Ensemble Background Error Covariance Research Articles

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.

Introducing large‐scale analysis constraints in regional hybrid EnVar data assimilation for the prediction of triple typhoons

AbstractLarge‐scale environment fields play an important role in the accurate prediction of typhoons. However, regional predictions for typhoons often suffer from inadequate representation of large‐scale flow pattern such as those from global models due to limited domain size and observations employed in regional models, especially when multiple typhoons that interact concurrently occur in a regional domain. This study merges the large‐scale information from global model forecasts with the mesoscale information from regional model forecasts in the hybrid ensemble‐variational (EnVar) data assimilation by adding an analysis constraint in the EnVar cost function, which is defined by the departure of the regional model EnVar analysis from the global model fields and takes advantage of flow‐dependent ensemble background error covariance for the introduction of large scales using data assimilation. The EnVar assimilation impacts of the large‐scale fields on predictions of triple typhoons are assessed by conducting cycling assimilation and forecast experiments for a 13‐day‐long period in July 2015 when three typhoons concurrently occurred. Results show that the large‐scale constraint for EnVar can clearly improve the triple‐typhoons' track and intensity forecasts of the regional model. The large‐scale information introduced by the proposed method is also shown to reduce forecast errors of wind, temperature and humidity, respectively. Predictions of the rainfall caused by typhoons are also ameliorated. Besides, the analysis‐constrained regional predictions provide better model dynamic fields in terms of sea surface pressure, geopotential height, and water vapor transport, as well as developed typhoon structures. In addition, the adaptive bias correction for radiance assimilation presents a stable performance under the influence of introducing extra background large‐scale fields. The results indicate that the large‐scale analysis constraint introduced in the hybrid EnVar takes advantages of the multiscale information from the global model and the regional model respectively, thus improving the final results of the predictions of multiple typhoons.

Data assimilation for the Model for Prediction Across Scales – Atmosphere with the Joint Effort for Data assimilation Integration (JEDI-MPAS 2.0.0-beta): ensemble of 3D ensemble-variational (En-3DEnVar) assimilations

Abstract. An ensemble of 3D ensemble-variational (En-3DEnVar) data assimilations is demonstrated with the Joint Effort for Data assimilation Integration (JEDI) with the Model for Prediction Across Scales – Atmosphere (MPAS-A) (i.e., JEDI-MPAS). Basic software building blocks are reused from previously presented deterministic 3DEnVar functionality and combined with a formal experimental workflow manager in MPAS-Workflow. En-3DEnVar is used to produce an 80-member ensemble of analyses, which are cycled with ensemble forecasts in a 1-month experiment. The ensemble forecasts approximate a purely flow-dependent background error covariance (BEC) at each analysis time. The En-3DEnVar BECs and prior ensemble-mean forecast errors are compared to those produced by a similar experiment that uses the Data Assimilation Research Testbed (DART) ensemble adjustment Kalman filter (EAKF). The experiment using En-3DEnVar produces a similar ensemble spread to and slightly smaller errors than the EAKF. The ensemble forecasts initialized from En-3DEnVar and EAKF analyses are used as BECs in deterministic cycling 3DEnVar experiments, which are compared to a control experiment that uses 20-member MPAS-A forecasts initialized from Global Ensemble Forecast System (GEFS) initial conditions. The experimental ensembles achieve mostly equivalent or better performance than the off-the-shelf ensemble system in this deterministic cycling setting, although there are many obvious differences in configuration between GEFS and the two MPAS ensemble systems. An additional experiment that uses hybrid 3DEnVar, which combines the En-3DEnVar ensemble BEC with a climatological BEC, increases tropospheric forecast quality compared to the corresponding pure 3DEnVar experiment. The JEDI-MPAS En-3DEnVar is technically working and useful for future research studies. Tuning of observation errors and spread is needed to improve performance, and several algorithmic advancements are needed to improve computational efficiency for larger-scale applications.

