一种基于历史样本投影的三维变分同化方法

对于中尺度数值天气预报来说,初始条件的准确与否已成为影响预报技巧的主要因素之一。现有的大气观测资料在时空分布上的不均匀,以及存在的观测误差,使得我们必须引进资料同化方法,为中尺度数值模式提供最优的初始场。由于传统的三维变分同化(3DVar)方法缺乏模式约束以及背景误差协方差矩阵(B矩阵)不具有流依赖性,因此本文提出一种基于历史样本投影的3DVar(HSP-3DVar)方法,它不仅具有流依赖的B矩阵,而且比传统的3DVar简单易行。为了评价HSP-3DVar的同化性能,我们基于区域暴雨预报模式AREM(Advanced Regional Eta Model)对其进行了观测系统模拟试验(OSSE),结果表明:HSP-3DVar能够有效融合观测信息,模式初值在各层的均方根误差都显著地降低。     

TOPEX/Poseidon高度计资料在全球海洋环流模式中的同化及分析

利用一个新的四维变分海洋资料同化系统LICOM-3DVM对TOPEX／Poseidon高度计资料进行了同化。该同化系统是在LASG／IAP气候海洋模式LICOM1．0的基础上建立起来的,所用的同化方法为三维变分映射资料同化方法3DVM。高度计观测资料是采取间接的方式进行同化,即先建立起二维海面高度距平场与三维温度场的统计关系,并由此通过观测的海面高度距平信息反演出“观测”的三维温度场,然后利用LICOM-3DVM四维变分同化系统将此反演的温度场同化到海洋模式中。作者设计了两组试验并对结果进行了比较分析,积分时间从1993年1月至2001年12月共9年时间。结果表明,由于上混合层相关系数较小,因此同化后海温没有改进;而在温跃层以及更深层次,同化后的海温均有很大程度的改善。从对赤道太平洋地区海温的气候态、季节变化和年际变化以及Nino3区的Nino指数的模拟情况来看,由于同化时将海面高度异常和海温异常之间的相关参数取为常数,没有考虑其季节和年际变化,因此,同化后对于赤道太平洋的年际变化没有改善。对于黑潮地区,由于模式的分辨率较低,同化之前没有很好地模拟出温度锋面,温度和盐度梯度都偏小,流速也偏弱;而同化后使得温度锋面和盐度梯度与WOA01更加吻合,流速增强。     

两种样本生成方法对DRP-4DVar同化方法性能影响的比较及分析

降维投影四维变分同化方法(DRP-4DVar)利用历史预报的集合来统计背景误差协方差,并将分析变量投影到样本空间下求解代价函数,因而集合样本的质量对DRP-4DVar同化方法的性能有着重要影响.文中尝试使用三维变分(3DVar)控制变量的扰动方法来产生集合样本,并与原来的历史预报扰动方法做比较.历史预报扰动样本具有随流...     

基于历史样本投影的四维变分陆面数据同化方法及其初步应用

法面临着计算量上的挑战。本研究将一种历史样本投影的四维变分同化方法(Historical-Sample-Projection4DVar,简写为HSP-4DVar)应用于陆面数据同化,建立起CoLM陆面模型的HSP-4DVar系统。相比其他四维变分同化方法,HSP-4DVar的分析值是显式求解,不需要编写和使用伴随模式,从而大大节省了计算量,是一种易于实现的同化方案。通过同化56个月的土壤湿度观测数据表明,新的陆面同化系统不仅省时,而且能够有效吸取观测信息,使得同化后的均方根误差显著降低,各层土壤湿度模拟都有所改善,陆表1000mm层的改善最为明显。     

