Assimilation of GOES-R Geostationary Lightning Mapper Flash Extent Density Data in GSI 3DVar, EnKF, and Hybrid En3DVar for the Analysis and Short-Term Forecast of a Supercell Storm Case

Capabilities to assimilate Geostationary Operational Environmental Satellite “R-series ”(GOES-R) Geostationary Lightning Mapper(GLM) flash extent density(FED) data within the operational Gridpoint Statistical Interpolation ensemble Kalman filter(GSI-EnKF) framework were previously developed and tested with a mesoscale convective system(MCS) case. In this study, such capabilities are further developed to assimilate GOES GLM FED data within the GSI ensemble-variational(EnVar) hybrid data assimilation(DA) framework. The results of assimilating the GLM FED data using 3DVar, and pure En3DVar(PEn3DVar, using 100% ensemble covariance and no static covariance) are compared with those of EnKF/DfEnKF for a supercell storm case. The focus of this study is to validate the correctness and evaluate the performance of the new implementation rather than comparing the performance of FED DA among different DA schemes. Only the results of 3DVar and pEn3DVar are examined and compared with EnKF/DfEnKF. Assimilation of a single FED observation shows that the magnitude and horizontal extent of the analysis increments from PEn3DVar are generally larger than from EnKF, which is mainly caused by using different localization strategies in EnFK/DfEnKF and PEn3DVar as well as the integration limits of the graupel mass in the observation operator. Overall, the forecast performance of PEn3DVar is comparable to EnKF/DfEnKF, suggesting correct implementation.

Application of the finite analytic numerical method to a flowdependent variational data assimilation

An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.

Progress and future prospects of decadal prediction and data assimilation:A review

年代际预测,也称为“近期气候预测”,旨在预测未来1-10年内的气候变化,是气候预测和气候变化研究领域的一个新关注点.它位于季节至年际预测和长期气候变化预测之间,结合了初值问题和外部强迫问题的两个方面.年代际预测的核心技术在于用于模式初始化的同化方法的准确性和效率,其目标是为模式提供准确的初始条件,其中包含观测到的气候系统内部变率,年代际预测的初始化通常涉及在耦合框架内同化海洋观测,其中观测到的信号通过耦合过程传递到其他分量,如大气和海冰.然而,最近的研究越来越关注在海洋-大气耦合模式中探索耦合数据同化(CDA),有人认为CDA有潜力显著提高年代际预测技巧.本文综合评述了该领域的三个方面的研究现状:初始化方法,年代际气候预测的可预测性和预测技巧,以及年代际预测的未来发展和挑战.

An Ensemble-Based Three-Dimensional Variational Assimilation Method for Land Data Assimilation

Land surface models are often highly nonlinear with model physics that contain parameterized discontinuities. These model attributes severely limit the application of advanced variational data assimilation methods into land data assimilation. The ensemble Kalman filter (EnKF) has been widely employed for land data assimilation because of its simple conceptual formulation and relative ease of implementation. An updated ensemble-based three-dimensional variational assimilation (En3-DVar) method is proposed for land data assimilation.This new method incorporates Monte Carlo sampling strategies into the 3-D variational data assimilation framework. The proper orthogonal decomposition (POD) technique is used to efficiently approximate a forecast ensemble produced by the Monte Carlo method in a 3-D space that uses a set of base vectors that span the ensemble. The data assimilation process is thus significantly simplified. Our assimilation experiments indicate that this new En3-DVar method considerably outperforms the EnKF method by increasing assimilation precision. Furthermore, computational costs for the new En3-DVar method are much lower than for the EnKF method.

