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.

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.

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.

Impact of FY-3D MWRI Radiance Assimilation in GRAPES 4DVar on Forecasts of Typhoon Shanshan

In this study, Fengyun-3 D(FY-3 D) Micro Wave Radiation Imager(MWRI) radiance data were directly assimilated into the Global/Regional Assimilation and Pr Ediction System(GRAPES) four-dimensional variational(4 DVar) system. Quality control procedures were developed for MWRI applications by using algorithms from similar microwave instruments. Compared with the FY-3 C MWRI, the bias of FY-3 D MWRI observations did not show a clear node-dependent difference from the numerical weather prediction background simulation. A conventional bias correction approach can therefore be used to remove systematic biases before the assimilation of data. After assimilating the MWRI radiance data into GRAPES, the geopotential height and humidity analysis fields were improved relative to the control experiment. There was a positive impact on the location of the subtropical high, which led to improvements in forecasts of the track of Typhoon Shanshan.

在模式参数有误差下使用四维变分同化的LAF法

为了有效利用各种观测资料改善观测误差来提高集合预报的效果,提出了一种新的预报方法,即拟在模式参数有误差的情况下,利用四维变分同化方法获取的初始场进行滞后时间集合预报(LAF)。通过比较在不同的观测误差方差、不同观测个数以及不同观测间隔的条件下,新方法与传统的滞后时间集合预报方法和单考虑最优初始场的四维同化确定性预报的预报效果的差异。实验结果表明:使用四维变分同化分析场的滞后时间集合预报在短期内的预报效果较好,但随着预报时长的增加,预报效果与单滞后时间集合预报的预报效果相接近。

基于VDRAS的快速更新雷达四维变分分析系统

基于雷达资料快速更新四维变分同化（RR4DVar）技术和三维数值云模式,初步研发了一个针对对流尺度数值模拟的快速更新雷达四维变分分析系统。系统通过对京津冀6部多普勒天气雷达资料进行RR4DVar同化,并融合5 min自动气象站观测和中尺度数值模式结果,可快速分析得到12-18 min更新的低层大气三维动力、热力场的对流尺度结构特征。针对2009年7月22日发生在京津冀的一次强风暴个例,通过一系列敏感性试验,并利用局地加密资料进行检验对比,表明有效的雷达资料RR4DVar同化及自动气象站和中尺度模式资料融合方案、恰当的中尺度背景场设置和动力约束方法是获得合理结果的关键。研究也表明：恰当的系统配置能够模拟出与对流生消发展密切相关的近风暴环境特征,包括低层入流、垂直风切变、低层辐合上升和暖舌等,以及风暴自身形成的冷池、出流等与风暴演变密切相关的对流尺度结构。

浅水潮波模式变分同化共轭码技术研究

以浅水潮波模式为例,详细讨论了共轭码技术的使用方法以及代码检验,并建立了海洋浅水模式的共轭模式。利用浅水潮波模式及其共轭模式进行了流速和水位的初始场优化试验。试验结果表明,初始场优化对于潮波系统数值模拟具有重要的作用,同时也说明利用共轭码技术可以有效地设计共轭模式,进行各种同化试验研究,显示了共轭码技术的诸多优点。

伴随方程在水汽资料四维同化中的应用 I.理论

由于水汽相变等过程为快过程，再考虑到水汽观测误差不服从正态分布，可以认为将水汽资料与其他观测误差进行正态分布的气象资料联合同化是一种不合适的方法。故应单独对水汽资料进行同化。在下边界为第三类边界条件下，推导了适合于数值天气预报的水汽方程的伴随方程；利用目标函数的极值性，得出了水汽的四维资料同化问题的伴随算法；证明了目标函数给出的极值点为最小值点，且是惟一的。

