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A four‐dimensional ensemble‐variational (4DEnVar) data assimilation (DA) system was developed based on the global forecast system of the Global/Regional Assimilation and Prediction System (GRAPES‐GFS). Instead of using the adjoint technique, this system utilizes a dimension‐reduced projection (DRP) technique to minimize the cost function of the standard four‐dimensional variational (4DVar) DA. It dynamically predicts ensemble background error covariance (BEC) and realizes the explicit flow‐dependence of BEC in the variational configuration. An inflation technique based on a linear combination of analysis increments and balanced random perturbations, is utilized to overcome the problem of underestimation of BEC matrix (B‐matrix) during the assimilation cycle. To mitigate the spurious correlations in the ensemble B‐matrix caused by the insufficient ensemble members, an ensemble‐sample‐based subspace localization method is utilized. In order to evaluate the new system, single‐point observation experiments (SOEs) and observing system simulation experiments (OSSEs) were conducted with sounding and cloud‐derived wind data based on GRAPES‐GFS. The explicit flow‐dependent characteristic of the 4DEnVar system using a localized ensemble covariance was verified in the SOEs. In the OSSEs, the ensemble mean analysis of 4DEnVar outperforms the analysis of 4DVar. The deterministic forecast initialized from the 4DEnVar ensemble mean analysis has better performance in the short‐range forecasts, better (worse) performance in the early (late) period of the medium‐range forecasts in the Northern Extratropics, and opposite performance in the Southern Extratropics, and exhibits slightly worse effects in the Tropics. Moreover, the ensemble mean forecast initialized by the 4DEnVar system has higher forecast skills. Plain Language Summary Medium‐range numerical weather prediction aims to predict weather states for future 1–10 days from the current state by solving the initial value problem of a set of partial differential equations. Data assimilation (DA) is one of the key techniques to improve forecast skills, which attempts to provide an optimal estimation of the current state by combining observations and forecasts. This study developed a four‐dimensional ensemble‐variational (4DEnVar) DA system based on the global forecast system of the Global/Regional Assimilation and Prediction System (GRAPES‐GFS) applying the dimension‐reduced projection (DRP) four‐dimensional variational (4DVar) approach. Compared with the standard 4DVar, which is generally recognized as one of the most advanced DA methods, this new system has three unique features. First, it dynamically estimates background error covariance (BEC) during the assimilation cycle instead of adopting a pre‐estimated static BEC as 4DVar does. Second, it uses a pure anisotropic ensemble covariance. Third, it can avoid using adjoint models and handle nonlinear problems well. The observing system simulation experiments based on GRAPES‐GFS verify that 4DEnVar has smaller analysis errors, and better ensemble mean forecast skills than 4DVar, and comparable skills of deterministic forecast initialized from the ensemble mean analysis to 4DVar. Key Points A DRP‐4DVar based 4DEnVar data assimilation system with the flow‐dependent background error covariance was developed for global numerical weather prediction The deterministic forecast initialized from the 4DEnVar ensemble mean analysis has performance comparable to 4DVar in the Extratropics Higher quality of analyses and ensemble forecasts can be produced by the 4DEnVar system relative to the 4DVar system

