Four-dimensional Variational Method Research Articles

FY-3A Microwave Data Assimilation Based on the POD-4DEnVar Method

A four-dimensional ensemble variational assimilation system for FY-3A satellite data is constructed using the Proper Orthogonal Decomposition (POD)-based ensemble four-dimensional variational (4DVar) assimilation method (referred to as POD-4DEnVar Satellite Assimilation System). Using the community radiative transfer model (CRTM) as the observation operator for satellite data, ensemble samples are mapped to the observation space and observation perturbations are generated. The observation perturbations matrix of satellite data is then decomposed to obtain the orthogonal eigenvectors and the eigenvalues for the observation perturbations matrix. The observation perturbations matrix and model perturbations matrix are transformed using orthogonal eigenvectors as basis functions and an explicit expression for the analysis increment is obtained. The expression includes the flow-dependent background error covariance and avoids the difficulty of solving the adjoint model for four-dimensional variational assimilation. In order to evaluate the capability of POD-4DEnVar Satellite Assimilation System, single observation experiments and observation system simulation experiments (OSSEs) for FY-3A MWHS and MWTS sensor data were designed to simulate a large-scale precipitation event occurring over the middle and lower reaches of the Yangtze River. The results of single observation experiments show that POD-4DEnVar Satellite Assimilation System can assimilate satellite data correctly, and the background error covariance of POD-4DEnVar Satellite Assimilation System has obvious flow-dependent characteristics. The results of the OSSEs show that the root-mean-square errors (RMSEs) of the assimilation analysis field with respect to the “true” field are lower than those of the background field, which indicates that the POD-4DEnVar Satellite Assimilation System can assimilate satellite data effectively. The sensitivity of the POD-4DEnVar Satellite Assimilation System to the percentage of truncated eigenvalues, the number of ensemble members, assimilation time window length, and the horizontal localization scale (which are key parameters for POD-4DEnVar Satellite Assimilation System) was tested in sensitivity experiments. These experiments show that if the percentage of truncated eigenvalues for POD decomposition is more than 80%, POD-4DEnVar Satellite Assimilation System has strong assimilation skill. Increasing the number of initial ensemble members has little influence on the assimilation ability of POD-4DEnVar Satellite Assimilation System. But, increasing the number of the physical ensemble members can clearly increase the assimilation ability. The assimilation skill of POD-4DEnVar Satellite Assimilation System is optimal when the length of the assimilation time window is 5 h or 3 h and the horizontal localization scale is 500 km or above. The assimilation ability of POD-4DEnVar Satellite Assimilation System is preliminarily tested by single observation experiments and OSSEs. The results show that it is feasible to assimilate satellite data using the POD-4DEnVar method. In the future, a variety of real satellite data and a variety of mesoscale weather cases will be used to further verify the stability of POD-4DEnVar Satellite Assimilation System.

Evaluation of Heavy Precipitation Simulated by the WRF Model Using 4D-Var Data Assimilation with TRMM 3B42 and GPM IMERG over the Huaihe River Basin, China

To obtain independent, consecutive, and high-resolution precipitation data, the four-dimensional variational (4D-Var) method was applied to directly assimilate satellite precipitation products into the Weather Research and Forecasting (WRF) model. The precipitation products of the Tropical Rainfall Measuring Mission 3B42 (TRMM 3B42) and its successor, the Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM IMERG) were assimilated in this study. Two heavy precipitation events that occurred over the Huaihe River basin in eastern China were studied. Before assimilation, the WRF model simulations were first performed with different forcing data to select more suitable forcing data and determine the control experiments for the subsequent assimilation experiments. Then, TRMM 3B42 and GPM IMERG were separately assimilated into the WRF. The simulated precipitation results in the outer domain (D01), with a 27-km resolution, and the inner domain (D02), with a 9-km resolution, were evaluated in detail. The assessments showed that (1) 4D-Var with TRMM 3B42 or GPM IMERG could both significantly improve WRF precipitation predictions at a time interval of approximately 12 h; (2) the WRF simulated precipitation assimilated with GPM IMERG outperformed the one with TRMM 3B42; (3) for the WRF output precipitation assimilated with GPM IMERG over D02, which has spatiotemporal resolutions of 9 km and 50 s, the correlation coefficients of the studied events in August and November were 0.74 and 0.51, respectively, at the point and daily scales, and the mean Heidke skill scores for the two studied events both reached 0.31 at the grid and hourly scales. This study can provide references for the assimilation of TRMM 3B42 or GPM IMERG into the WRF model using 4D-Var, which is especially valuable for hydrological applications of GPM IMERG during the transition period from the TRMM era into the GPM era.

