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.

Application of a Recursive Filter to a Three-Dimensional Variational Ocean Data Assimilation System

In order to improve the efficiency of the Ocean Variational Assimilation System （OVALS）, which has been widely used in various applications, an improved OVALS （OVALS2） is developed based on the recursive filter （RF） algorithm. The first advantage of OVALS2 is that memory storage can be substantially reduced in practice because it implicitly computes the background error covariance matrix; the second advantage is that there is no inversion of the background error covariance by preconditioning the control variable. For comparing the effectiveness between OVALS2 and OVALS, a set of experiments was implemented by assimilating expendable bathythermograph （XBT） and ARGO data into the Tropical Pacific circulation model. The results show that the efficiency of OVALS2 is much higher than that of OVALS. The computational time and the computer storage in the assimilation process were reduced by 83% and 77%, respectively. Additionally, the corresponding results produced by the RF are almost as good as those obtained by OVALS. These results prove that OVALS2 is suitable for operational numerical oceanic forecasting.

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.

Toward development of the 4Dvar data assimilation system in the Bering Sea:reconstruction of the mean dynamic ocean topography

The Bering Sea circulation is derived as a variational inverse of hydrographic profiles（ temperature and salinity） , atmospheric climatologies and historical observation of ocean curents. The important result of this study is estimate of the mean climatological sea surface height （SSH） that can be used as a reference for satellite altimetry sea level anomaly data in the Bering Sea region. Numerical experiments reveal that, when combined with satellite altimetry, the obtained reference SSH effectively constrains a realistic reconstruction of the Amukta Pass circulation.

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.

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.

Typhoon Track Forecast with a Hybrid GSI-ETKF Data Assimilation System

A hybrid grid-point statistical interpolation-ensemble transform Kalman filter (GSI-ETKF) data assimilation system for the Weather Research and Forecasting (WRF) model was developed and applied to typhoon track forecast with simulated dropsonde observations. This hybrid system showed significantly improved results with respect to tropical cyclone track forecast compared to the standard GSI system in the case of Muifa in 2011. Further analyses revealed that the flow-dependent ensemble covariance was the major contributor to the better performance of the GSI-ETKF system than the standard GSI system; the GSI-ETKF system was found to be potentially able to adjust the position of the typhoon vortex systematically and better update the environmental field.

An Ocean Data Assimilation System in the Indian Ocean and West Pacific Ocean

The development and application of a regional ocean data assimilation system are among the aims of the Global Ocean Data Assimilation Experiment. The ocean data assimilation system in the regions including the Indian and West Pacific oceans is an endeavor motivated by this goal. In this study, we describe the system in detail. Moreover, the reanalysis in the joint area of Asia, the Indian Ocean, and the western Pacific Ocean （hereafter AIPOcean） constructed using multi-year model integration with data assimilation is used to test the performance of this system. The ocean model is an eddy-resolving, hybrid coordinate ocean model. Various types of observations including in-situ temperature and salinity profiles （mechanical bathythermograph, expendable bathythermograph, Array for Real-time Geostrophic Oceanography, Tropical Atmosphere Ocean Array, conductivity-temperature-depth, station data）, remotely-sensed sea surface temperature, and altimetry sea level anomalies, are assimilated into the reanalysis via the ensemble optimal interpolation method. An ensemble of model states sampled from a long-term integration is allowed to change with season, rather than remaining stationary. The estimated background error covariance matrix may reasonably reflect the seasonality and anisotropy. We evaluate the performance of AIPOcean during the period 1993-2006 by comparisons with independent observations, and some reanalysis products. We show that AIPOcean reduces the errors of subsurface temperature and salinity, and reproduces mesoscale eddies. In contrast to ECCO and SODA products, AIPOcean captures the interannual variability and linear trend of sea level anomalies very well. AIPOcean also shows a good consistency with tide gauges.

Use of Microwave Radiances from Metop-C and Fengyun-3 C/D Satellites for a Northern European Limited-area Data Assimilation System

MetCoOp is a Nordic collaboration on operational Numerical Weather Prediction based on a common limited-area km-scale ensemble system. The initial states are produced using a 3-dimensional variational data assimilation scheme utilizing a large amount of observations from conventional in-situ measurements, weather radars, global navigation satellite system, advanced scatterometer data and satellite radiances from various satellite platforms. A version of the forecasting system which is aimed for future operations has been prepared for an enhanced assimilation of microwave radiances. This enhanced data assimilation system will use radiances from the Microwave Humidity Sounder, the Advanced Microwave Sounding Unit-A and the Micro-Wave Humidity Sounder-2 instruments on-board the Metop-C and Fengyun-3 C/D polar orbiting satellites. The implementation process includes channel selection, set-up of an adaptive bias correction procedure, and careful monitoring of data usage and quality control of observations. The benefit of the additional microwave observations in terms of data coverage and impact on analyses, as derived using the degree of freedom of signal approach, is demonstrated. A positive impact on forecast quality is shown, and the effect on the precipitation for a case study is examined. Finally, the role of enhanced data assimilation techniques and adaptions towards nowcasting are discussed.

