Flow-dependent Background Error Covariance Research Articles

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.

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.

Preliminary evaluation of all-sky radiance assimilation scheme with POD-3DEnVar method

To meet the challenges in satellite data assimilation involving cloud and precipitation processes, an all-sky radiance assimilation scheme (referred to as the ‘scheme’) that includes hydrometeor analysis is constructed based on the Proper Orthogonal Decomposition (POD)-3DEnVar method. Three key elements of the scheme are: (1) four hydrometeor mixing ratios for cloud-water, cloud-ice, rain, and snow in the control variables of the POD-3DEnVar method; (2) an extension of the Community Radiative Transfer Model interface to include hydrometeor profiles; and (3) multiple physical process model forecasts that use multiple microphysical and cumulus parameterization schemes as ensemble samples to estimate the flow-dependent background error covariance of the control variables, including those for hydrometeors.To evaluate the performance of the scheme, single-observation experiments and observation system simulation experiments (OSSEs) were designed for a binary typhoon case. Results for the single observation experiments show that the scheme can accurately assimilate satellite radiance near typhoon centers and produce reasonable increments for the hydrometeor variables. The background error covariances of the hydrometeor variables have reasonable flow-dependent characteristics. Results for the OSSEs have root-mean-square errors for all control variables of the assimilation analysis field with respect to the ‘true’ field that are lower than those obtained without assimilation. This indicates that the scheme effectively reduces error for all control variables, including those for hydrometeors. Forecasting experiments reveal that these improvements in the assimilation of control variables result in improved forecasts. However, improvements in the hydrometeor variables are of shorter duration than are those of the other control variables. The impact of improvements in the assimilation on typhoon track and intensity are obvious in the forecasting field.

Effects of Flow Dependency Introduced by Background Error in Frequent and Dense Assimilation of Radial Winds Using Observation Error Correlated in Time and Space

Abstract We investigated the effect of flow dependency in the assimilation of high-density, high-frequency observations. Radial winds from a Doppler radar are assimilated using a regional hybrid four-dimensional variational data assimilation (4D-Var) scheme with a flow-dependent background error covariance. To consistently assimilate 5 km × 5.625° cell-averaged radial winds at an interval of 10 min, the spatial and temporal correlations of the observation error are statistically diagnosed to be incorporated into the hybrid 4D-Var. The spatial correlation width is larger than that expected from instrument error, suggesting a contribution from representation error whose propagation is also considered to lead to temporal correlation, the width of which is diagnosed to increase with forecast time. The background error covariance also has an important role in incorporating observational information into the analysis. Single observation experiments show that the hybrid 4D-Var has more small-scale structure in its flow-dependent background error correlation than the 4D-Var limited from the climatological background error covariance mainly in the former part of the assimilation window. This suggests the higher potential of the hybrid 4D-Var to allow more higher-wavenumber components in the increment. A case study shows that the hybrid 4D-Var makes better use of the dense and frequent observations, reflecting more detailed representation of flow throughout the assimilation window, leading to promising results in the forecast. Sensitivity experiments also show that it is important to use the optimal observation error correlation. It is suggested that the flow-dependent background error becomes necessary to effectively use high-resolution, high-frequency observations.

Integrated Hybrid Data Assimilation for an Ensemble Kalman Filter

Abstract Hybrid ensemble–variational assimilation methods that combine static and flow-dependent background error covariances have been widely applied for numerical weather predictions. The commonly used hybrid assimilation methods compute the analysis increment using a variational framework and update the ensemble perturbations by an ensemble Kalman filter (EnKF). To avoid the inconsistencies that result from performing separate variational and EnKF systems, two integrated hybrid EnKFs that update both the ensemble mean and ensemble perturbations by a hybrid background error covariance in the framework of EnKF are proposed here. The integrated hybrid EnKFs approximate the static background error covariance by use of climatological perturbations through augmentation or additive approaches. The integrated hybrid EnKFs are tested in the Lorenz05 model given different magnitudes of model errors. Results show that the static background error covariance can be sufficiently estimated by climatological perturbations with an order of hundreds. The integrated hybrid EnKFs are superior to the traditional hybrid assimilation methods, which demonstrates the benefit to update ensemble perturbations by the hybrid background error covariance. Sensitivity results reveal that the advantages of the integrated hybrid EnKFs over traditional hybrid assimilation methods are maintained with varying ensemble sizes, inflation values, and localization length scales. Significance Statement Data assimilation is critical for providing the best possible initial condition for forecast and improving the numerical weather predictions. The hybrid ensemble–variational data assimilation method has been widely adopted and developed by many operational centers. The hybrid ensemble–variational assimilation method combines the advantages of ensemble and variational methods and minimizes the weaknesses of the two methods, and thus it outperforms the stand-alone variational and ensemble assimilation methods. The hybrid ensemble–variational assimilation method often computes the control analysis using a variational solver with hybrid background error covariances, but generates the ensemble perturbations by an ensemble Kalman filter (EnKF) system with pure flow-dependent background error covariances. The inconsistencies that result from performing separate variational and EnKF systems can lead to suboptimality in the hybrid ensemble–variational assimilation method. Therefore, integrated hybrid EnKF methods that utilize the framework of an EnKF to update both the ensemble mean and ensemble perturbations by the hybrid background error covariance, are proposed. The integrated hybrid EnKFs use climatological ensemble perturbations to approximate the static background error covariance. The integrated hybrid EnKFs are superior to the traditional hybrid ensemble–variational assimilation methods by producing smaller errors, and the advantages are persistent with varying assimilation parameters.

