Variational Data Assimilation Research Articles

Simultaneous Multiscale 4DEnVar With Scale Dependent Localization (SDL) in Hurricane Analysis and Forecast System (HAFS)

AbstractThis study presents the implementation and evaluation of scale‐dependent localization (SDL) in the hurricane analysis and forecast system 4D Ensemble Variational (4DEnVar) Data Assimilation (DA) system. The SDL capability is compared with the traditional Single‐Scale Localization (SSL) method to assess its benefits and necessity for hurricane prediction. The experiments focus on Hurricane Laura (2020) and involve single observation experiments as well as real observation DA cycling experiments. The results indicate that the SDL experiment, which incorporates the Fast Almost Gaussian Filtering approach for scale decomposition, consistently outperforms the corresponding SSL configurations in almost all aspects. Further diagnostics show that due to its multiscale nature, the SDL approach demonstrates better track prediction over small‐scale SSL due to improved environmental analysis and better analyzed vortex position and structure, and superior intensity prediction during the rapid intensification over both the large‐scale SSL and the small‐scale SSL owing to enhanced inner‐core thermodynamic analysis.

Improving Typhoon Muifa (2022) Forecasts with FY-3D and FY-3E MWHS-2 Satellite Data Assimilation under Clear Sky Conditions

This study investigates the impacts of assimilating the Microwave Humidity Sounder II (MWHS-2) radiance data carried on the FY-3D and FY-3E satellites on the analyses and forecasts of Typhoon Muifa in 2022 under clear-sky conditions. Data assimilation experiments are conducted using the Weather Research and Forecasting (WRF) model coupled with the Three-Dimensional Variational (3D-Var) Data Assimilation method to compare the different behaviors of FY-3D and FY-3E radiances. Additionally, the data assimilation strategies are assessed in terms of the sequence of applying the conventional and MWHS-2 radiance data. The results show that assimilating MWHS-2 data is able to enhance the dynamic and thermal structures of the typhoon system. The experiment with FY-3E MWHS-2 assimilated demonstrated superior performance in terms of simulating the typhoon’s structure and providing a prediction of the typhoon’s intensity and track than the experiment with FY-3D MWHS-2 did. The two-step assimilation strategy that assimilates conventional observations before the radiance data has improved the track and intensity forecasts at certain times, particularly with the FY-3E MWHS-2 radiance. It appears that large-scale atmospheric conditions are more refined by initially assimilating the Global Telecommunication System (GTS) data, with subsequent satellite data assimilation further adjusting the model state. This strategy has also confirmed improvements in precipitation prediction as it enhances the dynamic and thermal structures of the typhoon system.

Assimilation of Radar Reflectivity via a Full-Hydrometeor Assimilation Scheme Based on the WSM6 Microphysics Scheme in WRF 4D-Var

Abstract The microphysical parameterization scheme employed in four-dimensional variational data assimilation (4D-Var) plays an important role in the assimilation of humidity and cloud-sensitive observations. In this study, a newly developed full-hydrometeor assimilation scheme, integrating warm-rain and cold-cloud processes, has been implemented in the Weather Research and Forecasting (WRF) 4D-Var system. This scheme is based on the WRF single-moment 6-class microphysics scheme (WSM6). Its primary objective is to directly assimilate radar reflectivity observations, with the goal of evaluating its effects on model initialization and subsequent forecasting performance. Four assimilation experiments were conducted to assess the performance of the full-hydrometeor assimilation scheme against the warm-rain assimilation scheme. These experiments also investigated reflectivity assimilation using both indirect and direct methods. We found that the nonlinearity of the radar operator in the two direct reflectivity assimilation experiments requires more iterations for cost function reduction than in the indirect assimilation method. The hydrometeor fields were reasonably analyzed using the full-hydrometeor assimilation scheme, particularly improving the simulation of ice-phase hydrometeors and reflectivity above the melting layer. The assimilation of radar reflectivity led to improvements in short-term (0–3 h) precipitation forecasting with the full-hydrometeor assimilation scheme. Assimilation experiments across multiple case studies reaffirmed that assimilating radar reflectivity observations with the full-hydrometeor assimilation scheme accelerated model spinup and yielded enhancements in 0–3-h total accumulate precipitation forecasts for a range of precipitation thresholds.

