Background Error Statistics Research Articles

A Comparison of Channel Selection for the Assimilation of CrIS Radiances for NWP

Abstract With hyperspectral instruments measuring radiation emitted by Earth and its atmosphere in the thermal infrared range in multiple channels, several studies were made to select a subset of channels in order to reduce the number of channels to be used in a data assimilation system. An optimal selection of channels based on the information content depends on several factors related to observation and background error statistics and the assimilation system itself. An optimal channel selection for the Cross-track Infrared Sounder (CrIS) was obtained and then compared to selections made for different NWP systems. For instance, the channel selection of Carminati has 224 channels also present in our optimal selection, which includes 455 channels. However, in terms of analysis error variance, the difference between the two selections is small. Integrated over the whole profile, the relative difference is equal to 15.3% and 4.5% for temperature and humidity, respectively. Also, different observation error covariance matrices were considered to evaluate the impact of this matrix on channel selection. Even though the channels selected optimally were different in terms of which channels were selected for the various matrices, the results in terms of analysis error are similar. Significance Statement Satellites measure radiation from Earth and its atmosphere in the thermal infrared. Those radiance data contain thousands of measurements, called channels, and thus, a selection needs to be done retaining most of the information content since the large number of individual pieces of information is not usable for numerical weather prediction systems. The goal of this paper is to find an optimal selection for the instrument CrIS and to compare this selection with selections made for different numerical weather prediction systems. It was found that even though the channels selected optimally were different in terms of which channels were selected compared to other selections, the results in terms of precision of the analysis are similar and the results in terms of analysis error are similar due to the nature of hyperspectral instruments, which have multiple Jacobians overlapping.

Assessing the Accuracy of 3D-VAR in Supercell Thunderstorm Forecasting: A Regional Background Error Covariance Study

Data assimilation (DA) integrates observational data with numerical weather predictions to enhance weather forecast accuracy. This study evaluates three regional background error (BE) covariance statistics for numerical weather prediction (NWP) via a variational data assimilation (VAR) scheme. The best practices in DA are highlighted, as well as the impact of BE covariance calculation in DA procedures by employing the Weather Research and Forecasting (WRF) model. Forecasts initialized at different intervals were used to compute distinct regional background error statistics utilizing three control variable (CV) methodologies over a span of 20 days. These statistics are used by the three-dimensional VAR DA process of WRF DA software, producing analysis fields that lead to forecasts for a distinct convective supercell event during the summer of 2019 over northern Greece. This high-impact convective event underscores the importance of selecting appropriate BE over complex terrain areas. The results emphasize the significance of BE usage in DA, proposing the optimal DA approach for simulations of convective systems.

An Improved Coupled Data Assimilation System with a CGCM Using Multi-Time-Scale High-Efficiency EnOI-Like Filtering

Abstract Coupled data assimilation (CDA), which combines coupled models and observations from multiple Earth system domains, plays a critical role in climate studies by producing a four-dimensional estimation of Earth system states. Traditional ensemble Kalman filter (EnKF) CDA algorithms, while convenient to implement in multiple DA components in a coupled system, are, however, expensive and lack sufficient representativeness for low-frequency background flows. Here, a multi-time-scale high-efficiency approximate filter with ensemble optimal interpolation (MSHea-EnOI) scheme has been implemented with a global fully coupled model. It consists of stationary, low-frequency, and high-frequency filters constructed from the time series of a single-model solution with improved representativeness for low-frequency background error statistics and enhanced computational efficiency. The MSHea-EnOI is evaluated in a biased twin experiment framework with synthetic “observations” produced by another coupled model, and a three-decade coupled reanalysis experiment with real observations. Results show that with increased representativeness on multiscale background flows, while computationally costing only a small fraction of ensemble-based CDA, the MSHea-EnOI shows the potential to improve CDA quality with synthetic observations. The coupled reanalysis experiment with real observations also shows reasonable fittings to observations and comparable results to other reanalysis products using different DA schemes. While reconstructing a close-to-rapid Atlantic meridional overturning circulation, the coupled reanalysis reproduces most of the atmosphere and ocean reanalysis signals such as the Hadley circulation and upper ocean heat content. The MSHea-EnOI could have good application potential in ensemble-based DA systems in terms of its multiscale property and computational efficiency.