UNIFICATION AND APPLICATIONS OF MODERN OCEANIC/ATMOSPHERIC DATA ASSIMILATION ALGORITHMS

The key mathematics and applications of various modern atmospheric/oceanicdata assimilation methods including Optimal Interpolation (OI), 4-dimensional variational approach(4D-Var) and filters were systematically reviewed and classified. Based on the data assimilationphilosophy, i. e. , using model dynamics to extract the observational information, the commoncharacter of the problem, such as the probabilistic nature of the evolution of theatmospheric/oceanic system, noisy and irregularly spaced observations, and the advantages anddisadvantages of these data assimilation algorithms, were discussed. In the filtering framework, allmodern data assimilation algorithms were unified: OI/3D-Var is a stationary filter, 4D-Var is alinear (Kalman) filter and an ensemble of Kalman filters is able to construct a nonlinear filter.The nonlinear filter such as the Ensemble Kalman Filter (EN-KF), Ensemble Adjustment Kalman Filter(EAKF) and Ensemble Transformation Kalman Filter (ETKF) can, to some extent, account for thenon-Gaussian information of the prior distribution from the model. The flow-dependent covarianceestimated by an ensemble filter may be introduced to OI and 4D-Var to improve these traditionalalgorithms. In practice, the performance of algorithms may depend on the specific numerical modeland the choice of algorithm may depend on the specific problem. However, the unification ofalgorithms allows us to establish a unified test system to evaluate these algorithms, which providesmore insights into data assimilation philosophies and helps improve data assimilation techniques.

Role of the interaction between a gust front and a mesoscale air mass boundary in convection initiation:a case study

The local convection initiation(CI)mechanisms of a convective case that occurred on5 August 2017 in Cangzhou,northern China,were studied using Doppler radar and automatic weather station observational analysis,along with Variational Doppler Radar Analysis System assimilation analysis.During the convective process,a gust front appeared ahead of two existing convective systems,respectively.In the warm and moist environment ahead of the gust fronts in the south,there was a mesoscale air mass boundary.With the process of a gust front moving southward,approaching the mesoscale air mass boundary,the convergence intensified in the area between the gust front and the mesoscale air mass boundary.Finally,the strong convergent updraft exceeded the level of free convection and triggered the new convection.

A New Approach to Data Assimilation

A significant attempt to design a timesaving and efficient four-dimensional variational data assimilation （4DVar） has been made in this paper, and a new approach to data assimilation, which is noted as ＇threedimensional variational data assimilation of mapped observation （3DVM）＇ is proposed, based on the new concept of mapped observation and the new idea of backward 4DVar. Like the available 4DVar, 3DVM produces an optimal initial condition （IC） that is consistent with the prediction model due to the inclusion of model constraints and best fits the observations in the assimilation window through the model solution trajectory. Different from the 4DVar, the IC derived from 3DVM is located at the end of the assimilation window rather than at the beginning conventionally. This change greatly reduces the computing cost for the new approach, which is almost the same as that of the three-dimensional variational data assimilation （3DVar）. Especially, such a change is able to improve assimilation accuracy because it does not need the tangential linear and adjoint approximations to calculate the gradient of cost function. Therefore, in numerical test, the new approach produces better IC than 4DVar does for 72-h simulation of TY9914 （Dan）, by assimilating the three-dimensional fields of temperature and wind retrieved from the Advanced Microwave Sounding Unit-A （AMSU-A） observations. Meanwhile, it takes only 1/7 of the computing cost that the 4DVar requires for the same initialization with the same retrieved data.

Accounting for CO2 Variability over East Asia with a Regional Joint Inversion System and Its Preliminary Evaluation

A regional surface carbon dioxide （C02） flux inversion system, the Tan-Tracker-Region, was developed by incor- porating an assimilation scheme into the Community Multiscale Air Quality （CMAQ） regional chemical transport model to resolve fine-scale CO2 variability over East Asia. The proper orthogonal decomposition-based ensemble four-dimensional variational data assimilation approach （POD-4DVar） is the core algorithm for the joint assimilation framework, and simultaneous assimilations of CO2 concentrations and surface CO2 fluxes are applied to help reduce the uncertainty in initial CO2 concentrations. A persistence dynamical model was developed to describe the evolu- tion of the surface CO2 fluxes and help avoid the ＂signal-to-noise＂ problem; thus, CO2 fluxes could be estimated as a whole at the model grid scale, with better use of observation information. The performance of the regional inversion system was evaluated through a group of single-observation-based observing system simulation experiments （OSSEs）. The results of the experiments suggest that a reliable performance of Tan-Tracker-Region is dependent on certain assimilation parameter choices, for example, an optimized window length of approximately 3 h, an ensemble size of approximately 100, and a covariance localization radius of approximately 320 km. This is probably due to the strong diurnal variation and spatial heterogeneity in the fine-scale CMAQ simulation, which could affect the perform- ance of the regional inversion system. In addition, because all observations can be artificially obtained in OSSEs, the performance of Tan-Tracker-Region was further evaluated through different densities of the artificial observation net- work in different CO2 flux situations. The results indicate that more observation sites would be useful to systematic- ally improve the estimation of CO2 concentration and flux in large areas over the model domain. The work presented here forms a foundation for future research in which a thorough estimation of CO2 flux variability over East Asia could be performed with the regional inversion system.