EnKF Assimilation of Satellite-retrieved Cloud Water Path to Improve Tropical Cyclone Rainfall Forecast

Tropical cyclone(TC) rainfall forecast has remained a challenge. To create initial conditions with high quality for simulation, the present study implemented a data assimilation scheme based on the EnKF method to ingest the satellite-retrieved cloud water path(Cw) and tested it in WRF. The scheme uses the vertical integration of forecasted cloud water content to transform control variables to the observation space, and creates the correlations between Cw and control variables in the flow-dependent background error covariance based on all the ensemble members, so that the observed cloud information can affect the background temperature and humidity. For two typhoons in 2018(Yagi and Rumiba), assimilating Cw significantly increases the simulated rainfalls and TC intensities. In terms of the average equitable threat score of daily moderate to heavy rainfall(5-120 mm), the improvements are over 130%, and the dry biases are cut by about 30%. Such improvements are traced down to the fact that Cw assimilation increases the moisture content, especially that further away from the TC center, which provides more precipitable water for the rainfall, strengthens the TC and broadens the TC size via latent heat release and internal wind field adjustment.

Assimilation of Doppler Radar Data with an Ensemble 3DEnVar Approach to Improve Convective Forecasting

An ensemble three-dimensional ensemble-variational (3DEnVar) data assimilation (E3DA) system was developed within the Weather Research and Forecasting model’s 3DVar framework to assimilate radar data to improve convective forecasting. In this system, ensemble perturbations are updated by an ensemble of 3DEnVar and the ensemble forecasts are used to generate the flow-dependent background error covariance. The performance of the E3DA system was first evaluated against one experiment without radar DA and one radar DA experiment with 3DVar, using a severe storm case over southeastern China on 5 June 2009. Results indicated that E3DA improved the quantitative forecast skills of reflectivity and precipitation, as well as their spatial distributions in terms of both intensity and coverage over 3DVar. The root-mean-square error of radial velocity from 3DVar was reduced by E3DA, with stronger low-level wind closer to observation. It was also found that E3DA improved the wind, temperature and water vapor mixing ratio, with the lowest errors at the surface and upper levels. 3DVar showed moderate improvements in comparison with forecasts without radar DA. A diagnosis of the analysis revealed that E3DA increased vertical velocity, temperature, and humidity corresponding to the added reflectivity, while 3DVar failed to produce these adjustments, because of the lack of reasonable cross-variable correlations. The performance of E3DA was further verified using two convective cases over southern and southeastern China, and the reflectivity forecast skill was also improved over 3DVar.

The Impact of Stochastic Physics-Based Hybrid GSI/EnKF Data Assimilation on Hurricane Forecasts Using EMC Operational Hurricane Modeling System

The National Oceanic and Atmospheric Administration’s (NOAA) cloud-permitting high-resolution operational Hurricane Weather and Research Forecasting (HWRF) model includes the sophisticated hybrid grid-point statistical interpolation (GSI) and Ensemble Kalman Filter (EnKF) data assimilation (DA) system, which allows assimilating high-resolution aircraft observations in tropical cyclone (TC) inner core regions. In the operational HWRF DA system, the flow-dependent background error covariance matrix is calculated from the HWRF self-cycled 40-member ensemble. This DA system has proved to provide improved initial TC structure and therefore improved TC track and intensity forecasts. However, the uncertainties from the model physics are not taken into account in the FY2017 version of the HWRF DA system. In order to further improve the HWRF DA system, the stochastic physics perturbations are introduced in the HWRF DA, including the cumulus convection scheme, the planetary boundary layer (PBL) scheme, and model surface physics (drag coefficient), for HWRF-based ensembles. This study shows that both TC initial conditions and TC track and intensity forecast skills are improved by adding stochastic model physics in the HWRF self-cycled DA system. It was found that the improvements in the TC initial conditions and forecasts are the results of ensemble spread increases which realistically represent the model background error covariance matrix in HWRF DA. For all 2016 Atlantic storms, the TC track and intensity forecast skills are improved by about ~3% and 6%, respectively, compared to the control experiment. The case study shows that the stochastic physics in HWRF DA is especially helpful for those TCs that have inner-core high-resolution aircraft observations, such as tail Doppler radar (TDR) data.