A Multiresolution Ensemble Hybrid 4DEnVar with Variable Ensemble Sizes to Improve Global and Tropical Cyclone Track Numerical Prediction

Abstract The current global operational four-dimensional ensemble-variational (4DEnVar) data assimilation (DA) system at NCEP adopts a background ensemble at a reduced resolution, which restricts the range of spatial scales that the ensemble background error covariance can resolve. A prior study developed a multiresolution ensemble 4DEnVar method and determined that this approach can provide a comparable forecast to an approach using solely high-resolution members, while substantially reducing the computational cost. This study further develops the multiresolution ensemble 4DEnVar approach to allow for a flexible number of low- and high-resolution ensemble members as well as varying localization length scales between the high- and low-resolution ensembles. Three 4DEnVar experiments with the same computational costs are compared. The first experiment has an 80-member high-resolution background ensemble with single-scale optimally tuned localization (SR-High). The second and third experiments utilize the multiresolution background ensembles. One has 130 low-resolution and 40 high-resolution members (MR170) while the other has 180 low-resolution members and 24 high-resolution members (MR204). Both multiresolution ensemble experiments utilize differing localization radii with ensemble resolution. Despite having the same costs, both MR170 and MR204 improves global forecasts and decreases tropical cyclone track errors for up to 5 days’ lead time compared to SR-High. Improvements are most apparent in larger-scale features, such as jet streams and the environmental steering flow of tropical cyclones. Additionally, MR170 outperforms MR204 in terms of global and tropical cyclone track forecasts, demonstrating the value of both increasing sampling at large scales and retaining substantial information at small scales.

Assessment of the data assimilation framework for the Rapid Refresh Forecast System v0.1 and impacts on forecasts of a convective storm case study

Abstract. The Rapid Refresh Forecast System (RRFS) is currently under development and aims to replace the National Centers for Environmental Prediction (NCEP) operational suite of regional- and convective-scale modeling systems in the next upgrade. In order to achieve skillful forecasts comparable to the current operational suite, each component of the RRFS needs to be configured through exhaustive testing and evaluation. The current data assimilation component uses the hybrid three-dimensional ensemble–variational data assimilation (3DEnVar) algorithm in the Gridpoint Statistical Interpolation (GSI) system. In this study, various data assimilation algorithms and configurations in GSI are assessed for their impacts on RRFS analyses and forecasts of a squall line over Oklahoma on 4 May 2020. A domain of 3 km horizontal grid spacing is configured, and hourly update cycles are performed using initial and lateral boundary conditions from the 3 km grid High-Resolution Rapid Refresh (HRRR). Results show that a baseline RRFS run is able to represent the observed convection, although with stronger cells and large location errors. With data assimilation, these errors are reduced, especially in the 4 and 6 h forecasts using 75 % of the ensemble background error covariance (BEC) and 25 % of the static BEC with the supersaturation removal function activated in GSI. Decreasing the vertical ensemble localization radius from 3 layers to 1 layer in the first 10 layers of the hybrid analysis results in overall less skillful forecasts. Convection is greatly improved when using planetary boundary layer pseudo-observations, especially at 4 h forecast, and the bias of the 2 h forecast of temperature is reduced below 800 hPa. Lighter hourly accumulated precipitation is predicted better when using 100 % ensemble BEC in the first 4 h forecast, but heavier hourly accumulated precipitation is better predicted with 75 % ensemble BEC. Our results provide insight into the current capabilities of the RRFS data assimilation system and identify configurations that should be considered as candidates for the first version of RRFS.

Improving Short-Term Precipitation Forecasting with Radar Data Assimilation and a Multiscale Hybrid Ensemble–Variational Strategy

