基于雷达资料4DVar的低层热动力反演系统及其在北京奥运期间的初步应用分析

在变分多普勒雷达分析系统(VDRAS)中,通过对雷达资料的质量控制和预处理、云尺度模式的暖雨参数化方案、中尺度初猜场的插值分析方法、循环同化的冷启动和热启动中尺度背景场的计算方案等进行改进,实现了VDRAS对低层动力和热力场的分析反演及其在北京奥运期间的实时应用。改进后的VDRAS利用四维变分(4DVar)同化技术和一个包含简化暖雨参数化方案的云尺度模式,对北京和天津2部S波段天气雷达资料进行12min间隔的快速更新循环同化分析,反演与对流风暴生消发展密切相关的低层热动力三维结构,包括水平风场、垂直速度、辐合辐散、扰动温度、扰动温度梯度等,以及它们的时间增量。通过对北京奥运期间2个风暴个例的实时反演结果的分析表明,VDRAS反演的动力场能够反映低层的水平辐合、垂直抬升、风暴出流及它们的变化特征,而热力场则能够反映与风暴相伴随的冷池结构及其变化、阵风锋的相对位置及强弱。VDRAS的反演结果符合风暴发展传播与冷池、阵风锋、辐合抬升之间关系的概念模型。利用边界层风廓线雷达、地面自动站及地基微波辐射仪的观测资料,对VDRAS实时反演结果的初步统计检验表明,反演的风场和温度场与观测比较接近,风场能够反映出与风暴密切相关的低层风的垂直切变特征,温度场则能够反映出由于风暴过程所导致的地面温度的剧烈变化。与风廓线观测相比,反演的低层风速偏弱,偏差和均方根误差分别在-1.5m/s和2.5m/s以内,而风向的偏差和均方根误差分别在20°和45°以内。与地基微波辐射仪观测相比,反演的低层温度偏低,偏差和均方根误差分别在-1.9℃和2.8℃以内。

多普勒雷达资料4DVAR同化反演的模拟研究

利用Sun等建立的同化模式和四维变分同化方法对多普勒雷达资料反演大气风场、热力场和微物理场进行了模拟试验研究。反演的基本思路是 :将 4DVAR同化方法应用到三维云模式 ,定义价值函数表征雷达资料与模式预报结果之间的差别 ,通过极小化价值函数得到反演场 ,价值函数相对模式控制变量的梯度由伴随模式求取。试验结果表明 ,4DVAR同化技术能够从单 (双 )多普勒雷达资料反演大气三维风场、热力场和微物理场。各个变量反演精度高低与同化过程中变量受约束的大小程度呈正相关。速度场和雨水场反演精度较高 ,温度场、云水和水汽的反演精度次之 ,温度场的准确反演需要较长的同化时间。价值函数中加入背景场 ,哪怕是单点探空给出的平均场信息也有利于提高反演精度。在采用单部多普勒雷达资料进行反演时 ,速度场的反演误差较大。反演区相对雷达站的位置变化对速度场反演结果有一定的影响 ,而对其他变量的反演影响很小。两个时次的雷达观测资料基本足够提供反演所需的时间演变信息 ,同化更多时次的雷达资料 ,反演效果改进很小。雷达观测资料的缺值会显著降低同化效果 ,甚至可能导致同化失败 ,引入背景场可以改善这一状况。 4DVAR同化技术对于雷达观测资料误差不太敏感。利用双多普勒雷达合成风场提供水平风场边?

应用ATOVS资料和非对称Bogus资料对登陆台风韦帕的4DVAR数值模拟分析

前人研究中BDA方法采用的轴对称Bogus台风不能反映个别台风具体特征并弃掉了背景场的合理成分,也没有考虑大环境场的影响及湿热要素的同化。因此,提出一种充分融合分析场信息和实际观测信息并考虑副高影响的精细非对称台风Bogus方法,并在MM5的伴随同化系统中引入快速辐射传输模式RTTOV8,通过四维变分同化(4DVAR)技术,加入海面风场和气压场Bogus资料及多颗卫星多条轨道上的ATOVS红外和微波卫星辐射亮温资料并考虑Noah陆面过程方案来对登陆台风韦帕进行数值模拟,结果表明,单独同化海面Bogus资料的BDA方案可间接产生初始场非对称三维环流结构和暖心结构,但对湿度场及台风周围大环境场的调整不足,台风登陆后的路径预报改善也不明显;引入陆面过程方案弥补了Bogus资料对台风登陆后路径预报的不足;加入ATOVS资料能对湿度场及台风周围环境场做出调整,重构了大量中尺度结构信息,取得更为精细的初始台风环流和温压湿场结构,保持BDA方案路径及强度预报的优势的同时,使预报的降水强度增加,降水落区发生改变。