The Structure of Background-error Covariance in a Four-dimensional Variational Data Assimilation System:Single-point Experiment

A four dimensional variational data assimilation （4DVar） based on a dimension-reduced projection （DRP-4DVar） has been developed as a hybrid of the 4DVar and Ensemble Kalman filter （EnKF） concepts. Its good flow-dependent features are demonstrated in single-point experiments through comparisons with adjointbased 4DVar and three-dimensional variational data （3DVar） assimilations using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model （MM5）. The results reveal that DRP-4DVar can reasonably generate a background error covariance matrix （simply B-matrix） during the assimilation window from an initial estimation using a number of initial condition dependent historical forecast samples. In contrast, flow-dependence in the B-matrix of MM5 4DVar is barely detectable. It is argued that use of diagonal estimation in the B-matrix of the MM5 4DVar method at the initial time leads to this failure. The experiments also show that the increments produced by DRP-4DVar are anisotropic and no longer symmetric with respect to observation location due to the effects of the weather trends captured in its B-matrix. This differs from the MM5 3DVar which does not consider the influence of heterogeneous forcing on the correlation structure of the B-matrix, a condition that is realistic for many situations. Thus, the MM5 3DVar assimilation could only present an isotropic and homogeneous structure in its increments.

A New Global Four-Dimensional Variational Ocean Data Assimilation System and Its Application

A four-dimensional variational data assimilation （4DVar） system of the LASG/IAP Climate Ocean Model, version 1.0 （LICOM1.0）, named LICOM-3DVM, has been developed using the three-dimensional variational data assimilation of mapped observation （3DVM）, a 4DVar method newly proposed in the past two years. Two experiments with 12-year model integrations were designed to validate it. One is the assimilation run, called ASSM, which incorporated the analyzed weekly sea surface temperature （SST） fields from Reynolds and Smith （OISST） between 1990 and 2001 once a week by the LICOM-3DVM. The other is the control run without any assimilation, named CTL. ASSM shows that the simulated temperatures of the upper ocean （above 50 meters）, especially the SST of equatorial Pacific, coincide with the Tropic Atmosphere Ocean （TAO） mooring data, the World Ocean Atlas 2001 （WOA01） data and the Met Office Hadley Centre＇s sea ice and sea surface temperature （HadISST） data. It decreased the cold bias existing in CTL in the eastern Pacific and produced a Nifio index that agrees with observation well. The validation results suggest that the LICOM-3DVM is able to effectively adjust the model results of the ocean temperature, although it＇s hard to correct the subsurface results and it even makes them worse in some areas due to the incorporation of only surface data. Future development of the LICOM-3DVM is to include subsurface in situ observations and satellite observations to further improve model simulations.

The REMO Ocean Data Assimilation System into HYCOM(RODAS_H):General Description and Preliminary Results

The first version of the Brazilian Oceano- graphic Modeling and Observation Network （REMO） ocean data assimilation system into the Hybrid Coordi- nate Ocean Model （HYCOM） （RODAS H） has recently been constructed for research and operational purposes. The system is based on a multivariate Ensemble Optimal Interpolation （EnOI） scheme and considers the high fre- quency variability of the model error co-variance matrix. The EnOl can assimilate sea surface temperature （SST）, satellite along-track and gridded sea level anomalies （SLA）, and vertical profiles of temperature （T） and salinity （S） from Argo. The first observing system experiment was carried out over the Atlantic Ocean （78°S-50°N, 100°W-20°E） with HYCOM forced with atmospheric reanalysis from 1 January to 30 June 2010. Five integra- tions were performed, including the control run without assimilation. In the other four, different observations were assimilated： SST only （A SST）; Argo T-S profiles only （AArgo）; along-track SLA only （A_SLA）; and all data employed in the previous runs （A_All）. The A_SST, A_Argo, and A_SLA runs were very effective in improv- ing the representation of the assimilated variables, but they had relatively little impact on the variables that were not assimilated. In particular, only the assimilation of S was able to reduce the deviation of S with respect to ob- servations. Overall, the A_All run produced a good analy- sis by reducing the deviation of SST, T, and S with respect to the control run by 39%, 18%, and 30%, respectively, and by increasing the correlation of SLA by 81%.

