Variational Assimilation Method Research Articles

Anisotropic diffusion filters for flow-dependent variational data assimilation of sea surface temperature

It is well known that the background error covariance matrix in the data assimilation is anisotropic and varied with the flow field, that is, flow-dependent. However, it is generally assumed to be isotropic and static for ease of implementation. Therefore, to enhance the quality of the background error covariance, two easy-to-implement, flow-dependent three-dimensional variational analysis (3DVar) schemes, the advection–diffusion filter (ADF) and the Smagorinsky diffusion filter (SDF), are tentatively proposed. These serve as alternative schemes for the traditional methods that are based on the isotropic assumption. First, a correctness test of the gradient for the ADF is performed to verify the validity of the adjoint code. Then, the response analysis for the 1D advection–diffusion​ equation is investigated to validate the anisotropic characteristic of the ADF with various flow velocities. Second, the two flow-dependent 3DVar schemes are verified via single-observation assimilation experiments. Compared to the existing diffusion filter with a static diffusion coefficient, both new schemes show a flow-dependent capability in the assimilation experiment because they successfully spread the observational information anisotropically. Finally, a retroactive real-time forecast experiment framework based on a 3D baroclinic primitive equation ocean model is used to investigate the effects of the ADF/SDF on the analysis and forecast accuracy of sea surface temperature (SST). While the traditional variational assimilation method with an isotropic diffusion filter generally reduces initial field errors, both the ADF and SDF can further enhance the accuracy of the initial fields in strong current areas. In addition, better forecast skills can be obtained with the two flow-dependent schemes in the East China Sea.

Creation and Verification of a High-Resolution Multi-Parameter Surface Meteorological Assimilation Dataset for the Tibetan Plateau for 2010–2020 Available Online

The Qinghai–Tibet Plateau (QTP) is a crucial component of the global climate system, influencing the regional and global climate through complex thermal and dynamic mechanisms. The high-altitude region, which is the largest part of the extra-polar cryosphere, encompasses extensive mountain glaciers, permafrost, and seasonally frozen land, making it highly sensitive to global climate change. However, the challenging environmental conditions, such as the harsh terrain and high altitude, coupled with sparse weather station distribution and weak observatory representation, make it difficult to accurately quantify the atmospheric conditions and land–atmosphere coupling systems and their effects on the surrounding areas. To address these challenges, we utilized the Weather Research and Forecasting (WRF) model and a three-dimensional variational (3DVAR) assimilation method to create a high-resolution assimilated dataset (HRAD). The QTP-HRAD, covering the spatial range of 70 to 110°E and 25 to 40°N, was validated using both surface weather station observations and the European Center for Medium-Range Weather Forecasts Reanalysis V5, and can now be utilized for further studies on land–atmosphere interactions, water cycling and radiation energy transfer processes, and extreme weather events in the region.

Temperature Fusion of TIMED/SABER Data and COSMIC Data in Stratosphere

AbstractThe acquisition of accurate stratospheric temperature data is of great significance for the research on global climate system and numerical weather forecasting. To obtain high‐precision stratospheric temperature, the three‐dimensional variational assimilation method, combined with kriging interpolation, was applied for data fusion of the Thermosphere, Ionosphere, Mesosphere Energetics, and Dynamics/Sounding of the Atmosphere using Broadband Emission Radiometry (TIMED/SABER) temperature data and the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) radio occultation temperature data. As a sample, the two data sets of TIMED/SABER and COSMIC, during the time range from 5 December 2009, 09:00 to 5 December 2009, 15:00, were used to construct global stratospheric temperature field of 5 December 2009, 12:00. The cross‐validation results showed that temperature distribution from the variational fusion method was consistent with COSMIC observations at the height range of 15–35 km, which the mean deviations and standard deviations were within a range of −1 to 1 and 3 to 4 K, respectively. At the height range from 35 to 40 km, the temperature distribution from the variational fusion method was more consistent with TIMED/SABER observations. The mean deviations were within 0 and 0.5 K, and the standard deviations were between 1.8 and 2 K. Overall, the temperature field after variational fusion combines the high‐precision advantage of SABER observations around 40 km and the high‐precision advantage of COSMIC observations at the height range of 15–30 km, the effect of the variational fusion method is significant.