Forecasting of Asian dust storm that occurred on May 10-13, 2011, using an ensemble-based data assimilation system

An ensemble-based assimilation system that used the MASINGAR ink-2 （Model of Aerosol Species IN the Global AtmospheRe Mark 2） dust forecasting model and satellite-derived aerosol optical thickness （AOT） data. processed in the JAXA （Japan Aerospace Exploration Agency） Satellite Monitoring for Environmental Studies （JASMES） system with MODIS （Moderate Resolution Imaging Spectroradiometer） observations. was used to quantify the impact of assimilation on forecasts of a severe Asian dust storm during May 10-13. 2011. The modeled bidirectional reflectance function and observed vegetation index employed in JASMES enable AOT retrievals in areas of high surface reflectance, making JASMES effective for dust forecasting and early warning by enabling assimilations in dust storm source regions. Forecasts both with and without assimilation were validated using PM^0 observations from China, Korea, and Japan in the TEMM WG1 dataset. Only the forecast with assimilation successfully captured the contrast between the core and tail of the dust storm by increasing the AOT around the core by 70-150% and decreasing it around the tail by 20-30% in the 18-h forecast. The forecast with assimilation improved the agreement with observed PMlo concentrations, but the effect was limited at downwind sites in Korea and Japan because of the lack of observational constraints for a mis-forecasted dust storm due to cloud.

Assimilation of the FY-4A AGRI Clear-Sky Radiance Data in a Regional Numerical Model and Its Impact on the Forecast of the“21·7”Henan Extremely Persistent Heavy Rainfall

Assimilation of the Advanced Geostationary Radiance Imager(AGRI)clear-sky radiance in a regional model is performed.The forecasting effectiveness of the assimilation of two water vapor(WV)channels with conventional observations for the“21·7”Henan extremely heavy rainfall is analyzed and compared with a baseline test that assimilates only conventional observations in this study.The results show that the 24-h cumulative precipitation forecast by the assimilation experiment with the addition of the AGRI exceeds 500 mm,compared to a maximum value of 532.6 mm measured by the national meteorological stations,and that the location of the maximum precipitation is consistent with the observations.The results for the short periods of intense precipitation processes are that the simulation of the location and intensity of the 3-h cumulative precipitation is also relatively accurate.The analysis increment shows that the main difference between the two sets of assimilation experiments is over the ocean due to the additional ocean observations provided by FY-4A,which compensates for the lack of ocean observations.The assimilation of satellite data adjusts the vertical and horizontal wind fields over the ocean by adjusting the atmospheric temperature and humidity,which ultimately results in a narrower and stronger WV transport path to the center of heavy precipitation in Zhengzhou in the lower troposphere.Conversely,the WV convergence and upward motion in the control experiment are more dispersed;therefore,the precipitation centers are also correspondingly more dispersed.

A data assimilation-based forecast model of outer radiation belt electron fluxes

Because radiation belt electrons can pose a potential threat to the safety of satellites orbiting in space,it is of great importance to develop a reliable model that can predict the highly dynamic variations in outer radiation belt electron fluxes.In the present study,we develop a forecast model of radiation belt electron fluxes based on the data assimilation method,in terms of Van Allen Probe measurements combined with three-dimensional radiation belt numerical simulations.Our forecast model can cover the entire outer radiation belt with a high temporal resolution(1 hour)and a spatial resolution of 0.25 L over a wide range of both electron energy(0.1-5.0 MeV)and pitch angle(5°-90°).On the basis of this model,we forecast hourly electron fluxes for the next 1,2,and 3 days during an intense geomagnetic storm and evaluate the corresponding prediction performance.Our model can reasonably predict the stormtime evolution of radiation belt electrons with high prediction efficiency(up to~0.8-1).The best prediction performance is found for~0.3-3 MeV electrons at L=~3.25-4.5,which extends to higher L and lower energies with increasing pitch angle.Our results demonstrate that the forecast model developed can be a powerful tool to predict the spatiotemporal changes in outer radiation belt electron fluxes,and the model has both scientific significance and practical implications.

