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.

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.

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.

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.

Parallel Computing of a Variational Data Assimilation Model for GPS/MET Observation Using the Ray-Tracing Method

The Spectral Statistical Interpolation (SSI) analysis system of NCEP is used to assimilate meteorological data from the Global Positioning Satellite System (GPS/MET) refraction angles with the variational technique. Verified by radiosonde, including GPS/MET observations into the analysis makes an overall improvement to the analysis variables of temperature, winds, and water vapor. However, the variational model with the ray-tracing method is quite expensive for numerical weather prediction and climate research. For example, about 4 000 GPS/MET refraction angles need to be assimilated to produce an ideal global analysis. Just one iteration of minimization will take more than 24 hours CPU time on the NCEP's Cray C90 computer. Although efforts have been taken to reduce the computational cost, it is still prohibitive for operational data assimilation. In this paper, a parallel version of the three-dimensional variational data assimilation model of GPS/MET occultation measurement suitable for massive parallel processors architectures is developed. The divide-and-conquer strategy is used to achieve parallelism and is implemented by message passing. The authors present the principles for the code's design and examine the performance on the state-of-the-art parallel computers in China. The results show that this parallel model scales favorably as the number of processors is increased. With the Memory-IO technique implemented by the author, the wall clock time per iteration used for assimilating 1420 refraction angles is reduced from 45 s to 12 s using 1420 processors. This suggests that the new parallelized code has the potential to be useful in numerical weather prediction (NWP) and climate studies.

On the 4D Variational Data Assimilation with Constraint Conditions

An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint technology, penalty method and augmented Lagrangian method are used in constraint optimization field to minimize the defined constraint objective functions. The results of the numerical experiments show that the optimal solutions are obtained if the functions reach the minima. VDA with constraint conditions controlling the growth of gravity oscillations is efficient to eliminate perturbation and produces optimal initial field. It seems that this method can also be applied to the problem in numerical weather prediction. Key words Variational data assimilation - Constraint conditions - Penalty methods - finite-element model This research is supported by National Natural Science Foundation of China (Grant No. 49575269) and by National Key Basic Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters (Grant No. G1998040910).

Storm surge model based on variational data assimilation method

By combining computation and observation information, the variational data assimilation method has the ability to eliminate errors caused by the uncertainty of parameters in practical forecasting. It was applied to a storm surge model based on unstructured grids with high spatial resolution meant for improving the forecasting accuracy of the storm surge. By controlling the wind stress drag coefficient, the variation-based model was developed and validated through data assimilation tests in an actual storm surge induced by a typhoon. In the data assimilation tests, the model accurately identified the wind stress drag coefficient and obtained results close to the true state. Then, the actual storm surge induced by Typhoon 0515 was forecast by the developed model, and the results demonstrate its efficiency in practical application.

A temporal sliding procedure for ocean wave variational data assimilation and its application

For sequential performance of wave variational data assimilation, we proposed a temporal sliding method in which the temporal overlap is considered. The advantage of this method is that the initial wave spectrum of the optimization process is modified by the observations in latter and former times. This temporal sliding procedure is important for marginal region, such as the China seas, where the duration of assimilation effectiveness is 2-3 days. Experiments were performed in the whole course of Cyclone 9403 （Russ）. Around the cyclone center, the maximum value of wave elements did not change much by assimilation, because the extreme value was determined by wind energy input that was not yet optimized. In the area outside the cyclone center, this modification is evident especially for wind wave growth.

Optimal estimation of absolute geostrophic velocity field in vicinity of the Luzon Strait using variational data assimilation technique

A P - vector method is optimized using the variational data assimilation technique(VDAT). The absolute geostrophic velocity fields in the vicinity of the Luzon Strait (LS) are calculated, the spatial structures and seasonal variations of the absolute geostrophic velocity field are investigated. Our results show that the Kuroshio enters the South China Sea (SCS) in the south and middle of the Luzon Strait and flows out in the north, so the Kuroshio makes a slight clockwise curve in the Luzon Strait, and the curve is strong in winter and weak in summer. During the winter, a westward current appears in the surface, and locates at the west of the Luzon Strait. It is the north part of a cyclonic gyre which exits in the northeast of the SCS; an anti-cyclonic gyre occurs on the intermediate level, and it exits in the northeast of the SCS, and an eastward current exits in the southeast of the anti-cyclonic gyre.