Estimation and Correction of Model Bias in the NASA/GMAO GEOS5 Data Assimilation System:Sequential Implementation

This study presents a simplified multivariate bias correction scheme that is sequentially implemented in the GEOS5 data assimilation system and compared against a control experiment without model bias correction. The results show considerable improvement in terms of the mean biases of rawinsonde observation-minus-background （OmB） residuals for observed water vapor, wind and temperature variables. The time series spectral analysis shows whitening of bias-corrected OmB residuals, and mean biases for rawinsonde observation-minus-analysis （OmA） are also improved. Some wind and temperature biases in the control experiment near the equatorial tropopause nearly vanish from the bias-corrected experiment. Despite the analysis improvement, the bias correction scheme has only a moderate impact on forecast skill. Significant interaction is also found among quality-control, satellite observation bias correction, and background bias correction, and the latter positively impacts satellite bias correction.

Evaluation of an ocean data assimilation system for Chinese marginal seas with a focus on the South China Sea

Data assimilation is a powerful tool to improve ocean forecasting by reducing uncertainties in forecast initial conditions.Recently,an ocean data assimilation system based on the ensemble optimal interpolation(EnOI) scheme and HYbrid Coordinate Ocean Model(HYCOM) for marginal seas around China was developed.This system can assimilate both satellite observations of sea surface temperature(SST) and along-track sea level anomaly(SLA) data.The purpose of this study was to evaluate the performance of the system.Two experiments were performed,which spanned a 3-year period from January 1,2004 to December 30,2006,with and without data assimilation.The data assimilation results were promising,with a positive impact on the modeled fields.The SST and SLA were clearly improved in terms of bias and root mean square error over the whole domain.In addition,the assimilations provided improvements in some regions to the surface field where mesoscale processes are not well simulated by the model.Comparisons with surface drifter trajectories showed that assimilated SST and SLA also better represent surface currents,with drifter trajectories fitting better to the contours of SLA field than that without assimilation.The forecasting capacity of this assimilation system was also evaluated through a case study of a birth-and-death process of an anticyclone eddy in the Northern South China Sea(NSCS),in which the anticyclone eddy was successfully hindcasted by the assimilation system.This study suggests the data assimilation system gives reasonable descriptions of the near-surface ocean state and can be applied to forecast mesoscale ocean processes in the marginal seas around China.

IMPROVEMENT OF OCEAN DATA ASSIMILATION SYSTEM AND CLIMATE PREDICTION BY ASSIMILATING ARGO DATA

The Argo(Array for Real-time Geostrophic Oceanography) data from 1998 to 2003 were used in the Beijing Climate Center-Global Ocean Data Assimilation System(BCC-GODAS). The results show that the utilization of Argo global ocean data in BCC-GODAS brings about remarkable improvements in assimilation effects. The assimilated sea surface temperature(SST) of BCC-GODAS can well represent the climatological states of observational data. Comparison experiments based on a global coupled atmosphere-ocean general circulation model(AOCGM) were conducted for exploring the roles of ocean data assimilation system with or without Argo data in improving the climate predictability of rainfall in boreal summer. Firstly, the global ocean data assimilation system BCC-GODAS was used to obtain ocean assimilation data under the conditions with or without Argo data. Then, the global coupled atmosphere-ocean general circulation model(AOCGM) was utilized to do hindcast experiments with the two sets of the assimilation data as initial oceanic fields. The simulated results demonstrate that the seasonal predictability of rainfall in boreal summer, particularly in China, increases greatly when initial oceanic conditions with Argo data are utilized. The distribution of summer rainfall in China hindcast by the AOGCM under the condition when Argo data are used is more in accordance with observation than that when no Agro data are used. The area of positive correlation between hindcast and observation enlarges and the hindcast skill of rainfall over China in summer improves significantly when Argo data are used.

The climatology and interannual variability of the East Asian summer monsoonsimulated by a weakly coupled data assimilation system

With the motivation to improve the simulation of the East Asian summer monsoon(EASM) in coupled climate models, oceanic data assimilation(DA) was used in CAS-ESM-C(Chinese Academy of Sciences–Earth System Model–Climate Component) in this study. Observed sea surface temperature was assimilated into CAS-ESM-C. The climatology and interannual variability of the EASM simulated in CAS-ESM-C with DA were compared with a traditional AMIP-type run.Results showed that the climatological spatial pattern and annual cycle of precipitation in the western North Paci?c, and the ENSO-related and EASM-related EASM circulation and precipitation, were largely improved. As shown in this study, air–sea coupling is important for EASM simulation. In addition, oceanic DA synchronizes the coupled model with the real world without breaking the air–sea coupling process. These two successful factors make the assimilation experiment a more reasonable experimental design than traditional AMIP-type simulations.