基于NLS-4DVar方法的雷达资料同化及其在暴雨预报中的应用

在基于本征正交分解POD(Proper Orthogonal Decomposition)的集合四维变分同化方法(POD4DEn Var)建立的雷达资料同化系统(PRAS)的基础上,本文利用非线性最小二乘法的集合四维变分同化方法(NLS-4DVar)对PRAS进行改进,解决PRAS在高度非线性情况下的适应性问题,建立了新的雷达资料同化系统(NRAS)。通过观测系统模拟试验OSSEs(Observing System Simulation Experiments)和两次实际暴雨同化试验(2010年7月8日,中国中部地区;2014年3月30日,中国华南地区)对NRAS进行检验,并与PRAS的同化结果进行了对比。结果表明:无论是OSSEs还是实际雷达资料的同化,相对于PRAS,NRAS能够进一步提高同化效果。通过增加迭代的次数,NRAS能够有效地调整初始场的风场和水汽场,进一步提高了降水强度和位置的预报精度。但随着迭代次数的增加,对初始场的调整变小,进而对降水预报效果的改进也减小。试验结果表明NRAS能够有效解决PRAS在高度非线性情况下的应用问题,通过有限次数的迭代,即可得到近似收敛的结果。因而NRAS有望在数值预报中更有效地同化雷达资料,提高中小尺度天气的预报水平。

An Adjoint-Free CNOP–4DVar Hybrid Method for Identifying Sensitive Areas in Targeted Observations: Method Formulation and Preliminary Evaluation

This paper proposes a hybrid method, called CNOP–4 DVar, for the identification of sensitive areas in targeted observations, which takes the advantages of both the conditional nonlinear optimal perturbation(CNOP) and four-dimensional variational assimilation(4 DVar) methods. The proposed CNOP–4 DVar method is capable of capturing the most sensitive initial perturbation(IP), which causes the greatest perturbation growth at the time of verification;it can also identify sensitive areas by evaluating their assimilation effects for eliminating the most sensitive IP. To alleviate the dependence of the CNOP–4 DVar method on the adjoint model, which is inherited from the adjoint-based approach, we utilized two adjointfree methods, NLS-CNOP and NLS-4 DVar, to solve the CNOP and 4 DVar sub-problems, respectively. A comprehensive performance evaluation for the proposed CNOP–4 DVar method and its comparison with the CNOP and CNOP–ensemble transform Kalman filter(ETKF) methods based on 10 000 observing system simulation experiments on the shallow-water equation model are also provided. The experimental results show that the proposed CNOP–4 DVar method performs better than the CNOP–ETKF method and substantially better than the CNOP method.

Impacts of Multigrid NLS-4DVar-based Doppler Radar Observation Assimilation on Numerical Simulations of Landfalling Typhoon Haikui (2012)

We applied the multigrid nonlinear least-squares four-dimensional variational assimilation(MG-NLS4DVar)method in data assimilation and prediction experiments for Typhoon Haikui(2012)using the Weather Research and Forecasting(WRF)model.Observation data included radial velocity(Vr)and reflectivity(Z)data from a single Doppler radar,quality controlled prior to assimilation.Typhoon prediction results were evaluated and compared between the NLS-4DVar and MG-NLS4DVar methods.Compared with a forecast that began with NCEP analysis data,our radar data assimilation results were clearly improved in terms of structure,intensity,track,and precipitation prediction for Typhoon Haikui(2012).The results showed that the assimilation accuracy of the NLS-4DVar method was similar to that of the MG-NLS4DVar method,but that the latter was more efficient.The assimilation of Vr alone and Z alone each improved predictions of typhoon intensity,track,and precipitation;however,the impacts of Vr data were significantly greater that those of Z data.Assimilation window-length sensitivity experiments showed that a 6-h assimilation window with 30-min assimilation intervals produced slightly better results than either a 3-h assimilation window with 15-min assimilation intervals or a 1-h assimilation window with 6-min assimilation intervals.

