Variational Data Assimilation Research Articles

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.

Impact of Assimilating GK-2A All-Sky Radiance with a New Observation Error for Summer Precipitation Forecasting

In the assimilation of all-sky radiance (ASR), the non-Gaussian behaviour of observation-minus-background (OMB) departures has been the major issue. Treating observation error properly should give the distribution OMB departures closer to Gaussian on which data assimilation systems are based. This study introduces a look-up-table (LUT) observation error inflation (LOEI) for assimilating ASR from three water vapor channels of GEO-KOMPSAT-2A (GK-2A) geostationary satellite based on a three-dimensional variational data assimilation (3DVAR) framework. The impacts are assessed based on summer precipitation cases over South Korea. To confirm all kinds of radiance observations, the ASRs are assimilated without any quality control procedures. The LOEI adopt a pre-estimated radiance error statistics by using the higher order fitting function of cloud amount (CA) and standard deviation (STD) of OMB departures. This LOEI was produced during the summer period from August 1 to 30, 2020, representing the characteristics of the atmosphere condition during the experimental period. The promising impact of LOEI is demonstrated in comparison with the inflated observation error using a simple linier function proposed by Geer and Bauer (GBOEI). Study results revealed the LOEI normalized OMB departures into much more Gaussian form than the GBOEI. Hence, the assimilation of ASR using LOEI (ExpLOEI) produced BT analysis closer to the observation in four cloud phases in contrast with ASR assimilation using GBOEI (ExpGBOEI), which obviously found in the ice phase. The better BT analysis eventually simulated more realistic moisture and temperature variables in the background field. Consequently, the ExpLOEI exhibited more accuracy in precipitation location and intensity compared to the experiment with ExpGBOEI.

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.

East Asia Reanalysis System (EARS)

Abstract. Reanalysis data play a vital role in weather and climate study as well as meteorological resource development and application. In this work, the East Asia Reanalysis System (EARS) was developed using the Weather Research and Forecasting (WRF) model and the Gridpoint Statistical Interpolations (GSI) data assimilation system. The regional reanalysis system is forced by the European Centre for Medium-Range Weather Forecasts (ECMWF) global reanalysis ERA-Interim data at 6 h intervals. Hourly surface observations are assimilated by the Four-Dimension Data Assimilation (FDDA) scheme during the WRF model integration; upper observations are assimilated in three-dimensional variational data assimilation (3D-VAR) mode at the analysis moment. It should be highlighted that many of the assimilated observations have not been used in other reanalysis systems. The reanalysis runs from 1980 to 2018, producing a regional reanalysis dataset covering East Asia and surrounding areas at 12 km horizontal resolution, 74 sigma levels, and 3 h intervals. Finally, an evaluation of EARS has been performed with respect to the root mean square error (RMSE), based on the 10-year (2008–2017) observational data. Compared to the global reanalysis data of ERA-Interim, the regional reanalysis data of EARS are closer to the observations in terms of RMSE in both surface and upper-level fields. The present study provides evidence for substantial improvements seen in EARS compared to the ERA-Interim reanalysis fields over East Asia. The study also demonstrates the potential use of the EARS data for applications over East Asia and proposes further plans to provide the latest reanalysis in real-time operation mode. Simple data and updated information are available on Zenodo at https://doi.org/10.5281/zenodo.7404918 (Yin et al., 2022), and the full datasets are publicly accessible on the Data-as-a-Service platform of the China Meteorological Administration (CMA) at http://data.cma.cn (last access: 19 May 2023).

Anisotropic diffusion filters for flow-dependent variational data assimilation of sea surface temperature

It is well known that the background error covariance matrix in the data assimilation is anisotropic and varied with the flow field, that is, flow-dependent. However, it is generally assumed to be isotropic and static for ease of implementation. Therefore, to enhance the quality of the background error covariance, two easy-to-implement, flow-dependent three-dimensional variational analysis (3DVar) schemes, the advection–diffusion filter (ADF) and the Smagorinsky diffusion filter (SDF), are tentatively proposed. These serve as alternative schemes for the traditional methods that are based on the isotropic assumption. First, a correctness test of the gradient for the ADF is performed to verify the validity of the adjoint code. Then, the response analysis for the 1D advection–diffusion​ equation is investigated to validate the anisotropic characteristic of the ADF with various flow velocities. Second, the two flow-dependent 3DVar schemes are verified via single-observation assimilation experiments. Compared to the existing diffusion filter with a static diffusion coefficient, both new schemes show a flow-dependent capability in the assimilation experiment because they successfully spread the observational information anisotropically. Finally, a retroactive real-time forecast experiment framework based on a 3D baroclinic primitive equation ocean model is used to investigate the effects of the ADF/SDF on the analysis and forecast accuracy of sea surface temperature (SST). While the traditional variational assimilation method with an isotropic diffusion filter generally reduces initial field errors, both the ADF and SDF can further enhance the accuracy of the initial fields in strong current areas. In addition, better forecast skills can be obtained with the two flow-dependent schemes in the East China Sea.

