Static Background Error Covariance Research Articles

A Multivariate Additive Inflation Approach to Improve Storm‐Scale Ensemble‐Based Data Assimilation and Forecasts: Methodology and Experiment With a Tornadic Supercell

AbstractEnsemble‐based convective‐scale radar data assimilation commonly suffers from an underdispersive background ensemble. This study introduces a multivariate additive‐inflation method to address such deficiency. The multivariate additive inflation (AI) approach generates coherent random perturbations drawn from a newly constructed convective‐scale static background error covariance matrix for all state variables including hydrometeors and vertical velocity. This method is compared with a previously proposed univariate AI approach, which perturbs each variable individually without cross‐variable coherency. Comparisons are performed on the analyses and forecasts of the 8 May 2003 Oklahoma City tornadic supercell. Within assimilation cycles, the multivariate approach is more efficient in increasing reflectivity spread and thus has a reduced spinup time than the univariate approach; the additional inclusion of hydrometeors and vertical velocity results in more background spread for both reflectivity and radial velocity. Significant differences among AI experiments also exist in the subsequent forecasts and are more pronounced for the forecasts initialized from the earlier assimilation cycles. The multivariate approach yields better forecasts of low‐level rotation, reflectivity distributions, and storm maintenance for most lead times. The additional inclusion of hydrometeor and vertical velocity in the multivariate method is beneficial in forecasts. Conversely, the additional inclusion of hydrometeor and vertical velocity in the univariate method poses negative impacts for the majority of forecast lead times.

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.

Impact of Feature-Dependent Static Background Error Covariances for Satellite-Derived Humidity Assimilation on Analyses and Forecasts of Multiple Sea Fog Cases over the Yellow Sea

Assimilation of satellite-derived humidity with a homogenous static background error covariance (B) matrix computed over the entire computational domain (Full-B) tends to overpredict sea fog coverage. A feature-dependent B (Fog-B) is proposed to address this issue. In Fog-B, the static error statistics for clear air and foggy areas are calculated separately using a feature-dependent binning method. The resultant error statistics are used simultaneously at appropriate locations guided by the satellite-derived sea fog. Diagnostics show that Full-B generally has broader horizontal and vertical length scales and larger error variances than Fog-B below ~300 m except for the vertical length scale near the surface. Experiments on three sea fog cases over the Yellow Sea are conducted to understand and examine the impact of Fog-B on sea fog analyses and forecasts. Results show that using Full-B produces greater and broader water vapor mixing ratio increments and thus predicts larger sea fog coverage than using Fog-B. Further evaluations suggest that using Fog-B has greater forecast skills in sea fog coverage and more accurate moisture conditions than using Full-B.

Ensemble-based diurnally varying background error covariances and their impact on short-term weather forecasting

Background error covariance (BEC) plays an essential role in variational data assimilation. Most variational data assimilation systems still use static BEC. Actually, the characteristics of BEC vary with season, day, and even hour of the background. National Meteorological Center–based diurnally varying BECs had been proposed, but the diurnal variation characteristics were gained by climatic samples. Ensemble methods can obtain the background error characteristics that suit the samples in the current moment. Therefore, to gain more reasonable diurnally varying BECs, in this study, ensemble-based diurnally varying BECs are generated and the diurnal variation characteristics are discussed. Their impacts are then evaluated by cycling data assimilation and forecasting experiments for a week based on the operational China Meteorological Administration-Beijing system. Clear diurnal variation in the standard deviation of ensemble forecasts and ensemble-based BECs can be identified, consistent with the diurnal variation characteristics of the atmosphere. The results of one-week cycling data assimilation and forecasting show that the application of diurnally varying BECs reduces the RMSEs in the analysis and 6-h forecast. Detailed analysis of a convective rainfall case shows that the distribution of the accumulated precipitation forecast using the diurnally varying BECs is closer to the observation than using the static BEC. Besides, the cycle-averaged precipitation scores in all magnitudes are improved, especially for the heavy precipitation, indicating the potential of using diurnally varying BEC in operational applications.摘要背景场误差协方差在资料同化系统中具有非常重要的作用, 目前业务变分同化系统中常采用静态背景场误差协方差, 未考虑其具体的日变化特征. 为构建更为合理且便于业务系统应用的日变化背景误差协方差, 本文构建了高分辨率集合预报样本的日变化背景场误差协方差, 揭示了其日变化特征, 并应用到了CMA-BJ业务系统中, 开展了基于业务框架的批量循环同化预报试验. 结果表明, 背景场误差存在明显的日变化特征, 采用集合日变化背景场误差协方差能够改进模式的预报效果.

