Four-dimensional Variational Data Assimilation Research Articles

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.

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.

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.

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.

Hybrid IFDMB/4D-Var inverse modeling to constrain the spatiotemporal distribution of CO and NO2 emissions using the CMAQ adjoint model

We performed a hybrid approach that combines the iterative finite difference mass balance (IFDMB) and four-dimensional variational data assimilation (4D-Var) methods to effectively constrain the spatiotemporal distribution of emissions. To quantitatively compare the performance of inverse modeling in constraining CO and NO2 emissions in South Korea spatiotemporally, we conducted a model-based twin experiment for three inverse modeling methods: IFDMB, 4D-Var, and hybrid inversions. We performed numerical modeling using the Community Multi-scale Air Quality (CMAQ) and its adjoints to calculate the values required for inverse modeling. As a result, the IFDMB inversion can effectively constrain the average spatial distribution of emissions. Meanwhile, the 4D-Var inversion can help estimate temporal variations in emissions, but it is not effective in regions with large prior emission errors. The hybrid inversion showed the best performance in constraining the spatiotemporal distribution of emissions because it combined the strengths of the two aforementioned methods. Furthermore, to compare the performance of the inverse modeling of pollutants with different chemical properties, we conducted additional inverse modeling for highly reactive NO2. After the application of inverse modeling, the emission errors of NO2 (18.339%) were larger than those of CO (10.593%). This difference in inverse modeling errors was due to the greater nonlinear relationship between emissions and concentrations in the inverse modeling process for NO2, which is more reactive compared to CO. In this study, the ideal modeling tests were performed to quantitatively assess the performance of inverse modeling. In future studies, we expect to apply the hybrid inversion approach used in this study to inverse modeling using actual observations.

Large-eddy simulation-based reconstruction of turbulence in a neutral boundary layer using spectral-tensor regularization

We propose an efficient method to reconstruct the turbulent flow field in a neutrally stratified atmospheric boundary layer using large-eddy simulation (LES) and a series of lidar measurements. The reconstruction is formulated as a strong four-dimensional variational data assimilation problem, which involves optimizing two competing terms that contribute in the objective functional. The first term is a likelihood term, while the second contains the initial background distribution of turbulent velocity fluctuations and works as a regularization term. However, computing and storing the full background covariance tensor in turbulent flows is time consuming and resource intensive. In the current work, we investigate the possibility of replacing the complex background tensor by simple analytical approximations based on spectral tensors such as the Hunt–Graham–Wilson (HGW) model (Boundary-Layer Meteorol., vol. 85, 1997, pp. 35–52) or the Mann model (J. Fluid Mech., vol. 273, 1994, pp. 141–168). Afterwards, the problem is solved using a quasi-Newton algorithm and preconditioned to enhance the convergence rate. We test the method using virtual lidar measurements collected on a fine reference LES. Results show a super-linear convergence rate of the optimization algorithm to a local minimum and very good agreement between virtual lidar measurements and reconstruction in the scanning region. Furthermore, we demonstrate that incorporating the Saffman energy spectrum ( $E(k) \sim k^2$ where E is the energy spectrum and k is the magnitude of the wavenumber vector) at low wavenumbers into the Mann spectral tensor yields a longer streamwise correlation length, resulting in reduced reconstruction error when compared with the Batchelor spectrum ( $E(k) \sim k^4$ ). Finally, we observe that using the HGW model or Mann model with a Saffman spectrum yields similar results.

Enhancing the Assimilation of SWOT Simulated Observations Using a Multi-Scale 4DVAR Method in Regional Ocean Modeling System