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.

Hybrid Background Error Covariances for a Limited-Area Deterministic Weather Prediction System

Abstract This study introduces an experimental regional assimilation configuration for a 4D ensemble–variational (4D-EnVar) deterministic weather prediction system. A total of 16 assimilation experiments covering July 2014 are presented to assess both experimental regional climatological background error covariances and updates in the treatment of flow-dependent error covariances. The regional climatological background error covariances are estimated using statistical correlations between variables instead of using balance operators. These error covariance estimates allow the analyses to fit more closely with the assimilated observations than when using the lower-resolution global background error covariances (due to shorter correlation scales), and the ensuing forecasts are significantly improved. The use of ensemble-based background error covariances is also improved by reducing vertical and horizontal localization length scales for the flow-dependent background error covariance component. Also, reducing the number of ensemble members employed in the deterministic analysis (from 256 to 128) reduced computational costs by half without degrading the accuracy of analyses and forecasts. The impact of the relative contributions of the climatological and flow-dependent background error covariance components is also examined. Results show that the experimental regional system benefits from giving a lower (higher) weight to climatological (flow-dependent) error covariances. When compared with the operational assimilation configuration of the continental prediction system, the proposed modifications to the background error covariances improve both surface and upper-air RMSE scores by nearly 1%. Still, the use of a higher-resolution ensemble to estimate flow-dependent background error covariances does not yet provide added value, although it is expected to allow for a better use of dense observations in the future.

The impact of optimal selected historical forecasting samples on hybrid ensemble-variational data assimilation

A resampling method that selects historical forecasting samples as supplementary samples is proposed for the hybrid ensemble-variational data assimilation system to alleviate the computational burden of ensemble forecasting samples. To select reasonable samples from all historical forecasting samples, the first modes of absolute vorticity are abstracted by the empirical orthogonal function (EOF) as indicators of atmospheric dynamic features from the background and each of historical forecasting sample, then they are matched at the analysis time. A series of single observation tests and 19-day cycling data assimilation and forecasting experiments for a Mei-yu period are carried out to evaluate the impact of the selected historical forecasting samples.The single observation tests indicate that the use of selected historical forecasting samples is able to provide reasonable flow-dependent background error covariance for the data assimilation system. The cycling data assimilation and forecasting experiments demonstrate that the analyses and forecasts as well as precipitation forecast skills are improved by using the combination of selected historical forecasting samples and ensemble forecasting samples. The sample-combined experiment performs close to the experiment with full-size ensemble forecasting samples, but it spends fewer computational resources. The diagnosis of a heavy rainfall case is presented to further illustrate the role of the selected historical forecasting samples. It is found that the simulation of vertical velocity and relative humidity are improved for the case in the experiment of the combined samples, leading to better intensity and position forecasts of the precipitation.

Assimilation of radar radial velocity data with the WRF hybrid 4DEnVar system for the prediction of hurricane Ike (2008)

Four dimensional ensemble-variation data assimilation (4DEnVar) is the method that considers the flow dependent background error covariance (BEC) and asynchronous observations throughout the assimilation window, which avoids the maintenance of the adjoint model. The impacts of assimilation of radial velocity (Vr) data using hybrid-4DEnVar for the analyses and forecasts of hurricane Ike are investigated using Weather Research and Forecasting and Data Assimilation model (WRFDA). 4DEnVar is coupled with Ensemble Transform Kalman Filter (ETKF) by updating the ensemble mean by the hybrid scheme and the ensemble perturbations are updated by the ETKF. Single observation tests for typical Jet cast and tropical cyclone (TC) case are conducted before the real hurricane Ike (2008) case. It is found that the analysis increment moves downstream by the end of the assimilation window. The linear propagation represented by the 4DEnVar method is close to the full nonlinear model integration. For the real IKE case, it is found that positive and spiral temperature increments, best track and intensity forecast are found in 4DEnVar experiment, indicating a more realistic thermal structure of hurricane Ike. 3DEnVar and 3DVar-FGAT are limited due to the lack of the BEC description spatially and temporally. 3DVar experiment produces much smoother and weaker increments with cold temperature increments at the hurricane vortex center at lower levels.