Simulating carbon and water fluxes using a coupled process-based terrestrial biosphere model and joint assimilation of leaf area index and surface soil moisture

Abstract. Reliable modeling of carbon and water fluxes is essential for understanding the terrestrial carbon and water cycles and informing policy strategies aimed at constraining carbon emissions and improving water use efficiency. We designed an assimilation framework (LPJ-Vegetation and soil moisture Joint Assimilation, or LPJ-VSJA) to improve gross primary production (GPP) and evapotranspiration (ET) estimates globally. The integrated model, LPJ-PM (LPJ-PT-JPLSM Model) as the underlying model, was coupled from the Lund–Potsdam–Jena Dynamic Global Vegetation Model (LPJ-DGVM version 3.01) and a hydrology module (i.e., the updated Priestley–Taylor Jet Propulsion Laboratory model, PT-JPLSM). Satellite-based soil moisture products derived from the Soil Moisture and Ocean Salinity (SMOS) and Soil Moisture Active and Passive (SMAP) and leaf area index (LAI) from the Global LAnd and Surface Satellite (GLASS) product were assimilated into LPJ-PM to improve GPP and ET simulations using a proper orthogonal decomposition (POD)-based ensemble four-dimensional variational assimilation method (PODEn4DVar). The joint assimilation framework LPJ-VSJA achieved the best model performance (with an R2 ( coefficient of determination) of 0.91 and 0.81 and an ubRMSD (unbiased root mean square deviation) reduced by 40.3 % and 29.9 % for GPP and ET, respectively, compared with those of LPJ-DGVM at the monthly scale). The GPP and ET resulting from the assimilation demonstrated a better performance in the arid and semi-arid regions (GPP: R2 = 0.73, ubRMSD = 1.05 g C m−2 d−1; ET: R2 = 0.73, ubRMSD = 0.61 mm d−1) than in the humid and sub-dry humid regions (GPP: R2 = 0.61, ubRMSD = 1.23 g C m−2 d−1; ET: R2 = 0.66; ubRMSD = 0.67 mm d−1). The ET simulated by LPJ-PM that assimilated SMAP or SMOS data had a slight difference, and the SMAP soil moisture data performed better than SMOS data. Our global simulation modeled by LPJ-VSJA was compared with several global GPP and ET products (e.g., GLASS GPP, GOSIF GPP, GLDAS ET, and GLEAM ET) using the triple collocation (TC) method. Our products, especially ET, exhibited advantages in the overall error distribution (estimated error (μ): 3.4 mm per month; estimated standard deviation of μ: 1.91 mm per month). Our research showed that the assimilation of multiple datasets could reduce model uncertainties, while the model performance differed across regions and plant functional types. Our assimilation framework (LPJ-VSJA) can improve the model simulation performance of daily GPP and ET globally, especially in water-limited regions.

Comparison of sequential and variational assimilation methods to improve hydrological predictions in snow dominated mountainous catchments

• Assimilation of streamflow and snow data using variational and sequential techniques in a hydrological model. • Satellite snow coverage products are assimilated together with streamflow data. • Variational techniques outperform sequential techniques in two mountainous basins. • Average relative gains in variational assimilation are 49% for streamflow and 28% for snow data. Snowmelt modeling is vital issue for proper operational flow forecasting systems but still challenging in upstream mountainous basins due to limited observations and associated uncertainties. Data assimilation is a valuable tool to improve model state estimates to improve hydrological forecast. While assimilation of snow has been increasingly implemented in research, particularly using sequential data assimilation methods, less attention has been dedicated to compare different types of assimilation techniques. This study aims at comparing the well-known Ensemble Kalman Filter (EnKF) sequential data assimilation and the less known Moving Horizon Estimation (MHE) variational assimilation. Initial conditions of the hydrological model states are improved by assimilating in-situ streamflow and remotely sensed snow covered area data into the Hydrologiska Byråns Vattenbalansavdelning (HBV) conceptual rainfall-runoff model. The study is applied to improve runoff predictions over two mountainous basins: one in the uppermost catchment of the Karasu river, in Eastern Turkey, and the second in an alpine basin located in the headwaters of the Genil River in the northern flank of the Sierra Nevada Mountain in Southern Spain. The forecast models are tested in a hindcasting condition, i.e. closed loop environment, which simulates real-time forecasting systems. The results are analyzed using forecast verification metrics. Results showed that streamflow and snow state predictions using MHE outperform the commonly used EnKF based on the continuous ranked probability score (CRPS).