This paper presents an innovative approach to enhance the assimilation of high-resolution simulated observations, specifically targeting Surface Water Ocean Topography (SWOT) Ka-band Radar Interferometer Sea Surface Height (SSH) products, within the Regional Ocean Modeling System (ROMS). Responding to the demand for improved assimilation techniques, we developed a multi-scale Four-Dimensional Variational Data Assimilation (4DVAR) system, building upon validated fine-scale correction capabilities from prior studies. The multi-scale strategy was extended to the ROMS-4DVAR system, providing a comprehensive solution for assimilating high-resolution observations. Leveraging the Observing System Simulation Experiment (OSSE) framework, we conducted a twin experiment comprising a nature run and a free run case. Subsequently, synthetic SWOT SSH measurements were decomposed, considering the model configuration resolution. These components, derived from dense SSH observations, were integrated into a two-step 4DVAR assimilation scheme. The first cycle targets large-scale features for model field correction, and the updated analysis serves as the background for the second assimilation step, addressing fine-scale observation components. Comparisons with the primitive ROMS-4DVAR using a single-scale scheme highlight the superiority of the multi-scale strategy in reducing gaps between the model and the SSH observations. The Root Mean Squared Error (RMSE) is halved, and the Mean Absolute Percentage Error (MAPE) decreases from 2.237% to 0.93%. The two-step assimilation procedure ensures comprehensive multi-scale updates in the SSH field simulation, enhancing fine-scale features in the analysis fields. The quantification of three-dimensional-model dynamic fields further validates the efficiency and superiority of the multi-scale 4DVAR approach, offering a robust methodology for assimilating high-resolution observations within the ROMS.

Comparison of Cold Pool Characteristics of Two Distinct Gust Fronts over Bohai Sea Bay in China

Previous studies have demonstrated that cold pools play a pivotal role in the initiation and organization of convection, yet their influence on the evolution of gust fronts (GFs) remains inadequately understood. A destructive wind event associated with a rearward gust front (RGF; 8 grade gale after passing GF) and a prior gust front (PGF; 10 grade gale before passing GF) over the north coast of China on 10 June 2016 was analyzed. Using multiple forms of observation data, as well as the four-dimensional Variational Doppler Radar Data Assimilation System (VDRAS), we found that the depth and intensity of the cold pool in RGF are relatively shallower and weaker, leading to a correspondingly reduced strength in both outflow and convergence. In contrast, the enhanced vertical shear and boundary northeaster inflow of PGF generate intensified and more organized downdrafts, resulting in a deeper cold pool, robust outflow, and convergence. Two schematic models were proposed to explain the discrepancy between GFs and associated cold pools. We further show that there is an internal correlation between meso-γ-scale vortices (MVs) and cold pools, the collision of MVs strengthened low-level convergence and updraft between these two GFs. Moreover, the consolidation of the two cold pools exacerbates low-layer instability and rotation, generating an intense horizontal vorticity that leads to rapid convective storm intensification. These findings offer novel insights into the diversity of GFs and associated cold pools.

Four-dimensional variational data assimilation of a turbulent jet for super-temporal-resolution reconstruction

The super-temporal-resolution (STR) reconstruction of turbulent flows is an important data augmentation application for increasing the data reach in measurement techniques and understanding turbulence dynamics. This paper proposes a data assimilation (DA) strategy based on weak-constraint four-dimensional variation to conduct an STR reconstruction in a turbulent jet beyond the Nyquist limit from given low-sampling-rate observations. Highly resolved large-eddy simulation (LES) data are used to produce synthetic measurements, which are used as observations and for validation. A segregated assimilation procedure is realised to assimilate the initial condition, inflow boundary condition and model error separately. Different types of observational data are tested. The first type is down-sampled LES data containing many small-scale turbulence structures with or without synthetic noise. The DA results show that the temporal variation of the small-scale structures is well recovered even with noise in the observations. The spectra are resolved to a frequency approximately one order of magnitude higher than what can be captured within the Nyquist limit. The second type of observation is low-sampling-rate tomographic particle image velocimetry (tomo-PIV) data with or without the injection of small-scale structures. The modulation between the large-scale structures contained in the tomo-PIV fields and the small scales injected from the observations is improved. The resultant small scales in the STR reconstruction have the characteristics of authentic turbulence to a considerable extent. Additionally, DA yields much smaller errors in the prediction of particle positions when compared with the Wiener filter, demonstrating the great potential for Lagrangian particle tracking in measurement techniques.