GRAPES的新初始化方案

四维变分同化由于引入预报模式作为一项约束,理论上它的分析场已经具有较好的平衡性,但实施时还会有诸多因重力波导致的高频振荡过程,因此,四维变分同化(4DVar)分析仍需要初始化。文中描述了GRAPES全球四维变分同化系统(GRAPES-4DVar)的新初始化方案的科学设计、公式演绎以及试验结果。GRAPES-4DVar的新初始化方案采用数字滤波方案作为代价函数的一项约束控制重力波引发的不平衡结构,约束强加在分析增量上与极小化迭代过程同步进行。新的初始化方案是变分同化系统的一部分,数字滤波的积分时间与4DVar的同化时间窗一致,不会对4DVar产生额外的计算资源消耗;并能适应长时间窗的同化,不会因为时间窗的延长而削弱慢波过程。新初始化方案中,模式轨迹的光滑程度可在变分同化中通过重力波控制项的权重系数方便控制。GRAPES全球四维变分同化的理想和循环同化批量试验都表明,在四维变分同化中,重力波的控制依然非常重要,具有初始化的GRAPES试验,无论分析还是预报技巧都较无初始化的有明显优势。与以前分析和滤波独立实施的旧初始化方案相比,新方案的分析和预报效果略优,同时有效地节省循环同化系统的运行时间,这对四维变分同化来说非常重要。     

基于扰动模式的四维变分资料同化系统框架的设计完善和数值试验

为了建立一个应用于区域数值预报的四维变分资料同化（4DVar）系统,在近期开发的扰动预报模式GRAPES_PF基础上,开发完善增量四维变分同化系统框架。该框架中暂不包含物理过程（长短波辐射、边界层过程、对流参数化和云微物理等）。对比业务使用的GRAPES 3DVar系统,增加了温度控制变量。将无量纲Exner气压与流函数的线性风压平衡方程直接在地形追随垂直坐标面上求解,且通过广义共轭余差法（GCR）求解扰动亥姆霍兹（Helmholtz）伴随方程。利用人造“探空”资料对2015年10月台风“彩虹”进行了理想数值试验。试验结果表明,所开发的扰动四维变分同化框架得到了预期的结果,即同化更多资料并反复受到模式约束的四维变分同化系统能有效改善初值质量,进而改善区域数值预报。建立的区域四维变分同化框架合理可行,为进一步发展包含完整物理过程的区域四维变分同化系统奠定了研究基础。      

CMA-GFS全球预报系统中的台风初始化

在CMA-GFS(CMA Global Forecast System)全球四维变分资料同化系统(4DVar)基础上,参照BDA(Bogus Data Assimilation)方法,建立了一个全球模式台风初始化方案.该方案通过4DVar同化窗口吸收诊断处理后的1 h间隔台风中心定位及中心气压信息,利用模式动力物理约束...     

数值模式误差对降水四维变分资料同化及预报的影响

利用一个无量纲的水汽发展方程,针对同化时间窗口内出现和不出现降水两种情况,分析了不同模式误差和初始误差对降水四维变分资料同化预报效果的影响。结果表明,应用四维变分资料同化方法进行降水预报前,应该充分考虑数值模式中的误差,才能得到比较满意的同化及预报结果。假定同化窗口内获得的比湿观测场是准确的,当不存在模式误差时,四维变分资料同化方法可以有效地消除初始场误差,找到比湿真实初始场;而存在模式误差时,四维变分资料同化后的模式初始场会偏离真实的比湿初始场,并且模式误差越大,偏离程度越严重。在一些模式误差情况下,由于模式误差在同化窗口及延伸预报时段的作用不同,进行四维变分资料同化处理后,尽管累积降水量的预报结果在同化时间窗口内优于同化前的预报,而在最终预报时刻反而差于同化前。     