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.

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.

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.

Operational convective-scale data assimilation over Iran: A comparison between WRF and HARMONIE-AROME

The impact of applying three-dimensional variational data assimilation (3D-Var DA) on convective-scale forecasts is investigated by using two mesoscale models, the Weather Research and Forecasting model (WRF-ARW) and the Hirlam and Aladin Research Model On Non-hydrostatic-forecast Inside Europe (HARMONIE-AROME). One month (1 to 30 December 2013) of numerical experiments were conducted with these two models at 2.5 km horizontal resolution, in order to partly resolve convective phenomena, on the same domain over a mountainous area in Iran and neighboring areas. Furthermore, in order to estimate the domain specific background error statistics (BES) in convective scales, two months (1 November to 30 December 2017) of numerical experiments were carried out with both models by downscaling operational ECMWF forecasts. For setting the numerical experiments in an operational scenario, ECMWF operational forecast data were used as initial and lateral boundary conditions (ICs/LBCs). In order to examine the impact of data assimilation, the 3D-Var method in cycling mode was adopted and the forecasts were verified every 6 hours up to 36 hours for selected meteorological variables. In addition, 24 h accumulated precipitation forecasts were verified separately. Generally, the WRF and HARMONIE-AROME exhibit similar verification statistics for the selected forecast variables. The impact of DA on the numerical forecast shows some evidence of improvement in both models, and this effect decreases severely at longer lead times. Results from verifying the 24 h convective-scale precipitation forecasts from both models with and without DA suggest the superiority of the WRF model in forecasting more accurately the occurred precipitation over the simulation domain, even for the downscaling run.

Radar reflectivity and radial velocity assimilation in a hybrid ETKF‐3DVAR system for prediction of a heavy convective rainfall

AbstractReliable forecasting of heavy convective rainfall events continues to be one of the greatest challenges for numerical weather prediction models. Studies across the globe have indicated that Doppler weather radar (DWR) data assimilation through three‐dimensional variational methods (3D‐Var) has a considerable impact on improving the forecast skill of convective precipitation. However, the time‐averaged background error statistics (BES) employed in 3D‐Var fail to address the day‐to‐day variability of forecast errors in BES. To effectively represent the convective precipitation events through DWR assimilation, it is important to account for the day‐to‐day variability in background error's variance and correlations in the BES. In this study, the effect of assimilating DWR data using flow‐dependent BES within the variational assimilation system is analysed via the hybrid Ensemble Transform Kalman Filter (ETKF)‐3DVAR. For this, the functionality of ETKF in the hybrid ETKF‐3DVAR has been extended to assimilate both DWR radial velocity and reflectivity information. The results suggest that assimilating DWR observations through the hybrid ETKF‐3DVAR improves the forecast skills of convective precipitation as compared to the 3D‐Var. It has also been observed that updating the ensemble states through assimilation of DWR observations in the ETKF system shows an increased wind and moisture convergence.

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.

A Flow‐Dependent Targeted Observation Method for Ensemble Kalman Filter Assimilation Systems

AbstractIn this study, we developed a flow‐dependent sequential assimilation‐based targeted observation method by minimizing the analysis error variance under the framework of the ensemble Kalman filter (EnKF). This approach considers the flow‐dependent variation in background error statistics when identifying optimal observational sites through the sequential assimilation method. Covariance localization is also introduced in this method, enabling computational efficiency and eliminating impacts from spurious observations. By quantifying the reduction in analysis error variances, the proposed method could estimate the potential improvements by each optimal observation while assimilated. With this method, we design an optimal observational array for sea level anomaly (SLA) prediction in the tropical Indian Ocean (TIO), which is implemented using a fully coupled climate model, the Community Earth System Model (CESM), in conjunction with a coupled assimilation system. The optimal observational array detected from this method was found to theoretically reduce the initial uncertainty by up to approximately 60% of the error variance. An observing system simulation experiment (OSSE) using the CESM and the coupled assimilation system, which was designed for validation purposes, confirms the theoretical reduction in the analysis error variance by the optimal observation array.