A weakly coupled data assimilation system of a coupled physical–biological model for the northeastern South China Sea

A weakly coupled data assimilation system was established for a coupled physical–biological model for the northeastern South China Sea（NSCS）. The physical model used was the Regional Ocean Modeling System; the biological component was a seven-compartment nitrogen–phytoplankton–zooplankton–detritus ecosystem model; and the data assimilation method was Ensemble Optical Interpolation. To test the performance of the weakly coupled data assimilation system, two numerical experiments（i.e. control and assimilation runs） based on a process-oriented idealized case were conducted, and climatological SST was assimilated in the assimilation run. Only physical variables were adjusted in the weakly coupled data assimilation. The results showed that both the assimilated SST and other unassimilated physical variables had reasonable process responses. Due to the warmer SST observation, the water temperature（salinity） in the assimilation run increased（decreased） in coastal upwelling regions. Both the alongshore and bottom cross-shore currents were reduced, jointly demonstrating the weakening of the upwelling system. Meanwhile, ecosystem variables were also affected to some extent by the SST assimilation through the coupled model. For example, larger phytoplankton（chlorophyll） productivity was found in the upwelling region within the shallow layer due to the warmer waters in the assimilation run. Hence, the application of this data assimilation system could reasonably modify both physical and biological variables for the NSCS by SST assimilation.

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.

A Local Ensemble Transform Kalman Filter Data Assimilation System for the Global FSU Atmospheric Model

Data assimilation is the process by which measurements and model predictions are combined to obtain an accurate representation of the state of the modeled system. We implemented a data assimilation scheme called LETKF （local ensemble transform Kalman filter） with FSUGSM （Florida State University Global Spectral Model） and made an experiment to evaluate the initial condition generated to numerical weather prediction to FSUGSM model. The LETKF analysis carries out independently at each grid point with the use of ＂local＂ observations. An ensemble of estimates in state space represents uncertainty. The FSUGSM is a multilevel （27 vertical levels） spectral primitive equation model, where the variables are expanded horizontally in a truncated series of spherical harmonic functions （at resolution T63） and a transform technique is applied to calculate the physical processes in real space The assimilation cycle runs on the period 01/01/2001 to 31/01/2001 at （00, 06, 12 and 18 GMT） for each day. We examined the atmospheric fields during the period and the OMF （observation-minus-forecast） and the OMA （observation-minus-analysis） statistics to verify the analysis quality comparing with forecasts and observations. The analyses present stability and show suitable to initiate the weather predictions.

Construction and Application of a Regional Kilometer-Scale Carbon Source and Sink Assimilation Inversion System(CCMVS-R)

CO_(2)is one of the most important greenhouse gases(GHGs)in the earth’s atmosphere.Since the industrial era,anthropogenic activities have emitted excessive quantities of GHGs into the atmosphere,resulting in climate warming since the 1950s and leading to an increased frequency of extreme weather and climate events.In 2020,China committed to striving for carbon neutrality by 2060.This commitment and China’s consequent actions will result in significant changes in global and regional anthropogenic carbon emissions and therefore require timely,comprehensive,and objective monitoring and verification support(MVS)systems.The MVS approach relies on the top-down assimilation and inversion of atmospheric CO_(2)concentrations,as recommended by the Intergovernmental Panel on Climate Change(IPCC)Inventory Guidelines in 2019.However,the regional high-resolution assimilation and inversion method is still in its initial stage of development.Here,we have constructed an inverse system for carbon sources and sinks at the kilometer level by coupling proper orthogonal decomposition(POD)with four-dimensional variational(4DVar)data assimilation based on the weather research and forecasting-greenhouse gas(WRF-GHG)model.Our China Carbon Monito ring and Verification Support at the Regional level(CCMVS-R)system can continuously assimilate information on atmospheric CO_(2)and other related information and realize the inversion of regional and local anthropogenic carbon emissions and natural terrestrial ecosystem carbon exchange.Atmospheric CO_(2)data were collected from six ground-based monito ring sites in Shanxi Province,China to verify the inversion effect of regio nal anthropogenic carbon emissions by setting ideal and real experiments using a two-layer nesting method(at 27 and 9 km).The uncertainty of the simulated atmospheric CO_(2)decreased significantly,with a root-mean-square error of CO_(2)concentration values between the ideal value and the simulated after assimilation was close to 0.The total anthropogenic carbon emissions in Shanxi Province in 2019 from the assimilated inversions were approximately 28.6%(17%-38%)higher than the mean of five emission inventories using the bottomup method,showing that the top-down CCMVS-R system can obtain more comprehensive information on anthropogenic carbon emissions.