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.

Impact of Assimilating Aircraft Reconnaissance Observations on Tropical Cyclone Initialization and Prediction Using Operational HWRF and GSI Ensemble–Variational Hybrid Data Assimilation

Abstract This study evaluates the impact of assimilating high-resolution, inner-core reconnaissance observations on tropical cyclone initialization and prediction in the 2013 version of the operational Hurricane Weather Research and Forecasting (HWRF) Model. The 2013 HWRF data assimilation system is a GSI-based hybrid ensemble–variational system that, in this study, uses the Global Data Assimilation System ensemble to estimate flow-dependent background error covariance. Assimilation of inner-core observations improves track forecasts and reduces intensity error after 18–24 h. The positive impact on the intensity forecast is mainly found in weak storms, where inner-core assimilation produces more accurate tropical cyclone structures and reduces positive intensity bias. Despite such positive benefits, there is degradation in short-term intensity forecasts that is attributable to spindown of strong storms, which has also been seen in other studies. There are several reasons for the degradation of intense storms. First, a newly discovered interaction between model biases and the HWRF vortex initialization procedure causes the first-guess wind speed aloft to be too strong in the inner core. The problem worsens for the strongest storms, leading to a poor first-guess fit to observations. Though assimilation of reconnaissance observations results in analyses that better fit the observations, it also causes a negative intensity bias at the surface. In addition, the covariance provided by the NCEP global model is inaccurate for assimilating inner-core observations, and model physics biases result in a mismatch between simulated and observed structure. The model ultimately cannot maintain the analysis structure during the forecast, leading to spindown.

Practical Ensemble-Based Approaches to Estimate Atmospheric Background Error Covariances for Limited-Area Deterministic Data Assimilation

Abstract High-resolution flow-dependent background error covariances can allow for a better usage of dense observation networks in applications of data assimilation for numerical weather prediction. The generation of high-resolution ensembles, however, can be computationally cost prohibitive. In this study, practical and low-cost ensemble generation methods are presented and compared against both global and regional ensemble Kalman filters (G-EnKF and R-EnKF, respectively). The goal is to provide limited-area deterministic assimilation schemes with higher-resolution flow-dependent background error covariances that perform at least as well as those from the G-EnKF when assimilating the same observations. The low-cost methods are based on short-range regional ensemble forecasts initialized from 1) deterministic analysis plus balanced perturbations (filter free approach) and 2) a simplified ensemble square root filter (S-EnSRF), centered on deterministic analyses. The resulting ensembles from the different approaches are used within a 4D ensemble–variational (4D-EnVar) assimilation system covering most of Canada and the northern United States. Diagnostic results show that the mean is an important component of the ensembles. Results also show that the persistence of the homogeneous characteristics of the perturbations in the filter free approach makes this method unsuited for short assimilation time windows since some error structures take longer to develop. The S-EnSRF approach overcomes this limitation by recycling part of the prior perturbations. Results from 1-month assimilation experiments show that the S-EnSRF and R-EnKF experiments provide forecasts of similar quality to those from G-EnKF. Furthermore, results from precipitation verification indicate that the R-EnKF experiment provides the best precipitation accumulation predictions over 24-h periods.

A Comparison between 3DVAR and EnKF for Data Assimilation Effects on the Yellow Sea Fog Forecast

The data assimilation method to improve the sea fog forecast over the Yellow Sea is usually three-dimensional variational assimilation (3DVAR), whereas ensemble Kalman filter (EnKF) has not yet been applied to this weather phenomenon. In this paper, two sea fog cases over the Yellow sea, one spread widely and the other spread narrowly along the coastal area, are studied in detail by a series of numerical experiments with 3DVAR and EnKF based on the Grid-point Statistical Interpolation (GSI) system and the Weather Research and Forecasting (WRF) model. The results show that the assimilation effect of EnKF outperforms that of 3DVAR: for the widespread-fog case, the probability of detection and equitable threat scores of the forecasted sea fog area are improved respectively by ~57.9% and ~55.5%; the sea fog formation of the other case completely mis-forecasted by 3DVAR was produced successfully by EnKF. These improvements of EnKF relative to 3DVAR benefit from its flow-dependent background error covariances, resulting in more realistic depiction of sea surface wind for the widespread-fog case and better moisture distribution for the other case in the initial conditions. More importantly, the correlation between temperature and humidity in the background error covariances of EnKF plays a vital role in the response of moisture to the assimilation of temperature, which leads to a great improvement in the initial moisture conditions for sea fog forecast. Extra sensitivity experiments of EnKF indicate that the forecast result is sensitive to ensemble inflation and localization factors, in particular, highly sensitive to the latter.