Abstract This paper presents a multiscale hybrid ensemble–variational (EnVar) data assimilation strategy with an hourly rapid update aiming to improve analysis of convection via radar observations and of convective environment via conventional observations. In this multiscale hybrid EnVar strategy, the ensemble members are updated by assimilating conventional data using an EnKF to provide the hybrid EnVar with flow-dependent background error covariance (BEC). A two-step approach is employed in the hybrid EnVar to achieve improved multiscale analysis by assimilating radar data and conventional data, respectively, in two successive steps. This two-step procedure enables the applications of different BEC tuning factors and different hybrid weights for radar and conventional observations. In addition, this study also examines the impacts of the flow-dependent BEC generated with and without radar data assimilation in EnKF on the performance of hybrid EnVar analysis and ensuing convective forecasting. The multiscale hybrid EnVar strategy was first evaluated through a comparison with 3DVar and EnKF using a convective rainfall case. Quantitative verifications for both precipitation and environmental variables demonstrated that the hybrid EnVar system with an optimal multiscale configuration outperformed both the 3DVar and EnKF. The multiscale hybrid EnVar strategy was then evaluated through a series of sensitivity experiments. It was shown that the two-step assimilation strategy outperformed the one-step for both the precipitation and environmental variables, and the ensemble BEC generated without radar data assimilation led to improved hybrid EnVar analysis over that with radar data assimilation by better representing uncertainties in convective environment and reducing spurious spatial and multivariate correlations.

A Four‐Dimensional Ensemble‐Variational (4DEnVar) Data Assimilation System Based on GRAPES‐GFS: System Description and Primary Tests

AbstractA four‐dimensional ensemble‐variational (4DEnVar) data assimilation (DA) system was developed based on the global forecast system of the Global/Regional Assimilation and Prediction System (GRAPES‐GFS). Instead of using the adjoint technique, this system utilizes a dimension‐reduced projection (DRP) technique to minimize the cost function of the standard four‐dimensional variational (4DVar) DA. It dynamically predicts ensemble background error covariance (BEC) and realizes the explicit flow‐dependence of BEC in the variational configuration. An inflation technique based on a linear combination of analysis increments and balanced random perturbations, is utilized to overcome the problem of underestimation of BEC matrix (B‐matrix) during the assimilation cycle. To mitigate the spurious correlations in the ensemble B‐matrix caused by the insufficient ensemble members, an ensemble‐sample‐based subspace localization method is utilized. In order to evaluate the new system, single‐point observation experiments (SOEs) and observing system simulation experiments (OSSEs) were conducted with sounding and cloud‐derived wind data based on GRAPES‐GFS. The explicit flow‐dependent characteristic of the 4DEnVar system using a localized ensemble covariance was verified in the SOEs. In the OSSEs, the ensemble mean analysis of 4DEnVar outperforms the analysis of 4DVar. The deterministic forecast initialized from the 4DEnVar ensemble mean analysis has better performance in the short‐range forecasts, better (worse) performance in the early (late) period of the medium‐range forecasts in the Northern Extratropics, and opposite performance in the Southern Extratropics, and exhibits slightly worse effects in the Tropics. Moreover, the ensemble mean forecast initialized by the 4DEnVar system has higher forecast skills.

Assimilating FY-4A Lightning and Radar Data for Improving Short-Term Forecasts of a High-Impact Convective Event with a Dual-Resolution Hybrid 3DEnVAR Method

A dual-resolution, hybrid, three-dimensional ensemble-variational (3DEnVAR) data assimilation method combining static and ensemble background error covariances is used to assimilate radar data, and pseudo-water vapor observations to improve short-term severe weather forecasts with the Weather Research and Forecast (WRF) model. The higher-resolution deterministic forecast and the lower-resolution ensemble members have 3 and 9 km horizontal resolution, respectively. The water vapor pseudo-observations are derived from the combined use of total lightning data and cloud top height from the Fengyun-4A(FY-4A) geostationary satellite. First, a set of single-analysis experiments are conducted to provide a preliminary performance evaluation of the effectiveness of the hybrid method for assimilating multisource observations; second, a set of cycling analysis experiments are used to evaluate the forecast performance in convective-scale high-frequency analysis; finally, different hybrid coefficients are tested in both the single and cycling experiments. The single-analysis results show that the combined assimilation of radar data and water vapor pseudo-observations derived from the lightning data is able to generate reasonable vertical velocity, water vapor and hydrometeor adjustments, which help to trigger convection earlier in the forecast/analysis and reduce the spin-up time. The dual-resolution hybrid 3DEnVAR method is able to adjust the wind fields and hydrometeor variables with the assimilation of lightning data, which helps maintain the triggered convection longer and partially suppress spurious cells in the forecast compared with the three-dimensional variational (3DVAR) method. A cycling analysis that introduced a large number of observations with more frequent small adjustments is able to better resolve the observed convective events than a single-analysis approach. Different hybrid coefficients can affect the forecast results, either in the single deterministic or cycling analysis experiments. Overall, we found that a static coefficient of 0.4 and an ensemble coefficient of 0.6 yields the best forecast skill for this event.