Object-Based Verification of GSI EnKF and Hybrid En3DVar Radar Data Assimilation and Convection-Allowing Forecasts within a Warn-on-Forecast Framework

Abstract The Center for Analysis and Prediction of Storms has recently developed capabilities to directly assimilate radar reflectivity and radial velocity data within the GSI-based ensemble Kalman filter (EnKF) and hybrid ensemble three-dimensional variational (En3DVar) system for initializing convective-scale forecasts. To assess the performance of EnKF and hybrid En3DVar with different hybrid weights (with 100%, 20%, and 0% of static background error covariance corresponding to pure 3DVar, hybrid En3DVar, and pure En3DVar) for assimilating radar data in a Warn-on-Forecast framework, a set of data assimilation and forecast experiments using the WRF Model are conducted for six convective storm cases of May 2017. Using an object-based verification approach, forecast objects of composite reflectivity and 30-min updraft helicity swaths are verified against reflectivity and rotation track objects in Multi-Radar Multi-Sensor data on space and time scales typical of National Weather Service warnings. Forecasts initialized by En3DVar or the best performing EnKF ensemble member produce the highest object-based verification scores, while forecasts from 3DVar and the worst EnKF member produce the lowest scores. Averaged across six cases, hybrid En3DVar using 20% static background error covariance does not improve forecasts over pure En3DVar, although improvements are seen in some individual cases. The false alarm ratios of EnKF members for both composite reflectivity and updraft helicity at the initial time are lower than those from variational methods, suggesting that EnKF analysis reduces spurious reflectivity and mesocyclone objects more effectively.

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.

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.

An Analytical Four‐Dimensional Ensemble‐Variational Data Assimilation Scheme

AbstractThe usage of four‐dimensional variational (4DVar) scheme is limited by the static background error covariance and the adjoint model. In a hybrid frame of the four‐dimensional ensemble‐variational data assimilation scheme (4DEnVar), being able to avoid the tangent linear and adjoint models in the 4DVar and nowadays developed into a cutting‐edge research topic of the next‐generation data assimilation methods, an analytical 4DEnVar (A‐4DEnVar) scheme is designed. First, an analytical expression for explicit evolution of the background error covariances is derived. The expression collects the innovation of observations over an assimilation window simultaneously and propagates information to the initial background field by temporal cross covariances. Second, to estimate the adjoint model, the temporal covariances are constructed with ensemble members being centralized with respect to the model states integrated from the initial condition. Third, an iterative linear search process is introduced to minimize the cost function to update the analysis field until convergence. Twin experiments based on the Lorenz chaos model with three variables are conducted for the validation of the A‐4DEnVar scheme. Comparisons to the conventional 4DVar show that the A‐4DEnVar is comparable in accuracy even with a long assimilation window and sparse observations. The assimilation results also show that the A‐4DEnVar scheme can be implemented with a very small ensemble size which means that under circumstances without the tangent linear and adjoint models it can be easily incorporated into data assimilation systems in use.

Comparisons of Hybrid En3DVar with 3DVar and EnKF for Radar Data Assimilation: Tests with the 10 May 2010 Oklahoma Tornado Outbreak

AbstractIn this study, a hybrid En3DVar data assimilation (DA) scheme is compared with 3DVar, EnKF, and pure En3DVar for the assimilation of radar data in a real tornadic storm case. Results using hydrometeor mixing ratios (CVq) or logarithmic mixing ratios (CVlogq) as the control variables are compared in the variational DA framework. To address the lack of radial velocity impact issues when using CVq, a procedure that assimilates reflectivity and radial velocity data in two separate analysis passes is adopted. Comparisons are made in terms of the root-mean-square innovations (RMSIs) as well as the intensity and structure of the analyzed and forecast storms. For pure En3DVar that uses 100% ensemble covariance, CVlogq and CVq have similar RMSIs in the velocity analyses, but errors grow faster during forecasts when using CVlogq. Introducing static background error covariance at 5% in hybrid En3DVar (with CVlogq) significantly reduces the forecast error growth. Pure En3DVar produces more intense reflectivity analyses than EnKF that more closely match the observations. Hybrid En3DVar with 50% outperforms other weights in terms of the RMSIs and forecasts of updraft helicity and is thus used in the final comparison with 3DVar and EnKF. The hybrid En3DVar is found to outperform EnKF in better capturing the intensity and structure of the analyzed and forecast storms and outperform 3DVAR in better capturing the intensity and evolution of the rotating updraft.