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。     

GRAPES全球三维变分同化中卫星微波温度计亮温的背景误差及在质量控制中的应用

模式变量背景误差在观测空间的投影,也即观测变量的背景误差包含了变分同化系统的重要信息,其在诊断和分析变分同化系统中资料的影响等方面具有重要作用,特别是在背景场检查质量控制中。在GRAPES全球三维变分同化(3DVar)系统中仅给定了控制变量的背景误差,并未直接给定观测变量的背景误差。为了能够对GRAPES全球3DVar进行全面的诊断和分析,改进卫星微波温度计资料的质量控制,推导出GRAPES全球3DVar同化系统控制变量随机扰动方法估计观测变量的背景误差的公式,为分析和改进GRAPES全球3DVar提供了一个有力工具,并进而估计了AMSU-A亮温的背景误差,分析了AMSU-A不同通道亮温的背景误差特征,将其应用于GRAPES全球3DVar的AMSU-A亮温的背景场检查质量控制中。结果表明,控制变量随机扰动方法估计的GRAPES全球3DVar同化系统AMSU-A亮温的背景误差正确合理。同化循环预报试验结果表明,亮温的背景误差在背景场检查中的应用显著提高了GRAPES全球3DVar同化的亮温资料的数量,显著提高了GRAPES南半球对流层中高层位势高度场的预报技巧。在GRAPES全球3DVar同化系统中推导和实现的控制变量扰动方法为诊断和分析GRAPES全球3DVar观测资料同化效果提供了有力工具。      

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 'three-dimensional 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.     

Numerical experiments for Typhoon Dan incorporating AMSU-A retrieved data with 3DVM

Two sets of assimilation experiments on a landfalling typhoon—Typhoon Dan(1999)over the western North Pacific were designed to compare the performances of two kinds of variational data assimilation schemes that are the 3-Dimensional Variational data assimilation of Mapped observation(3DVM)and the 4-dimensional variational data assimilation(4DVar).Results show that:(1)both the 3DVM and 4DVar successfully improved the simulations of typhoon intensity and track incorporating the satellite AMSU-A retrieved temperature and wind data into the initial conditions,and the 3DVM more significantly due to the flow-dependent of background error covariance matrix and observation error covariance matrix like 3-dimensional variational data assimilation(3DVar)circle;(2)inclusions of extra model integration iterations at each observation time in the 3DVM make it more consistent with prediction model;(3)the 3DVM is much more time-saving due to the exclusion of the adjoint technique in it.     

Initialization and simulation of a landfalling typhoon using a variational bogus mapped data assimilation (BMDA)

Summary Recently, a new data assimilation method called “3-dimensional variational data assimilation of mapped observation (3DVM)” has been developed by the authors. We have shown that the new method is very efficient and inexpensive compared with its counterpart 4-dimensional variational data assimilation (4DVar). The new method has been implemented into the Penn State/NCAR mesoscale model MM5V1 (MM5_3DVM). In this study, we apply the new method to the bogus data assimilation (BDA) available in the original MM5 with the 4DVar. By the new approach, a specified sea-level pressure (SLP) field (bogus data) is incorporated into MM5 through the 3DVM (for convenient, we call it variational bogus mapped data assimilation – BMDA) instead of the original 4DVar data assimilation. To demonstrate the effectiveness of the new 3DVM method, initialization and simulation of a landfalling typhoon – typhoon Dan (1999) over the western North Pacific with the new method are compared with that with its counterpart 4DVar in MM5. Results show that the initial structure and the simulated intensity and track are improved more significantly using 3DVM than 4DVar. Sensitivity experiments also show that the simulated typhoon track and intensity are more sensitive to the size of the assimilation window in the 4DVar than that in the 3DVM. Meanwhile, 3DVM takes much less computing cost than its counterpart 4DVar for a given time window.     