Development of Convective-Scale Static Background Error Covariance within GSI-Based Hybrid EnVar System for Direct Radar Reflectivity Data Assimilation

AbstractA convective-scale static background-error covariance (BEC) matrix is further developed to include the capability of direct reflectivity assimilation and evaluated within the GSI-based three-dimensional variational (3DVar) and hybrid ensemble–variational (EnVar) methods. Specific developments are summarized as follows: 1) Control variables (CVs) are extended to include reflectivity, vertical velocity, and all hydrometeor types. Various horizontal momentum and moisture CV options are included. 2) Cross correlations between all CVs are established. 3) A storm intensity-dependent binning method is adopted to separately calculate static error matrices for clear-air and storms with varying intensities. The resultant static BEC matrices are simultaneously applied at proper locations guided by the observed reflectivity. 4) The EnVar is extended to adaptively incorporate static BECs based on the quality of ensemble covariances. Evaluation and examination of the new static BECs are first performed on the 8 May 2003 Oklahoma City supercell. Detailed diagnostics and 3DVar examinations suggest zonal/meridional winds and pseudo–relative humidity are selected as horizontal momentum and moisture CVs for direct reflectivity assimilation, respectively; inclusion of cross correlations favors spin up and maintains the analyzed storms; application of binning improves characteristics and persistence of the simulated storm. Relative to an experiment using the full ensemble BECs (Exp-PureEnVar), incorporating static BECs in hybrid EnVar reduces spinup time and better analyzes reflectivity distributions while the background ensemble is deficient in sampling errors. Compared to both pure 3DVar and Exp-PureEnVar, hybrid EnVar better predicts reflectivity distributions and better maintains a strong mesocyclone. Further examination through the 20 May 2013 Oklahoma supercells confirms these results and additionally demonstrates the effectiveness of adaptive hybridization.

Doppler weather radar data assimilation at convective-allowing grid spacing for predicting an extreme weather event in Southern India

ABSTRACT Thunderstorms and heavy rainfall are the most devastating and dangerous weather phenomena over the tropical region. Southern Peninsula India in general and regions close to Western Ghats in particular are very prone to such severe weather activity. To improve the short-range forecasting of such extreme weather hazards, tremendous efforts are made to develop Doppler Weather Radar (DWR) network over Indian region for detection and continuous monitoring of weather activities. In this study, the Weather Research and Forecasting (WRF) model and its three-dimensional variational (3D-Var) data assimilation system are used to evaluate the importance of the frequently available DWR observations at convective-allowing grid spacing for predicting an extreme weather event. Various assimilation experiments are performed using background error covariance statistics generated from the National Meteorological Center (NMC) method and Ensemble method, quality control in radial winds, and with/without Digital Filter Initialization (DFI) schemes for DWR data assimilation. Results suggest that with the assimilation of DWR observations, the WRF model is able to predict selected rainfall events with less temporal, spatial and intensity error. Moreover, synoptic conditions are more favourable after DWR assimilation. Due to lack of precise initial conditions, control experiments are not able to capture this extreme weather activity. Results suggest that better skill is seen when the DFI method is used in combination with ensemble background error covariance as compared to other experiments. The maximum rainfall prediction skill is enhanced with DWR data assimilation experiment with DFI method and ensemble background error covariance statistics.