Grain growth prediction based on data assimilation by implementing 4DVar on multi-phase-field model

We propose a method to predict grain growth based on data assimilation by using a four-dimensional variational method (4DVar). When implemented on a multi-phase-field model, the proposed method allows us to calculate the predicted grain structures and uncertainties in them that depend on the quality and quantity of the observational data. We confirm through numerical tests involving synthetic data that the proposed method correctly reproduces the true phase-field assumed in advance. Furthermore, it successfully quantifies uncertainties in the predicted grain structures, where such uncertainty quantifications provide valuable information to optimize the experimental design.

A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 2: Optimization scheme and identical twin experiment of atmospheric CO<sub>2</sub> inversion

Abstract. A four-dimensional variational method (4D-Var) is a popular technique for source/sink inversions of atmospheric constituents, but it is not without problems. Using an icosahedral grid transport model and the 4D-Var method, a new atmospheric greenhouse gas (GHG) inversion system has been developed. The system combines offline forward and adjoint models with a quasi-Newton optimization scheme. The new approach is then used to conduct identical twin experiments to investigate optimal system settings for an atmospheric CO2 inversion problem, and to demonstrate the validity of the new inversion system. In this paper, the inversion problem is simplified by assuming the prior flux errors to be reasonably well known and by designing the prior error correlations with a simple function as a first step. It is found that a system of forward and adjoint models with smaller model errors but with nonlinearity has comparable optimization performance to that of another system that conserves linearity with an exact adjoint relationship. Furthermore, the effectiveness of the prior error correlations is demonstrated, as the global error is reduced by about 15 % by adding prior error correlations that are simply designed when 65 weekly flask sampling observations at ground-based stations are used. With the optimal setting, the new inversion system successfully reproduces the spatiotemporal variations of the surface fluxes, from regional (such as biomass burning) to global scales. The optimization algorithm introduced in the new system does not require decomposition of a matrix that establishes the correlation among the prior flux errors. This enables us to design the prior error covariance matrix more freely.

A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 1: Offline forward and adjoint transport models

Abstract. A four-dimensional variational (4D-Var) method is a popular algorithm for inverting atmospheric greenhouse gas (GHG) measurements. In order to meet the computationally intense 4D-Var iterative calculation, offline forward and adjoint transport models are developed based on the Nonhydrostatic ICosahedral Atmospheric Model (NICAM). By introducing flexibility into the temporal resolution of the input meteorological data, the forward model developed in this study is not only computationally efficient, it is also found to nearly match the transport performance of the online model. In a transport simulation of atmospheric carbon dioxide (CO2), the data-thinning error (error resulting from reduction in the time resolution of the meteorological data used to drive the offline transport model) is minimized by employing high temporal resolution data of the vertical diffusion coefficient; with a low 6-hourly temporal resolution, significant concentration biases near the surface are introduced. The new adjoint model can be run in discrete or continuous adjoint mode for the advection process. The discrete adjoint is characterized by perfect adjoint relationship with the forward model that switches off the flux limiter, while the continuous adjoint is characterized by an imperfect but reasonable adjoint relationship with its corresponding forward model. In the latter case, both the forward and adjoint models use the flux limiter to ensure the monotonicity of tracer concentrations and sensitivities. Trajectory analysis for high CO2 concentration events are performed to test adjoint sensitivities. We also demonstrate the potential usefulness of our adjoint model for diagnosing tracer transport. Both the offline forward and adjoint models have computational efficiency about 10 times higher than the online model. A description of our new 4D-Var system that includes an optimization method, along with its application in an atmospheric CO2 inversion and the effects of using either the discrete or continuous adjoint method, is presented in an accompanying paper Niwa et al.(2016).