非线性集合四维变分同化方法NLS-4DVar之局地化改进

四维变分同化可利用同化窗口内所有可能的观测信息优化大气、海洋模式的初始场,从而极大地提高大气、海洋模式模拟性能,而作为4DVar标准算法的伴随方法始终无法避免繁琐与复杂的预报模式伴随方程的编程、维护以及更新。为避免伴随模式的使用,集合四维变分方法,4DEnVar方法被逐渐开发,为4DVar的求解提供了一种便捷的途径。4DEnVar一般通过局地化过程消除样本不足所造成的虚假相关,而局地化方案的不同也必然会影响到其最终的同化效果。本文将一种集合样本扩展的局地化方案引入到基于Gaussian-Newton迭代算法的非线性集合四维变分同化方法NLS-4DVar中,从而避免了原算法中为进行局地化过程而额外需要的线性化假设,使得算法收敛更稳定。另外,通过将原Gaussian-Newton迭代序列进行变形、避免了矩阵的直接求逆,极大地提高了同化算法的计算效率。利用非线性动力模型Lorenz-96所开展的观测系统模拟试验表明:采用新的样本扩展型局地化方案的NLS-4DVar算法,其同化精度略优于NLS-4DVar原始算法,由于避免了矩阵的直接求逆,其计算效率反而有所提高,同化所需时间有所降低,对于大气与海洋数据同化领域的应用具有极大的潜力。

Impact of 4DVAR Assimilation of Rainfall Data on the Simulation of Mesoscale Precipitation Systems in a Mei-yu Heavy Rainfall Event

The multi-scale weather systems associated with a mei-yu front and the corresponding heavy precipitation during a particular heavy rainfall event that occurred on 4 5 July 2003 in east China were successfully simulated through rainfall assimilation using the PSU/NCAR non-hydrostatic, mesoscale, numerical model （MM5） and its four-dimensional, variational, data assimilation （4DVAR） system. For this case, the improvement of the process via the 4DVAR rainfall assimilation into the simulation of mesoscale precipitation systems is investigated. With the rainfall assimilation, the convection is triggered at the right location and time, and the evolution and spatial distribution of the mesoscale convective systems （MCSs） are also more correctly simulated. Through the interactions between MCSs and the weather systems at different scales, including the low-level jet and mei-yu front, the simulation of the entire mei-yu weather system is significantly improved, both during the data assimilation window and the subsequent 12-h period. The results suggest that the rainfall assimilation first provides positive impact at the convective scale and the influences are then propagated upscale to the meso- and sub-synoptic scales. Through a set of sensitive experiments designed to evaluate the impact of different initial variables on the simulation of mei-yu heavy rainfall, it was found that the moisture field and meridional wind had the strongest effect during the convection initialization stage, however, after the convection was fully triggered, all of the variables at the initial condition seemed to have comparable importance.

4DVAR同化反演多普勒雷达资料在一次强降水中的应用

利用秦皇岛多普勒天气雷达资料,应用干模式的4DVAR系统反演发生在河北省昌黎县的一次强降水过程的二维风场,得到较为真实的中小尺度天气系统状况。强降水发生在"人"字形切变线的暖式切变线的前侧,当暖式切变线附近出现中-γ尺度闭合气旋性环流时,降水进一步增强。由于采用干模式的变分方法,每4 min就可完成一次风场的反演,其业务化前景非常乐观。

Impact of Analysis-time Tuning on the Performance of the DRP-4DVar Approach

In this study we extend the dimension-reduced projection-four dimensional variational data assimilation （DRP-4DVar） approach to allow the analysis time to be tunable, so that the intervals between analysis time and observation times can be shortened. Due to the limits of the perfect-model assumption and the tangentlinear hypothesis, the analysis-time tuning is expected to have the potential to further improve analyses and forecasts. Various sensitivity experiments using the Lorenz-96 model are conducted to test the impact of analysistime tuning on the performance of the new approach under perfect and imperfect model scenarios, respectively. Comparing three DRP-4DVar schemes having the analysis time at the start, middle, and end of the assimilation window, respectively, it is found that the scheme with the analysis time in the middle of the window outperforms the others, on the whole. Moreover, the advantage of this scheme is more pronounced when a longer assimilation window is adopted or more observations are assimilated.