A Novel Localized Fast Multipole Method for Computations With Spatially Correlated Observation Error Statistics in Data Assimilation

AbstractSeveral observation types (e.g., geostationary satellite and Doppler radar observations) have recently been found to exhibit strong spatial error correlations. Including these error statistics in data assimilation for numerical weather prediction can improve analysis quality and forecast skill. Moreover, it allows for increases in the spatial density of observations assimilated, which is needed for the provision of information on appropriate scales for high‐resolution forecasting. However, introducing correlated error statistics may increase the computational complexity and parallel communication costs of matrix‐vector products involving observation precision matrices (inverse observation error covariance matrices). Without new approaches, we cannot take full advantage of new observation uncertainty estimates. We develop a new numerical approximation method based on a particular type of fast multipole method and a domain localization approach. The basic idea is to divide the observation domain into boxes and then separate calculations of matrix‐vector products according to the partition. These calculations can be done in parallel with very low communication overheads. The new method is easy to implement and parallelize, and it is applicable to a wide variety of observation precision matrices. We applied the new method to a simple variational data assimilation problem and found that the computational cost of the variational minimization was dramatically reduced while preserving analysis accuracy across a range of scales. The new method has the potential to be used as an efficient technique for practical applications where a large number of observations with mutual error correlations need to be assimilated quickly.

Inversion of Sea Surface Currents From Satellite‐Derived SST‐SSH Synergies With 4DVarNets

AbstractSatellite altimetry offers a unique approach for direct sea surface current observation, but it is limited to measuring the surface‐constrained geostrophic component. Ageostrophic dynamics, prevalent at horizontal scales below 100 km and time scales below 10 days, are often underestimated by ocean reanalyzes employing data assimilation schemes. To address this limitation, we introduce a novel deep learning scheme, rooted in a variational data assimilation formulation with trainable observations and a priori terms, that harnesses the synergies between satellite‐derived sea surface observations, namely sea surface height (SSH) and sea surface temperature (SST), to enhance sea surface current reconstruction. Numerical experiments, conducted using realistic simulations, in a case study area of the Gulf Stream, demonstrate the potential of the proposed scheme to capture ageostrophic dynamics at time scales of 2.5–3.0 days and horizontal scales of 0.5°–0.7°. The analysis of diverse observation configurations, encompassing nadir along‐track altimetry, wide‐swath SWOT (Surface Water and Ocean Topography) altimetry, and SST data, highlights the pivotal role of SST features in retrieving a significant portion of the ageostrophic dynamics (approximately 47%). These findings underscore the potential of deep learning and 4DVarNet schemes in improving ocean reanalyzes and enhancing our understanding of ocean dynamics.

Combining neural networks and data assimilation to enhance the spatial impact of Argo floats in the Copernicus Mediterranean biogeochemical model

Abstract. Biogeochemical-Argo (BGC-Argo) float profiles provide substantial information on key vertical biogeochemical dynamics and have been successfully integrated in biogeochemical models via data assimilation approaches. Although BGC-Argo assimilation results have been encouraging, data scarcity remains a limitation with respect to their effective use in operational oceanography. To address availability gaps in the BGC-Argo profiles, an observing system experiment (OSE) that combines a neural network (NN) and data assimilation (DA) was performed here. A NN was used to reconstruct nitrate profiles, starting from oxygen profiles and associated Argo variables (pressure, temperature, and salinity), while a variational data assimilation scheme (3DVarBio) was upgraded to integrate BGC-Argo and reconstructed observations in the Copernicus Mediterranean operational forecast system (MedBFM). To ensure the high quality of oxygen data, a post-deployment quality control method was developed with the aim of detecting and eventually correcting potential sensors drift. The Mediterranean OSE features three different set-ups: a control run without assimilation; a multivariate run with assimilation of BGC-Argo chlorophyll, nitrate, and oxygen; and a multivariate run that also assimilates reconstructed observations. The general improvement in the skill performance metrics demonstrated the feasibility of integrating new variables (oxygen and reconstructed nitrate). Major benefits have been observed with respect to reproducing specific biogeochemical-process-based dynamics such as the nitracline dynamics, primary production, and oxygen vertical dynamics. The assimilation of BGC-Argo nitrate corrects a generally positive bias of the model in most of the Mediterranean areas, and the addition of reconstructed profiles makes the corrections even stronger. The impact of enlarged nitrate assimilation propagates to ecosystem processes (e.g. primary production) at a basin-wide scale, demonstrating the importance of the assimilation of BGC-Argo profiles in forecasting the biogeochemical ocean state.