Significance of 4DVAR Radar Data Assimilation in Weather Research and Forecast Model‐Based Nowcasting System

AbstractAccurate nowcasting of short‐lived extreme weather events is essential for saving millions of lives and property. Traditional methods of nowcasting are majorly focused on extrapolation of precipitation derived from radar reflectivity data, which often fail to capture the initiation and decay of weather systems. Earlier studies have shown the ability of high‐resolution Numerical Weather Prediction (NWP) models to better capture the structure and lifecycle of storms compared to data‐driven methods. However, the initial value problem of NWP makes it more challenging to be implemented for nowcasting applications. To handle such uncertainty from initial conditions, we have designed an NWP nowcasting system based on variational approach using WRF model. One of the major challenges of the variational methods in the nowcasting system is the choice of control variables used for generating background error statistics. Thus, we have investigated the impact of control variable options on improving the skill of variational‐based NWP nowcasting system. The proposed nowcasting system was tested for a heavy rainfall event that occurred over the Chennai city, India, on 1 December 2015, by assimilating Doppler Weather Radar data using different control variable options in Weather Research and Forecast—three‐dimensional (3DVAR)‐ and four‐dimensional variational data assimilation (4DVAR)‐based nowcasting system. Results show that control variables choices have a positive impact on 4DVAR analysis, particularly on radial velocity. Our results also indicate that assimilation of Doppler Weather Radar data with zonal and meridional momentum control variable in a 4DVAR system shows more than 30% improvement in precipitation forecast skill compared to the 3DVAR system.

Background error statistics in the Tropics: Structures and impact in a convective‐scale numerical weather prediction system

AbstractThe background error covariance matrix plays a vital role in any data assimilation system. Proper specification, which is determined by the forecast system set‐up, is often required. Previous studies have investigated its relevance in various global and regional numerical weather prediction (NWP) systems; however, very few have explored it in tropical NWP systems. Here, we present and evaluate the structures of the background error covariance matrix for a tropical convective‐scale NWP system. A total of 12 background error covariance matrices are modelled using differences between pairs of forecasts of different lengths but valid at the same time, based on the application of the vertical‐first and horizontal‐first transform order formulations on six permutations of the training data. Through pseudo‐single observation tests, we extract and test the sensitivity of their structures to the training data period (seasons), forecast lag and transform order. The structures typically exhibit more dependence on forecast lag and transform order; horizontal‐first transform order covariances had structures with shorter horizontal length‐scales for wind and larger wind background error standard deviations. We also note that some covariances had horizontal and vertical structures with stronger mass–wind coupling, closely resembling an equatorial Kelvin wave. To assess the performance of each of the covariances, 12 month‐long data assimilation trials in May 2018 (characterised by frequent occurrences of localised thunderstorm events) are performed. We show improved short‐range precipitation forecasts in trials using some of the covariances compared to the current operational covariance. These covariances generally have structures with weak mass–wind coupling, shorter horizontal length‐scales for wind and larger wind background error standard deviations, compared to other covariances which led to poorer forecasts. These may be desirable factors when modelling the background error covariance matrix for tropical convective‐scale data assimilation systems.