Adjoint-based data assimilation for reconstruction of thermal convection in a highly viscous fluid from surface velocity and temperature snapshots

SUMMARY It is a general problem in geoscience to estimate the time-series of velocity and temperature fields for a fluid based on limited observations, such as the flow velocity at the fluid surface and/or a temperature snapshot after flow. In this study, an adjoint-based data assimilation method (also known as 4-D variational data assimilation) was used to reconstruct the thermal convection in a highly viscous fluid (e.g. Earth’s mantle) to investigate which observations constrain the thermal convection and how accurately the convection can be reconstructed for different wavelengths. The data assimilated to the adjoint-based model were generated synthetically from forward models with convecting cells of different length-scales. Based on the surface velocity and temperature snapshot, our simulations successfully reconstructed thermal convection over 50 Myr in the case that the wavelength of the convective cells is sufficiently large. We obtained two main results from this parametric study. (1) When we only considered instantaneous thermal structure fitting in the cost function, the convection reconstruction tended to fail. However, there are some cases where the laminar thermal convection can be reconstructed by assimilating only the velocity along the fluid surface. (2) There is a limit to the reconstruction of thermal convection in the case that the convecting cells are small (∼1000 km for a 50 Myr reconstruction). We propose that (1) is related to the balance of forces due to the thermal buoyancy and viscous stress around the thermal anomalies and (2) is related to how information is preserved (i.e. how the previous thermal structure is maintained in the observable state throughout the convection process). The results enable the use of geological records to estimate time-series of velocity and temperature in Earth’s deep interior, even though the records may only contain information from shallow parts of Earth.

Time-Limited Balanced Truncation for Data Assimilation Problems

Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced truncation has been drawn (Qian et al in Sci Comput 91:29, 2022). Although this connection is new, the application of balanced truncation to data assimilation is not a novel idea: it has already been used in four-dimensional variational data assimilation (4D-Var). This paper discusses the application of balanced truncation to linear Gaussian Bayesian inference, and, in particular, the 4D-Var method, thereby strengthening the link between systems theory and data assimilation further. Similarities between both types of data assimilation problems enable a generalisation of the state-of-the-art approach to the use of arbitrary prior covariances as reachability Gramians. Furthermore, we propose an enhanced approach using time-limited balanced truncation that allows to balance Bayesian inference for unstable systems and in addition improves the numerical results for short observation periods.

Evaluating Alternate Methods of 4D-Var Data Assimilation in a Coupled Hydrodynamic—Four-Component Biogeochemical Model of the California Current System

Assimilating biogeochemical (BGC) data into ocean models using traditional four-dimensional variational data assimilation (4D-Var) includes the technical challenge of constructing tangent-linear (TLM) and adjoint (ADJ) models corresponding to the non-linear BGC model. This hurdle can be time-consuming, particularly for non-linear BGC models experiencing active development, with regular updates to functional types or representation of key BGC processes. We evaluate two alternate approaches that greatly simplify TLM and ADJ construction and eliminate the need for code updates when the underlying, non-linear BGC model changes. One form of model-reduced data assimilation represents BGC interactions as a linear combination of orthogonal modes; we use empirical orthogonal functions and refer to this as the BioEOFs method. The second approach treats BGC variables as passive tracers that experience advection and diffusion by TLM and ADJ physics over an assimilation cycle, but are biochemically inactive. We evaluate the efficacy of these methods in a realistically configured, data-assimilative implementation of the Regional Ocean Modeling System with a simple nutrient–phytoplankton–zooplankton–detritus (NPZD) BGC model for the U.S. west coast. In a series of sequential data-assimilative model cycles, observations of temperature, salinity, sea-level anomaly, and phytoplankton biomass constrain the modeled state over the period spanning January–June 2019. We perform the assimilation in both physical and logarithmic-transformed space and compare results of the two approximate methods to traditional 4D-Var using TLM and ADJ models with BGC processes corresponding explicitly to the BGC model. While the full-adjoint 4D-Var results in the best correction to phytoplankton fields for analyses and forecasts, the BioEOFs and passive-tracer approaches also significantly reduce the model-observation misfit compared to a non-assimilative run and do so at reduced computational expense. The passive tracer performs generally better than BioEOFs, whose corrections exhibit large-scale structure across the domain. While the most accurate state estimate will result from development and application of the full TLM and ADJ, the log-transformed passive-tracer approach may be a viable alternative for performing BGC 4D-Var for state estimation when a full-adjoint option is not yet available.