Comparison of the Performance of Hybrid ETKF-3DVAR and 3DVAR Data Assimilation Systems on Short-Range Forecasts during Indian Summer Monsoon Season in a Limited-Area Model

The impact of deploying a flow-dependent ensemble error covariance in Weather Research and Forecasting (WRF) three-dimensional variational (3DVAR) data assimilation (DA) system is examined for short-range rainfall forecasts during an Indian summer monsoon season. The flow-dependent background error covariance (BEC) is generated using a 50-member ensemble, which is further updated using the ensemble transform Kalman filter (ETKF). Assimilation is performed using a Hybrid variational-ensemble (“Hybrid”) and traditional 3DVAR DA system during the 4 weeks of July 2013. The forecasted wind, temperature, and rainfall from the assimilation experiments are verified against corresponding observations. The results indicate that the flow-dependent ensemble background error covariance in 3DVAR has systematically improved the forecasted wind and temperature when compared to the traditional 3DVAR. Similarly, rainfall forecast skill is superior in the Hybrid experiments relative to that of 3DVAR. Convection-permitting resolution rainfall forecast is validated against 746 telemetric rain gauge observations over the state of Karnataka. The Hybrid experiments show higher quantitative precipitation forecast skill than 3DVAR, particularly towards the later stages of data assimilation cycling. Spatially, the 3DVAR experiment shows a dry bias over the upper peninsular regions and a slight wet bias over the central and the northern Indian regions, while the magnitude of such wet and dry biases is smaller in forecasts from Hybrid analysis. Additionally, the westerly wind over the peninsular Indian landmass analyzed by 3DVAR is considerably weaker than that analyzed by the Hybrid experiments. This is proposed as a possible reason for the reduced dry bias in rainfall forecasts over the Indian landmass in Hybrid versus 3DVAR experiments.

A Multiresolution Ensemble Hybrid 4DEnVar for Global Numerical Prediction

Abstract A multiresolution ensemble (MR-ENS) method is developed to resolve a wider range of scales of the background error covariance (BEC) in the hybrid four-dimensional ensemble–variational (4DEnVar) while saving computational costs. MR-ENS is implemented in the NCEP Global Forecast System (GFS) gridpoint statistical interpolation (GSI) hybrid 4DEnVar. MR-ENS generates analysis increment by incorporating high-resolution static BEC and flow-dependent ensemble BECs from both high and low resolutions. MR-ENS is compared with three 4DEnVar update approaches: 1) the single-resolution (SR)-Low approach where the analysis increments are generated from the ensemble BEC and the static BEC at the same low resolution; 2) the dual-resolution (DR) approach where the analysis increment is generated using the high-resolution static BEC and low-resolution ensemble BEC; and 3) the SR-High approach, which is the same as 1) except that all covariances are at high-resolution. Experiments show that MR-ENS improves global and tropical cyclone track forecasts compared to SR-Low and DR. Inclusion of the high-resolution ensemble leads to increased background ensemble spread, better fitting of the background to observations, increased effective ranks, more accurate ensemble error correlation, and increased power of analysis increment at small scales. The majority of the improvement of MR-ENS relative to SR-Low is due to the partial use of high-resolution background ensemble. Compared to SR-High, MR-ENS decreases the overall cost by about 40% and shows comparable global and tropical cyclone track forecast performances. Diagnostics show that particularly in the tropics, MR-ENS improves the analysis increment over a wide range of scales and increases the effective rank of the ensemble BEC to the degree comparable to SR-High.

Forecast Sensitivity Observation Impact in the 4DVAR and Hybrid-4DVAR Data Assimilation Systems

