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In November 2021, the Royal Meteorological Society Data Assimilation (DA) Special Interest Group and the University of Reading hosted a virtual meeting on the topic of DA for convection‐permitting numerical weather prediction. The goal of the meeting was to discuss recent developments and review the challenges including methodological developments and progress in making the best use of observations. The meeting took place over two half days on the 10 and 12 November, and consisted of six talks and a panel discussion. The scientific presentations highlighted some recent work from Europe and the USA on convection‐permitting DA including novel developments in the assimilation of observations such as cloud‐affected satellite radiances in visible channels, ground‐based profiling networks, aircraft data, and radar reflectivity data, as well as methodological advancements in background and observation error covariance modelling and progress in operational systems. The panel discussion focused on key future challenges including the handling of multiscales (synoptic‐, meso‐, and convective‐scales), ensemble design, the specification of background and observation error covariances, and better use of observations. These will be critical issues to address in order to improve short‐range forecasts and nowcasts of hazardous weather. We report on a meeting on progress and challenges in convection‐permitting data assimilation. Novel developments include the assimilation of novel observations such as cloud‐affected satellite radiances, ground‐based profiling networks and aircraft data, as well as methodological advancements in error covariance modelling, and progress in operational systems. Key future challenges include the handling of multiple scales, the design of ensembles and observation networks: these will be critical issues for short‐range forecasts and nowcasts of hazardous weather.

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.

The ionosphere's dynamic structure affects electromagnetic radiation by altering radio wave propagation, impacting daily communications. The characteristics of the ionosphere are primarily characterized by electron density parameters. This paper proposes a method to construct Three‐Dimensional (3‐D) electron density distributions with arbitrary spatiotemporal resolution in ISR observational regions. The method, termed Artificial Intelligence‐based data assimilation (AI‐Assim), integrates data assimilation directly into a neural network. It assimilates electron density from the IRI‐2020 model to fill ISR observation gaps. Experiments conducted using the Sanya Incoherent Scatter Radar (SYISR) in Hainan, China, successfully constructed a 3‐D electron density structure over the region, with a 0.2° latitude/longitude resolution and 1 km height resolution. The method's effectiveness was validated by calculating the mean square error and comparing the results with digisonde measurements. Plain Language Summary This study leverages the most powerful ionospheric observation tool, the ISR, to construct 3‐D electron density distributions with arbitrary spatial resolution. Relying solely on empirical models often leads to accuracy issues, while 3‐D electron density models based purely on observational methods typically suffer from low resolution. All observational methods encounter difficulties in achieving continuous, high spatial resolution monitoring of the entire sky, and ISR is one of the most effective techniques available. However, even with interpolation methods, the coverage area of ISR remains limited. Therefore, this study explores a method that uses the neural network to assimilate electron density values from the IRI‐2020 model, aiming to fill the gaps in ISR detection. By assimilating International Reference Ionosphere values to approximate observed values, the accuracy of the 3‐D electron density results is enhanced. Multiple iterations of AI‐ Assim enable the construction of 3‐D electron density distributions with arbitrary spatial resolution. Key Points We developed a method for constructing 3‐D electron density distributions with arbitrary spatiotemporal resolution at ISR stations The method termed AI‐Assim, continuously assimilating electron density from the IRI‐2020 model to fill ISR observation gaps Experiments using SYISR data achieved a 3‐D electron density model with 0.2° map resolution and 1 km height resolution