Estimating of the Global Ionosphere Maps Using Hybrid Data Assimilation Method and Their Background Influence Analysis

AbstractThe increasing amount of the Global Navigation Satellite System (GNSS) ground receivers provides extremely abundant data resource to ionospheric community. In present paper, a hybrid data assimilation method is proposed to derive the global ionosphere maps (GIM) using the GNSS measurements. This method can balance the weights of background information from the International Reference Ionosphere model (IRI‐2016) and actual observations to reach a reasonable estimation, and its background error covariance (BEC) is a weighted linear combination of climatological static BEC and ensemble‐based flow‐dependent BEC. The results show that this method is capable of improving the background outputs significantly. To evaluate the quantitative contribution of background information on the estimated GIM, the background influence analysis is performed. The background information contributes less in the data‐rich areas and more in the data‐sparse areas. The mean background influence is up to 0.93 for the reconstructed GIM; that is, about 93% of the contribution is due to the background information, and the complementary 7% is the influence of the assimilated observations.

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.

A radar reflectivity operator with ice-phase hydrometeors for variational data assimilation (version 1.0) and its evaluation with real radar data

Abstract. A reflectivity forward operator and its associated tangent linear and adjoint operators (together named RadarVar) were developed for variational data assimilation (DA). RadarVar can analyze both rainwater and ice-phase species (snow and graupel) by directly assimilating radar reflectivity observations. The results of three-dimensional variational (3D-Var) DA experiments with a 3 km grid mesh setting of the Weather Research and Forecasting (WRF) model showed that RadarVar was effective at producing an analysis of reflectivity pattern and intensity similar to the observed data. Two to three outer loops with 50–100 iterations in each loop were needed to obtain a converged 3-D analysis of reflectivity, rainwater, snow, and graupel, including the melting layers with mixed-phase hydrometeors. It is shown that the deficiencies in the analysis using this operator, caused by the poor quality of the background fields and the use of the static background error covariance, can be partially resolved by using radar-retrieved hydrometeors in a preprocessing step and tuning the spatial correlation length scales of the background errors. The direct radar reflectivity assimilation using RadarVar also improved the short-term (2–5 h) precipitation forecasts compared to those of the experiment without DA.

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 AMSU-A Radiances in a Column Ensemble Kalman Filter

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.

Value-added Impact of Geostationary Hyperspectral Infrared Sounders on Local Severe Storm Forecasts—via a Quick Regional OSSE

Accurate atmospheric temperature and moisture information with high temporal/spatial resolutions are two of the key parameters needed in regional numerical weather prediction (NWP) models to reliably predict high-impact weather events such as local severe storms (LSSs). High spectral resolution or hyperspectral infrared (HIR) sounders from geostationary orbit (GEO) provide an unprecedented source of near time-continuous, three-dimensional information on the dynamic and thermodynamic atmospheric fields—an important benefit for nowcasting and NWP-based forecasting. In order to demonstrate the value of GEO HIR sounder radiances on LSS forecasts, a quick regional OSSE (Observing System Simulation Experiment) framework has been developed, including high-resolution nature run generation, synthetic observation simulation and validation, and impact study on LSS forecasts. Results show that, on top of the existing LEO (low earth orbit) sounders, a GEO HIR sounder may provide value-added impact [a reduction of 3.56% in normalized root-mean-square difference (RMSD)] on LSS forecasts due to large spatial coverage and high temporal resolution, even though the data are assimilated every 6 h with a thinning of 60 km. Additionally, more frequent assimilations and smaller thinning distances allow more observations to be assimilated, and may further increase the positive impact from a GEO HIR sounder. On the other hand, with denser and more frequent observations assimilated, it becomes more difficult to handle the spatial error correlation in observations and gravity waves due to the limitations of current assimilation and forecast systems (such as a static background error covariance). The peak reduction of 4.6% in normalized RMSD is found when observations are assimilated every 3 h with a thinning distance of 30 km.