Reconstructing urban wind flows for urban air mobility using reduced-order data assimilation

Advancements in uncrewed aircrafts and communications technologies have led to a wave of interest and investment in unmanned aircraft systems(UASs)and urban air mobility(UAM)vehicles over the past decade.To support this emerging aviation application,concepts for UAS/UAM traffic management(UTM)systems have been explored.Accurately characterizing and predicting the microscale weather conditions,winds in particular,will be critical to safe and efficient operations of the small UASs/UAM aircrafts within the UTM.This study implements a reduced order data assimilation approach to reduce discrepancies between the predicted urban wind speed with computational fluid dynamics(CFD)Reynolds-averaged Navier Stokes(RANS)model with real-world,limited and sparse observations.The developed data assimilation system is UrbanDA.These observations are simulated using a large eddy simulation(LES).The data assimilation approach is based on the time-independent variational framework and uses space reduction to reduce the memory cost of the process.This approach leads to error reduction throughout the simulated domain and the reconstructed field is different than the initial guess by ingesting wind speeds at sensor locations and hence taking into account flow unsteadiness in a time when only the mean flow quantities are resolved.Different locations where wind sensors can be installed are discussed in terms of their impact on the resulting wind field.It is shown that near-wall locations,near turbulence generation areas with high wind speeds have the highest impact.Approximating the model error with its principal mode provides a better agreement with the truth and the hazardous areas for UAS navigation increases by more than 10%as wind hazards resulting from buildings wakes are better simulated through this process.

Prediction of landslide block movement based on Kalman filtering data assimilation method

Compared with the study of single point motion of landslides,studying landslide block movement based on data from multiple monitoring points is of great significance for improving the accurate identification of landslide deformation.Based on the study of landslide block,this paper regarded the landslide block as a rigid body in particle swarm optimization algorithm.The monitoring data were organized to achieve the optimal state of landslide block,and the 6-degree of freedom pose of the landslide block was calculated after the regularization.Based on the characteristics of data from multiple monitoring points of landslide blocks,a prediction equation for the motion state of landslide blocks was established.By using Kalman filtering data assimilation method,the parameters of prediction equation for landslide block motion state were adjusted to achieve the optimal prediction.This paper took the Baishuihe landslide in the Three Gorges reservoir area as the research object.Based on the block segmentation of the landslide,the monitoring data of the Baishuihe landslide block were organized,6-degree of freedom pose of block B was calculated,and the Kalman filtering data assimilation method was used to predict the landslide block movement.The research results showed that the proposed prediction method of the landslide movement state has good prediction accuracy and meets the expected goal.This paper provides a new research method and thinking angle to study the motion state of landslide block.

Time-Expanded Sampling for Ensemble-Based Filters:Assimilation Experiments with Real Radar Observations

By sampling perturbed state vectors from each ensemble prediction run at properly selected time levels in the vicinity of the analysis time, the recently proposed time-expanded sampling approach can enlarge the ensemble size without increasing the number of prediction runs and, hence, can reduce the computational cost of an ensemble-based filter. In this study, this approach is tested for the first time with real radar data from a tornadic thunderstorm. In particular, four assimilation experiments were performed to test the time-expanded sampling method against the conventional ensemble sampling method used by ensemble- based filters. In these experiments, the ensemble square-root filter （EnSRF） was used with 45 ensemble members generated by the time-expanded sampling and conventional sampling from 15 and 45 prediction runs, respectively, and quality-controlled radar data were compressed into super-observations with properly reduced spatial resolutions to improve the EnSRF performances. The results show that the time-expanded sampling approach not only can reduce the computational cost but also can improve the accuracy of the analysis, especially when the ensemble size is severely limited due to computational constraints for real-radar data assimilation. These potential merits are consistent with those previously demonstrated by assimilation experiments with simulated data.

SAR Data Assimilation for Crop Biomass Simulation Based on Crop Growth Model

Biomass from SAR data was assimilated into crop growth model to describe relationship between crop biomass and crop growth time to improve estimation accuracy of biomass. In addition, inverse model was established in order to estimate biomass according to relationship between biomass and backscattering coefficients from SAR data. Based on cost function, parameters of growth model were optimized as per conjugate gradient method, minimizing the differences between estimated biomass and inversion values from SAR data. The results indicated that the simulated biomass using the revised growth model with SAR data was consistent with the measured one in time distribution and even higher in accuracy than that without SAR data. Hence, the key parameters of crop growth model could be revised by real-time growth information from SAR data and accuracy of the simulated biomass could be improved accordingly.

