow‐dependent vertical component need to be recomputed on each cycle. This result is of significant practical interest since the vertical diffusion operator employs an inexpensive direct solver and thus can be applied on each cycle with a large random sample to obtain a good approximation of the normalization matrix. [ABSTRACT FROM AUTHOR]

Kilometre‐scale numerical weather prediction addresses the challenge of forecasting accurately clouds and precipitation. Ensemble‐based data assimilation methods make use of background‐error covariances that are sampled from an ensemble of forecasts. These methods can be considered in order to include hydrometeor variables and their flow‐dependent error covariances in the data assimilation system. Yet, because of limited ensemble size, rank deficiency of the resulting covariances and sampling noise occur, which can be mitigated by a localization procedure. In order to optimally localize covariances for hydrometeor variables, previous work by the authors has been extended. This approach estimates localization as a linear filtering on covariances, optimal in the sense of minimizing sampling noise. The zero‐variance and the high spatial variability issues met with hydrometeor variables are addressed by using an improved method for spatial sampling, based on geographical masks. Diagnosed optimal horizontal localization lengths appear to be much shorter for hydrometeors than for other classical thermodynamic variables. Conversely, we report optimal vertical localization to be very broad for precipitating species. Great variability between different meteorological situations has also been noticed, which reflects the high flow dependency of hydrometeor forecast errors. This suggests that ensemble‐based data assimilation schemes that consider hydrometeors as control variables should adopt more refined localization schemes than the common "one‐size‐fits‐all" approach. [ABSTRACT FROM AUTHOR]

The AROME-EPS convection-permitting ensemble prediction system has been evaluated over the HyMeX-SOP1 period. Objective verification scores are computed using dense observing networks prepared for the HyMeX experiment. In probabilistic terms, the AROME-EPS ensemble performs better than the AROME-France deterministic prediction system, and a state-of-the-art ensemble at a lower resolution. The strengths and weaknesses of AROME-EPS are discussed. Here, impact experiments are used to study perturbation schemes for the initial conditions and the model surface. Both have a significant effect on the ensemble performance. The interactions between the perturbations of lateral boundaries, initial conditions and surface perturbations are studied. The consistency between initial and lateral perturbations is found to be unimportant from a meteorological point of view. Ensemble data assimilation is not as effective as a simpler surface perturbation scheme, and it is noted that both approaches could be usefully combined. [ABSTRACT FROM AUTHOR]