AbstractIn this study, the observation impacts on 24-h forecast error reduction (FER), based on the adjoint method in the four-dimensional variational (4DVAR) data assimilation (DA) and hybrid-4DVAR DA systems coupled with the Unified Model, were evaluated from 0000 UTC 5 August to 1800 UTC 26 August 2014. The nonlinear FER in hybrid-4DVAR was 12.2% greater than that in 4DVAR due to the use of flow-dependent background error covariance (BEC), which was a weighted combination of the static BEC and the ensemble BEC based on ensemble forecasts. In hybrid-4DVAR, the observation impacts (i.e., the approximated nonlinear FER) for most observation types increase compared to those in 4DVAR. The increased observation impact from using hybrid-4DVAR instead of 4DVAR changes depending on the analysis time and regions. To calculate the ensemble BEC in hybrid-4DVAR, analyses at 0600 and 1800 UTC (0000 and 1200 UTC) used 3-h (9-h) ensemble forecasts. Greater observation impact was obtained when 3-h ensemble forecasts were used for the ensemble BEC at 0600 and 1800 UTC, than with 9-h ensemble forecasts at 0000 and 1200 UTC. Different from other observations, the atmospheric motion vectors (AMVs) deduced from geostationary satellite are more frequently observed in the same area. When the ensemble forecasts with longer integration times were used for the ensemble BEC in hybrid-4DVAR, the observation impact of the AMVs decreased the most in East Asia. This implies that the observation impact of AMVs in East Asia shows the highest sensitivity to the integration time of the ensemble members used for deducing the flow-dependent BEC in hybrid-4DVAR.

An Efficient Local Correlation Matrix Decomposition Approach for the Localization Implementation of Ensemble‐Based Assimilation Methods

AbstractEnsemble‐based data assimilation methods often use the so‐called localization scheme to improve the representation of the ensemble background error covariance (Be). Extensive research has been undertaken to reduce the computational cost of these methods by using the localized ensemble samples to localize Be by means of a direct decomposition of the local correlation matrix C. However, the computational costs of the direct decomposition of the local correlation matrix C are still extremely high due to its high dimension. In this paper, we propose an efficient local correlation matrix decomposition approach based on the concept of alternating directions. This approach is intended to avoid direct decomposition of the correlation matrix. Instead, we first decompose the correlation matrix into 1‐D correlation matrices in the three coordinate directions, then construct their empirical orthogonal function decomposition at low resolution. This procedure is followed by the 1‐D spline interpolation process to transform the above decompositions to the high‐resolution grid. Finally, an efficient correlation matrix decomposition is achieved by computing the very similar Kronecker product. We conducted a series of comparison experiments to illustrate the validity and accuracy of the proposed local correlation matrix decomposition approach. The effectiveness of the proposed correlation matrix decomposition approach and its efficient localization implementation of the nonlinear least‐squares four‐dimensional variational assimilation are further demonstrated by several groups of numerical experiments based on the Advanced Research Weather Research and Forecasting model.

Extraction of wind and temperature information from hybrid 4D-Var assimilation of stratospheric ozone using NAVGEM

Abstract. Extraction of wind and temperature information from stratospheric ozone assimilation is examined within the context of the Navy Global Environmental Model (NAVGEM) hybrid 4-D variational assimilation (4D-Var) data assimilation (DA) system. Ozone can improve the wind and temperature through two different DA mechanisms: (1) through the “flow-of-the-day” ensemble background error covariance that is blended together with the static background error covariance and (2) via the ozone continuity equation in the tangent linear model and adjoint used for minimizing the cost function. All experiments assimilate actual conventional data in order to maintain a similar realistic troposphere. In the stratosphere, the experiments assimilate simulated ozone and/or radiance observations in various combinations. The simulated observations are constructed for a case study based on a 16-day cycling truth experiment (TE), which is an analysis with no stratospheric observations. The impact of ozone on the analysis is evaluated by comparing the experiments to the TE for the last 6 days, allowing for a 10-day spin-up. Ozone assimilation benefits the wind and temperature when data are of sufficient quality and frequency. For example, assimilation of perfect (no applied error) global hourly ozone data constrains the stratospheric wind and temperature to within ∼ 2 m s−1 and ∼ 1 K. This demonstrates that there is dynamical information in the ozone distribution that can potentially be used to improve the stratosphere. This is particularly important for the tropics, where radiance observations have difficulty constraining wind due to breakdown of geostrophic balance. Global ozone assimilation provides the largest benefit when the hybrid blending coefficient is an intermediate value (0.5 was used in this study), rather than 0.0 (no ensemble background error covariance) or 1.0 (no static background error covariance), which is consistent with other hybrid DA studies. When perfect global ozone is assimilated in addition to radiance observations, wind and temperature error decreases of up to ∼ 3 m s−1 and ∼ 1 K occur in the tropical upper stratosphere. Assimilation of noisy global ozone (2 % errors applied) results in error reductions of ∼ 1 m s−1 and ∼ 0.5 K in the tropics and slightly increased temperature errors in the Northern Hemisphere polar region. Reduction of the ozone sampling frequency also reduces the benefit of ozone throughout the stratosphere, with noisy polar-orbiting data having only minor impacts on wind and temperature when assimilated with radiances. An examination of ensemble cross-correlations between ozone and other variables shows that a single ozone observation behaves like a potential vorticity (PV) “charge”, or a monopole of PV, with rotation about a vertical axis and vertically oriented temperature dipole. Further understanding of this relationship may help in designing observation systems that would optimize the impact of ozone on the dynamics.

