Background Error Covariance Research Articles

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.

Progress, challenges, and future steps in data assimilation for convection‐permitting numerical weather prediction: Report on the virtual meeting held on 10 and 12 November 2021

AbstractIn November 2021, the Royal Meteorological Society Data Assimilation (DA) Special Interest Group and the University of Reading hosted a virtual meeting on the topic of DA for convection‐permitting numerical weather prediction. The goal of the meeting was to discuss recent developments and review the challenges including methodological developments and progress in making the best use of observations. The meeting took place over two half days on the 10 and 12 November, and consisted of six talks and a panel discussion. The scientific presentations highlighted some recent work from Europe and the USA on convection‐permitting DA including novel developments in the assimilation of observations such as cloud‐affected satellite radiances in visible channels, ground‐based profiling networks, aircraft data, and radar reflectivity data, as well as methodological advancements in background and observation error covariance modelling and progress in operational systems. The panel discussion focused on key future challenges including the handling of multiscales (synoptic‐, meso‐, and convective‐scales), ensemble design, the specification of background and observation error covariances, and better use of observations. These will be critical issues to address in order to improve short‐range forecasts and nowcasts of hazardous weather.

Multi-scale three-dimensional variational data assimilation for high-resolution aerosol observations: Methodology and application

With an increasing number of air quality monitoring stations installed around the Chinese mainland, high-resolution aerosol observations become available, allowing improvements in air pollution monitoring and aerosol forecasting. However, the multi scales (especially small-scale) information included in high-resolution aerosol observations could not be effectively utilized by the traditional three-dimensional variational method (3DVAR). This study attempted to extend the traditional 3DVAR to a multi-scale 3DVAR with two iteration steps, two-scale-3DVAR (TS-3DVAR), to improve the effectiveness of assimilating high-resolution observations. In TS-3DVAR, the large-scale and small-scale components of observation information were decomposed from the original high-resolution observations using a Gaussian smoothing method and then assimilated using the corresponding large-scale or small-scale background error covariances which were derived from the partitioned background error samples. The data assimilation (DA) analysis field generated by TS-3DVAR is more accurate than 3DVAR in reproducing the field’s multi-scale characteristics, which could thus be used as the initial chemical field of the air quality model to improve aerosol forecasting. Particulate matter with an aerodynamic diameter of less than 2.5 μm (PM2.5) and 10.0 μm (PM10) from the surface air quality monitoring stations from November 01 to November 30, 2018 at 00:00 were assimilated daily to verify the effects of TS-3DVAR and 3DVAR on the aerosol analysis and forecast accuracy. The results showed that TS-3DVAR better constrained both large-scale and small-scale, especially the spatial wavelengths in a range of 54–216 km and those above 351 km. The average power spectra of the TS-3DVAR assimilation increment in the two wavelength ranges were 71.70% and 35.33% higher than those of 3DVAR. As a result, the TS-3DVAR was more effective than 3DVAR in improving the accuracy of the initial chemical field, and thereby the forecasting capability for PM2.5. In the initial chemical field, the 30-day average correlation coefficient (Corr) of PM2.5 of TS-3DVAR was 0.052 (6.12%) higher than that of 3DVAR, and the root mean square error (RMSE) of TS-3DVAR was 3.446 μg m−3 (16.4%) lower than that of 3DVAR. For the forecasting capability for PM2.5 mass concentration, the 30-day average Corr of TS-3DVAR during the 0–24 hour forecast period was 0.025 (5.08%) higher than that of 3DVAR, and the average RMSE was 2.027 μg m−3 (4.85%) lower. The positive effect of TS-3DVAR on the improvement of forecasting capability can last for more than 24 h.

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.