A Simple Method of Calculating the Optimal Step Size in 4DVAR Technique

In four—dimensional variational data assimilation (4DVAR) technology, how to calculate the optimal step size is always a very important and indeed difficult task. It is directly related to the computational efficiency. In this research, a new method is proposed to calculate the optimal step size more effectively. Both nonlinear one—dimensional advection equation and two—dimensional inertial wave equation are used to test and compare the influence of different methods of the optimal step size calculations on the iteration steps, as well as the simulation results of 4DVAR processes. It is in evidence that the different methods have different influences. The calculating method is very important to determining whether the iteration is convergent or not and whether the convergence rate is large or small. If the calculating method of optimal step size is properly determined as demonstrated in this paper, then it can greatly enlarge the convergence rate and further greatly decrease the iteration steps. This research is meaningful since it not only makes an important improvement on 4DVAR theory, but also has useful practical application in improving the computational efficiency and saving the computational time. Key words 4DVAR - Optimal step size - Iterative convergence rate This work was supported by the National Natural Science Foundation under grants: 49735180 and 49675259, the “973 Project? CHERES(G 1998040907), the Project of Natural Science Foundation of Jiangsu Province(BK99020), and the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars.

Application of multigrid NLS-4DVar in radar radial velocity data assimilation with WRF-ARW

非线性最小二乘法的集合四维变分同化方法是一种结合了集合卡尔曼滤波和四维变分同化优势的混合同化方法。引入多重网格策略的NLS-4DVar方法不仅可以避免使用伴随模式,而且可以从大尺度到小尺度依次修正误差得到精度更高的分析场。本文将高效的多重网格策略的NLS-4DVar方法应用于雷达径向风数据同化中。通过一组基于ARW-WRF模式的观测系统模拟试验检验该方法对雷达径向风的同化能力和同化效率。试验结果显示,同化雷达径向风数据后,初始场得到明显改进且24小时累计降水预报精度有大幅度提高。与此同时,多重网格策略的NLS-4DVar方法还减少了计算代价,明显提高了计算效率。

A Local Implementation of the POD-Based Ensemble 4DVar with R-Localization

The purpose of this paper is to provide a robust and flexible implementation of a proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method(PODEn4DVar) through Rlocalization.With R-localization,the implementation of the local PODEn4DVar analysis can be coded for parallelization with enhanced assimilation precision.The feasibility and effectiveness of the PODEn4DVar local implementation with R-localization are demonstrated in a two-dimensional shallow-water equation model with simulated observations(OSSEs) in comparison with the original version of the PODEn4DVar with B-localization and that without localization.The performance of the PODEn4DVar with localization shows a significant improvement over the scheme with no localization,particularly under the imperfect model scenario.Moreover,the R-localization scheme is capable of outperforming the Blocalization case to a certain extent.Further,the assimilation experiments also demonstrate that PODEn4DVar with R-localization is most efficient due to its easy parallel implementation.

基于历史预报的四维变分资料同化(4DVar)方法中的滤波

基于历史预报的四维变分同化方法在降维的样本空间最小化代价函数,避免切线性伴随模式,是一种比较经济的算法。但是因为选取的集合样本不可能无限多,实际样本数远远小于观测资料数以及模式变量的自由度,会导致观测站点和模式格点间产生虚假的相关。介绍了在历史预报4DVar中引入的局地化滤波技术,并通过3组试验,比较了局地化前后的结果。试验结果表明:引入局地化技术后,其能有效滤去初始场中的虚假相关关系,同时由于Schur算子的作用,滤波后的分析场是光滑连续的。而且实际个例研究结果表明,局地化后能改进6h和12h累积降水的均方根误差,进一步提高预报效果。

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.

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.

Dynamical and Microphysical Retrieval from Simulated Doppler Radar Observations Using the 4DVAR Assimilation Technique