3DVAR Aerosol Data Assimilation and Evaluation Using Surface PM2.5, Himawari-8 AOD and CALIPSO Profile Observations in the North China

Based on the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) aerosol scheme of the Weather Research and Forecasting model coupled with online Chemistry (WRF-Chem) and the three-dimensional variational (3DVAR) assimilation method, a 3DVAR data assimilation (DA) system for aerosol optical depth (AOD) and aerosol concentration observations was developed. A case study on assimilating the Himawari-8 satellite AOD and/or fine particulate matter (PM2.5) was conducted to investigate the improvement of DA on the analysis accuracy and forecast skills of the spatial distribution characteristics of aerosols, especially in the vertical dimension. The aerosol extinction coefficient (AEC) profile data from The Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), surface PM2.5 and Himawari-8 AOD measurements were used for verification. One control experiment (without DA) and two DA experiments including a PM2.5 DA experiment denoted by Da_PM and a combined PM2.5 and AOD DA experiment denoted by Da_AOD_PM were conducted. Both DA experiments had positive effects on the surface PM2.5 mass concentration forecast skills for more than 60 h. However, the Da_PM showed a slight improvement in the analysis accuracy of the AOD distribution compared with the control experiment, while the Da_AOD_PM showed a considerable improvement. The Da_AOD_PM had the best positive effect on the AOD forecast skills. The correlation coefficient (CORR), root mean square error (RMSE), and mean fraction error (MFE) of the 24 h AOD forecasts for the Da_AOD_PM were 0.73, 0.38, and 0.54, which are 0.09 (14.06%), 0.08 (17.39%), and 0.22 (28.95%) better than that of the control experiment, and 0.05 (7.35%), 0.06 (13.64%), and 0.19 (26.03%) better than that of the Da_PM, respectively. Moreover, improved performance for the Da_AOD_PM occurred when the AEC profile was used for verification, as when the AOD was used for verification. The Da_AOD_PM successfully simulated the first increasing and then decreasing trend of the aerosol extinction coefficients below 1 km, while neither the control nor the Da_PM did. This indicates that assimilating AOD can effectively improve the analyses and forecast accuracy of the aerosol structure in both the horizontal and vertical dimensions, thereby compensating for the limitations associated with assimilating traditional surface aerosol observations alone.

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.

Impact of assimilation of SCATSAT-1 data on coupled ocean-atmospheric simulations of tropical cyclones over Bay of Bengal

This study examines the impact of assimilation of the surface winds obtained from SCATterometer SATellite-1 (SCATSAT-1) in predicting the tropical cyclones over the Bay of Bengal using a coupled ocean-atmospheric model. Three sets of numerical experiments are conducted for six cyclones during post-monsoon (VARDAH, GAJA, PHETHAI) and pre-monsoon cyclones (MORA, FANI, AMPHAN). The first experiment, ‘CONTROL’, is conducted with the Weather Research and Forecasting - Ocean Mixed Layer (WRF-OML) model initialized using Global Forecasting System analysis and ocean initial conditions obtained from the HYbrid Coordinated Ocean Model (HYCOM) model. The second experiment, ‘PREPBUFR’, is conducted by assimilating the National Center for Environmental Prediction (NCEP) prepared BUFR observations with the WRF-OML model and three-dimensional variational assimilation method. Further, the 'SCATSAT' experiment is conducted as PREPBUFR, but additionally, the SCATSAT-1 surface wind vectors are assimilated. Our results of the simulated tracks from three experiments suggest that CONTROL and PREPBUFR simulations exhibit faster translation speed and more track deviations than the India Meteorological Department (IMD) observations. The realistic representation of low-level cyclonic vortex through the assimilation of SCATSAT-1 winds seems to produce positive feedback to both track and intensity, producing a significant improvement in predicting intensity and marginal enhancement on simulation of track and translation speed. The assimilation of winds further improved the representation of different life cycles of the storms as seen in IMD. The analysis of air-sea parameters, in terms of mixed layer deepening, sea surface temperatures, and air-sea flux exchanges, suggests that the response of air-sea feedback is strong in SCATSAT compared to PREPBUFR and CONTROL. Overall, the assimilation of SCATSAT surface winds improved the WRF-OML performance on the prediction of track and intensity, upper ocean response, primary and secondary circulations of tropical cyclones, and the rainfall distributions.