Improving Convective Precipitation Forecasts Using Ensemble‐Based Background Error Covariance in 3DVAR Radar Assimilation System

AbstractSkillful quantitative precipitation forecast using the numerical weather prediction model relies on an accurate estimate of the atmospheric state as an initial condition. Variational assimilation methods (VAR) have the potential to provide improved initial state estimation to the numerical weather prediction model using observations, prior data (background), and their respective error covariance. The quality of variational assimilation hinges on the background error statistics (BES) as it weights the error in prior state and determines the spread of assimilated observations in model space. Traditional approaches used to model stationary BES in a three‐dimensional variational assimilation system often fail to represent the model error in BES. In this study, we have proposed an ensemble method using Stochastically Perturbed Parameterization Tendency to represent the model error in BES. The characteristics of the proposed BES are compared with the traditional approaches using the National Meteorological Centre method for different control variables choices. We have further tested the performance of the proposed method in improving the skill of precipitation forecast for an extreme rainfall event, which caused devastating flood over Chennai city, India, on December 2015. Results demonstrate that the use of the proposed method results in better forecast skill of convective precipitation in terms of both position and intensity than traditional National Meteorological Centre‐based BES. Best results are obtained when zonal and meridional momentum control variables are used for modeling ensemble‐based BES.

Techniques and challenges in the assimilation of atmospheric water observations for numerical weather prediction towards convective scales

AbstractWhile contemporary numerical weather prediction models represent the large‐scale structure of moist atmospheric processes reasonably well, they often struggle to maintain accurate forecasts of small‐scale features such as convective rainfall. Even though high‐resolution models resolve more of the flow, and are therefore arguably more accurate, moist convective flow becomes increasingly nonlinear and dynamically unstable. Importantly, the models' initial conditions are typically sub‐optimal, leaving scope to improve the accuracy of forecasts with improved data assimilation. To address issues regarding the use of atmospheric water‐related observations – especially at convective scales (also known as storm scales) – this article discusses the observation and assimilation of water‐related quantities. Special emphasis is placed on background error statistics for variational and hybrid methods which need special attention for water variables. The challenges of convective‐scale data assimilation of atmospheric water information are discussed, which are more difficult to tackle than at larger scales. Some of the most important challenges include the greater degree of inhomogeneity and lower degree of smoothness of the flow, the high volume of water‐related observations (e.g. from radar, microwave and infrared instruments), the need to analyse a range of hydrometeors, the increasing importance of position errors in forecasts, the greater sophistication of forward models to allow use of indirect observations (e.g. cloud‐ and precipitation‐affected observations), the need to account for the flow‐dependent multivariate “balance” between atmospheric water and both dynamical and mass fields, and the inherent non‐Gaussian nature of atmospheric water variables.

Ensemble of 4DVARs (En4DVar) data assimilation in a coastal ocean circulation model, Part I: Methodology and ensemble statistics

The ocean state off Oregon-Washington, U.S. West coast, is highly variable in time. Under these conditions the assumption made in traditional 4-dimensional variational data assimilation (4DVAR) that the prior model (background) error covariance is the same in every data assimilation (DA) window can be limiting. A DA system based on an ensemble of 4DVARs (En4DVar) has been developed in which the background error covariance is estimated from an ensemble of model runs and is thus time-varying. This part describes details of the En4DVar method and ensemble statistics verification tests. The control run and 39 ensemble members are forced by perturbed wind fields and corrected by DA in a series of 3-day windows. Wind perturbations are represented as a linear combination of empirical orthogonal functions (EOFs) for the larger scales and Daubechies wavelets for the smaller scales. The variance of the EOF expansion coefficients is based on estimates of the wind field error statistics derived using scatterometer observations and a Bayesian Hierarchical Model. It is found that the variance of the wind errors relative to the natural wind variability increases as the horizontal spatial scales decrease. DA corrections to the control run and ensemble members are calculated in parallel by the newly developed, cost-effective cluster search minimization method. For a realistic coastal ocean application, this method can generate a 30% wall time reduction compared to the restricted B-conjugate gradient (RBCG) method. Ensemble statistics are generally found to be consistent with background error statistics. In particular, ensemble spread is maintained without inflating. However, sea-surface height background errors cannot be fully reproduced by the ensemble perturbations.

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.