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.

Four-Dimensional Variational Data Assimilation Experiments for a Heavy Rain Case During the 2002 IOP in China

A heavy rainfall event along the mei-yu front during 22-23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the mesoscale heavy rainfall forecast, a series of four-dimensional variational (4DVAR) data assimilation and model simulation experiments was conducted using nonhydrostatic mesoscale model MM5 and the MM5 4DVAR system. The effects of the intensive observations in the different areas on the heavy rainfall forecast were also investigated. The results showed that improvement of the forecast skill for mesoscale heavy rainfall intensity was possible from the assimilation of the IOP radiosonde observations. However, the impact of the IOP observations on the forecast of the rainfall pattern was not significant. Initial conditions obtained through the 4DVAR experiments with a 12-h assimilation window were capable of improving the 24-h forecast. The simulated results after the assimilation showed that it would be best to perform the intensive radiosonde observations in the upstream of the rainfall area and in the moisture passageway area at the same time. Initial conditions created by the 4DVAR led to the low-level moisture convergence over the rainfall area, enhanced frontogenesis and upward motion within the mei-yu front, and intensified middle- and high-level unstable stratification in front of the mei-yu front. Consequently, the heavy rainfall forecast was improved.

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.

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

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

Estimation of eddy viscosity on the South China Sea shelf with adjoint assimilation method

The eddy viscosity of the ocean is an important parameter indicating the small-scale mixing process in the oceanic interior water column. Ekman wind-driven current model and adjoint assimilation technique are used to calculate the vertical profiles of eddy viscosity by fitting model results to the observation data. The data used in the paper include observed wind data and ADCP data obtained at Wenchang Oil Rig on the SCS （the South China Sea） shelf in August 2002. Different simulations under different wind conditions are analyzed to explore how the eddy viscosity develops with varying wind field. The results show that the eddy viscosity endured gradual variations in the range of 10^-3 -10^-2 m^2 /s during the periods of wind changes. The mean eddy viscosity undergoing strong wind could rise by about 25% as compared to the value under weak wind.

Adjoint Assimilation in Marine Ecosystem Models and an Example of Application

This paper aims at a review of the work carried out to date on the adjoint assimilation of data in marine ecosys-tem models since 1995. The structure and feature of the adjoint assimilation in marine ecosystem models are also introduced. To illustrate the application of the adjoint technique and its merits, a 4-variable ecosystem model coupled with a 3-D physical model is established for the Bohai Sea and the Yellow Sea. The chlorophyll concentration data derived from the SeaWiFS o-cean colour data are assimilated in the model with the technique. Some results are briefly presented.

The Study of Single Station Inverting the Sea Surface Current by HF Ground Wave Radar Based on Adjoint Assimilation Technology

This paper introduces the assimilation technology in an ocean dynamics model and discusses the feasibility of inverting the sea surface current in the detection zone by assimilating the sea current radial velocity detected by single station HF ground wave radar in ocean dynamics model. Based on the adjoint assimilation and POM model, the paper successfully inverts the sea surface current through single station HF ground wave radar in the Zhoushan sea area. The single station HF radar inversion results are also compared with the bistatic HF radar composite results and the fixed point measured results by Annderaa current meter. The error analysis shows that acquisition of flow velocity and flow direction data from the single station HF radar based on adjoint assimilation and POM model is viable and the data obtained have a high correlation and consistency with the flow field observed by HF radar.

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

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

Diagnosis of Physical and Biological Control over Phytoplankton in the Gulf of Maine-Georges Bank Region Using an Adjoint Data Assimilation Approach

The linkage between physical and biological processes, particularly the effect of the circulation field on the distribution of phytoplankton, is studied by applying a two-dimensional model and an adjoint data assimilation approach to the Gulf of Maine-Georges Bank region. The model results, comparing well with observation data, reveal seasonal and geographic variations of phytoplankton concentration and verify that the seasonal cycles of phytoplankton are controlled by both biological sources and advection processes which are functions of space and time and counterbalance each other. Although advective flux divergences have greater magnitudes on Georges Bank than in the coastal region of the western Gulf of Maine, advection control over phytoplankton concentration is more significant in the coastal region of the western Gulf of Maine. The model results also suggest that the two separated populations in the coastal regions of the western Gulf of Maine and on Georges Bank are self-sustaining.

The Nonlinear Interaction Process in the Wave Assimilation Model and Its Experiments

This paper presents a composite interaction formula based on the discrete-interaction operator of wave-wave nonlinear interaction for deriving its adjoint source function in the wave assimilation model. Assimilation experiments were performed using the significant wave heights observed by the TOPES/POSEIDON satellite, and the gradient distribution in the physical space was also analyzed preliminarily.