Implementation of Scale-Dependent Background-Error Covariance Localization in the Canadian Global Deterministic Prediction System

Abstract The approach of applying different amounts of horizontal localization to different ranges of background-error covariance horizontal scales as proposed by Buehner and Shlyaeva was recently implemented in the four-dimensional ensemble–variational (4DEnVar) data assimilation scheme of the global deterministic prediction system (GDPS) at Environment and Climate Change Canada operations. To maximize the benefits from this approach to reduce the sampling noise in the ensemble-derived background-error covariances, it was necessary to adopt a new weighting between the climatological and flow-dependent covariances that increases significantly the role of the latter. Thus, in December 2021 the GDPS became the first operational global deterministic medium-range weather forecasting system to rely completely on flow-dependent covariances in the troposphere and the lower stratosphere. The experiments that led to the adoption of these two related changes and their impacts on the forecasts up to 7 days for various regions of the globe during the boreal summer of 2019 and winter of 2020 are presented here. It is also illustrated that relying more on ensemble-derived covariances amplifies the positive impacts on the GDPS when the background ensemble generation strategy is improved.

Developing 4D-Var for Strongly Coupled Data Assimilation Using a Coupled Atmosphere–Ocean Quasigeostrophic Model

Abstract Four-dimensional variational (4D-Var) data assimilation (DA) is developed for a coupled atmosphere–ocean quasigeostrophic application. Complications arise in coupled data assimilation (CDA) systems due to the presence of multiple spatiotemporal scales. Various formulations of the background error covariance matrix (), using different localization strategies, are explored to evaluate their impact on 4D-Var performance in a CDA setting. 4D-Var requires access to tangent linear and adjoint models (TLM/AM) to propagate information about the misfit between the forecast and observations within an optimization window. In practice, particularly for coupled models, the TLM and adjoint are often difficult to produce, and for some models are nonexistent in analytic form. Accordingly, a statistical data-driven alternative is also employed and evaluated to determine its feasibility for a 4D-Var CDA system. Using experiments conducted with a coupled atmosphere–ocean quasigeostrophic model, it is found that ensemble generation of flow-dependent error covariance statistics can increase the accuracy of 4D-Var CDA. When observing all variables, the hybrid climatological/flow-dependent constructions outperform either independently. The use of a hybrid matrix combined with a rapid updating ensemble transform Kalman filter (RU-ETKF) using either strongly or weakly CDA resulted in lower overall RMSE. The ocean component achieved its lowest RMSE when using a fully flow-dependent matrix generated using 4D-ETKF and using weakly CDA. These results show the importance of time scales and analysis update frequencies. The use of a statistically derived TLM/AM generated from the ETKF ensemble perturbations produces results similar to cases using the analytical coupled TLM/AM in 4D-Var.

Hybrid ensemble-variational data assimilation in ABC-DA within a tropical framework

Abstract. Hybrid ensemble-variational data assimilation (DA) methods have gained significant traction in recent years. These methods aim to alleviate the limitations and maximise the advantages offered by ensemble or variational methods. Most existing hybrid applications focus on the mid-latitudinal context; almost none have explored its benefits in the tropical context. In this article, hybrid ensemble-variational DA is introduced to a tropical configuration of a simplified non-hydrostatic convective-scale fluid dynamics model (the ABC model, named after its three key parameters: the pure gravity wave frequency A, the controller of the acoustic wave speed B, and the constant of proportionality between pressure and density perturbations C), and its existing variational framework, the ABC-DA system. The hybrid ensemble-variational DA algorithm is developed based on the alpha control variable approach, often used in numerical weather prediction. Aspects of the algorithm such as localisation (used to mitigate sampling error caused by finite ensemble sizes) and weighting parameters (used to weight the ensemble and climatological contributions to the background error covariance matrix) are implemented. To produce the flow-dependent error modes (ensemble perturbations) for the ensemble-variational DA algorithm, an ensemble system is also designed for the ABC model which is run alongside the hybrid DA system. A random field perturbations method is used to generate an initial ensemble which is then propagated using the ensemble bred vectors method. This setup allows the ensemble to be centred on the hybrid control analysis. Visualisation software has been developed to focus on the diagnosis of the ensemble system. To demonstrate the hybrid ensemble-variational DA in the ABC-DA system, sensitivity tests using observing system simulation experiments are conducted within a tropical framework. A 30-member ensemble was used to generate the error modes for the experiments. In general, the best performing configuration (with respect to the “truth”) for the hybrid ensemble-variational DA system used an 80%/20% weighting on the ensemble-derived/climatological background error covariance matrix contributions. For the horizontal wind variables though, full weight on the ensemble-derived background error covariance matrix (100%/0%) resulted in the smallest cycle-averaged analysis root mean square errors, mainly due to large errors in the meridional wind field when contributions from the climatological background error covariance matrix were involved, possibly related to a sub-optimal background error covariance model. The ensemble bred vectors method propagated a healthy-looking DA-centred ensemble without bimodalities or evidence of filter collapse. The ensemble was under-dispersive for some variables but for others, the ensemble spread approximately matched the corresponding root mean square errors. Reducing the number of ensemble members led to slightly larger errors across all variables due to the introduction of larger sampling errors into the system.