Characteristics of topographic submesoscale eddies off the Crimea coast from high-resolution satellite optical measurements

Long-term arrays of satellite optical measurements of Landsat-5,7,8 and Sentinel-2 were used to describe the characteristics of submesoscale eddy (SE) dynamics in different parts of the Crimean coast: their geometric and kinematic characteristics, the main sites and mechanisms of formation, and impact on the redistribution of suspended matter. The dynamic characteristics of SE were computed on the base of the 4D variational assimilation method from the pair of consecutive Landsat-8/Sentinel-2 images. The orbital velocity of submesoscale cyclonic eddies (SCE) with a diameter of 1 km reaches 0.15 m/s, indicating the cyclostrophic balance with a high Rossby number (RO) exceeding 2. Submesoscale cyclones were detected much more frequently than the usually larger submesoscale anticyclones. High-resolution satellite imagery gives a possibility to observe complex submesoscale dynamic processes, such as the generation of chains of SCE, large cyclones behind the capes consisting of densely packed arrays of SCEs, topographic submesoscale anticyclones with a number of attached SCEs, mushroom-like current structures, and frontal SE. Despite the diversity of the processes considered, several basic mechanisms of formation of submesoscale eddies can be identified on the basis of satellite data: (1) Separation of the boundary current, often wind-driven, behind the capes; (2) barotropic instability due to the horizontal shear on the coastal periphery of mesoscale anticyclones or alongshore currents; (3) formation of the mushroom-like structure due to the interaction of offshore currents with deep waters near the capes or due to offshore winds; and (4) frontal instabilities on the coastal upwelling. The results of the analysis were used to create a scheme of the spatial variability of submesoscale processes near the Crimean coast and compare it to the results of the high-resolution modeling. The model was able to describe the main areas of SE formation, which was located near the major capes. It provides additional data about SE generation near the rocky capes of the South Crimea, where satellite data was limited by the absence of optical tracers.

Application of radar data assimilation on convective precipitation forecasts based on water vapor retrieval

Based on a short-time heavy rainfall in Anhui and the weather research and forecasting (WRF) model, the water vapor in the initial field of the model is retrieved using the statistical relationships of the reflectivity factor from the Doppler weather radar with the relative humidity and hydrometeor. Three-dimensional variational (3DVAR) assimilation method is used to assimilate the radar reflectivity factor and radial velocity, and then the impact of assimilating retrieved water vapor on the analysis and forecast of the torrential rain is assessed. The results show that, after assimilating the retrieved water vapor, the water vapor field in the model is significantly improved. The water vapor content in the middle layer of the model in the analyzed field is increased, corresponding well with the convective region. Meanwhile, the precipitation distribution during this weather process is successfully simulated. The mesoscale characteristics are better presented by the imageries of radar reflectivity factor, and false echoes are partially reduced. Besides, the prediction of short-time heavy rainfall regions is closer to the actual observations. After assimilating the retrieved water vapor, the simulated one-hour accumulated rainfall is closer to the actual observation, and the fraction skill score (FSS) is higher.

Water quality modelling based on 4-dimensional variational assimilation method in the Nanfei River, Lake Chaohu Basin<sup>*</sup>