Variational Assimilation of GPS Precipitable Water Vapor and Hourly Rainfall Observations for a Meso-βScale Heavy Precipitation Event During the 2002 Mei-Yu Season

Recent advances in Global Positioning System （GPS） remote sensing technology allow for a direct estimation of the precipitable water vapor （PWV） from delayed signals transmitted by GPS satellites, which can be assimilated into numerical models with four-dimensional variational （4DVAR） data assimilation. A mesoscale model and its 4DVAR system are used to access the impacts of assimilating GPS-PWV and hourly rainfall observations on the short-range prediction of a heavy rainfall event on 20 June 2002. The heavy precipitation was induced by a sequence of meso-β-scale convective systems （MCS） along the mei-yu front in China. The experiments with GPS-PWV assimilation cluster and also eliminated the erroneous rainfall successfully simulated the evolution of the observed MCS systems found in the experiment without 4DVAR assimilation. Experiments with hourly rainfall assimilation performed similarly both on the prediction of MCS initiation and the elimination of erroneous systems, however the MCS dissipated much sooner than it did in observations. It is found that the assimilation-induced moisture perturbation and mesoscale low-level jet are helpful for the MCS generation and development. It is also discovered that spurious gravity waves may post serious limitations for the current 4DVAR algorithm, which would degrade the assimilation efficiency, especially for rainfall data. Sensitivity experiments with different observations, assimilation windows and observation weightings suggest that assimilating GPS-PWV can be quite effective, even with the assimilation window as short as 1 h. On the other hand, assimilating rainfall observations requires extreme cautions on the selection of observation weightings and the control of spurious gravity waves.

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.

Study on the Transport of COD in the Sea Area Around Maidao off Qingdao Coast Using Data Assimilation

A two-layer pollutant advection-diffusion model is built to investigate the pollutant transport in the sea area around Maidao off Qingdao coast. An adjoint data assimilation technique is applied to estimate the optimal values of the model parameters. The experimental results on the initial field of pollutant indicate that the distribution of Chemical Oxygen Demand (COD) concentra- tion is sensitive to the horizontal eddy diffusivity. An appropriate value of horizontal eddy diffusivity is necessary in order to depict the influence of the initial field precisely, and it is also essential to the simulation of the advection-diffusion process of the pollutant. By inversion of the model parameters and optimization of the initial COD concentrations, the simulation results are improved sig- nificantly. The cost function is reduced to 40% of its first step value. The average misfit between the model outputs and the observa- tions in the upper layer decreases from 0.46 to 0.25 mg L-1, and that in the lower layer decreases from 0.22 to 0.14 mg L-1.

WAVE ASSIMILATION AND NUMERICAL PREDICTION

An adjoint variational method for wave data assimilation in the LAGFD WAM wave model is proposed. The adjoint equation of the wavenumber energy spectrum balance equation is derived. And fortunately, its characteristic equations are the same as those in the LAGFD WAM wave model. Simple experiments on the functional optimization and assimilation effectiveness during the prediction period indicated that the adjoint variational method is effective for wave assimilation and that the initial optimization of the wave model is important for the short range wave prediction. All of this is under the assumption that the wind field is accurate, the method is the important first step for combined wind and wave data assimilation systems.

内蒙古区域数值预报对探空和地面观测资料的敏感性试验研究

基于内蒙古睿图预报系统的低分辨率版本和WRFDA-FSO诊断工具,评估2021年7月现有探空和地面观测对内蒙古睿图预报系统预报的影响。该方法计算代价相对低廉,并允许根据观测变量、观测类型、气压层次、地理区域等观测的子集对观测影响进行划分。代价函数为以干总能量为度量的背景场和分析场的预报误差之间的差异。结果表明:观测影响的总体总和为负,观测对预报起正贡献作用。对12 h预报误差减小贡献最大的观测来自探空观测的动力变量(U、V风分量)。而单时次单位数量平均观测影响,探空观测的贡献约为地面观测的1/2。探空观测对12 h预报误差减小从近地面层至模式层顶均保持正贡献作用,并在对流层中低层和对流层高空急流层存在两个极大值区域;地面观测在850 hPa以下低层正贡献占比明显。探空观测在被同化系统同化时均总体具有有利的影响,也反映出探空观测数据稳定、质量较高的特征;地面观测对12 h预报误差减小起正贡献作用次数最多的区域在河套地区尤为显著。同时,探讨了需进一步提高地面观测资料同化率的问题。

An explicit four-dimensional variational data assimilation method

A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are ex-pressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost func-tion with respect to the control variables, is no longer needed. The new technique significantly simpli-fies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method.

Forming proper ensemble forecast initial members with four-dimensional variational data assimilation method

A method has been presented to improve ensemble forecast by utilizing these initial members generated by four-dimensional variational data assimilation (4-D VDA), to conquer limitation of those initial members generated by Monte Carlo forecast (MCF) or lagged average forecast (LAF). This method possesses significant statistical characteristic of MCF, and by virtue of LAF that contains multi-time information and its initial members are harmonic with