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.

On the dual advantage of placing observations through forward sensitivity analysis

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.

Improving sea surface temperature in a regional ocean model through refined sea surface temperature assimilation

Abstract. Infrared (IR) and passive microwave (PMW) satellite sea surface temperature (SST) retrievals are valuable to assimilate into high-resolution regional ocean forecast models. Still, there are issues related to these SSTs that need to be addressed to achieve improved ocean forecasts. Firstly, satellite SST products tend to be biased. Assimilating SSTs from different providers can thus cause the ocean model to receive inconsistent information. Secondly, while PMW SSTs are valuable for constraining models during cloudy conditions, the spatial resolution of these retrievals is rather coarse. Assimilating PMW SSTs into high-resolution ocean models will spatially smooth the modeled SST and consequently remove finer SST structures. In this study, we implement a bias correction scheme that corrects satellite SSTs before assimilation. We also introduce a special observation operator, called the supermod operator, into the Regional Ocean Modeling System (ROMS) four-dimensional variational data assimilation algorithm. This supermod operator handles the resolution mismatch between the coarse observations and the finer model. We test the bias correction scheme and the supermod operator using a setup of ROMS covering the shelf seas and shelf break off Norway. The results show that the validation statistics in the modeled SST improve if we apply the bias correction scheme. We also find improvements in the validation statistics when we assimilate PMW SSTs in conjunction with the IR SSTs. However, our supermod operator must be activated to avoid smoothing the modeled SST structures on spatial scales smaller than twice the PMW SST footprint. Both the bias correction scheme and the supermod operator are easy to apply, and the supermod operator can easily be adapted for other observation variables.

Inverse Modeling of Formaldehyde Emissions and Assessment of Associated Cumulative Ambient Air Exposures at Fine Scale

Among air toxics, formaldehyde (HCHO) is an important contributor to urban cancer risk. Emissions of HCHO in the United States are systematically under-reported and may enhance atmospheric ozone and particulate matter, intensifying their impacts on human health. During the 2021 Michigan-Ontario Ozone Source Experiment (MOOSE), mobile real-time (~1 s frequency) measurements of ozone, nitrogen oxides, and organic compounds were conducted in an industrialized area in metropolitan Detroit. The measured concentrations were used to infer ground-level and elevated emissions of HCHO, CO, and NO from multiple sources at a fine scale (400 m horizontal resolution) based on the 4D variational data assimilation technique and the MicroFACT air quality model. Cumulative exposure to HCHO from multiple sources of both primary (directly emitted) and secondary (atmospherically formed) HCHO was then simulated assuming emissions inferred from inverse modeling. Model-inferred HCHO emissions from larger industrial facilities were greater than 1 US ton per year while corresponding emission ratios of HCHO to CO in combustion sources were roughly 2 to 5%. Moreover, simulated ambient HCHO concentrations depended significantly on wind direction relative to the largest sources. The model helped to explain the observed HCHO concentration gradient between monitoring stations at Dearborn and River Rouge in 2021.

The Impact of Dropsonde Data on the Performance of the NCEP Global Forecast System during the 2020 Atmospheric Rivers Observing Campaign. Part II: Dynamic Variables and Humidity