A 4DEnVar‐Based Ensemble Four‐Dimensional Variational (En4DVar) Hybrid Data Assimilation System for Global NWP: System Description and Primary Tests

AbstractThis study developed an ensemble four‐dimensional variational (En4DVar) hybrid data assimilation system. Different from most of the available En4DVar systems that adopted ensemble Kalman Filter class or ensemble data assimilation approaches to produce ensemble covariances for their hybrid background error covariances (BECs), it used a four‐dimensional ensemble variational (4DEnVar) system to obtain the ensemble covariance. The localization scheme for 4DEnVar applied orthogonal functions to decompose the correlation matrix so that it was implemented easily and rapidly. In terms of analysis quality and forecast skill, the En4DVar system was evaluated in the single‐point observation experiments and observing system simulation experiments (OSSEs) with sounding and cloud‐derived wind observations, using its standalone four‐dimensional variational (4DVar) and 4DEnVar components as references. The single‐point observation experiments visually verified the explicit flow‐dependent characteristic of the BEC due to the introduction of the ensemble covariance from the 4DEnVar system. The OSSE‐based sensitivity experiments revealed different contributions of the weight for the ensemble covariance in the En4DVar system to the forecasts in the Northern and Southern Extratropics and Tropics. A much higher weight for the ensemble covariance in a properly inflated hybrid covariance helped En4DVar produce the most reasonable analysis. The forecast initialized by En4DVar is overall better than by 4DVar and 4DEnVar, although the quality of En4DVar analysis is between those of 4DVar and 4DEnVar ensemble mean analyses. It indicates that the flow‐dependent ensemble covariance provided by 4DEnVar dominantly contributes to the improvements in the En4DVar‐initialized forecast, with certain but necessary constraint from the balanced climatological covariance.

Revisiting the 2003–18 Deep Ocean Warming through Multiplatform Analysis of the Global Energy Budget