STUDY ON THE ADJOINT METHOD IN DATA ASSIMILATION AND THE RELATED PROBLEMS

It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.

Coupling Ensemble Kalman Filter with Four-dimensional Variational Data Assimilation

This study examines the performance of coupling the deterministic four-dimensional variational assimilation system （4DVAR） with an ensemble Kalman filter （EnKF） to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme （E4DVAR） benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence： the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.

Impact of the Assimilation Frequency of Radar Data with the ARPS 3DVar and Cloud Analysis System on Forecasts of a Squall Line in Southern China

Assimilation configurations have significant impacts on analysis results and subsequent forecasts. A squall line system that occurred on 23 April 2007 over southern China was used to investigate the impacts of the data assimilation frequency of radar data on analyses and forecasts. A three-dimensional variational system was used to assimilate radial velocity data,and a cloud analysis system was used for reflectivity assimilation with a 2-h assimilation window covering the initial stage of the squall line. Two operators of radar reflectivity for cloud analyses corresponding to single-and double-moment schemes were used. In this study, we examined the sensitivity of assimilation frequency using 10-, 20-, 30-, and 60-min assimilation intervals. The results showed that analysis fields were not consistent with model dynamics and microphysics in general;thus, model states, including dynamic and microphysical variables, required approximately 20 min to reach a new balance after data assimilation in all experiments. Moreover, a 20-min data assimilation interval generally produced better forecasts for both single-and double-moment schemes in terms of equitable threat and bias scores. We conclude that a higher data assimilation frequency can produce a more intense cold pool and rear inflow jets but does not necessarily lead to a better forecast.

Assimilating Surface Observations in a Four-Dimensional Variational Doppler Radar Data Assimilation System to Improve the Analysis and Forecast of a Squall Line Case

This paper examines how assimilating surface observations can improve the analysis and forecast ability of a four- dimensional Variational Doppler Radar Analysis System （VDRAS）. Observed surface temperature and winds are assimilated together with radar radial velocity and reflectivity into a convection-permitting model using the VDRAS four-dimensional variational （4DVAR） data assimilation system. A squall-line case observed during a field campaign is selected to investigate the performance of the technique. A single observation experiment shows that assimilating surface observations can influence the analyzed fields in both the horizontal and vertical directions. The surface-based cold pool, divergence and gust front of the squall line are all strengthened through the assimilation of the single surface observation. Three experiments--assimilating radar data only, assimilating radar data with surface data blended in a mesoscale background, and assimilating both radar and surface observations with a 4DVAR cost function--are conducted to examine the impact of the surface data assimilation. Independent surface and wind profiler observations are used for verification. The result shows that the analysis and forecast are improved when surface observations are assimilated in addition to radar observations. It is also shown that the additional surface data can help improve the analysis and forecast at low levels. Surface and low-level features of the squall line-- including the surface warm inflow, cold pool, gust front, and low-level wind--are much closer to the observations after assimilating the surface data in VDRAS.

Evaluation of Two Momentum Control Variable Schemes and Their Impact on the Variational Assimilation of Radar Wind Data:Case Study of a Squall Line

Different choices of control variables in variational assimilation can bring about different influences on the analyzed atmospheric state. Based on the WRF model＇s three-dimensional variational assimilation system, this study compares the be- havior of two momentum control variable options-streamfunction velocity potential （ψ-χ） and horizontal wind components （U-V）-in radar wind data assimilation for a squall line case that occurred in Jiangsu Province on 24 August 2014. The wind increment from the single observation test shows that the ψ-χ control variable scheme produces negative increments in the neighborhood around the observation point because streamfunction and velocity potential preserve integrals of velocity. On the contrary, the U-V control variable scheme objectively reflects the information of the observation itself. Furthermore, radial velocity data from 17 Doppler radars in eastern China are assimilated. As compared to the impact of conventional observation, the assimilation of radar radial velocity based on the U-V control variable scheme significantly improves the mesoscale dynamic field in the initial condition. The enhanced low-level jet stream, water vapor convergence and low-level wind shear result in better squall line forecasting. However, the ψ-χ control variable scheme generates a discontinuous wind field and unrealistic convergence/divergence in the analyzed field, which lead to a degraded precipitation forecast.