Mesoscale Factors Contributing to the Extreme Rainstorm on 20 July 2021 in Zhengzhou, China, as Revealed by Rapid Update 4DVar Analysis

Abstract The purpose of this study is to diagnose mesoscale factors responsible for the formation and development of an extreme rainstorm that occurred on 20 July 2021 in Zhengzhou, China. The rainstorm produced 201.9 mm of rainfall in 1 h, breaking the record of mainland China for 1-h rainfall accumulation in the past 73 years. Using 2-km continuously cycled analyses with 6-min updates that were produced by assimilating observations from radar and dense surface networks with a four-dimensional variational (4DVar) data assimilation system, we illustrate that the modification of environmental easterlies by three mesoscale disturbances played a critical role in the development of the rainstorm. Among the three systems, a mesobeta-scale low pressure system (mesolow) that developed from an inverted trough southwest of Zhengzhou was key to the formation and intensification of the rainstorm. We show that the rainstorm formed via sequential merging of three convective cells, which initiated along the convergence bands in the mesolow. Further, we present evidence to suggest that the mesolow and two terrain-influenced flows near the Taihang Mountains north of Zhengzhou, including a barrier jet and a downslope flow, contributed to the local intensification of the rainstorm and the intense 1-h rainfall. The three mesoscale features coexisted near Zhengzhou in the several hours before the extreme 1-h rainfall and enhanced local wind convergence and moisture transport synergistically. Our analysis also indicated that the strong midlevel south/southwesterly winds from the mesolow along with the gravity-current-modified low-level northeasterly barrier jet enhanced the vertical wind shear, which provided favorable local environment supporting the severe rainstorm.

A Multiscale Four-Dimensional Variational Data Assimilation Scheme: A Squall-Line Case Study

Abstract This study presents a multiscale four-dimensional variational data assimilation (MS-4DVar) scheme that aims to assimilate multiscale information from conventional and radar observations. The MS-4DVar scheme separately assimilates conventional and radar data in different outer loop iterations of an incremental 4DVar with varied resolutions in the tangent linear and adjoint models (TLM/ADM) and time window lengths in the 4DVar. The MS-4DVar scheme was evaluated through a series of single observation tests and several cycled assimilation and forecasting experiments for a real squall-line case. Our results indicated that different TLM/ADM resolutions and time window lengths applied to the conventional and radar observations improved the multiscale analysis. In addition, the MS-4DVar scheme was more efficient than the common 4DVar because of the low-resolution TLM/ADM used for conventional data and the shortened time window length for radar data. Verification of the squall-line forecasts suggested that the MS-4DVar scheme improved the hourly accumulated precipitation and radar reflectivity forecast skills and reduced the forecast errors of both large-scale environmental and convective-scale states. Further diagnosis revealed that the improvement of precipitation forecast skill was attributable to the stronger cold pool, deeper saturated water vapor layer, and stronger updraft of the simulated squall-line system, as well as a more favorable convective environment.

Assimilating AMSU-A Radiance Observations with an Ensemble Four-Dimensional Variational (En4DVar) Hybrid Data Assimilation System