Assimilation of Remotely-Sensed Leaf Area Index into a Dynamic Vegetation Model for Gross Primary Productivity Estimation

Quantitative estimation of the magnitude and variability of gross primary productivity (GPP) is required to study the carbon cycle of the terrestrial ecosystem. Using ecosystem models and remotely-sensed data is a practical method for accurately estimating GPP. This study presents a method for assimilating high-quality leaf area index (LAI) products retrieved from satellite data into a process-oriented Lund-Potsdam-Jena dynamic global vegetation model (LPJ-DGVM) to acquire accurate GPP. The assimilation methods, including the Ensemble Kalman Filter (EnKF) and a proper orthogonal decomposition (POD)-based ensemble four-dimensional (4D) variational assimilation method (PODEn4DVar), incorporate information provided by observations into the model to achieve a better agreement between the model-estimated and observed GPP. The LPJ-POD scheme performs better with a correlation coefficient of r = 0.923 and RMSD of 32.676 gC/m2/month compared with the LPJ-EnKF scheme (r = 0.887, RMSD = 38.531 gC/m2/month) and with no data assimilation (r = 0.840, RMSD = 45.410 gC/m2/month). Applying the PODEn4DVar method into LPJ-DGVM for simulating GPP in China shows that the annual amount of GPP in China varied between 5.92 PgC and 6.67 PgC during 2003–2012 with an annual mean of 6.35 PgC/yr. This study demonstrates that integrating remotely-sensed data with dynamic global vegetation models through data assimilation methods has potential in optimizing the simulation and that the LPJ-POD scheme shows better performance in improving GPP estimates, which can provide a favorable way for accurately estimating dynamics of ecosystems.

Handling non-linearity in radar data assimilation using the non-linear least squares enhanced POD-4DVar

The Proper Orthogonal Decomposition (POD)-based ensemble four-dimensional variational (4DVar) assimilation method (POD4DEnVar) was proposed to combine the strengths of EnKF (i.e., the ensemble Kalman filter) and 4DVar assimilation methods. Recently, a POD4DEnVar-based radar data assimilation scheme (PRAS) was built and its effectiveness was demonstrated. POD4DEnVar is based on the assumption of a linear relationship between the model perturbations (MPs) and the observation perturbations (OPs); however, this assumption is likely to be destroyed by the highly non-linear forecast model or observation operator. To address this issue, using the Gauss-Newton iterative method, the nonlinear least squares enhanced POD4DEnVar algorithm (referred to as NLS-4DVar) was proposed. Naturally, the PRAS was upgraded to form the NLS-4DVar-based radar data assimilation scheme (NRAS). To evaluate the performance of NRAS against PRAS, observing system simulation experiments (OSSEs) were conducted to assimilate reflectivity and radial velocity individually, with one, two, and three iterations. The results demonstrated that the NRAS outperformed PRAS in improving the initial condition and the forecasting of model variables and rainfall. The NRAS, with a smaller number of iterations, can yield a convergent result. In contrast to the situation when assimilating radial velocity, the advantages of NRAS over PRAS were more obvious when assimilating reflectivity.

Data assimilation in a coupled physical-biogeochemical model of the California Current System using an incremental lognormal 4-dimensional variational approach: Part 2—Joint physical and biological data assimilation twin experiments

Coupled physical and biological data assimilation is performed within the California Current System using model twin experiments. The initial condition of physical and biological variables is estimated using the four-dimensional variational (4DVar) method under the Gaussian and lognormal error distributions assumption, respectively. Errors are assumed to be independent, yet variables are coupled by assimilation through model dynamics. Using a nutrient-phytoplankton-zooplankton-detritus (NPZD) model coupled to an ocean circulation model (the Regional Ocean Modeling System, ROMS), the coupled data assimilation procedure is evaluated by comparing results to experiments with no assimilation and with assimilation of physical data and biological data separately. Independent assimilation of physical (biological) data reduces the root-mean-squared error (RMSE) of physical (biological) state variables by more than 56% (43%). However, the improvement in biological (physical) state variables is less than 7% (13%). In contrast, coupled data assimilation improves both physical and biological components by 57% and 49%, respectively. Coupled data assimilation shows robust performance with varied observational errors, resulting in significantly smaller RMSEs compared to the free run. It still produces the estimation of observed variables better than that from the free run even with the physical and biological model error, but leads to higher RMSEs for unobserved variables. A series of twin experiments illustrates that coupled physical and biological 4DVar assimilation is computationally efficient and practical, capable of providing the reliable estimation of the coupled system with the same and ready to be examined in a realistic configuration.