针对河流模拟中未知不确定性源对模拟精度的影响，以巢湖流域南淝河为研究对象，建立了基于四维变分同化方法的南淝河干流水质模型，研究了含未知污染源的南淝河水质过程模拟.模型以未知污染负荷的动态变化过程为控制变量，通过同化沿河不同断面的逐日水质监测数据，识别不同河段的逐日入河污染负荷过程来实现水质过程的模拟，改变了常规模型模拟需提前预知并输入污染负荷的应用前提.模拟结果表明，采用四维变分同化方法的水质模拟结果有明显改进，重点河段水质模拟的纳什效率系数从小于0提高到0.5以上.识别的入河污染过程与降雨过程波动总体一致，证实南淝河的入河污染与降雨过程密切；同时，模型也可识别异常的入河负荷，提高模型对水环境问题的诊断分析能力.该方法可推广应用于复杂河流系统，为巢湖等流域污染来源定量解析、水质预测预警及污染管控提供支持.;To reduce model accuracy caused by unknown uncertain pollutant sources, a water quality model based on a 4-dimensional variational assimilation method was established. Water quality modelling was conducted in the mainstream of the Nanfei River, Lake Chaohu Basin, in which water quality is highly unstable influenced by unmeasured pollutant sources. The proposed model takes the unsteady process of non-point source loads as the control variable. By assimilating the daily water quality monitoring data in different gauges along the river, the water quality process was successfully reproduced by identifying the daily pollution load process of each reach. It changes the premise that the traditional model simulation needs the right pollution load in advance. The numerical experiment shows that the results of water quality simulation using variational assimilation method are significantly improved, and the Nash efficiency coefficient of water quality simulation in key river reaches is increased from less than 0 to more than 0.5. The identified pollution process consistent with the observed rainfall process proves that the pollution into the river is closely related to the rainfall. The model can also identify some abnormal pollutant loads into the river and improve the diagnosis and analysis ability of the model for water environment problems.

Input Parameters Variational Identifying Procedures of the Passive Impurity Transfer Model

The paper presents a method for input parameters variational identification of passive impurity transfer model as a result of assimilation of measurement data. The assimilation is carried out by minimizing the quadratic functional of the forecast quality, and the solution of the adjoint problem is used to construct gradients of the functional in the parameter space. Formulas for calculating such gradients in the case of identification of the initial concentration fields, turbulent diffusion coefficients and the power of pollution sources are presented. When solving environmental problems based on the use of numerical dynamic models and models describing the processes of propagation of certain pollutants, the task naturally arises of improving the predicted model fields by identifying the input parameters of the models. One of the ways of such identification is the variational assimilation method based on minimizing the forecast residuals and solving conjugate problems of a special type. The development of such algorithms is an important and urgent task due to the increasing anthropogenic load and the need to create environmental monitoring systems.

Observation Strategies Based on Singular Value Decomposition for Ocean Analysis and Forecast

In this article, we discuss possible observing strategies for a simplified ocean model (Double Gyre (DG)), used as a preliminary tool to understand the observation needs for real analysis and forecasting systems. Observations are indeed fundamental to improve the quality of forecasts when data assimilation techniques are employed to obtain reliable analysis results. In addition, observation networks, particularly in situ observations, are expensive and require careful positioning of instruments. A possible strategy to locate observations is based on Singular Value Decomposition (SVD). SVD has many advantages when a variational assimilation method such as the 4D-Var is available, with its computation being dependent on the tangent linear and adjoint models. SVD is adopted as a method to identify areas where maximum error growth occurs and assimilating observations can give particular advantages. However, an SVD-based observation positioning strategy may not be optimal; thus, we introduce other criteria based on the correlation between points, as the information observed on neighboring locations can be redundant. These criteria are easily replicable in practical applications, as they require rather standard studies to obtain prior information.

Study on variational assimilation in chemical hazard leakage accidents

In this paper, the problem is studied and analyzed by introducing variational assimilation method and combining with the gaussian plume model.Through the analysis and study of background error covariance, observation error covariance and diffusion parameters, the variational assimilation scheme of chemical hazards was designed and the mathematical modeling was carried out.Then, through Matlab platform programming, numerical experiments are carried out on the established model and an example analysis is made. The results show that the concentration prediction field after assimilation can effectively reduce the prediction error and achieve convergence.

Evaluation of Combined Satellite and Radar Data Assimilation with POD-4DEnVar Method on Rainfall Forecast

Satellite and radar observations represent two fundamentally different remote sensing observation types, providing independent information for numerical weather prediction (NWP). Because the individual impact on improving forecast has previously been examined, combining these two resources of data potentially enhances the performance of weather forecast. In this study, satellite radiance, radar radial velocity and reflectivity are simultaneously assimilated with the Proper Orthogonal Decomposition (POD)-based ensemble four-dimensional variational (4DVar) assimilation method (referred to as POD-4DEnVar). The impact is evaluated on continuous severe rainfall processes occurred from June to July in 2016 and 2017. Results show that combined assimilation of satellite and radar data with POD-4DEnVar has the potential to improve weather forecast. Averaged over 22 forecasts, RMSEs indicate that though the forecast results are sensitive to different variables, generally the improvement is found in different pressure levels with assimilation. The precipitation skill scores are generally increased when assimilation is carried out. A case study is also examined to figure out the contributions to forecast improvement. Better intensity and distribution of precipitation forecast is found in the accumulated rainfall evolution with POD-4DEnVar assimilation. These improvements are attributed to the local changes in moisture, temperature and wind field. In addition, with radar data assimilation, the initial rainwater and cloud water conditions are changed directly. Both experiments can simulate the strong hydrometeor in the precipitation area, but assimilation spins up faster, strengthening the initial intensity of the heavy rainfall. Generally, the combined assimilation of satellite and radar data results in better rainfall forecast than without data assimilation.