Abstract The impact of assimilating dropsonde data from the 2020 Atmospheric River (AR) Reconnaissance (ARR) field campaign on operational numerical weather forecasts was assessed. Two experiments were executed for the period from 24 January to 18 March 2020 using the National Centers for Environmental Prediction (NCEP) Global Forecast System version 15 (GFSv15) with a four-dimensional hybrid ensemble–variational (4DEnVar) data assimilation system. The control run (CTRL) used all of the routinely assimilated data and included data from 628 ARR dropsondes, whereas the denial run (DENY) excluded the dropsonde data. Results from 17 intensive observing periods (IOPs) indicate a mixed impact for mean sea level pressure and geopotential height over the Pacific–North American (PNA) region in CTRL compared to DENY. The overall local impact over the U.S. West Coast and Gulf of Alaska for the 17 IOPs is neutral (−0.45%) for integrated vapor transport (IVT), but positive for wind and moisture profiles (0.5%–1.0%), with a spectrum of statistically significant positive and negative impacts for various IOPs. The positive dropsonde data impact on precipitation forecasts over U.S. West Coast domains appears driven, in part, by improved low-level moisture and wind fields at short-forecast lead times. Indeed, data gaps, especially for accurate and unbiased moisture profiles and wind fields, can be at least partially mitigated to improve U.S. West Coast precipitation forecasts.

Data Assimilation for the Two-Dimensional Ambipolar Diffusion Equation in Earth’s Ionosphere Model

The problem of variational data assimilation for the INM RAS two-dimensional diffusion model of the Earth’s ionosphere F region is considered. Total integral electron contents along given paths are used as observation data. The general statement of the problem in differential form is formulated, and its solvability is analyzed. Based on a regularized statement, an iterative algorithm for solving the assimilation problem is constructed, and its convergence is demonstrated. A finite-dimensional approximation is constructed, the numerical solution of the problem is implemented, and the stability and convergence of the difference scheme are proved. The quality of the reconstruction of electron concentration fields is examined in test numerical experiments. It is shown that a weakly perturbed solution is reconstructed with acceptable accuracy for both stationary and evolutionary statements in the case of vertical and slant integration paths.

A WRF/WRF-Hydro Coupled Forecasting System with Real-Time Precipitation–Runoff Updating Based on 3Dvar Data Assimilation and Deep Learning

This study established a WRF/WRF-Hydro coupled forecasting system for precipitation–runoff forecasting in the Daqing River basin in northern China. To fully enhance the forecasting skill of the coupled system, real-time updating was performed for both the WRF precipitation forecast and WRF-Hydro forecasted runoff. Three-dimensional variational (3Dvar) multi-source data assimilation was implemented using the WRF model by incorporating hourly weather radar reflectivity and conventional meteorological observations to improve the accuracy of the forecasted precipitation. A deep learning approach, i.e., long short-term memory (LSTM) networks, was adopted to improve the accuracy of the WRF-Hydro forecasted flow. The results showed that hourly data assimilation had a positive impact on the range and trends of the WRF precipitation forecasts. The quality of the WRF precipitation outputs had a significant impact on the performance of WRF-Hydro in forecasting the flow at the catchment outlet. With the runoff driven by precipitation forecasts being updated by 3Dvar data assimilation, the error of flood peak flow was decreased by 3.02–57.42%, the error of flood volume was decreased by 6.34–39.30%, and the Nash efficiency coefficient was increased by 0.15–0.52. The implementation of LSTM can effectively reduce the forecasting errors of the coupled system, particularly those of the time-to-peak and peak flow volumes.

Application of a Three-Dimensional Wind Field from a Phased-Array Weather Radar Network in Severe Convection Weather

In 2019–2020, an array weather radar (AWR) network consisting of seven X-band phased-array radars (PARs), with a detection spatial resolution of 30 m and a temporal resolution of 30 s, was built in the city of Foshan in China’s Guangdong Province. The detection time deviation in the same space is within 5 s. Through variational data assimilation, the three-dimensional wind field inside the storm can be obtained. This study selected instances of hail, thunderstorms, strong winds, and short-duration heavy precipitation in 2020 to conduct a detailed analysis. The results show the following: (1) The fine detection ability enables phased-array radars to detect the complete evolution process of convective storms, including development, strengthening, and weakening, providing a useful reference for judging the future variation trends of convective storms. (2) Through evolutionary analysis of the three-dimensional wind field, the dynamic mechanisms of storm strengthening and weakening could be obtained, which could serve as a reference to predict the development of storms. The gust wind index and convection index calculated based on the three-dimensional wind field could provide advanced warning for nowcasting. When the gust wind index was greater than 263, the probability of gale-force wind (above 17.0 m/s) was determined to be high. Moreover, the warning could be provided 10–20 min in advance. A convection index greater than 35 and the presence of concentrated contour lines were found to be conducive to the strengthening and formation of a convection, and the warning could be provided 20 min in advance. These results show that the application of PAR can provide important technical support for nowcasting severe convective weather.

