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.

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.

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.

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.

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.

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.

New data assimilation system DNDAS for high-dimensional models

The tangent linear（TL） models and adjoint（AD） models have brought great difficulties for the development of variational data assimilation system. It might be impossible to develop them perfectly without great efforts, either by hand, or by automatic differentiation tools. In order to break these limitations, a new data assimilation system, dual-number data assimilation system（DNDAS）, is designed based on the dual-number automatic differentiation principles. We investigate the performance of DNDAS with two different optimization schemes and subsequently give a discussion on whether DNDAS is appropriate for high-dimensional forecast models. The new data assimilation system can avoid the complicated reverse integration of the adjoint model, and it only needs the forward integration in the dual-number space to obtain the cost function and its gradient vector concurrently. To verify the correctness and effectiveness of DNDAS, we implemented DNDAS on a simple ordinary differential model and the Lorenz-63 model with different optimization methods. We then concentrate on the adaptability of DNDAS to the Lorenz-96 model with high-dimensional state variables. The results indicate that whether the system is simple or nonlinear, DNDAS can accurately reconstruct the initial condition for the forecast model and has a strong anti-noise characteristic. Given adequate computing resource, the quasi-Newton optimization method performs better than the conjugate gradient method in DNDAS.

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.

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.

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.

Optimal estimation of zonal velocity and transport through Luzon Strait using variational data assimilation technique

A P-vector method was optimized using variational data assimilation technique, with which the vertical structures and seasonal variations of zonal velocities and transports were investigated. The results showed that westward and eastward flowes occur in the Luzon Strait in the same period in a year. However the net volume transport is westward. In the upper level (0m -500m),the westward flow exits in the middle and south of the Luzon Strait, and the eastward flow exits in the north. There are two centers of westward flow and one center of eastward flow. In the middle of the Luzon Strait, westward and eastward flowes appear alternately in vertical direction. The westward flow strengthens in winter and weakens in summer. The net volume transport is strong in winter (5.53 Sv) but weak in summer (0.29 Sv). Except in summer, the volume transport in the upper level accounts for more than half of the total volume transport (0m bottom). In summer, the net volume transport in the upper level is eastward (1.01 Sv), but westward underneath.

An Examination of the Predictability of Tropical Cyclone Genesis in High-Resolution Coupled Models with Dynamically Downscaled Coupled Data Assimilation Initialization

Predicting tropical cyclone(TC)genesis is of great societal importance but scientifically challenging.It requires fineresolution coupled models that properly represent air−sea interactions in the atmospheric responses to local warm sea surface temperatures and feedbacks,with aid from coherent coupled initialization.This study uses three sets of highresolution regional coupled models(RCMs)covering the Asia−Pacific(AP)region initialized with local observations and dynamically downscaled coupled data assimilation to evaluate the predictability of TC genesis in the West Pacific.The APRCMs consist of three sets of high-resolution configurations of the Weather Research and Forecasting−Regional Ocean Model System(WRF-ROMS):27-km WRF with 9-km ROMS,and 9-km WRF with 3-km ROMS.In this study,a 9-km WRF with 9-km ROMS coupled model system is also used in a case test for the predictability of TC genesis.Since the local sea surface temperatures and wind shear conditions that favor TC formation are better resolved,the enhanced-resolution coupled model tends to improve the predictability of TC genesis,which could be further improved by improving planetary boundary layer physics,thus resolving better air−sea and air−land interactions.

Impacts of XBT,TAO,Altimetry and ARGO Observations on the Tropical Pacific Ocean Data Assimilation

This study aims at assessing the relative impacts of four major components of the tropical Pacific Ocean observing system on assimilation of temperature and salinity fields. Observations were collected over a period between January 2001 through June 2003 including temperature data from the expendable bathythermographs （XBT）, thermistor data from the Tropical Ocean Global Atmosphere Tropical Atmosphere-Ocean （TOGA-TAO） mooring array, sea level anomalies from the Topex/Poseidon and Jason-1 altimetry （T/P-J）, and temperature and salinity profiles from the Array for Real-time Geostrophic Oceanography （ARGO） floats. An efficient three-dimensional variational analysis-based method was introduced to assimilate the above data into the tropical-Pacific circulation model. To evaluate the impact of the individual component of the observing system, four observation system experiments were carried out. The experiment that assimilated all four components of the observing system was taken as the reference. The other three experiments were implemented by withholding one of the four components. Results show that the spatial distribution of the data influences its relative contribution. XBT observations produce the most distinguished effects on temperature analyses in the off-equatorial region due to the large amount of measurements and high quality. Similarly, the impact of TAO is dominant in the equatorial region due to the focus of the spatial distribution. The Topex/Poseidon-Jason-1 can be highly complementary where the XBT and TAO observations are sparse. The contribution of XBT or TAO on the assimilated salinity is made by the model dynamics because no salinity observations from them are assimilated. Therefore, T/P-J, as a main source for providing salinity data, has been shown to have greater impacts than either XBT or TAO on the salinity analysis. Although ARGO includes the subsurface observations, the relatively smaller number of observation makes it have the smallest contribution to the assimilation system.