Blending of global and regional ensembles in cycling hybrid ensemble-variational data assimilation for the convection-permitting prediction of typhoon Merbok (2017)

Several blending approaches have been implemented in regional cycling data assimilation to introduce the large-scale weather features of the global model forecast or analysis effectively into regional model forecasts. While in previous studies the blending schemes for data assimilation have generally been applied in stand-alone variational data assimilation systems, here we incorporate the new large-scale ensemble blending schemes into the regional hybrid ensemble-variational (EnVar) data assimilation system. It uses a low-pass Raymond tangent implicit filter to introduce the large-scale background or analysis information from global ensembles. Five parallel cycling hybrid ensemble-variational data assimilation experiments for the convection-permitting prediction of typhoon Merbok in 2017 show that the large-scale ensemble information from Global Ensemble Forecast System (GEFS) can suppress cumulative error growth in data assimilation cycles. On the other hand, the large-scale part of the global ensemble improves the typhoon track and intensity forecasts, possibly due to a better description of the horizontal and vertical structure of the typhoon. In addition, the blending scheme using global ensemble analysis provides more accurate rainfall forecasts of typhoon than the other blending schemes.

Three-dimensional variational assimilation with a multivariate background error covariance for the Model for Prediction Across Scales – Atmosphere with the Joint Effort for Data assimilation Integration (JEDI-MPAS 2.0.0-beta)

Abstract. 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.

Variational data assimilation with finite-element discretization for second-order parabolic interface equation

Abstract In this paper, we propose and analyze a finite-element method of variational data assimilation for a second-order parabolic interface equation on a two-dimensional bounded domain. The Tikhonov regularization plays a key role in translating the data assimilation problem into an optimization problem. Then the existence, uniqueness and stability are analyzed for the solution of the optimization problem. We utilize the finite-element method for spatial discretization and backward Euler method for the temporal discretization. Then based on the Lagrange multiplier idea, we derive the optimality systems for both the continuous and the discrete data assimilation problems for the second-order parabolic interface equation. The convergence and the optimal error estimate are proved with the recovery of Galerkin orthogonality. Moreover, three iterative methods, which decouple the optimality system and significantly save computational cost, are developed to solve the discrete time evolution optimality system. Finally, numerical results are provided to validate the proposed method.

An ensemble-based data assimilation system for forecasting variability of the Northwestern Pacific ocean

An adjoint-free four-dimensional variational (a4dVar) data assimilation (DA) is implemented in an operational ocean forecast system based on an eddy-resolving ocean general circulation model for the Northwestern Pacific. Validation of the system against independent observations demonstrates that fitting the model to time-dependent satellite altimetry during a 10-day DA window leads to substantial skill improvements in the succeeding 60-day hindcast. The a4dVar corrects representation of the Kuroshio path variation south of Japan by adjusting the dynamical balance between amplitude/wavelength of the meander and flow advection. A larger ensemble spread tends to reduce the skill in representing the observed sea surface height anomaly, suggesting that it is possible to use the ensemble information for quantifying the forecast error. The ensemble information is also utilized for modification of the background error covariance (BEC), which improves the accuracy of temperature and salinity distributions. The modified BEC yields the skill decline of the Kuroshio path variation during the 60-day hindcast period, and the ensemble sensitivity analysis shows that changes in the dynamical balance caused by the ensemble BEC result in such skill deterioration.

How frequent and which variables of automatic weather station data should be assimilated into WRF-3DVar model? A case study of a squall line event in Beijing