Adjoint free four-dimensional variational data assimilation for a storm surge model of the German North Sea

In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.

PODEn4DVar-based radar data assimilation scheme: formulation and preliminary results from real-data experiments with advanced research WRF (ARW)

The Proper Orthogonal Decomposition (POD)-based ensemble four-dimensional variational (4DVar) assimilation method (referred to as PODEn4DVar) is a hybrid assimilation method that exploits the strengths of both the ensemble Kalman filter (EnKF) and the 4DVar assimilation method. Its feasibility and validity have been demonstrated using ideal models through observing system simulation experiments (OSSEs). In this study, we further utilise this approach to build a PODEn4DVar-based radar data assimilation scheme (PRAS). In a PRAS, radar observations including radial velocity and reflectivity, after some necessary data preprocessing, are assimilated directly to improve model initialisation. A group of single-observation-based OSSEs are first designed to generally evaluate the validity of PRAS. Subsequently, a group of comparison experiments are also carried out between PRAS and an LETKF-based radar assimilation scheme (LRAS), which shows that PRAS is able to produce results better than (at least as good as) LRAS. Thirdly, to evaluate the potential impact for PRAS in the operational context, a group of cycling assimilation experiments of radar data are performed, which demonstrates that PRAS can gradually improve the accuracy of analysis field by cycling assimilation. Finally, a heavy convective-rainfall case study was selected to investigate the performance of PRAS in assimilating real radar observations and the impacts of assimilating radar observations on numerical forecasts, with the Weather Research and Forecasting (WRF) model as our forecasting model. The results show that significant improvements in predicting heavy rainfall can be achieved due to the improved initial conditions for the convective system's dynamics and microphysics after assimilating the radar observations with PRAS. In summary, the results show that the PODEn4DVar is a promising method for atmospheric data assimilation.

An Economical Approach to Flow-Adaptive Moderation of Spurious Ensemble Correlations and Its Application in the Proper Orthogonal Decomposition-Based Ensemble Four Dimensional Variational Assimilation Method

AbstractThe purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method (PODEn4DVar). Owing to the applications of the sparse processing and EOF decomposition techniques, the computational costs of this proposed sparse flow-adaptive moderation (SFAM) localization scheme are significantly reduced. The effectiveness of PODEn4DVar with SFAM localization is demonstrated by using the Lorenz-96 model in comparison with the Smoothed ENsemble Correlations Raised to a Power (SENCORP) and static localization schemes, separately. The performance of PODEn4DVar with SFAM localization shows a moderate improvement over the schemes with SENCORP and static localization, with low computational costs under the imperfect model.

Investigation of the Effects of Considering Balloon Drift Information on Radiosonde Data Assimilation Using the Four-Dimensional Variational Method

Abstract Effects of balloon drift information (i.e., position and elapsed ascent time of the balloon) on the assimilation of radiosonde observations are investigated by using the Weather Research and Forecasting (WRF) Model and its data assimilation (WRFDA) system. Special radiosonde observations over the Korean Peninsula, which include the exact position and elapsed time of the balloon, are used instead of estimating the balloon drift information. To consider the balloon drift information appropriately, the four-dimensional variational data assimilation (4DVAR) and a high horizontal resolution (6 km) are used. Cycling experiments over the observation period from 20 June to 4 July 2013 are carried out to obtain the statistical robustness of the effects of considering the balloon drift information, and a single-case experiment is also conducted to show further details about the effects. The verification results of cycling experiments, such as root-mean-square errors (RMSEs) for meteorological-variable forecasts verified against the radiosonde observations and threat and bias scores for rainfall forecasts, show the positive impacts of considering the balloon drift information. Results of the single-case experiment also reveal that the simulated rainfall distribution, time series of hourly rainfall, and quantitative precipitation forecast (QPF) skills are improved through the assimilation of radiosonde observations while considering the balloon drift information. Additionally, forecasts of meteorological variables such as horizontal wind components, temperature, and dewpoint temperature are also improved by considering the balloon drift information in the single-case experiment.