Abstract Recent estimates of the global warming rates suggest that approximately 9% of Earth’s excess heat has been cumulated in the deep and abyssal oceans (below 2000-m depth) during the last two decades. Such estimates assume stationary trends deducted as long-term rates. To reassess the deep ocean warming and potentially shed light on its interannual variability, we formulate the balance between Earth’s energy imbalance (EEI), the steric sea level, and the ocean heat content (OHC), at yearly time scales during the 2003–18 period, as a variational problem. The solution is achieved through variational minimization, merging observational data from top-of-atmosphere EEI, inferred from Clouds and the Earth’s Radiant Energy System (CERES), steric sea level estimates from altimetry minus gravimetry, and upper-ocean heat content estimates from in situ platforms (mostly Argo floats). Global ocean reanalyses provide background-error covariances for the OHC analysis. The analysis indicates a 2000-m–bottom warming of 0.08 ± 0.04 W m−2 for the period 2003–18, equal to 13% of the total ocean warming (0.62 ± 0.08 W m−2), slightly larger than previous estimates but consistent within the error bars. The analysis provides a fully consistent optimized solution also for the steric sea level and EEI. Moreover, the simultaneous use of the different heat budget observing networks is able to decrease the analysis uncertainty with respect to the observational one, for all observation types and especially for the 0–700-m OHC and steric sea level (more than 12% reduction). The sensitivity of the analysis to the choice of the background time series proved insignificant. Significance Statement Several observing networks provide complementary information about the temporal evolution of the global energy budget. Here, satellite observations of Earth’s energy imbalance (EEI) and steric sea level and in situ–derived estimates of ocean heat content anomalies are combined in a variational analysis framework, with the goal of assessing the deep ocean warming. The optimized solution accounts for the uncertainty of the different observing networks. Furthermore, it provides fully consistent analyses of global ocean heat content, steric sea level, and EEI, which show smaller uncertainty than the original observed time series. The deep ocean (below 2000-m depth) exhibits a significant warming of 0.08 ± 0.04 W m−2 for the period 2003–18, equal to the 13% of the total ocean warming.

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

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

Analytical Four-Dimensional Ensemble Variational Data Assimilation for Joint State and Parameter Estimation

The joint state and parameter estimation problem is an important issue in data assimilation. An adjoint free data assimilation method, namely analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method, was developed to provide a solution for the joint estimation problem. In the algorithm, to estimate the adjoint model reasonably, the ensemble initial conditions and parameters are generated by Gaussian noise whose covariance is constructed by multiplying a very small factor by their background error covariance. The ensemble perturbations are calculated with respect to background states rather than the ensemble mean. Next, the usage of temporal cross covariances makes it possible to avoid the adjoint model and estimate the gradient in 4DVar. Furthermore, we update the solution iteratively with a linear search process to improve the stability and ensure the convergence of the algorithm. The method is tested using the three-variable Lorenz model (Lorenz-1963) to illustrate its efficiency. It is shown that A-4DEnVar results in similar performance with 4DVar. Sensitivity experiments show that A-4DEnVar is able to assimilate observations successfully with different settings. The proposed method is able to work as well as 4DVar and avoid adjoint models for the joint state and parameter estimation.

Variational data assimilation for a sea dynamics model

Abstract The 4D variational data assimilation technique is presented for modelling the sea dynamics problems, developed at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The approach is based on the splitting method for the mathematical model of sea dynamics and the minimization of cost functionals related to the observation data by solving an optimality system that involves the adjoint equations and observation and background error covariances. Efficient algorithms for solving the variational data assimilation problems are presented based on iterative processes with a special choice of iterative parameters. The technique is illustrated for the Black Sea dynamics model with variational data assimilation to restore the sea surface heat fluxes.

Impact of all‐sky water vapour channel radiance from INSAT‐3D/3DR satellite over South Asia region using WRF model

AbstractThe objective of this study is to explore and present a methodology to assimilate all‐sky water vapour (WV) radiance from Indian geostationary satellites (INSAT‐3D and INSAT‐3DR) in the Weather Research and Forecasting (WRF) model. For all‐sky assimilation, hydrometeors are considered as control variables by adding in background error covariance. Additionally, this study uses the application of Global Satellite based Inter‐Calibration System (GSICS) based bias correction mechanism on WV radiances before their assimilation. To fulfil these objectives, three sets of experiments have been performed with and without WV radiance assimilation for the month of July 2018 over the South Asia region. The impact assessment of assimilation has been performed by comparing radiative transfer (RT) model‐simulated analysed and predicted brightness temperature against independent satellite observations from SAPHIR (Sondeur Atmosphérique du Profil d'Humidité Intertropicale par Radiométrie) and MHS (Microwave Humidity Sounder) sensors. Results not only show the number of assimilated observations increased significantly (∼250%) in all‐sky assimilation compared to clear‐sky assimilation but also present that the all‐sky analyses are closer to actual satellite observations. Due to the multivariate nature of variational data assimilation, noteworthy changes are also noticed in hydrometeors analyses in all‐sky assimilation. The short‐range forecasts confirm the positive impact of all‐sky assimilation as compared to clear‐sky assimilation when verified against SAPHIR and MHS measurements.