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

Total 550 nm aerosol optical depth (AOD) retrievals from Moderate Resolution Imaging Spectroradiometer (MODIS) sensors and surface fine particulate matter (PM2.5) observations were assimilated with the National Centers for Environmental Prediction (NCEP) Gridpoint Statistical Interpolation (GSI) three‐dimensional variational (3DVAR) data assimilation (DA) system. Parallel experiments assimilated AOD and surface PM2.5observations both individually and simultaneously. New 3DVAR aerosol analyses were produced every 6 h between 0000 UTC 01 June and 1800 UTC 14 July 2010 over a domain encompassing the continental United States. The analyses initialized Weather Research and Forecasting‐Chemistry (WRF‐Chem) model forecasts. Assimilating AOD, either alone or in conjunction with PM2.5 observations, produced better AOD forecasts than a control experiment that did not perform DA. Additionally, individual assimilation of both AOD and PM2.5 improved surface PM2.5 forecasts compared to when no DA occurred. However, the best PM2.5 forecasts were produced when both AOD and PM2.5 were assimilated. Considering the goodness of both AOD and PM2.5 forecasts, the results unequivocally show that concurrent DA of PM2.5 and AOD observations produced the best overall forecasts, illustrating how simultaneous DA of different aerosol observations can work synergistically to improve aerosol forecasts. Key Points Simultaneous 3DVAR data assimilation of MODIS AOD and surface PM2.5 observations Aerosol data assimilation substantially improves aerosol forecasts Forecasts are best when both AOD and surface PM2.5 are assimilated concurrently

Recent studies have started to explore coupled data assimilation (CDA) in coupled ocean–atmosphere models because of the great potential of CDA to improve climate analysis and seamless weather–climate prediction on weekly-to-decadal time scales in advanced high-resolution coupled models. In this review article, we briefly introduce the concept of CDA before outlining its potential for producing balanced and coherent weather–climate reanalysis and minimizing initial coupling shocks. We then describe approaches to the implementation of CDA and review progress in the development of various CDA methods, notably weakly and strongly coupled data assimilation. We introduce the method of coupled model parameter estimation (PE) within the CDA framework and summarize recent progress. After summarizing the current status of the research and applications of CDA-PE, we discuss the challenges and opportunities in high-resolution CDA-PE and nonlinear CDA-PE methods. Finally, potential solutions are laid out.

In this paper, the latest progress, major achievements and future plans of Chinese meteorological satellites and the core data processing techniques are discussed. First, the latest three FengYun (FY) meteorological satellites (FY-2H, FY-3D, and FY-4A) and their primary objectives are introduced. Second, the core image navigation techniques and accuracies of the FY meteorological satellites are elaborated, including the latest geostationary (FY-2/4) and polar-orbit (FY-3) satellites. Third, the radiometric calibration techniques and accuracies of reflective solar bands, thermal infrared bands, and passive microwave bands for FY meteorological satellites are discussed. It also illustrates the latest progress of real-time calibration with the onboard calibration system and validation with different methods, including the vicarious China radiance calibration site calibration, pseudo invariant calibration site calibration, deep convective clouds calibration, and lunar calibration. Fourth, recent progress of meteorological satellite data assimilation applications and quantitative science produce are summarized at length. The main progress is in meteorological satellite data assimilation by using microwave and hyper-spectral infrared sensors in global and regional numerical weather prediction models. Lastly, the latest progress in radiative transfer, absorption and scattering calculations for satellite remote sensing is summarized, and some important research using a new radiative transfer model are illustrated.

Inflation of ensemble perturbations is employed in ensemble Kalman filters to account for unrepresented error sources. The authors propose a multiplicative inflation algorithm that inflates the posterior ensemble in proportion to the amount that observations reduce the ensemble spread, resulting in more inflation in regions of dense observations. This is justified since the posterior ensemble variance is more affected by sampling errors in these regions. The algorithm is similar to the “relaxation to prior” algorithm proposed by Zhang et al., but it relaxes the posterior ensemble spread back to the prior instead of the posterior ensemble perturbations. The new inflation algorithm is compared to the method of Zhang et al. and simple constant covariance inflation using a two-level primitive equation model in an environment that includes model error. The new method performs somewhat better, although the method of Zhang et al. produces more balanced analyses whose ensemble spread grows faster. Combining the new multiplicative inflation algorithm with additive inflation is found to be superior to either of the methods used separately. Tests with large and small ensembles, with and without model error, suggest that multiplicative inflation is better suited to account for unrepresented observation-network-dependent assimilation errors such as sampling error, while model errors, which do not depend on the observing network, are better treated by additive inflation. A combination of additive and multiplicative inflation can provide a baseline for evaluating more sophisticated stochastic treatments of unrepresented background errors. This is demonstrated by comparing the performance of a stochastic kinetic energy backscatter scheme with additive inflation as a parameterization of model error.

