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.

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.

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.

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.

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.

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.

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.

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 multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

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.

Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).Alternatively,physical space analysis system(4D-PSAS)is proposed to reduce the computation cost,in which the 4D-Var problem is solved in physical space(i.e.,observation space).In this study,the conjugate gradient(CG)algorithm,implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process.The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed.In order to overcome the non-monotonic variation of gradient norm,a new algorithm,Minimum Residual(MINRES)algorithm,is implemented in the process of assimilation iteration in this study.Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function,greatly improves the convergence properties of 4D-PSAS as well,and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.

Electromagnetic response function for the semi-annual variations estimated by the single-station method using the night-time values of the geomagnetic fields

The geomagnetic night-time values were used to estimate the electromagnetic response function Q1 for half-year period. If the spatial structure of the source field can be described by the approximation, one can estimate the Q1 value using the single-station Z/H method. This technique enables us to carry out regional deep gcomagnetic sounding by the method. The data used for analyses are geomagnetic night-time values for about, typically, 26 years from 5 good-quality stations and for several years from 34 stations distributed over the globe. The results indicate that the night-time values yield more reliable response estimates for half-year period compared to the usual estimates obtained from daily means. It implies that the approximation for the night-time fields holds good for the half-year period, but the daily means are not suitable for estimating the response function of the semi-annual variations by using the single-station method. Source field analyses for daily means data and night-time means data have also been carried out in this paper.

DEA Scores’ Confidence Intervals with Past-Present and Past-Present-Future Based Resampling

In data envelopment analysis (DEA), input and output values are subject to change for several reasons. Such variations differ in their input/output items and their decision-making units (DMUs). Hence, DEA efficiency scores need to be examined by considering these factors. In this paper, we propose new resampling models based on these variations for gauging the confidence intervals of DEA scores. The first model utilizes past-present data for estimating data variations imposing chronological order weights which are supplied by Lucas series (a variant of Fibonacci series). The second model deals with future prospects. This model aims at forecasting the future efficiency score and its confidence interval for each DMU. We applied our models to a dataset composed of Japanese municipal hospitals.

Intelligent Optimization Algorithms to VDA of Models with on/off Parameterizations

Some variational data assimilation （VDA） problems of time- and space-discrete models with on/off parameterizations can be regarded as non-smooth optimization problems. Same as the sub-gradient type method, intelligent optimization algorithms, which are widely used in engineering optimization, can also be adopted in VDA in virtue of their no requirement of cost function＇s gradient （or sub-gradient） and their capability of global convergence. Two typical intelligent optimization algorithms, genetic algorithm （GA） and particle swarm optimization （PSO）, are introduced to VDA of modified Lorenz equations with on-off parameterizations, then two VDA schemes are proposed, that is, GA based VDA （GA-VDA） and PSO based VDA （PSO-VDA）. After revealing the advantage of GA and PSO over conventional adjoint methods in the ability of global searching at the existence of cost function＇s discontinuity induced by on-off switches, sensitivities of GA-VDA and PSO-VDA to population size, observational noise, model error and observational density are detailedly analyzed. It＇s shown that, in the context of modified Lorenz equations, with proper population size, GA-VDA and PSO-VDA can effectively estimate the global optimal solution, while PSO-VDA consumes much less computational time than GA-VDA with the same population size, and requires a much lower population size with nearly the same results, both methods are not very sensitive to observation noise and model error, while PSO-VDA shows a better performance with observational noise than GA-VDA. It is encouraging that both methods are not sensitive to observational density, especially PSO-VDA, using which almost the same perfect assimilation results can be obtained with comparatively sparse observations.

四维变分同化方法在台风初始化及其数值模拟中的应用——对9608号(Herb)台风的研究结果(英)

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.

Retrieval of Atmospheric and Oceanic Parameters and the Relevant Numerical Calculation

It is well known that retrieval of parameters is usually ill-posed and highly nonlinear, so parameter retrieval problems are very difficult. There are still many important theoretical issues under research, although great success has been achieved in data assimilation in meteorology and oceanography. This paper reviews the recent research on parameter retrieval, especially that of the authors. First, some concepts and issues of parameter retrieval are introduced and the state-of-the-art parameter retrieval technology in meteorology and oceanography is reviewed briefly, and then atmospheric and oceanic parameters are retrieved using the variational data assimilation method combined with the regularization techniques in four examples： retrieval of the vertical eddy diffusion coefficient; of the turbulivity of the atmospheric boundary layer; of wind from Doppler radar data, and of the physical process parameters. Model parameter retrieval with global and local observations is also introduced.

Satellite All-sky Infrared Radiance Assimilation:Recent Progress and Future Perspectives

Satellite infrared(IR)sounder and imager measurements have become one of the main sources of data used by data assimilation systems to generate initial conditions for numerical weather prediction(NWP)models and atmospheric analysis/reanalysis.This paper reviews the development of satellite IR data assimilation in NWP in recent years,especially the assimilation of all-sky satellite IR observations.The major challenges and future directions are outlined and discussed.