Testing a Four-Dimensional Variational Data Assimilation Method Using an Improved Intermediate Coupled Model for ENSO Analysis and Prediction

A four-dimensional variational （4D-Var） data assimilation method is implemented in an improved intermediate coupled model （ICM） of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The ＂observation＂ of the SST anomaly, which is sampled from a ＂truth＂ model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction.

An Adaptive Estimation of Forecast Error Covariance Parameters for Kalman Filtering Data Assimilation

An adaptive estimation of forecast error covariance matrices is proposed for Kalman filtering data assim- ilation. A forecast error covariance matrix is initially estimated using an ensemble of perturbation forecasts. This initially estimated matrix is then adjusted with scale parameters that are adaptively estimated by minimizing -2log-likelihood of observed-minus-forecast residuals. The proposed approach could be applied to Kalman filtering data assimilation with imperfect models when the model error statistics are not known. A simple nonlinear model （Burgers＇ equation model） is used to demonstrate the efficacy of the proposed approach.

Evaluation on data assimilation of a global high resolution wave-tide-circulation coupled model using the tropical Pacific TAO buoy observations

In order to evaluate the assimilation results from a global high resolution ocean model, the buoy observations from tropical atmosphere ocean（TAO） during August 2014 to July 2015 are employed. The horizontal resolution of wave-tide-circulation coupled ocean model developed by The First Institute of Oceanography（FIOCOM model） is 0.1°×0.1°, and ensemble adjustment Kalman filter is used to assimilate the sea surface temperature（SST）, sea level anomaly（SLA） and Argo temperature/salinity profiles. The simulation results with and without data assimilation are examined. First, the overall statistic errors of model results are analyzed. The scatter diagrams of model simulations versus observations and corresponding error probability density distribution show that the errors of all the observed variables, including the temperature, isotherm depth of 20°C（D20）, salinity and two horizontal component of velocity are reduced to some extent with a maximum improvement of 54% after assimilation. Second, time-averaged variables are used to investigate the horizontal and vertical structures of the model results. Owing to the data assimilation, the biases of the time-averaged distribution are reduced more than70% for the temperature and D20 especially in the eastern Pacific. The obvious improvement of D20 which represents the upper mixed layer depth indicates that the structure of the temperature after the data assimilation becomes more close to the reality and the vertical structure of the upper ocean becomes more reasonable. At last,the physical processes of time series are compared with observations. The time evolution processes of all variables after the data assimilation are more consistent with the observations. The temperature bias and RMSE of D20 are reduced by 76% and 56% respectively with the data assimilation. More events during this period are also reproduced after the data assimilation. Under the condition of strong 2014/2016 El Ni？o, the Equatorial Undercurrent（EUC） from the TAO is gradually increased during August to November in 2014, and followed by a decreasing process. Since the improvement of the structure in the upper ocean, these events of the EUC can be clearly found in the assimilation results. In conclusion, the data assimilation in this global high resolution model has successfully reduced the model biases and improved the structures of the upper ocean, and the physical processes in reality can be well produced.

Initialization and Simulation of a Typhoon Using 4-Dimensional Variational Data Assimilation——Research on Typhoon Herb (1996)

The MM5 and its four dimensional variational data assimilation (4D-Var) system are used in this paper. Based on the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis data, the authors generate an optimal initial condition for a typhoon by using the bogus data assimilation (BDA) scheme. BDA is able to recover many of the structural features of typhoons including a warm-core vertex, the correct center position, and the strong circulation. As a result of BDA using a bogus surface low, dramatic improvement is achieved in the 72 h prediction of typhoon Herb. Through several cases, the initialization by BDA effectively generates the harmonious inner structure of the typhoon, but which is lacking in the original analysis field. Therefore the intensity forecast is improved greatly. Some improvements are made in the track forecast, but more work still needs to be done.