4D-Var data assimilation in a nested model of the Mid-Atlantic Bight

The Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation platform has been extended to include nested grid configurations using both one-way and two-way nesting strategies. The efficacy of this new ROMS utility is demonstrated in a model comprising three nested grids with horizontal refinement and configured for the Mid-Atlantic Bight. The three nested grids have a horizontal resolution ranging from ∼7 km to ∼0.8 km thereby capturing circulation regimes that span the Gulf Stream western boundary current, through the mesoscale eddy field, and down to the rapidly evolving and energetic submesoscale. These circulation regimes represent a challenge for any data assimilation system, and the nested 4D-Var system was found to perform well across the range of resolved space and time scales. The observational data used to constrain the ocean state estimates come from a wide range of remote sensing, in situ, and mobile platforms, along with the U.S. National Science Foundation’s Ocean Observatories Initiative Pioneer Array. Several aspects of the system performance are explored and described here, including the fit of the model to the observations, the influence of data assimilation on the wave number spectra at the submesoscale, and the downscaling and upscaling of information captured by the observations.

4DVarNet-SSH: end-to-end learning of variational interpolation schemes for nadir and wide-swath satellite altimetry

Abstract. The reconstruction of sea surface currents from satellite altimeter data is a key challenge in spatial oceanography, especially with the upcoming wide-swath SWOT (Surface Water and Ocean and Topography) altimeter mission. Operational systems, however, generally fail to retrieve mesoscale dynamics for horizontal scales below 100 km and timescales below 10 d. Here, we address this challenge through the 4DVarnet framework, an end-to-end neural scheme backed on a variational data assimilation formulation. We introduce a parameterization of the 4DVarNet scheme dedicated to the space–time interpolation of satellite altimeter data. Within an observing system simulation experiment (NATL60), we demonstrate the relevance of the proposed approach, both for nadir and nadir plus SWOT altimeter configurations for two contrasting case study regions in terms of upper ocean dynamics. We report a relative improvement with respect to the operational optimal interpolation between 30 % and 60 % in terms of the reconstruction error. Interestingly, for the nadir plus SWOT altimeter configuration, we reach resolved space–timescales below 70 km and 7 d. The code is open source to enable reproducibility and future collaborative developments. Beyond its applicability to large-scale domains, we also address the uncertainty quantification issues and generalization properties of the proposed learning setting. We discuss further future research avenues and extensions to other ocean data assimilation and space oceanography challenges.

Effect of meteorological data assimilation using 3DVAR on high-resolution simulations of atmospheric CO2 concentrations in East Asia

In this study, the effects of meteorological data assimilation (DA) on high-resolution CO2 concentration simulations in East Asia were investigated using the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) and three-dimensional variational data assimilation (3DVAR). Experiments with and without meteorological DA were performed for June and December 2018. To determine an appropriate DA cycling interval, two experiments were performed at cycling intervals of 6 and 12 h. Compared to the meteorological fields simulated from experiment without DA, those simulated from experiments with DA were more similar to atmospheric observations. The CO2 concentrations simulated from the experiment with a 6 h DA cycling interval were highly similar to the observed CO2 concentrations. Compared to the root mean square error (RMSE) of the experiment without DA, the RMSE of simulated CO2 concentrations in the experiment with a 6 h DA interval decreased by 8.19% in June and 1.43% in December with respect to surface CO2 concentration observations, and decreased by 2.52% in June and 0.47% in December against column-averaged CO2 concentration (XCO2) observations of the Orbiting Carbon Observatory 2 (OCO-2). The improved 2 m temperature forecasts by DA enhanced biogenic CO2 simulations using the Vegetation Photosynthesis and Respiration Model (VPRM) in WRF-Chem. The improved wind speed and direction forecasts by DA led to improved simulations of the horizontal transport of CO2 concentrations and planetary boundary layer height. Overall, enhanced meteorological forecasts by meteorological DA using 3DVAR improved the accuracy of high-resolution CO2 concentration simulations using WRF-Chem in East Asia.

Sensitivity of Functionals of the Solution to the Variational Assimilation Problem to the Input Data on the Heat Flux for a Model of Sea Thermodynamics

For the mathematical model of the sea thermodynamics developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, the problem of variational assimilation of observational data in order to recover heat fluxes on the sea surface is considered. The sensitivity of functionals of the solution to the input data on the heat flux in this problem is studied, and the results of numerical experiments for the model of Black Sea dynamics are presented.