This study developed an ensemble four‐dimensional variational (En4DVar) hybrid data assimilation system. Different from most of the available En4DVar systems that adopted ensemble Kalman Filter class or ensemble data assimilation approaches to produce ensemble covariances for their hybrid background error covariances (BECs), it used a four‐dimensional ensemble variational (4DEnVar) system to obtain the ensemble covariance. The localization scheme for 4DEnVar applied orthogonal functions to decompose the correlation matrix so that it was implemented easily and rapidly. In terms of analysis quality and forecast skill, the En4DVar system was evaluated in the single‐point observation experiments and observing system simulation experiments (OSSEs) with sounding and cloud‐derived wind observations, using its standalone four‐dimensional variational (4DVar) and 4DEnVar components as references. The single‐point observation experiments visually verified the explicit flow‐dependent characteristic of the BEC due to the introduction of the ensemble covariance from the 4DEnVar system. The OSSE‐based sensitivity experiments revealed different contributions of the weight for the ensemble covariance in the En4DVar system to the forecasts in the Northern and Southern Extratropics and Tropics. A much higher weight for the ensemble covariance in a properly inflated hybrid covariance helped En4DVar produce the most reasonable analysis. The forecast initialized by En4DVar is overall better than by 4DVar and 4DEnVar, although the quality of En4DVar analysis is between those of 4DVar and 4DEnVar ensemble mean analyses. It indicates that the flow‐dependent ensemble covariance provided by 4DEnVar dominantly contributes to the improvements in the En4DVar‐initialized forecast, with certain but necessary constraint from the balanced climatological covariance. Plain Language Summary Dynamically balanced complete error structure and explicit flow dependence of the background error covariance (BEC) are two key factors which affect the analysis quality of a data assimilation (DA) system. The untruncated and balanced BEC in the four‐dimensional variational (4DVar) DA approach has no explicit flow dependence, while the localized flow‐dependent ensemble BEC usually breaks the balance. The hybrid of the 4DVar approach and an ensemble class DA method can achieve these two important characteristics of BEC. In this study, a hybrid DA system called ensemble 4DVar (En4DVar) system was developed. It has two unique features. First, it uses a four‐dimensional ensemble‐variational (4DEnVar) system to dynamically provide the ensemble covariance, which differs from most of the available En4DVar systems that estimate their dynamic covariances with the ensemble Kalman Filter class approaches or ensemble of 4DVars method. Second, the ensemble covariance is localized in the sample space using a limited number of leading eigenvectors of the correlation function. In the single‐point observation experiments and observing system simulation experiments, the new En4DVar system exhibited obvious flow‐dependent characteristic and higher forecast skill than both the 4DVar and 4DEnVar systems although its analysis error is between those of the latter two. Key Points An ensemble four‐dimensional variational (En4DVar) data assimilation system with a hybrid background error covariance was developed for global numerical weather prediction The hybrid covariance is realized by linearly combining the climatological covariance of four‐dimensional variational (4DVar) system and the ensemble covariance of four‐dimensional ensemble‐variational (4DEnVar) system The En4DVar‐initialized forecast is improved relative to 4DVar‐ and 4DEnVar‐initialized forecasts

The current NCEP operational four‐dimensional ensemble‐variational data assimilation system uses a control forecast at T1534 resolution coupled with an 80 member ensemble at T574 resolution. Given an increase in computing resources, and assuming the control forecast resolution is fixed, would it be better to increase the ensemble size and keep the ensemble resolution the same, or increase the ensemble resolution and keep the ensemble size the same? To answer this question, experiments are conducted at reduced resolutions. Two sets of experiments are conducted which both use approximately four times more computational resources than the control experiment that uses a control forecast at T670 and an 80 member ensemble at T254. One increases the ensemble size to 320 but keeps the ensemble resolution at T254; and the other increases the ensemble resolution to T670 but retains an 80 ensemble size. When ensemble size increases to 320, turning off the static component of the background‐error covariance does not degrade performance. When the data assimilation parameters are tuned for optimal performance, increasing either ensemble size or ensemble resolution can improve the forecast performance. Increasing ensemble resolution is slightly, but significantly better than increasing ensemble size for these experiments, particularly when considering errors at smaller scales. Much of the benefit of increasing ensemble resolution comes about by eliminating the need for a deterministic control forecast and running all of the background forecasts at the same resolution. In this “single‐resolution” mode, the control forecast is replaced by an ensemble average, which reduces small‐scale errors significantly. Key Points The trade‐offs between ensemble size and ensemble resolution for an ensemble‐variational data assimilation system are evaluated Increasing either ensemble size or ensemble resolution can improve the forecast performance Increasing ensemble resolution is better than increasing ensemble size, particularly when considering errors at smaller scales