A theoretical study of the multigrid three-dimensional variational data assimilation scheme using a simple bilinear interpolation algorithm

In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.

ASSIMILATION OF REAL OBSERVATIONAL DATA WITH THE GSI-HYBRID DATA ASSIMILATION SYSTEM TO IMPROVE TYPHOON FORECAST

A hybrid GSI （Grid-point Statistical Interpolation）-ETKF （Ensemble Transform Kalman Filter） data assimila- tion system has been recently developed for the WRF （Weather Research and Forecasting） model and tested with simu- lated observations for tropical cyclone （TC） forecast. This system is based on the existing GSI but with ensemble back- ground information incorporated. As a follow-up, this work extends the new system to assimilate real observations to further understand the hybrid scheme. As a first effort to explore the system with real observations, relatively coarse grid resolution （27 km） is used. A case study of typhoon Muifa （2011） is performed to assimilate real observations in- cluding conventional in-situ and satellite data. The hybrid system with flow-dependent ensemble eovariance shows sig- nificant improvements with respect to track forecast compared to the standard GSI system which in theory is three di- mensional variational analysis （3DVAR）. By comparing the analyses, analysis increments and forecasts, the hybrid sys- tem is found to be potentially able to recognize the existence of TC vortex, adjust its position systematically, better de- scribe the asymmetric structure of typhoon Muifa and maintain the dynamic and thermodynamic balance in typhoon ini- tial field. In addition, a cold-start hybrid approach by using the global ensembles to provide flow-dependent error is test- ed and similar results are revealed with those from cycled GSI-ETKF approach.

Aerosol Data Assimilation Using Data from Fengyun-3A and MODIS:Application to a Dust Storm over East Asia in 2011

Aerosol optical depth （AOD） is the most basic paxalneter that describes the optical properties of atmospheric aerosols, and it can be used to indicate aerosol content. In this study, we assimilated AOD data from the Fengyun-3A （FY-3A） and MODIS meteorological satellite using the Gridpoint Statistical Interpolation three-dimensional variational data assimilation system. Experiments were conducted for a dust storm over East Asia in April 2011. Each 0600 UTC analysis initialized a 24-h Weather Research and Forecasting with Chemistry model forecast. The results generally showed that the assimilation of satellite AOD observational data can significantly improve model aerosol mass prediction skills. The AOD distribution of the analysis field was closer to the observations of the satellite after assimilation of satellite AOD data. In addition, the analysis resulting from the experiment assimilating both FY-3A/MERSI （Medium-resolution Spectral Imager） AOD data and MODIS AOD data had closer agreement with the ground-based values than the individual assimilation of the two datasets for the dust storm over East Asia. These results suggest that the Chinese FY-3A satellite aerosol products can be effectively applied to numerical models and dust weather analysis.

VARIATIONAL DATA ASSIMILATION USING WAVELET BACKGROUND ERROR COVARIANCE: INITIALIZATION OF TYPHOON KAEMI (2006)

Background error covariance plays an important role in any variational data assimilation system, because it determines how information from observations is spread in model space and between different model variables. In this paper, the use of orthogonal wavelets in representation of background error covariance over a limited area is studied. Based on the WRF model and its 3D-VAR system, an algorithm using orthogonal wavelets to model background error covariance is developed. Because each wavelet function contains information on both position and scale, using a diagonal correlation matrix in wavelet space gives the possibility to represent some anisotropic and inhomogeneous characteristics of background error covariance. The experiments show that local correlation functions are better modeled than spectral methods. The formulation of wavelet background error covariance is tested with the typhoon Kaemi (2006). The results of experiments indicate that the subsequent forecasts of typhoon Kaemi’s track and intensity are significantly improved by the new method.

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.