Variational Estimation of Wave-Affected Parameters in a Two-Equation Turbulence Model

AbstractA variational method is used to estimate wave-affected parameters in a two-equation turbulence model with assimilation of temperature data into an ocean boundary layer model. Enhancement of turbulent kinetic energy dissipation due to breaking waves is considered. The Mellor–Yamada level 2.5 turbulence closure scheme (MY2.5) with the two uncertain wave-affected parameters (wave energy factor α and Charnock coefficient β) is selected as the two-equation turbulence model for this study. Two types of experiments are conducted. First, within an identical synthetic experiment framework, the upper-layer temperature “observations” in summer generated by a “truth” model are assimilated into a biased simulation model to investigate if (α, β) can be successfully estimated using the variational method. Second, real temperature profiles from Ocean Weather Station Papa are assimilated into the biased simulation model to obtain the optimal wave-affected parameters. With the optimally estimated parameters, the upper-layer temperature can be well predicted. Furthermore, the horizontal distribution of the wave-affected parameters employed in a high-order turbulence closure scheme can be estimated optimally by using the four-dimensional variational method that assimilates the upper-layer available temperature data into an ocean general circulation model.

GRACE terrestrial water storage data assimilation based on the ensemble four-dimensional variational method PODEn4DVar: Method and validation

Seasonal and interannual changes in the Earth’s gravity field are mainly due to mass exchange among the atmosphere, ocean, and continental water sources. The terrestrial water storage changes, detected as gravity changes by the Gravity Recovery and Climate Experiment (GRACE) satellites, are mainly caused by precipitation, evapotranspiration, river transportation and downward infiltration processes. In this study, a land data assimilation system LDAS-G was developed to assimilate the GRACE terrestrial water storage (TWS) data into the Community Land Model (CLM3.5) using the POD-based ensemble four-dimensional variational assimilation method PODEn4DVar, disaggregating the GRACE large-scale terrestrial water storage changes vertically and in time, and placing constraints on the simulation of vertical hydrological variables to improve land surface hydrological simulations. The ideal experiments conducted at a single point and assimilation experiments carried out over China by the LDAS-G data assimilation system showed that the system developed in this study improved the simulation of land surface hydrological variables, indicating the potential of GRACE data assimilation in large-scale land surface hydrological research and applications.

Comparison of Hybrid-4DEnVar and Hybrid-4DVar Data Assimilation Methods for Global NWP

Abstract The Met Office has developed an ensemble-variational data assimilation method (hybrid-4DEnVar) as a potential replacement for the hybrid four-dimensional variational data assimilation (hybrid-4DVar), which is the current operational method for global NWP. Both are four-dimensional variational methods, using a hybrid combination of a fixed climatological model of background error covariances with localized covariances from an ensemble of current forecasts designed to describe the structure of “errors of the day.” The fundamental difference between the methods is their modeling of the time evolution of errors within each data assimilation window: 4DVar uses a linear model and its adjoint and 4DEnVar uses a localized linear combination of nonlinear forecasts. Both hybrid-4DVar and hybrid-4DEnVar beat their three-dimensional versions, which are equivalent, in NWP trials. With settings based on the current operational system, hybrid-4DVar performs better than hybrid-4DEnVar. Idealized experiments designed to compare the time evolution of covariances in the methods are described: the basic 4DEnVar represents the evolution of ensemble errors as well as 4DVar. However, 4DVar also represents the evolution of errors from the climatological covariances, whereas 4DEnVar does not. This difference is the main cause of the superiority of hybrid-4DVar. Another difference is that the authors’ 4DVar explicitly penalizes rapid variations in the analysis increment trajectory, while the authors’ 4DEnVar contains no dynamical constaints on imbalance. The authors describe a four-dimensional incremental analysis update (4DIAU) method that filters out the high-frequency oscillations introduced by the poorly balanced 4DEnVar increments. Possible methods for improving hybrid-4DEnVar are discussed.

An adjoint sensitivity-based data assimilation method and its comparison with existing variational methods