The Advantages of Hybrid 4DEnVar in the Context of the Forecast Sensitivity to Initial Conditions

AbstractHybrid four‐dimensional ensemble variational data assimilation (hybrid 4DEnVar) is a prospective successor to three‐dimensional variational data assimilation (3DVar) in operational weather prediction centers currently developing a new weather prediction model and those that do not operate adjoint models. In experiments using real observations, hybrid 4DEnVar improved Northern Hemisphere (NH; 20°N–90°N) 500 hPa geopotential height forecasts up to 5 days in a NH summer month compared to 3DVar, with statistical significance. This result is verified against ERA‐Interim through a Monte Carlo test. By a regression analysis, the sensitivity of 5 day forecast is associated with the quality of the initial condition. The increased analysis skill for midtropospheric midlatitude temperature and subtropical moisture has the most apparent effect on forecast skill in the NH including a typhoon prediction case. Through attributing the analysis improvements by hybrid 4DEnVar separately to the ensemble background error covariance (BEC), its four‐dimensional (4‐D) extension, and climatological BEC, it is revealed that the ensemble BEC contributes to the subtropical moisture analysis, whereas the 4‐D extension does to the midtropospheric midlatitude temperature. This result implies that hourly wind‐mass correlation in 6 h analysis window is required to extract the potential of hybrid 4DEnVar for the midlatitude temperature analysis to the maximum. However, the temporal ensemble correlation, in hourly time scale, between moisture and another variable is invalid so that it could not work for improving the hybrid 4DEnVar analysis.

GSI Three-Dimensional Ensemble–Variational Hybrid Data Assimilation Using a Global Ensemble for the Regional Rapid Refresh Model

The Rapid Refresh (RAP) is an hourly updated regional meteorological data assimilation/short-range model forecast system running operationally at NOAA/National Centers for Environmental Prediction (NCEP) using the community Gridpoint Statistical Interpolation analysis system (GSI). This paper documents the application of the GSI three-dimensional hybrid ensemble–variational assimilation option to the RAP high-resolution, hourly cycling system and shows the skill improvements of 1–12-h forecasts of upper-air wind, moisture, and temperature over the purely three-dimensional variational analysis system. Use of perturbation data from an independent global ensemble, the Global Data Assimilation System (GDAS), is demonstrated to be very effective for the regional RAP hybrid assimilation. In this paper, application of the GSI-hybrid assimilation for the RAP is explained. Results from sensitivity experiments are shown to define configurations for the operational RAP version 2, the ratio of static and ensemble background error covariance, and vertical and horizontal localization scales for the operational RAP version 3. Finally, a 1-week RAP experiment from a summer period was performed using a global ensemble from a winter period, suggesting that a significant component of its multivariate covariance structure from the ensemble is independent of time matching between analysis time and ensemble valid time.