Based on a cloud model and the four-dimensional variational (4DVAR) dataassimilation method developed by Sun and Crook (1997), simulated experiments of dynamical andmicrophysical retrieval from Doppler radar data were performed. The 4DVAR data assimilationtechnique was applied to a cloud scale model with a warm rain parameterization scheme. The 3D wind,thermodynamical, and microphysieal fields were determined by minimizing a cost function, defined bythe difference between both radar observed radial velocities and reflectivities and their modelpredictions. The adjoint of the numerical model was used to provide the gradient of the costfunction with respect to the control variables. Experiments have demonstrated that the 4DVARassimilation method is able to retrieve the detailed structure of wind, thermodynamics, andmicrophysics by using either dual-Doppler or single-Doppler information. The quality of retrievaldepends strongly on the magnitude of constraint with respect to the variables. Retrieving thetemperature field, cloud water and water vapor is more difficult than the recovery of the wind fieldand rainwater. Accurate thermodynamic retrieval requires a longer assimilation period. Theinclusion of a background term, even mean fields from a single sounding, helped reduce the retrievalerrors. Less accurate velocity fields were obtained when single-Doppler data were used. It wasfound that the retrieved velocity is sensitive to the location of the retrieval domain relative tothe radars while the other fields have very little changes. Two radar volumetric scans are generallyadequate for providing the evolution, although the use of additional volumes improves theretrieval. As the amount of the observations decreases, the performance of the retrieval isdegraded. However, the missing observations can be compensated by adding a background term to thecost function. The technique is robust to random errors in radial velocity and calibration errors inreflectivity. The boundary conditions from the dual-Doppler synthesized winds are sufficient forthe retrieval. When the retrieval is mainly controlled by the observations in the regions away fromthe boundaries, the simple boundary conditions from velocity azimuth display (VAD) analysis are alsoavailable. The microphysical retrieval is sensitive to model errors.

Effects of 4DVAR with multifold observed data on the typhoon track forecast

Effects of 4-dimension variational data assimi-lation (4DVAR) with multifold observed data on the typhoontrack forecast are studied, by using the MM5V3 model, theRTTOVS-5 model and their adjoint models. The data usedfor assimilation include large-scale background fields data,bogus data, cloud-derived wind data, satellite inverse data,and high resolution infrared radiation sounder data (HIRS).There are 5 typhoon cases are used to perform the numericalexperiments and assimilation experiments. The numericalresults show that with 4DVAR the initial fields can be greatlyimproved and the initial typhoon structure can be clearlydescribed.

Mesoscale Structure of Rainstorm Retrieved from Dual-Doppler Radar Observations Using the 4DVAR Assimilation Technique

The four-dimensional variational （4DVAR） data assimilation method was applied to dual-Doppler radar data about two Meiyu rainstorms observed during CHeRES （China Heavy Rain Experiment and Study）. The purpose of this study is to examine the performance of the 4DVAR technique in retrieving rainstorm mesoscale structure and to reveal the feature of rainstorm mesoscale structure. Results demonstrated that the 4DVAR assimilation method was able to retrieve the detailed structure of wind, thermodynamics, and microphysics fields from dual-Doppler radar observations. The retrieved wind fields agreed with the dual- Doppler synthesized winds and were accurate. The distributions of the retrieved perturbation pressure, perturbation temperature, and microphysics fields were also reasonable through the examination of their physical consistency. Both of the two heavy rainfalls were caused by merging cloud processes. The wind shear and convergence lines at middle and lower levels were their primary dynamical characteristics. The convective system was often related to low-level convergence and upper-level divergence coupled with up- drafts. During its mature stage, the convective system was characterized by low pressure at lower level and high pressure at upper level, associated with warmer at middle level and colder at lower and upper levels than the environment. However, a region of cooling and high pressure occurred in the lower and middle levels compared to warming and low pressure in the upper level during its dissipating ＇.stage. The water vapor, cloud water, and rainwater corresponded to the convergence, the updraft and the intensive reflectivity, respectively.

A Soil Moisture Data Assimilation System for Pakistan Using PODEn4DVar and CLM4.5

Soil moisture is an important state variable for land–atmosphere interactions.It is a vital land surface variable for research on hydrology,agriculture,climate,and drought monitoring.In current study,a soil moisture data assimilation framework has been developed by using the Community Land Model version 4.5(CLM4.5)and the proper orthogonal decomposition(POD)-based ensemble four-dimensional variational assimilation(PODEn4 DVar)algorithm.Assimilation experiments were conducted at four agricultural sites in Pakistan by assimilating in-situ soil moisture observations.The results showed that it was a reliable system.To quantify further the feasibility of the data assimilation(DA)system,soil moisture observations from the top four soil-depths(0–5,5–10,10–20,and 20–30 cm)were assimilated.The evaluation results indicated that the DA system improved soil moisture estimation.In addition,updating the soil moisture in the upper soil layers of CLM4.5 could improve soil moisture estimation in deeper soil layers[layer 7(L7,62.0 cm)and layer 8(L8,103.8 cm)].To further evaluate the DA system,observing system simulation experiments(OSSEs)were designed for Pakistan by assimilating daily observations.These idealized experiments produced statistical results that had higher correlation coefficients,reduced root mean square errors,and lower biases for assimilation,which showed that the DA system is able to produce and improve soil moisture estimation in Pakistan.