To better understand the assimilation contribution and influence mechanism of different satellite platforms and different microwave instruments, the radiance data of Advanced Microwave Sounding Unit-A (AMSU-A) and the Microwave Humidity Sounder (MHS) onboard NOAA-15 and NOAA-18 are assimilated to investigate various assimilation effects on the prediction of path and intensity of Typhoon Megi (2016) based on Weather Research and Forecasting (WRF) three-dimensional variation and the WRF model. The community radiative transfer model is employed as the forward operator. The quality control and bias correction procedures before the radiance data assimilation (DA) are performed to improve the simulations. Impact of AMSU-A and MHS radiances assimilation on Typhoon Megi (2016)’s path and intensity is investigated by six experiments (without and with AMSU-A and MHS DA) with initial conditions at 1200 UTC on 25 September 2016 and 60 h forecast integration. The results are compared to the observational data from the China Meteorological Administration tropical cyclone database. The impact mechanisms of DA adjustments to the initial fields and assimilation increment analysis of each physical quantity field are investigated in detail. The findings show that NOAA-15 AMSU-A assimilation produces the best output over the course of the 60 h simulation, demonstrating that assimilation satellite data from multiple platforms is not always better than assimilation satellite data from a single platform. In comparison, MHS assimilation has a favorable effect on short-term path and strength forecasts, but has a negative impact on long-term forecasts. The effect of MHS DA needs to be further investigated.

Tropical cyclone track is strongly controlled by the large‐scale environmental circulation. In limited‐area models (LAMs) driven by global analyses or forecasts through a conventional lateral boundary nesting approach, the global analyses are often distorted by the use of “sponge zone” or interpolation when they are passed into the LAM. In this study, a dynamical downscaling approach based on scale‐selective data assimilation (SSDA) is applied to a limited‐area numerical weather prediction model with emphasis on tropical cyclone track simulation. The idea of the SSDA approach is to drive the LAM not only from the lateral boundary but also from the model domain interior. The large‐scale flow from global analyses or forecasts is assimilated into the regional model using 3‐D variational data assimilation. The large‐scale features in the LAM are thus constrained to follow the global analyses while allowing the regional model itself to develop the regional and small‐scale characteristics. The results from the case study of Hurricane Katrina (2005) show that both large‐ and small‐scale flows in the regional model benefited from the SSDA approach, leading to an improvement in the accuracy of storm track simulation when provided with an accurate large‐scale circulation from global analyses. In addition, the SSDA procedure is shown to be an effective method to construct a nested‐grid regional modeling system that reduces model sensitivity to model domain geometry and location.

Data assimilation (DA) holds considerable potential for improving hydrologic predictions as demonstrated in numerous research studies. However, advances in hydrologic DA research have not been adequately or timely implemented in operational forecast systems to improve the skill of forecasts for better informed real-world decision making. This is due in part to a lack of mechanisms to properly quantify the uncertainty in observations and forecast models in real-time forecasting situations and to conduct the merging of data and models in a way that is adequately efficient and transparent to operational forecasters. The need for effective DA of useful hydrologic data into the forecast process has become increasingly recognized in recent years. This motivated a hydrologic DA workshop in Delft, the Netherlands in November 2010, which focused on advancing DA in operational hydrologic forecasting and water resources management. As an outcome of the workshop, this paper reviews, in relevant detail, the current status of DA applications in both hydrologic research and operational practices, and discusses the existing or potential hurdles and challenges in transitioning hydrologic DA research into cost-effective operational forecasting tools, as well as the potential pathways and newly emerging opportunities for overcoming these challenges. Several related aspects are discussed, including (1) theoretical or mathematical aspects in DA algorithms, (2) the estimation of different types of uncertainty, (3) new observations and their objective use in hydrologic DA, (4) the use of DA for real-time control of water resources systems, and (5) the development of community-based, generic DA tools for hydrologic applications. It is recommended that cost-effective transition of hydrologic DA from research to operations should be helped by developing community-based, generic modeling and DA tools or frameworks, and through fostering collaborative efforts among hydrologic modellers, DA developers, and operational forecasters.