Accurate precipitation forecasting is one of the most challenging problems in mesoscale Numerical Weather Prediction (NWP) models. The utilization of 3-Dimensional Variational (3DVar) Data Assimilation technique based on automatic weather station (AWS) data can significantly enhance the accuracy of precipitation simulations and forecasts using the Weather Research and Forecasting (WRF) model. However, the impacts of different assimilation frequencies and meteorological variables on the accuracy of precipitation forecasts remain unclear. This study comprehensively evaluated the impact of different assimilation frequencies and meteorological variables on precipitation forecasts, as illustrated by a case study of a squall line event on August 2, 2017, in Beijing. Eight experiments were conducted by assimilating different combinations of meteorological variables (air pressure, temperature, relative humidity, wind speed, and wind direction) at various time intervals (1 h, 3 h, and 6 h). The results indicated that the WRF model roughly simulated the evolution of this event but overestimated the precipitation amount, accompanied by a large deviation in precipitation areas. Assimilating detailed AWS data significantly improves the model performance in precipitation forecasts. The experiment assimilating all variables at a 3 h interval yielded the most accurate forecasts, with the maximum threat score (TS) increasing from 0.02 to 0.56. Higher assimilation frequencies do not guarantee a better performance. In practice, a 3 h assimilation frequency emerges as an optimal choice for AWS data assimilation. The assimilation of various variables enhanced precipitation forecasts to varying degrees, with the optimum results achieved when all variables were assimilated. Wind speed and direction were the most significant factors in dynamically enhancing the simulation of precipitation areas. Relative humidity and temperature influenced the precipitation intensity by affecting the evolution of convective precipitation thermodynamically. The findings of this study can contribute to the development of AWS data assimilation strategies for the WRF-3DVar model, thereby enhancing the precipitation forecast accuracy.

An Enhanced Long-Term Wind Speed Prediction Using Dynamic Unified Ensemble Learning and Data Assimilation Techniques: A Case Study in Tamil Nadu, India

Reliable wind speed prediction is essential for effective grid management since wind energy is a key component of renewable energy generation. However, controlling wind speed just right is no easy feat since the wind flow changes constantly. This paper presents an innovative method for predicting wind speeds in the future. It uses state-of-the-art data assimilation methods and a dynamic unified ensemble learning model. For efficient wind energy planning and monitoring, WSP accuracy is crucial. Data from a single site limited the accuracy of WSPs in previous research. An improved accuracy of long-term wind speed predictions is achieved by the proposed model via the integration of data assimilation and ensemble learning. To increase forecast accuracy, the model uses sophisticated data assimilation methods like the Kalman filter to combine data from many sources. Specifically, the model employs the Stacked CNN + BiLSTM with Data Assimilator (SCBLSTM+DA) technique, which integrates Wind Speed (WS) data from adjacent areas with the CNN + BiLSTM-based Ensemble Learning Model (ELM) and the Four-Dimensional Variational and Ensemble Kalman Filter (4DVar/EnKF) Data Assimilation method. Using real-world wind speed data from nine meteorological stations in Tamil Nadu, India, we find that current prediction models, including both classical statistical and cutting-edge machine learning models, perform better. Further, unlike standalone models, the suggested model shows less susceptibility to changes in prediction time scales. Promising a solution to improve long-term wind speed predictions accuracy, this study has significant consequences for wind energy management and production.

Data assimilation with machine learning for dynamical systems: Modelling indoor ventilation

Data assimilation is a method of combining physical observations with prior knowledge (for instance, a computational simulation) in order to produce an improved estimate of the state of a system; that is, improved over what the physical observations or the computational simulation, alone, could offer. Recently, machine learning techniques have been deployed in order to address the significant computational burden that is associated with the procedures involved in data assimilation.In this paper we propose an approach that uses a non-intrusive reduced-order model (NIROM) as a surrogate for a high-resolution model thereby saving computational effort. The mismatch between observations and the surrogate model is propagated forwards and backwards in time in a manner similar to 4D-variational data assimilation methods. The observations and prior are reconciled in a new way which takes full advantage of the neural network used in the NIROM and also means that there is no need to form the sensitivities explicitly when propagating the mismatch. Instead, the observations are part of the input and output of the network. The key advantages of this data assimilation approach are its simplicity (as we can avoid differentiating the forward model and bypass the use of an optimisation method), and its ability to integrate with control and uncertainty quantification methodologies.Modelling the air quality in a school classroom is the test case for our demonstration. After comparing the proposed data assimilation approach with 4D Variational Data Assimilation, we investigate two scenarios. The first of these is a dual-twin type experiment, for which the proposed approach is shown to perform very well, and the second is a test case which assimilates predictions from the NIROM with observations collected from a classroom in Houndsfield Primary School.