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.

A Prototype Regional GSI-based EnKF-Variational Hybrid Data Assimilation System for the Rapid Refresh Forecasting System: Dual-Resolution Implementation and Testing Results

A dual-resolution (DR) version of a regional ensemble Kalman filter (EnKF)-3D ensemble variational (3DEnVar) coupled hybrid data assimilation system is implemented as a prototype for the operational Rapid Refresh forecasting system. The DR 3DEnVar system combines a high-resolution (HR) deterministic background forecast with lower-resolution (LR) EnKF ensemble perturbations used for flow-dependent background error covariance to produce a HR analysis. The computational cost is substantially reduced by running the ensemble forecasts and EnKF analyses at LR. The DR 3DEnVar system is tested with 3-h cycles over a 9-day period using a 40/∼13-km grid spacing combination. The HR forecasts from the DR hybrid analyses are compared with forecasts launched from HR Gridpoint Statistical Interpolation (GSI) 3D variational (3DVar) analyses, and single LR hybrid analyses interpolated to the HR grid. With the DR 3DEnVar system, a 90% weight for the ensemble covariance yields the lowest forecast errors and the DR hybrid system clearly outperforms the HR GSI 3DVar. Humidity and wind forecasts are also better than those launched from interpolated LR hybrid analyses, but the temperature forecasts are slightly worse. The humidity forecasts are improved most. For precipitation forecasts, the DR 3DEnVar always outperforms HR GSI 3DVar. It also outperforms the LR 3DEnVar, except for the initial forecast period and lower thresholds.

Evaluation of precipitation forecasts from 3D-Var and hybrid GSI-based system during Indian summer monsoon 2015

This paper presents a systematic investigation of medium-range rainfall forecasts from two versions of the National Centre for Medium Range Weather Forecasting (NCMRWF)-Global Forecast System based on three-dimensional variational (3D-Var) and hybrid analysis system namely, NGFS and HNGFS, respectively, during Indian summer monsoon (June–September) 2015. The NGFS uses gridpoint statistical interpolation (GSI) 3D-Var data assimilation system, whereas HNGFS uses hybrid 3D ensemble–variational scheme. The analysis includes the evaluation of rainfall fields and comparisons of rainfall using statistical score such as mean precipitation, bias, correlation coefficient, root mean square error and forecast improvement factor. In addition to these, categorical scores like Peirce skill score and bias score are also computed to describe particular aspects of forecasts performance. The comparison results of mean precipitation reveal that both the versions of model produced similar large-scale feature of Indian summer monsoon rainfall for day-1 through day-5 forecasts. The inclusion of fully flow-dependent background error covariance significantly improved the wet biases in HNGFS over the Indian Ocean. The forecast improvement factor and Peirce skill score in the HNGFS have also found better than NGFS for day-1 through day-5 forecasts.

A comparison of limited-area 3DVAR and ETKF-En3DVAR data assimilation using radar observations at convective scale for the prediction of Typhoon Saomai (2006)

The ensemble transform Kalman filter based ensemble 3D variational (ETKF-En3DVAR) data assimilation (DA) system is employed to evaluate the potential value of assimilating radar radial wind (Vr) data for the analysis and forecasting of Typhoon Saomai (2006). The DA system conducted cycling assimilation every 30 min when Saomai started to enter radar coverage. Within the DA cycles, the control analysis was updated by the ETKF-En3DVAR algorithm whereas the forecast ensemble perturbations in the hybrid scheme were updated by the ETKF algorithm. The benefits from the use of the flow-dependent ensemble covariance are explored by comparing the analysis increments, analysis and subsequent forecasts from the hybrid scheme with those from a pure 3DVAR using static background error covariance. Sensitivity to the horizontal correlation scale in the 3DVAR and the vertical covariance localization in the hybrid are also explored. The reduced horizontal correlation scale in the 3DVAR yields much more reasonable circulation analyses than the default scale. The vertical covariance localization scale specified in terms of geometric height instead of model levels allows for desirable spreading of Vr data to the surface. It seems that the assimilation with the hybrid method leads to further improved vortex intensity forecast and track forecast of the typhoon compared to those in the analyses from the global forecast system and 3DVAR. The results also indicated that the hybrid has a significant effect on the 12 h accumulated rainfall forecasts. Such improvements for analysis and forecast are probably due to the use of the flow-dependent background error covariance.