GENERALIZED VARIATIONAL DATA ASSIMILATION METHOD AND NUMERICAL EXPERIMENT FOR NON-DIFFERENTIAL SYSTEM

The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR (Four-dimensional variational) of non-differential partial differential system with local observations.

Some theoretical problems on variational data assimilation

Theoretical aspects of variational data assimilation （VDA） for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions and parameters for the model are revisited and the model itself is modified. The estimates of both error and convergence rate are theoretically made and the vahdity of the method is proved. For VDA problem with local observation data, the conventional VDA method are out of use due to the ill-posedness of the problem. In order to overcome the difficulties caused by the ill-posedness, the initial conditions and parameters of the model are modified by using the improved VDA method, and the estimates of both error and convergence rate are also made. Finally, the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example, and a theoretical criterion of the regularization parameters is proposed.

Variational Data Assimilation Method Using Parallel Dual Populations Particle Swarm Optimization Algorithm

In recent years,numerical weather forecasting has been increasingly emphasized.Variational data assimilation furnishes precise initial values for numerical forecasting models,constituting an inherently nonlinear optimization challenge.The enormity of the dataset under consideration gives rise to substantial computational burdens,complex modeling,and high hardware requirements.This paper employs the Dual-Population Particle Swarm Optimization(DPSO)algorithm in variational data assimilation to enhance assimilation accuracy.By harnessing parallel computing principles,the paper introduces the Parallel Dual-Population Particle Swarm Optimization(PDPSO)Algorithm to reduce the algorithm processing time.Simulations were carried out using partial differential equations,and comparisons in terms of time and accuracy were made against DPSO,the Dynamic Weight Particle Swarm Algorithm(PSOCIWAC),and the TimeVarying Double Compression Factor Particle Swarm Algorithm(PSOTVCF).Experimental results indicate that the proposed PDPSO outperforms PSOCIWAC and PSOTVCF in convergence accuracy and is comparable to DPSO.Regarding processing time,PDPSO is 40%faster than PSOCIWAC and PSOTVCF and 70%faster than DPSO.

A Prototype Regional GSI-based EnKF-Variational Hybrid Data Assimilation System for the Rapid Refresh Forecasting System：Dual-Resolution Implementation and Testing Results

A dual-resolution（DR） version of a regional ensemble Kalman filter（EnKF）-3D ensemble variational（3DEnVar） coupled hybrid data assimilation system is implemented as a prototype for the operational Rapid Refresh forecasting system. The DR 3DEnVar system combines a high-resolution（HR） deterministic background forecast with lower-resolution（LR） EnKF ensemble perturbations used for flow-dependent background error covariance to produce a HR analysis. The computational cost is substantially reduced by running the ensemble forecasts and EnKF analyses at LR. The DR 3DEnVar system is tested with 3-h cycles over a 9-day period using a 40/13-km grid spacing combination. The HR forecasts from the DR hybrid analyses are compared with forecasts launched from HR Gridpoint Statistical Interpolation（GSI） 3D variational（3DVar）analyses, and single LR hybrid analyses interpolated to the HR grid. With the DR 3DEnVar system, a 90% weight for the ensemble covariance yields the lowest forecast errors and the DR hybrid system clearly outperforms the HR GSI 3DVar.Humidity and wind forecasts are also better than those launched from interpolated LR hybrid analyses, but the temperature forecasts are slightly worse. The humidity forecasts are improved most. For precipitation forecasts, the DR 3DEnVar always outperforms HR GSI 3DVar. It also outperforms the LR 3DEnVar, except for the initial forecast period and lower thresholds.

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.