Impacts of Multigrid NLS-4DVar-based Doppler Radar Observation Assimilation on Numerical Simulations of Landfalling Typhoon Haikui (2012)

We applied the multigrid nonlinear least-squares four-dimensional variational assimilation (MG-NLS4DVar) method in data assimilation and prediction experiments for Typhoon Haikui (2012) using the Weather Research and Forecasting (WRF) model. Observation data included radial velocity (Vr) and reflectivity (Z) data from a single Doppler radar, quality controlled prior to assimilation. Typhoon prediction results were evaluated and compared between the NLS-4DVar and MG-NLS4DVar methods. Compared with a forecast that began with NCEP analysis data, our radar data assimilation results were clearly improved in terms of structure, intensity, track, and precipitation prediction for Typhoon Haikui (2012). The results showed that the assimilation accuracy of the NLS-4DVar method was similar to that of the MG-NLS4DVar method, but that the latter was more efficient. The assimilation of Vr alone and Z alone each improved predictions of typhoon intensity, track, and precipitation; however, the impacts of Vr data were significantly greater that those of Z data. Assimilation window-length sensitivity experiments showed that a 6-h assimilation window with 30-min assimilation intervals produced slightly better results than either a 3-h assimilation window with 15-min assimilation intervals or a 1-h assimilation window with 6-min assimilation intervals.

Variational Assimilation of the Impervious Surfaces Temperature

Impervious surface temperature is a key parameter in impervious surface energy balance. Urban canopy models are now widely used to simulate impervious surface temperatures, but the physical assimilation method for the urban canopy model is still under development and the use of high temporal resolution observation data are limited. In this paper, a physical assimilation method was used to improve the simulation of the impervious surface temperature for the first time. A variational assimilation method was developed and coupled with the integrated urban land model, using the impervious surface energy balance equation as the adjoint physical constraint. The results showed that when the observed impervious surface temperature data of every timestep were assimilated into the integrated urban land model, the bias of the impervious surface temperature was reduced about 86 %. For the operational run, the observed data were assimilated twice per day, and the bias of the impervious surface temperature was reduced by about 78%.

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.

Application of multigrid NLS-4DVar in radar radial velocity data assimilation with WRF-ARW

The nonlinear least-squares four-dimensional variational assimilation (NLS-4DVar) method introduced here combines the merits of the ensemble Kalman filter and 4DVar assimilation methods. The multig...

An Adjoint-Free CNOP–4DVar Hybrid Method for Identifying Sensitive Areas Targeted Observations: Method Formulation and Preliminary Evaluation

This paper proposes a hybrid method, called CNOP–4DVar, for the identification of sensitive areas in targeted observations, which takes the advantages of both the conditional nonlinear optimal perturbation (CNOP) and four-dimensional variational assimilation (4DVar) methods. The proposed CNOP–4DVar method is capable of capturing the most sensitive initial perturbation (IP), which causes the greatest perturbation growth at the time of verification; it can also identify sensitive areas by evaluating their assimilation effects for eliminating the most sensitive IP. To alleviate the dependence of the CNOP–4DVar method on the adjoint model, which is inherited from the adjoint-based approach, we utilized two adjoint-free methods, NLS-CNOP and NLS-4DVar, to solve the CNOP and 4DVar sub-problems, respectively. A comprehensive performance evaluation for the proposed CNOP–4DVar method and its comparison with the CNOP and CNOP–ensemble transform Kalman filter (ETKF) methods based on 10 000 observing system simulation experiments on the shallow-water equation model are also provided. The experimental results show that the proposed CNOP–4DVar method performs better than the CNOP–ETKF method and substantially better than the CNOP method.