An adjoint sensitivity-based data assimilation (ASDA) method is proposed and applied to a heavy rainfall case over the Korean Peninsula. The heavy rainfall case, which occurred on 26 July 2006, caused torrential rainfall over the central part of the Korean Peninsula. The mesoscale convective system (MCS) related to the heavy rainfall was classified as training line/adjoining stratiform (TL/AS)-type for the earlier period, and back building (BB)-type for the later period. In the ASDA method, an adjoint model is run backwards with forecast-error gradient as input, and the adjoint sensitivity of the forecast error to the initial condition is scaled by an optimal scaling factor. The optimal scaling factor is determined by minimising the observational cost function of the four-dimensional variational (4D-Var) method, and the scaled sensitivity is added to the original first guess. Finally, the observations at the analysis time are assimilated using a 3D-Var method with the improved first guess. The simulated rainfall distribution is shifted northeastward compared to the observations when no radar data are assimilated or when radar data are assimilated using the 3D-Var method. The rainfall forecasts are improved when radar data are assimilated using the 4D-Var or ASDA method. Simulated atmospheric fields such as horizontal winds, temperature, and water vapour mixing ratio are also improved via the 4D-Var or ASDA method. Due to the improvement in the analysis, subsequent forecasts appropriately simulate the observed features of the TL/AS- and BB-type MCSs and the corresponding heavy rainfall. The computational cost associated with the ASDA method is significantly lower than that of the 4D-Var method.

Radar radial wind data assimilation using the time-incremental 4D-Var method implemented to the WRFDA system

In this study, we selected a heavy rainfall case over the Korean Peninsula, which was characterised by two localised rainfall maxima. Neither of the two maxima is accurately simulated when no radar data are assimilated or when radar data are assimilated using the three-dimensional variational (3D-Var) method of the Weather Research and Forecasting Data Assimilation (WRFDA) system. Using the four-dimensional variational (4D-Var) method included in the WRFDA system improves the rainfall forecast partially. To obtain further improvements in the rainfall forecast, outer loops and the time-incremental 4D-Var method are used. In the time-incremental 4D-Var method, the length of the assimilation window is increased gradually, and the starting point of the current minimisation task comes from the minimiser of the previous minimisation task. The analysis of the experiment using outer loops or the time-incremental 4D-Var method is closer to the observations than that of the experiment using the 4D-Var method. This is because the first guess is improved progressively by using outer loops or the time-incremental 4D-Var method. The gap between nonlinear and linear growth is reduced via outer loops or the time-incremental 4D-Var method compared to the 4D-Var method, because the nonlinearity is accounted for by consistently updating the nonlinear model trajectory. However, the rainfall forecast is improved only in the experiment using the time-incremental 4D-Var method. Analysis increments of the horizontal wind and convective available potential energy (CAPE) result in proper modifications to the analysis, and finally, an improved subsequent forecast. The quasi-static adjustment in the time-incremental 4D-Var method may contribute to finding the global minimum under the high degree of nonlinearity present in the original minimisation problem.

State estimates and forecasts of the loop current in the Gulf of Mexico using the MITgcm and its adjoint

[1] An ocean state estimate has been developed for the Gulf of Mexico (GoM) using the MIT general circulation model and its adjoint. The estimate has been tested by forecasting loop current (LC) evolution and eddy shedding in the GoM. The adjoint (or four-dimensional variational) method was used to match the model evolution to observations by adjusting model temperature and salinity initial conditions, open boundary conditions, and atmospheric forcing fields. The model was fit to satellite-derived along-track sea surface height, separated into temporal mean and anomalies, and gridded sea surface temperature for 2 month periods. The optimized state at the end of the assimilation period was used to initialize the forecast for 2 months. Forecasts explore practical LC predictability and provide a cross-validation test of the state estimate by comparing it to independent future observations. The model forecast was tested for several LC eddy separation events, including Eddy Franklin in May 2010 during the deepwater horizon oil spill disaster in the GoM. The forecast used monthly climatological open boundary conditions, atmospheric forcing, and run-off fluxes. The model performance was evaluated by computing model-observation root-mean-square difference (rmsd) during both the hindcast and forecast periods. The rmsd metrics for the forecast generally outperformed persistence (keeping the initial state fixed) and reference (forecast initialized using assimilated Hybrid Coordinate Ocean Model 1/12° global analysis) model simulations during LC eddy separation events for a period of 12 months.

E4DVar: Coupling an Ensemble Kalman Filter with Four-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model

A hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2003. After verifying the forecasts from each analysis against standard sounding observations, it is found that the E4DVar substantially outperforms both the EnKF and 4DVar during this active summer month, which featured several episodes of severe convective weather. On average, the forecasts produced from E4DVar analyses have considerably smaller errors than both of the stand-alone EnKF and 4DVar systems for forecast lead times up to 60 h.

A POD-based ensemble four-dimensional variational assimilation method

A POD-based ensemble four-dimensional variational assimilation method