Role of Ocean Initialization in Skillful Prediction of Sahel Rainfall on the Decadal Time Scale

Abstract Sahel summer rainfall has undergone persistent drought from the 1970s to 1980s, causing severe human life and economic losses. Many studies pointed out that the decadal variations of Sahel rainfall are mainly modulated by low-frequency sea surface temperature (SST) variations in different ocean basins. However, how this modulation contributes to the decadal prediction skill of Sahel rainfall remains unknown. This study provided an affirmative response using the decadal hindcasts initialized by a dimensional-reduced projection four-dimensional variational (DRP-4DVar) data assimilation method to incorporate only ocean analysis data into the gridpoint version 2 of the Flexible Global Ocean–Atmosphere–Land System Model (FGOALS-g2). The hindcasts reveal the benefits of the DRP-4DVar approach for improving the Sahel rainfall decadal prediction skill measured by the anomaly correlation coefficient (ACC), root-mean-square error, ACC difference, and mean square skill score. The decadal variations of SSTs in the Atlantic, Mediterranean Sea, Indian Ocean, and Pacific as well as correct representations of the associated Sahel rainfall–SST relationships are well predicted, thus leading to skillful predictions of Sahel rainfall. In particular, the initialization of SSTs in the Atlantic and Mediterranean Sea plays a more important role in skillful Sahel rainfall predictions than in the other basins. The prediction skill of Sahel rainfall by the FGOALS-g2 prediction system is significantly higher than those by most phase 5 and 6 of the Coupled Model Intercomparison Project (CMIP5&6) prediction systems initialized only with ocean analysis data. This result is likely attributed to a more accurate relationship between Sahel rainfall and SST by the FGOALS-g2 prediction system than by the CMIP5&6 prediction systems. Significance Statement Previous studies have shown limited success in predicting Sahel rainfall. By using an advanced coupled data assimilation method constrained only by ocean observational data, we achieve a high decadal prediction skill for Sahel rainfall. The successful prediction is attributed to accurately predicted decadal variations of sea surface temperatures in the Atlantic, Mediterranean Sea, Indian Ocean, and Pacific as well as their relationships with Sahel rainfall. Our results can provide references for future decadal predictions of Sahel rainfall and motivate the need to evaluate the contributions of the initialization of the ocean versus the other climate components (e.g., atmosphere or land) to Sahel rainfall predictions.

Met Office MOGREPS‐G initialisation using an ensemble of hybrid four‐dimensional ensemble variational (En‐4DEnVar) data assimilations

AbstractThe Met Office Global and Regional Ensemble Prediction System–Global (MOGREPS‐G) used an ensemble transform Kalman filter (ETKF) to perturb its initial conditions from its operational implementation in September 2008 until December 2019. In 2019, MOGREPS‐G became the first operational atmospheric ensemble to apply hybrid four‐dimensional ensemble variational data assimilation (En‐4DEnVar) to each of the 44 perturbed ensemble members. Other enhancements have also been added, including to the inflation used to improve ensemble spread. The combined impact of these changes on ensemble forecasts is overwhelmingly positive but initially more neutral for deterministic forecasts, which also use the ensemble to represent flow‐dependent forecast errors in their hybrid data assimilation updates. The latter result is not a surprise, because the deterministic forecast's hybrid data assimilation was initially weighted more strongly to the modelled stationary covariance component and not optimised to take full advantage of the upgraded ensemble. A subsequent operational upgrade in December 2020 has introduced shifting in addition to lagging to exploit the ensemble better in the deterministic forecast's hybrid data assimilation by including ensemble members from a previous cycle and also from adjacent forecast lead times to augment the ensemble without having to run additional forecasts. More weight has since been given to the ensemble in the deterministic forecast's hybrid data assimilation in May 2022. A key motive for adopting hybrid 4DEnVar in MOGREPS‐G is to reduce maintenance overheads by virtue of sharing much of the deterministic forecast system's data assimilation code. This also enables the ensemble to assimilate almost all observation types used by the deterministic forecast. The updated system also exploits parallelism better so as to be fast enough for operational use, despite assimilating more observations and being more computationally expensive than the Met Office's ETKF.