Ensemble-based release estimation for accidental river pollution with known source position

Dispersion model is an important tool for decision makers to accurately assess risks and effectively plan countermeasures during river pollution accidents, but their applications suffer from significant modeling uncertainties, primarily due to the scarce information of the source. A fully sequential inverse estimation method is proposed to reconstruct the temporal release for accidental river pollution. The method is based on a one-dimensional advection-dispersion model in conjunction with the augmented ensemble Kalman filter method. Detailed analysis of the ensemble background error covariance (BEC) matrix is conducted to elucidate the “flow-dependent” mechanism, which enables the inversion method to simultaneously take into account the uncertainties in the hydrological parameters (mean flow velocity and longitudinal dispersion coefficient). The method is evaluated with six field tracer experiments with various mean flow velocities, ranging from 0.085 to 0.889ms−1, and also compared with the commonly used Tikhonov regularization inverse estimation method to demonstrate its performance improvement. The results indicate that it successfully reconstructs the temporal release and reduces the relative errors of the total release estimation by about 12.4% on average compared with the Tikhonov method, since the errors caused by the uncertainties in mean flow velocity and longitudinal dispersion coefficient are effectively alleviated.

An Ensemble Kalman Filter for Numerical Weather Prediction Based on Variational Data Assimilation: VarEnKF

AbstractSeveral NWP centers currently employ a variational data assimilation approach for initializing deterministic forecasts and a separate ensemble Kalman filter (EnKF) system both for initializing ensemble forecasts and for providing ensemble background error covariances for the deterministic system. This study describes a new approach for performing the data assimilation step within a perturbed-observation EnKF. In this approach, called VarEnKF, the analysis increment is computed with a variational data assimilation approach both for the ensemble mean and for all of the ensemble perturbations. To obtain a computationally efficient algorithm, a much simpler configuration is used for the ensemble perturbations, whereas the configuration used for the ensemble mean is similar to that used for the deterministic system. Numerous practical benefits may be realized by using a variational approach for both deterministic and ensemble prediction, including improved efficiency for the development and maintenance of the computer code. Also, the use of essentially the same data assimilation algorithm would likely reduce the amount of numerical experimentation required when making system changes, since their impacts in the two systems would be very similar. The variational approach enables the use of hybrid background error covariances and may also allow the assimilation of a larger volume of observations. Preliminary tests with the Canadian global 256-member system produced significantly improved ensemble forecasts with VarEnKF as compared with the current EnKF and at a comparable computational cost. These improvements resulted entirely from changes to the ensemble mean analysis increment calculation. Moreover, because each ensemble perturbation is updated independently, VarEnKF scales perfectly up to a very large number of processors.

Influence of the Self-Consistent Regional Ensemble Background Error Covariance on Hurricane Inner-Core Data Assimilation with the GSI-Based Hybrid System for HWRF

Abstract An initial vortex spindown, or strong adjustment to the structure and intensity of a hurricane’s initial vortex, presents a significant problem in hurricane forecasting, as with the NCEP Hurricane Weather Research and Forecasting Model (HWRF), because it can cause significantly degraded intensity forecasts. In this study, the influence of the self-consistent regional ensemble background error covariance on assimilating hurricane inner-core tail Doppler radar (TDR) observations in HWRF is examined with the NCEP gridpoint statistical interpolation (GSI)-based ensemble–three-dimensional variational (3DVAR) hybrid data assimilation system. It is found that the resolution of the background error covariance term, coming from the ensemble forecasts, has notable influence on the assimilation of hurricane inner-core observations and subsequent forecasting results. Specifically, the use of ensemble forecasting at high-resolution native grids results in significant reduction of the vortex spindown problem and thus leads to improved hurricane intensity forecasting. Further diagnoses are conducted to examine the spindown problem with a gradient wind balance. It is found that artificial vortex initialization, performed before data assimilation, can cause strong supergradient winds or imbalance in the vortex inner-core region. Assimilation of hurricane inner-core TDR data can significantly mitigate this imbalance by reducing the supergradient effects. Compared with the use of a global ensemble background error term, application of the self-consistent regional ensemble background covariance to inner-core data assimilation leads to better representation of the mesoscale hurricane inner-core structures. It can also result in more realistic vortex structures in data assimilation even when the observational data are unevenly distributed.