A variational data assimilation approach for sparse velocity reference data in coarse RANS simulations through a corrective forcing term

The Reynolds-averaged Navier–Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their accuracy. To address this issue, recent research has explored data-driven techniques such as data assimilation and machine learning.An efficient variational data assimilation (DA) approach is presented to enhance steady-state eddy viscosity based RANS simulations. To account for model deficiencies, a corrective force term is introduced in the momentum equation. In the case of only velocity reference data, this term can be represented by a potential field and is divergence-free. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation.The implementation is based on a two-dimensional coupled RANS solver in OpenFOAM, which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is used to minimize the difference between the simulation results and the reference data. To evaluate this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the data assimilation, sparsely distributed reference data from averaged high-fidelity simulation results are used.The results suggest that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. The method works well for different reference data configurations and runs efficiently by leveraging coarse meshes.

Assessing the impact of subsurface temperature observations from fishing vessels on temperature and heat content estimates in shelf seas: a New Zealand case study using Observing System Simulation Experiments

We know that extremes in ocean temperature often extend below the surface, and when these extremes occur in shelf seas they can significantly impact ecosystems and fisheries. However, a key knowledge gap exists around the accuracy of model estimates of the ocean’s subsurface structure, particularly in continental shelf regions with complex circulation dynamics. It is well known that subsurface observations are crucial for the correct representation of the ocean’s subsurface structure in reanalyses and forecasts. While Argo floats sample the deep waters, subsurface observations of shelf seas are typically very sparse in time and space. A recent initiative to instrument fishing vessels and their equipment with temperature sensors has resulted in a step-change in the availability of in situ data in New Zealand’s shelf seas. In this study we use Observing System Simulation Experiments to quantify the impact of the recently implemented novel observing platform on the representation of temperature and ocean heat content around New Zealand. Using a Regional Ocean Modelling System configuration of the region with 4-Dimensional Variational Data Assimilation, we perform a series of data assimilating experiments to demonstrate the influence of subsurface temperature observations at two different densities and of different data assimilation configurations. The experiment period covers the 3 months during the onset of the 2017-2018 Tasman Sea Marine Heatwave. We show that assimilation of subsurface temperature observations in concert with surface observations results in improvements of 44% and 38% for bottom temperature and heat content in shelf regions (water depths< 400m), compared to improvements of 20% and 28% for surface-only observations. The improvement in ocean heat content estimates is sensitive to the choices of prior observation and background error covariances, highlighting the importance of the careful development of the assimilation system to optimize the way in which the observations inform the numerical model estimates.

Error Model for the Assimilation of All-Sky FY-4A/AGRI Infrared Radiance Observations.

The Advanced Geostationary Radiation Imager (AGRI) carried by the FengYun-4A (FY-4A) satellite enables the continuous observation of local weather. However, FY-4A/AGRI infrared satellite observations are strongly influenced by clouds, which complicates their use in all-sky data assimilation. The presence of clouds leads to increased uncertainty, and the observation-minus-background (O-B) differences can significantly deviate from the Gaussian distribution assumed in the variational data assimilation theory. In this study, we introduce two cloud-affected (Ca) indices to quantify the impact of cloud amount and establish dynamic observation error models to address biases between O-B and Gaussian distributions when assimilating all-sky data from FY-4A/AGRI observations. For each Ca index, we evaluate two dynamic observation error models: a two-segment and a three-segment linear model. Our findings indicate that the three-segment linear model we propose better conforms to the statistical characteristics of FY-4A/AGRI observations and improves the Gaussianity of the O-B probability density function. Dynamic observation error models developed in this study are capable of handling cloud-free or cloud-affected FY-4A/AGRI observations in a uniform manner without cloud detection.

A robust computational framework for variational data assimilation of mean flows with sparse measurements corrupted by strong outliers

A variational framework for the reconstruction of time-averaged mean flows using a sparse set of observations with large magnitudes of noise (referred to as outliers), is presented. The observations constitute a set of point-wise measurements of the mean flow with outliers at certain measurement locations and are incorporated into a numerical simulation governed by the two-dimensional, incompressible Reynolds-averaged Navier-Stokes (RANS) equations with an unknown momentum forcing. This forcing, which corresponds to the divergence of the Reynolds stress tensor, is calculated from a direct-adjoint optimization procedure to reduce the deviation between the measured and estimated mean velocities. ℓ2, ℓ1, Huber, and hybrid loss functions are used to represent the discrepancy in the mean velocity field between the measurements and the predictions. A variety of algorithms are considered to solve the optimization problem with these loss functions and a performance comparison in terms of the quality and physical features of the recovered mean flow is presented. The Huber loss function performed best as it remained robust to strong outliers in the measurements with its ℓ1 contribution and also ensured the uniqueness of the optimal solution with its ℓ2 contribution. Huber loss functions restrict the effect of outliers at the local measurement locations, thereby not affecting the quality of the high-dimensional reconstructed mean flow field. The hybrid loss function, a modified form of the continuous Huber loss function, also recovered the mean flow with high accuracy. We demonstrate the performance of the data assimilation framework for the case of two-dimensional laminar flow around a circular cylinder at Re=100. We then extend the analysis to the case of two-dimensional laminar flow over a backward-facing step at Re=500, to further assess the efficacy and robustness of the data assimilation framework.