The sensitivity of the WRF-4DVar data assimilation system to the control variables: A study on heavy rainfall events over India

The impact of different formulations of background error covariances (BECs) is examined for three heavy rainfall episodes over north India with a regional 4-dimensional variational (4DVar) data assimilation (DA) system. Three BEC formulations are analyzed, in which two of them employ stream function and velocity potential (ψ and χ) and the third one uses zonal and meridional velocity components (v and v) as momentum control variables. The uv-based formulation is completely univariate whereas, the correlations among the control variables are taken into account in the ψχ-based formulations through linear regression relations. Among the two ψχ-based BECs, one uses univariate relation and the other one uses multivariate relations for the moisture field. The multivariate relationship allows for impacting the moisture analysis through the assimilation of temperature or wind observations. Three experiments are carried out for each case with cyclic 4DVar assimilation. The conventional surface and upper-air observations are assimilated in combination with atmospheric motion vectors (AMVs) and ocean surface winds. Free forecast for 48 h is performed from respective final analysis fields for all the experiments. The results indicate that the uv-based analysis fields are closer to the observations. A comparative analysis of the 4DVar experiments with the 3DVar DA system provided a critical insight on the role of the 4DVar DA system on implicitly accounting for the multivariate correlations. The precipitation forecasts confirm the improved performance of the ψχ-based experiment, when multivariate nature of the humidity is incorporated. The time evolution of the intense rainfall episodes over the location of maximum rainfall are relatively well reproduced in the uv-based experiment. The results indicate that the inclusion of multivariate humidity variable in the BEC formulation does have a significant impact on suppressing the excessive overestimation in rainfall intensity.

A Variational Method for Analyzing Vortex Flows in Radar-Scanned Tornadic Mesocyclones. Part III: Sensitivities to Vortex Center Location Errors

Abstract When the vortex center location is estimated from a radar-scanned tornadic mesocyclone, the estimated location is not error-free. This raises an important issue concerning the sensitivities of analyzed vortex flow (VF) fields by the VF-Var (formulated in Part I of this paper series and tested in Part II) to vortex center location errors, denoted by Δxc. Numerical experiments are performed to address this issue with the following findings: The increase of |Δxc| from zero to a half of vortex core radius causes large analysis error increases in the vortex core but the increased analysis errors decrease rapidly away from the vortex core especially for dual-Doppler analyses. The increased horizontal-velocity errors in the vortex core are mainly in the Δxc-normal component, because this component varies much more rapidly than the other component along the Δxc direction in the vortex core. The vertical variations of Δxc distort the vertical correlation structure of Δxc-dislocated VF-dependent background error covariance, which can increase the analysis errors in the vortex core. The dual-Doppler analyses have adequate accuracies outside the vortex core even when |Δxc| increases to a half of vortex core radius, while single-Doppler analyses can also have adequate accuracies outside the vortex core mainly for the single-Doppler-observed velocity component. The sensitivities to Δxc are largely unaffected by the vortex slanting. The above findings are important and useful for assessing the accuracies of analyzed VFs for real radar-observed tornadic mesocyclones. Significance Statement When the vortex center location is estimated from a radar-scanned tornadic mesocyclone, the estimated location is not error-free. This raises an issue concerning the sensitivity of analyzed vortex flow (VF) by the VF-Var (formulated in Part I of this paper series and tested with simulated radar observations in Part II) to vortex center location error. This issue and its required investigations are very important for the VF-Var to be applied to real radar-observed tornadic mesocyclones, especially in an operational setting with the WSR-88Ds. Numerical experiments are performed to address this issue. The findings from these experiments are important and useful for assessing the accuracies of VF-Var analyzed VF fields for real radar-observed tornadic mesocyclones.