A Study of the HWRF Analysis and Forecast Impact of Realistically Simulated CYGNSS Observations Assimilated as Scalar Wind Speeds and as VAM Wind Vectors

Abstract In preparation for the launch of the NASA Cyclone Global Navigation Satellite System (CYGNSS), a variety of observing system simulation experiments (OSSEs) were conducted to develop, tune, and assess methods of assimilating these novel observations of ocean surface winds. From a highly detailed and realistic hurricane nature run (NR), CYGNSS winds were simulated with error characteristics that are expected to occur in reality. The OSSE system makes use of NOAA’s HWRF Model and GSI data assimilation system in a configuration that was operational in 2012. CYGNSS winds were assimilated as scalar wind speeds and as wind vectors determined by a variational analysis method (VAM). Both forms of wind information had positive impacts on the short-term HWRF forecasts, as shown by key storm and domain metrics. Data assimilation cycle intervals of 1, 3, and 6 h were tested, and the 3-h impacts were consistently best. One-day forecasts from CYGNSS VAM vector winds were the most dynamically consistent with the NR. The OSSEs have a number of limitations; the most noteworthy is that this is a case study, and static background error covariances were used.

Multi-resolution Hybrid Data Assimilation Core on a Cubed-sphere Grid (HybDA)

This study illustrates the characteristics of the data assimilation system at the Korea Institute of Atmospheric Prediction Systems (KIAPS), based on the cubed-sphere grid system. The most interesting feature is the use of spherical harmonic functions defined on cubed-sphere grid points, which makes it possible to control the allowable physical wavenumber for the analysis increments. The relevant computational costs and parallel scalability are represented. The multiple-resolution approach is a distinguishable aspect of this data assimilation system. The wavenumber, up to which the analysis is conducted, increases as the outer iteration progresses. This multiresolution strategy is based on an investigation into the change of spectral components of analysis increments. The multi-resolution outer-loop provides cost-effective analysis-improvement, by explicitly controlling the analysis increments entered into the observation operator. To utilize the high-resolution deterministic forecast as a background state, it is subtracted from the forecast ensemble, to produce ensemble forecast perturbation that is hybridized with static background error covariance. Based on the cycled analysis experiments, the higher-resolution deterministic forecast is shown to preserve the high-frequency feature of the analysis increment relative to the ensemble mean forecast.

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.

Development of a Hybrid En3DVar Data Assimilation System and Comparisons with 3DVar and EnKF for Radar Data Assimilation with Observing System Simulation Experiments

Abstract A hybrid ensemble–3DVar (En3DVar) system is developed and compared with 3DVar, EnKF, “deterministic forecast” EnKF (DfEnKF), and pure En3DVar for assimilating radar data through perfect-model observing system simulation experiments (OSSEs). DfEnKF uses a deterministic forecast as the background and is therefore parallel to pure En3DVar. Different results are found between DfEnKF and pure En3DVar: 1) the serial versus global nature and 2) the variational minimization versus direct filter updating nature of the two algorithms are identified as the main causes for the differences. For 3DVar (EnKF/DfEnKF and En3DVar), optimal decorrelation scales (localization radii) for static (ensemble) background error covariances are obtained and used in hybrid En3DVar. The sensitivity of hybrid En3DVar to covariance weights and ensemble size is examined. On average, when ensemble size is 20 or larger, a 5%–10% static covariance gives the best results, while for smaller ensembles, more static covariance is beneficial. Using an ensemble size of 40, EnKF and DfEnKF perform similarly, and both are better than pure and hybrid En3DVar overall. Using 5% static error covariance, hybrid En3DVar outperforms pure En3DVar for most state variables but underperforms for hydrometeor variables, and the improvement (degradation) is most notable for water vapor mixing ratio qυ (snow mixing ratio qs). Overall, EnKF/DfEnKF performs the best, 3DVar performs the worst, and static covariance only helps slightly via hybrid En3DVar.