Estimating spatially distributed hydrological parameters in ungauged catchments poses a challenging regionalization problem and requires imposing spatial constraints given the sparsity of discharge data. A possible approach is to search for a transfer function that quantitatively relates physical descriptors to conceptual model parameters. This paper introduces a Hybrid Data Assimilation and Parameter Regionalization (HDA-PR) approach incorporating learnable regionalization mappings, based on either multi-linear regression or artificial neural networks (ANNs), into a differentiable hydrological model. This approach demonstrates how two differentiable codes can be linked and their gradients chained, enabling the exploitation of heterogeneous data sets across extensive spatio-temporal computational domains within a high-dimensional regionalization context, using accurate adjoint-based gradients. The inverse problem is tackled with a multi-gauge calibration cost function accounting for information from multiple observation sites. HDA-PR was tested on high-resolution, hourly and kilometric regional modeling of 126 flash-flood-prone catchments in the French Mediterranean region. The results highlight a strong regionalization performance of HDA-PR especially in the most challenging upstream-to-downstream extrapolation scenario with ANN, achieving median Nash-Sutcliffe efficiency (NSE) scores from 0.6 to 0.71 for spatial, temporal, spatio-temporal validations, and improving NSE by up to 30% on average compared to the baseline model calibrated with lumped parameters. Multiple evaluation metrics based on flood-oriented hydrological signatures also indicate that the use of an ANN leads to better performances than a multi-linear regression in a validation context. ANN enables to learn a non-linear descriptors-to-parameters mapping which provides better model controllability than a linear mapping for complex calibration cases.

The unprecedented hydraulic visibility of rivers surfaces deformation with SWOT satellite offers tremendous information for improving hydrological‐hydraulic models and discharge estimations for rivers worldwide. However, estimating the uncertain or unknown parameters of hydraulic models, such as inflow discharges, bathymetry, and friction parameters, poses a high‐dimensional inverse problem, which is ill‐posed if based solely on altimetry observations. To address this, we couple the hydraulic model with a semi‐distributed hydrological model, to constrain the ill‐posed inverse problem with sufficiently accurate initial estimates of inflows at the network upstreams. A robust variational data assimilation of water surface elevation (WSE) data into a 1D Saint‐Venant river network model, enables the inference of inflow hydrographs, effective bathymetry, and spatially distributed friction at network scale. The method is demonstrated on the large, complex, and poorly gauged Maroni basin in French Guiana. The pre‐processing chain enables (a) building an effective hydraulic model geometry from drifting ICESat‐2 WSE altimetry and Sentinel‐1 width; (b) filtering noisy SWOT Level 2 WSE data before assimilation. A systematic improvement is achieved in fitting the assimilated WSE (85% cost improvement), and in validating discharge at 5 gauges within the network. For assimilation of SWOT data alone, 70% of data‐model fit is in [−0.25;0.25m] $[-0.25;\\,0.25\\,\\mathrm{m}]$ and the discharge NRMSE ranges between 0.05 and 0.18 (18%–71% improvement from prior). The high density of SWOT WSE enables the inferrence of detailed spatial variability in channel bottom elevation and friction, and inflows timeseries. The approach is transferable to other rivers networks worldwide.

Estimating and modeling background‐error covariances remains a core challenge in variational data assimilation (DA). Operational systems typically approximate these covariances by transformations that separate geostrophically balanced components from unbalanced inertia‐gravity modes—an approach well‐suited for the midlatitudes but less applicable in the tropics, where different physical balances prevail. This study estimates background‐error covariances in a reduced‐dimension latent space learned by a neural‐network autoencoder (AE). The AE was trained using 40 years of ERA5 reanalysis data, enabling it to capture flow‐dependent atmospheric balances from a diverse set of weather states. We demonstrate that performing DA in the latent space yields analysis increments that preserve multivariate horizontal and vertical physical balances in both tropical and midlatitude atmosphere. Assimilating a single 500 hPa geopotential height observation in the midlatitudes produces increments consistent with geostrophic and thermal wind balance, while assimilating a total column water vapor observation with a positive departure in the nearly‐saturated tropical atmosphere generates an increment resembling the tropical response to (latent) heat‐induced perturbations. The resulting increments are localized and flow‐dependent, and shaped by orography and land‐sea contrasts. Forecasts initialized from these analyses exhibit realistic weather evolution, including the excitation of an eastward‐propagating Kelvin wave in the tropics. Finally, we explore the transition from using synthetic ensembles and a climatology‐based background error covariance matrix to an operational ensemble of data assimilations. Despite significant compression‐induced variance loss in some variables, latent‐space assimilation produces balanced, flow‐dependent increments—highlighting its potential for ensemble‐based latent‐space 4D‐Var. Plain Language Summary Accurately estimating the current state of the atmosphere is essential for reliable weather forecasting. This estimate, called the initial condition, is produced through data assimilation (DA)—a process that combines previous short forecast with new observations. An important part of this process involves describing how forecast errors relate across space and between atmospheric variables. This relationship determines how the influence of each new observation is spread in a physically consistent way. Traditional weather models rely on statistical or theoretical assumptions to describe these error relationships. While effective in the midlatitudes, these assumptions often fail in the tropics, where different physical processes dominate. In this study, we explore a new approach that learns a simplified low‐dimensional representation of the atmosphere using a neural network trained on 40 years of reconstructed weather data. We show that performing DA of new observations in this learned “latent space” produces realistic updates that respect known atmospheric balances both in the tropics and midlatitudes and adapt to the current weather situation. It also works with forecast ensembles used in operational weather centers. These results suggest that DA in latent space could offer a more flexible and efficient way to improve weather forecasts. Key Points The background‐error covariances in a machine learning‐based variational data assimilation framework are studied The method captures both tropical and midlatitude atmospheric balances in the background‐error covariance model The approach works with both climatological and ensemble‐based background‐error covariance matrices