Assimilation of Radar Reflectivity Using a Time‐Lagged Ensemble Based Ensemble Kalman Filter With the “Cloud‐Dependent” Background Error Covariances

AbstractThis study proposes a method for direct assimilation of radar reflectivity in cycled deterministic forecast systems using a time‐lagged ensemble based ensemble Kalman filter with the “cloud‐dependent” background error covariances. With this method, forecasts from multiple deterministic forecast cycles that are initialized at different times but valid at the same time, are collected as a time‐lagged ensemble to compute the background error covariances. An algorithm to compute the specified “cloud‐dependent” background error covariances was devised, in which the vertical background error covariance is computed for each of the “cloud‐feature” bins which are divided according to the column maximum radar reflectivity and cloud top height. The single‐observation experiments and the observing system simulation experiments (OSSEs) indicate that the radar reflectivity data assimilation method was able to capture the main thermodynamic and microphysical features of convective clouds and was effective in reducing the spin‐up time of convection, and generating convective cells which were missed in the background. Meanwhile, assimilating “zero‐reflectivity” observations helped suppress spurious convection. The method provided overall more accurate thermodynamic analysis, radar reflectivity and precipitation analysis and forecast of the MCS, while did not significantly increase computational cost, compared to a cloud‐analysis based latent‐heat nudging approach.

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.

An Improved 1D-VAR Retrieval Algorithm of Temperature Profiles from an Ocean-Based Microwave Radiometer

In this study, a one-dimensional variational algorithm that combines brightness temperatures (BTs), measured by ocean-based microwave radiometers (MWR), with reanalysis data was developed to generate high accuracy temperature profiles. A forward radiative transfer model was used to simulate the BTs. For the V band (50–70 GHz), there is a good agreement between observations and simulations, but for K band (20–30 GHz), which is more affected by water vapor, large errors are observed. To reduce the errors, a combined temperature and water vapor background error covariance matrix is applied to the 1D-Var algorithm. In addition, a correction factor is added to the 1D-Var iterative equation to improve retrieval accuracy. The results of the improved 1D-Var method have been compared with the MWR built-in neural network (NN) method, original 1D-Var method, and radiosonde data, which shows that the retrievals of the combined 1D-Var method showed significant improvements between 0 to 10 km. The statistical results show that the maximum mean absolute error of the combined 1D-Var method is less than 2 K in clear sky and cloudy conditions. This paper demonstrates that the proposed combined 1D-Var method has better performance than many known retrieval methods.

An Analog Offline EnKF for Paleoclimate Data Assimilation

AbstractAn analog offline ensemble Kalman filter (AOEnKF) is proposed, which constructs ensemble priors from a control climate simulation for each assimilation time based on an analog criterion using proxy observations. Even though AOEnKF is an offline scheme and is therefore computationally economical, it has the ability to capture “flow‐dependent” background error covariances that help spread observation information through climate fields. Extensive tests in the Lorenz05 model demonstrate that, compared to the online cycling EnKF (CEnKF), AOEnKF generates smaller posterior errors and requires much less computational cost. Compared to the commonly applied offline EnKF (OEnKF), AOEnKF has the advantages of having a more accurate prior ensemble mean and “flow‐dependent” background error covariances, even though the assimilation time scale is beyond significant forecast skill of the climate model. With varying ensemble sizes, sample sizes, observation error covariances and observing networks, AOEnKFs generally produce statistically significant error reduction relative to OEnKF, especially for larger sample sizes, increased observation uncertainties and sparser observing networks. The AOEnKF can be applied based on either the error of state variables from observations (AOEnKF_E) or the spatial correlation of state variables with observations (AOEnKF_C), with generally comparable results.

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.