Strongly coupled data assimilation (SCDA) views the Earth as one unified system. This allows observations to have an instantaneous impact across boundaries such as the air‐sea interface when estimating the state of each individual component. Operational prediction centers are moving toward Earth system modeling for all forecast timescales, ranging from days to months. However, there have been few studies that examine fundamental aspects of SCDA and the transition from traditional approaches that apply data assimilation only to a single component, whether forecasts were derived from a coupled model or an uncoupled forced model. The SCDA approach is examined here in detail using numerical experiments with a simple coupled atmosphere‐ocean quasi‐geostrophic model. The impact of coupling is explored with respect to its impact on the Lyapunov spectrum and on data assimilation system stability. Different data assimilation methods are compared within the context of SCDA, including the 3‐D and 4‐D Variational methods, the ensemble Kalman filter, and the hybrid gain method. The impact of observing system coverage is also investigated. We find that SCDA is generally superior to weakly coupled or uncoupled approaches. Dynamically defined background error covariance estimates are essential for SCDA to achieve an accurate coupled state estimate as the observing system becomes sparser. As a clarification of seemingly contradictory findings from previous studies, it is shown that ocean observations can adequately constrain atmospheric state estimates provided that the analysis‐observing frequency is sufficiently high and the ensemble size determining the background error covariance is sufficiently large. Plain Language Summary To make accurate predictions of weather and climate, scientists develop complex computer models of the Earth that couple smaller models of the atmosphere, oceans, land, etc. Measurements from satellites, ground stations, and ocean buoys are limited, so these give an incomplete picture. Forecasters combine past predictions with new observations to make an informed guess about what the entire Earth looks like at any instant. This guess is used to initialize computer model forecasts. However, since the atmosphere is a chaotic system, small inaccuracies in this initial guess can lead to wildly diverging forecasts further out in time. This study investigates a new method for initializing the Earth models. In the past, physical inconsistencies between the atmosphere and ocean arose because each was initialized independently. We use atmospheric observations to improve our best guess of the ocean conditions, and vice versa, to improve this consistency. This may improve daily weather forecasts and seasonal guidance when adopted by operational weather prediction centers. Given the growing urgency to respond to near‐term climate change risks, improved methods to initialize Earth system models provide the potential to generate accurately initialized climate predictions that can better anticipate the coming changes over the next decade. Key Points Strongly coupled data assimilation produces more accurate state estimates and forecasts than traditional approaches to data assimilation Dynamic background error covariance estimates are essential for strongly coupled data assimilation, especially with limited observations Ocean observations can constrain the atmosphere, provided that the analysis‐observing frequency and the ensemble size are sufficiently high

Nonlinear variable interactions are essential for the development and evolution of extreme events. However, the conventional assimilation approaches, such as the ensemble Kalman filter (EnKF), tend to underestimate extreme events due to their inability to capture these nonlinear coupling features, given their reliance on linear background error covariance estimation. In this study, a nonlinear and machine learning‐based assimilation method is proposed to address this limitation and improve the quality of analysis ensemble for extreme events. This data‐driven approach effectively characterizes the time‐variant and complex multivariate relationships, thereby nonlinearly projecting the innovation onto the ensemble subspace. This significant improvement enables the ML‐based approach to increase the analysis accuracy for extreme phenomena by up to 66% over EnKF, and its ensemble increment distribution is well‐aligned with that of the target increments, showing the potential of data‐driven assimilation approach for advancing the capabilities of capturing and triggering the extreme events.