A global Four‐Dimensional Ensemble Variational (4DEnVar) data assimilation system for the Atmospheric component of the Model for Prediction Across Scales (MPAS‐A) is presented that uses the Joint Effort for Data assimilation Integration (JEDI). Dual‐resolution cycling experiments with a 30 km analysis but an ensemble run at a coarser (60 km) resolution are shown to perform well, thereby reducing the computational cost. Month long global cycling data assimilation experiments show that 4DEnVar updates have lower mean errors in both observation and model space than comparable 3DEnVar experiments. Additional improvements over 4DEnVar are then demonstrated when using Hybrid‐4DEnVar, which leverages the benefits of both flow‐dependent ensemble covariance and a static climatological covariance, and when assimilating all‐sky Advanced Microwave Sounding Unit‐A (AMSU‐A) radiance observations. Lastly, extended forecasts initialized from the four‐dimensional analyses are compared with forecasts initialized from three‐dimensional analyses. A particular focus is on the prediction of clouds and precipitation in forecasts initialized from Hybrid‐4DEnVar versus Hybrid‐3DEnVar analyses. Results from extended forecasts show that both forecasts of traditional meteorological fields and precipitation are improved through use of Hybrid‐4DEnVar. However, improvements in precipitation forecasts from 4D methods are shown to be most significant in the southern hemisphere, consistent with where the largest improvements in other meteorological fields are found. Significant improvements in precipitation forecasts in the tropics are found in both 3D and 4D experiments assimilating all‐sky AMSU‐A radiance observations. In summary, 4DEnVar and Hybrid‐4DEnVar capabilities are available through MPAS‐JEDI—an open‐source community developed tool—and perform well during continuous global cycling experiments across traditional verification metrics. Plain Language Summary Weather forecasts rely on combining real‐world observations with computer weather models to get the most accurate starting point for predictions—a process known as data assimilation. One such model, the Atmospheric component of the Model for Prediction Across Scales (MPAS‐A), is a widely used community‐based model for global and regional weather modeling. In this study, we introduce a new tool for improving predictions with MPAS‐A using advanced four‐dimensional data assimilation methods. These methods better account for the timing of observations, leading to a more accurate starting point for predictions. These methods are implemented within the Joint Effort for Data assimilation Integration framework, a flexible, community‐based data assimilation framework designed to work with different weather models and assimilation methodologies. Through a series of month‐long global experiments, we show these new methods outperform previous approaches. In particular, the new methods led to more accurate forecasts—especially for rainfall—and better agreement between the model and real‐world data. Key Points Global four‐dimensional hybrid‐ensemble data assimilation approaches are available and presented for the Model for Prediction Across Scales Four‐dimensional data assimilation improves upon previous benchmark experiments using three‐dimensional methods, including for rainfall forecasts Assimilation of cloudy radiances with four‐dimensional methods improves the short‐term prediction of precipitation