Many ensemble-based data assimilation (DA) methods use observation space localization to mitigate the sampling errors due to the insufficient ensemble members. Observation space localization is simpler and more timesaving than model space localization in implementation, but more difficult to directly assimilate satellite radiance observations, a kind of non-local observations. The vertical locations of radiance observations are undetermined and the transmission of observational information is thereby obstructed. To determine the vertical coordinates of radiance observations, a weighted average hypsometry is proposed. Using this hypsometry, AMSU-A radiance observations are directly assimilated with an ensemble four-dimensional variational (En4DVar) DA system. It consists of a four-dimensional ensemble-variational (4DEnVar) system providing ensemble covariance and a 4DVar system. Observing system simulation experiments show that the hypsometry alleviates the degradations in the late period of medium-range forecast in the Northern Extratropics that occur in the traditional peak-based hypsometry. It obviously improves the analysis qualities and forecast skills of the En4DVar system and its two components, especially in the Southern Extratropics, when incorporating AMSU-A radiance observations. The improvement in the En4DVar-initialized forecast is comparable to that in the 4DVar-initialized forecast in the Southern Extratropics and Tropics. It indicates that a proper hypsometry enables efficient extraction of useful information from AMSU-A radiance observations by 4DEnVar with observation space localization. Therefore, the 4DEnVar provides high-quality ensemble covariances for En4DVar.

Four-Dimensional Variational Data Assimilation and Sensitivity of Ocean Model State Variables to Observation Errors

The use of Four-Dimensional variational (4D-Var) data assimilation technology in the context of sea dynamics problems, with a sensitivity analysis of model results to observation errors, is presented. The technology is applied to a numerical model of ocean circulation developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), with the use of the splitting method and complemented by 4D-Var data assimilation with covariance matrices of background and observation errors. The variational data assimilation involves iterative procedures to solve inverse problems so as to correct sea surface heat fluxes for the model under consideration. An algorithm is formulated to study the sensitivity of the model outputs, considered as output functions after assimilation, to the observation errors. The algorithm reveals the regions where the output function gradient is the largest for the average sea surface temperature (SST) in a selected area, obtained by assimilation. In the numerical experiments, a 4D variational problem of SST assimilation for the Baltic Sea area is solved.

Construction and Application of a Regional Kilometer-Scale Carbon Source and Sink Assimilation Inversion System (CCMVS-R)

CO2 is one of the most important greenhouse gases (GHGs) in the earth’s atmosphere. Since the industrial era, anthropogenic activities have emitted excessive quantities of GHGs into the atmosphere, resulting in climate warming since the 1950s and leading to an increased frequency of extreme weather and climate events. In 2020, China committed to striving for carbon neutrality by 2060. This commitment and China’s consequent actions will result in significant changes in global and regional anthropogenic carbon emissions and therefore require timely, comprehensive, and objective monitoring and verification support (MVS) systems. The MVS approach relies on the top-down assimilation and inversion of atmospheric CO2 concentrations, as recommended by the Intergovernmental Panel on Climate Change (IPCC) Inventory Guidelines in 2019. However, the regional high-resolution assimilation and inversion method is still in its initial stage of development. Here, we have constructed an inverse system for carbon sources and sinks at the kilometer level by coupling proper orthogonal decomposition (POD) with four-dimensional variational (4DVar) data assimilation based on the weather research and forecasting–greenhouse gas (WRF-GHG) model. Our China Carbon Monitoring and Verification Support at the Regional level (CCMVS-R) system can continuously assimilate information on atmospheric CO2 and other related information and realize the inversion of regional and local anthropogenic carbon emissions and natural terrestrial ecosystem carbon exchange. Atmospheric CO2 data were collected from six ground-based monitoring sites in Shanxi Province, China to verify the inversion effect of regional anthropogenic carbon emissions by setting ideal and real experiments using a two-layer nesting method (at 27 and 9 km). The uncertainty of the simulated atmospheric CO2 decreased significantly, with a root-mean-square error of CO2 concentration values between the ideal value and the simulated after assimilation was close to 0. The total anthropogenic carbon emissions in Shanxi Province in 2019 from the assimilated inversions were approximately 28.6% (17%–38%) higher than the mean of five emission inventories using the bottom-up method, showing that the top-down CCMVS-R system can obtain more comprehensive information on anthropogenic carbon emissions.