Influence of Assimilation of NEXRAD-Derived 2D Inner-Core Structure Data from Single Radar on Numerical Simulations of Hurricane Charley (2004) near Its Landfall

This study presents the first research that assimilates the ground-based NEXRAD observations-derived two-dimensional (2D), azimuthally averaged radar radial velocity and reflectivity within 60 km of radius from the hurricane center to examine their influence on the analysis and prediction of a hurricane near and after its landfall. The mesoscale community Weather Research and Forecasting (WRF) model and its four-dimensional variational (4D-VAR) data assimilation system are utilized to conduct data assimilation experiments for Hurricane Charley (2004). Results show that assimilation of the radar inner-core data leads to better forecasts of hurricane tracks, intensity, and precipitation. The improved forecast outcomes imply that the changes in dynamical, thermal, and moisture structures from data assimilations made more reasonable conditions for the hurricane development near and after its landfall. Overall results indicate that the assimilation of the radar-derived 2D inner-core structure could be a feasible way to utilize the radar data for improved hurricane prediction.

Variable-Dependent and Selective Multivariate Localization for Ensemble–Variational Data Assimilation in the Tropics

Abstract Two aspects of ensemble localization for data assimilation are explored using the simplified nonhydrostatic ABC model in a tropical setting. The first aspect (i) is the ability to prescribe different localization length scales for different variables (variable-dependent localization). The second aspect (ii) is the ability to control (i.e., to knock out by localization) multivariate error covariances (selective multivariate localization). These aspects are explored in order to shed light on the cross-covariances that are important in the tropics and to help determine the most appropriate localization configuration for a tropical ensemble–variational (EnVar) data assimilation system. Two localization schemes are implemented within the EnVar framework to achieve (i) and (ii). One is called the isolated variable-dependent localization (IVDL) scheme and the other is called the symmetric variable-dependent localization (SVDL) scheme. Multicycle observation system simulation experiments are conducted using IVDL or SVDL mainly with a 100-member ensemble, although other ensemble sizes are studied (between 10 and 1000 members). The results reveal that selective multivariate localization can reduce the cycle-averaged root-mean-square error (RMSE) in the experiments when cross-covariances associated with hydrostatic balance are retained and when zonal wind/mass error cross-covariances are knocked out. When variable-dependent horizontal and vertical localization are incrementally introduced, the cycle-averaged RMSE is further reduced. Overall, the best performing experiment using both variable-dependent and selective multivariate localization leads to a 3%–4% reduction in cycle-averaged RMSE compared to the traditional EnVar experiment. These results may inform the possible improvements to existing tropical numerical weather prediction systems that use EnVar data assimilation.

3D‐Var data assimilation using a variational autoencoder

AbstractData assimilation of atmospheric observations traditionally relies on variational and Kalman filter methods. Here, an alternative neural network data assimilation (NNDA) with variational autoencoder (VAE) is proposed. The three‐dimensional variational (3D‐Var) data assimilation cost function is utilised to determine the analysis that optimally fuses simulated observations and the encoded short‐range persistence forecast (background), accounting for their errors. The minimisation is performed in the reduced‐order latent space discovered by the VAE. The variational problem is autodifferentiable, simplifying the computation of the cost‐function gradient necessary for efficient minimisation. We demonstrate that the background‐error covariance (B) matrix measured and represented in the latent space is quasidiagonal. The background‐error covariances in the grid‐point space are flow‐dependent, evolving seasonally and depending on the current state of the atmosphere. Data assimilation experiments with a single temperature observation in the lower troposphere indicate that the B matrix describes both tropical and extratropical background‐error covariances simultaneously.