IMPACT OF DIABATIC PROCESSES IN AGCM ON 4-DIMENSIONAL VARIATIONAL DATA ASSIMILATION

The impact of diabatic processes on 4-dimensional variational data assimilation (4D-Var) was studied using the 1995 version of NCEP's global spectral model with and without full physics.The adjoint was coded manually.A cost function measuring spectral errors of 6-hour forecasts to 'observation' (the NCEP reanalysis data) was minimized using the L-BFGS (the limited memory quasi-Newton algorithm developed by Broyden,Fletcher,Goldfard and Shanno) for optimizing parameters and initial conditions.Minimization of the cost function constrained by an adiabatic version of the NCEP global model converged to a minimum with a significant amount of decrease in the value of the cost function.Minimization of the cost function using the diabatic model, however,failed after a few iterations due to discontinuities introduced by physical parameterizations.Examination of the convergence of the cost function in different spectral domains reveals that the large-scale flow is adjusted during the first 10 iterations,in which discontinuous diabatic parameterizations play very little role.The adjustment produced by the minimization gradually moves to relatively smaller scales between 10-20th iterations.During this transition period,discontinuities in the cost function produced by 'on-off' switches in the physical parameterizations caused the cost function to stay in a shallow local minimum instead of continuously decreasing toward a deeper minimum. Next,a mixed 4D-Var scheme is tested in which large-scale flows are first adiabatically adjusted to a sufficient level,followed by a diabatic adjustment introduced after 10 to 20 iterations. The mixed 4D-Var produced a closer fit of analysis to observations,with 38% and 41% more decrease in the values of the cost function and the norm of gradient,respectively,than the standard diabatic 4D-Var,while the CPU time is reduced by 21%.The resulting optimal initial conditions improve the short-range forecast skills of 48-hour statistics.The detrimental effect of parameterization discontinuities on minimization was also reduced.

Application of Nonlinear Balance Scheme in Three-Dimensional Variational Data Assimilation

The dynamical constrains in three-dimensional variational data assimilation are discussed when considering the impact of stream divergence and convergence on the pressure and wind fields. For the analysis of severe tropical cyclone, frontal structures, and other rapidly changing structures, the geostrophic balance and linear balance cannot properly represent the relationship between wind and pressure fields. However, the nonlinear balance incremental equation takes into account the information of flow-dependent background, and makes response to the flow-dependent background covariance in the 3D-Var system. Results indicate that the application of the nonlinear balance equation to 3D-Var system improves the quality of severe tropical cyclone assimilation system, which has some positive effects on intensity prediction of tropical cyclones.

Studies of Variational Assimilation for the Inversion of the Coupled Air-sea Model

For the prediction of ENSO, the accuracy of the model including the parameters, initial value and others of the model is important, which can be retrieved by the variational data assimilation methods developed in recent years. However, when the nonlinearity of the model is quite strong, the effect of the improvement made by the 4-D variational data assimilation may be poor due to the bad approximation of the tangent linear model to the original model. So in the paper the ideas in the optimal control is introduced to improve the effect of 4-DVAR in the inversion of the parameters of a nonlinear dynamic ENSO model. The results indicate that when the terminal controlling term is added to the cost functional of 4DVAR, which originated from the optimal control, the effect of the inversion may be largely improved comparing to the traditional 4DVAR, as can be especially obvious from the phase orbit of the model variables. The results in the paper also suggest that the method of 4DVAR in combination with optimal control cannot only reduce the error resulting from the inaccuracy of the model parameters but also can correct the parameters itself. This gives a good method in modifying the model and improving the quality of prediction of ENSO.

Variational Assimilation of Satellite Cloud Water/Ice Path and Microphysics Scheme Sensitivity to the Assimilation of a Rainfall Case

Hydrometeor variables （cloud water and cloud ice mixing ratios） are added into the WRF three-dimensional variational assimilation system as additional control variables to directly analyze hydrometeors by assimilating cloud observations. In addition, the background error covariance matrix of hydrometeors is modeled through a control variable transform, and its characteristics discussed in detail. A suite of experiments using four microphysics schemes （LIN, SBU-YLIN, WDM6 and WSM6） are performed with and without assimilating satellite cloud liquid/ice water path. We find analysis of hydrometeors with cloud assimilation to be significantly improved, and the increment and distribution of hydrometeors are consistent with the characteristics of background error covariance. Diagnostic results suggest that the forecast with cloud assimilation represents a significant improvement, especially the ability to forecast precipitation in the first seven hours. It is also found that the largest improvement occurs in the experiment using the WDM6 scheme, since the assimilated cloud information can sustain for longer in this scheme. The least improvement, meanwhile, appears in the experiment using the SBU-YLIN scheme.

Rainfall Assimilation Using a New Four-Dimensional Variational Method:A Single-Point Observation Experiment

Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread attention from the public because it caused catastrophic damage in China. Several numerical studies have shown that many forecast models, including Pennsylvania State University National Center for Atmospheric Research’s fifth-generation mesoscale model （MM5）, failed to simulate the heavy precipitation over the Yangzi River valley. This study demonstrates that with the optimal initial conditions from the dimension-reduced projection four-dimensional variational data assimilation （DRP-4DVar） system, MM5 can successfully reproduce these observed rainfall amounts and can capture many important mesoscale features, including the southwestward shear line and the low-level jet stream. The study also indicates that the failure of previous forecasts can be mainly attributed to the lack of mesoscale details in the initial conditions of the models.