Combined assimilation of hourly rainfall data and every 10-min AHI radiance with WRF 4DVar for the short-range heavy rainfall forecast in Eastern China

Rainfall observations and geostationary satellite water vapor radiances account for complementary humidity information over rainy areas and large-scale environments, respectively. This study investigates the simultaneous assimilation of China Hourly Merged Precipitation Analysis (CHMPA) data and clear-sky water vapor radiances provided by the Himawari-8 Advanced Himawari Imager (AHI) with Four-Dimensional Variational (4DVar) data assimilation method using Weather Research and Forecasting (WRF) model with an hourly rapid-update cycling data assimilation configuration. The rapid-update 4DVar assimilation is configured as 10-min interval for AHI radiances and 1-h interval for CHMPA rainfall data in a same 1-h assimilation time window. Generally positive impacts from assimilating CHMPA rainfall and AHI water vapor radiance observations are achieved for the 12-h short-term precipitation forecast. Error reductions are found after assimilating CHMPA rainfall and AHI water vapor radiance observations for both analyses and forecasts when compared to ERA5 reanalysis. It is found that combined assimilation of CHMPA rainfall and AHI water vapor radiance data has clearly positive impacts on heavy rainfall forecasts. A heavy rainfall case that occurred in Jiangsu Province on 28 June 2020 is examined in details. The combined assimilation of infrared radiances from AHI water vapor channels together with CHMPA rainfall data improves the vertical and horizontal transport of humidity conditions, which better adjusts the humidity distribution. The over-estimation of rainfall forecast caused by the assimilation of CHMPA is alleviated. This result can provide reference for quantitative precipitation forecasts of regional numerical weather model.

Unsteady flow enhancement on an airfoil using sliding window weak-constraint four-dimensional variational data assimilation

This study establishes a continuous sliding window weak-constraint four-dimensional variational approach for reproducing a complete instantaneous flow from sparse spatiotemporal velocity observations. The initial condition, boundary condition, and model-form uncertainties are corrected simultaneously by a spatiotemporally varying additive forcing, coupled with the large eddy simulation (LES) framework, which reinforces subgrid-scale viscosity stresses and simplifies gradient computation. The additive force undergoes a Stokes–Helmholtz decomposition to ensure divergence-free projection and natural pressure determination. The model is theoretically derived to minimize discrepancies between the sparse velocity observations and the numerical predictions of the primary-adjoint system, enabling optimal contribution of the additive force. Synthetic data from a fine-grid LES of the vortical flow over an NACA0012 airfoil are used as observations. The algorithm is evaluated on a benchmark case, where observations are subsampled at 1/400 000 spatiotemporal resolution required for an LES. The sliding window strategy expands the dependence domain of the observations and mitigates the impact of primary-adjoint chaos, achieving over 90% pointwise correlation for filtered parameters and 80% spectral correlation for all of the resolved wavenumbers. Despite the lack of near-wall observations, streaks are accurately recovered due to the convective sensitivity of the observations from the outer flow. While the pressure fluctuation in the inflow region is not as well excited as in LES, recovery is augmented downstream. In both the inner and outer wall layers, the pressure distributions are obtained reasonably well by capturing the signatures of the vortical structure and their downstream convection. The robustness of the algorithm to observation noise is demonstrated. Finally, the impact of temporal resolution on estimation is evaluated, establishing a resolution threshold for successful reconstruction.

Stein-based preconditioners for weak-constraint 4D-var

Algorithms for data assimilation try to predict the most likely state of a dynamical system by combining information from observations and prior models. Variational approaches, such as the weak-constraint four-dimensional variational data assimilation formulation considered in this problem, can ultimately be interpreted as a minimization problem. One of the main challenges of such a formulation is the solution of large linear systems of equations which arise within the inner linear step of the adopted nonlinear solver. Depending on the adopted approach, these linear algebraic problems amount to either a saddle point linear system or a symmetric positive definite (SPD) one. Both formulations can be solved by means of a Krylov method, like GMRES or CG, that needs to be preconditioned to ensure fast convergence in terms of the number of iterations. In this paper we illustrate novel, efficient preconditioning operators which involve the solution of certain Stein matrix equations. In addition to achieving better computational performance, the latter machinery allows us to derive tighter bounds for the eigenvalue distribution of the preconditioned linear system for certain problem settings. A panel of diverse numerical results displays the effectiveness of the proposed methodology compared to current state-of-the-art approaches.