CMA-MESO三维变分同化系统2 m相对湿度资料同化研究

为了提高CMA-MESO （China Meteorological Administration Mesoscale model）（原GRAPES）三维变分同化系统中2 m相对湿度资料的应用效果,改善模式中相对湿度的分析和降水预报效果,分析了2015年6—8月T639（T639L60全球中期数值预报系统,0.28125°×0.28125°）分析场低层相对湿度和2 m相对湿度之差与表征稳定度的理查森数（Ri）的关系,发现二者有很好的相关,Ri＜0时,模式低层相对湿度与2 m相对湿度的差异较小,基本在同化观测误差范围内。依据该统计结果,对CMA-MESO同化系统中2 m相对湿度同化方案进行优化,Ri＜0时,将观测站地形低于模式地形的2 m相对湿度观测由观测站高度改为模式最低层高度进行同化,形成新的2 m相对湿度同化方案,旨在解决2 m相对湿度资料同化时模式地形高度与观测站高度不同的影响。2018年7月CMA-MESO三维变分同化系统（3DVar）个例和连续试验结果显示:新的2 m相对湿度同化方案同化分析资料数量明显增加,且08时多于20时（北京时）,新增观测点新息向量（背景减观测）与周围原有观测新息向量保持基本一致,分析残差偏差和均方根误差减小,降水预报效果明显改善。新2 m相对湿度同化方案通过提高观测站低于模式地形高度的观测资料合理应用,从而改善了3 km模式系统同化分析和预报效果。      

System of Multigrid Nonlinear Least-squares Four-dimensional Variational Data Assimilation for Numerical Weather Prediction (SNAP): System Formulation and Preliminary Evaluation

A new forecasting system—the System of Multigrid Nonlinear Least-squares Four-dimensional Variational (NLS-4DVar) Data Assimilation for Numerical Weather Prediction (SNAP)—was established by building upon the multigrid NLS-4DVar data assimilation scheme, the operational Gridpoint Statistical Interpolation (GSI)?based data-processing and observation operators, and the widely used Weather Research and Forecasting numerical model. Drawing upon lessons learned from the superiority of the operational GSI analysis system, for its various observation operators and the ability to assimilate multiple-source observations, SNAP adopts GSI-based data-processing and observation operator modules to compute the observation innovations. The multigrid NLS-4DVar assimilation framework is used for the analysis, which can adequately correct errors from large to small scales and accelerate iteration solutions. The analysis variables are model state variables, rather than the control variables adopted in the conventional 4DVar system. Currently, we have achieved the assimilation of conventional observations, and we will continue to improve the assimilation of radar and satellite observations in the future. SNAP was evaluated by case evaluation experiments and one-week cycling assimilation experiments. In the case evaluation experiments, two six-hour time windows were established for assimilation experiments and precipitation forecasts were verified against hourly precipitation observations from more than 2400 national observation sites. This showed that SNAP can absorb observations and improve the initial field, thereby improving the precipitation forecast. In the one-week cycling assimilation experiments, six-hourly assimilation cycles were run in one week. SNAP produced slightly lower forecast RMSEs than the GSI 4DEnVar (Four-dimensional Ensemble Variational) as a whole and the threat scores of precipitation forecasts initialized from the analysis of SNAP were higher than those obtained from the analysis of GSI 4DEnVar.     

An Economical Approach to Four-dimensional Variational Data Assimilation

Four-dimensional variational data assimilation (4DVar) is one of the most promising methods to provide optimal analysis for numerical weather prediction (NWP). Five national NWP centers in the world have successfully applied 4DVar methods in their global NWPs, thanks to the increment method and adjoint technique. However, the application of 4DVar is still limited by the computer resources available at many NWP centers and research institutes. It is essential, therefore, to further reduce the computational cost of 4DVar. Here, an economical approach to implement 4DVar is proposed, using the technique of dimension-reduced projection (DRP), which is called ``DRP-4DVar." The proposed approach is based on dimension reduction using an ensemble of historical samples to define a subspace. It directly obtains an optimal solution in the reduced space by fitting observations with historical time series generated by the model to form consistent forecast states, and therefore does not require implementation of the adjoint of tangent linear approximation. To evaluate the performance of the DRP-4DVar on assimilating different types of mesoscale observations, some observing system simulation experiments are conducted using MM5 and a comparison is made between adjoint-based 4DVar and DRP-4DVar using a 6-hour assimilation window.     

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.     

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.