GRAPeS三维变分同化系统的理想试验

文中介绍了一种新的、适合格点模式的三维变分同化方案GRAPeS 3DVAR。该方案采用相互独立的流函数、非平衡速度势函数、非平衡位势和水汽作为分析变量。通过变量变换对目标函数进行预调节 ,不仅避免了直接计算背景误差协方差逆矩阵的困难 ,而且改善了Hessian矩阵的性状 ,提高了收敛速度。采用EOF分解方法 ,将三维分析变量投影到垂直摸态上 ,分解成为二维场 ;水平方向采用数字 (递归 )滤波器代替矩阵运算 ,实现和简化了方案的求解。此外 ,还考虑了质量场和风场之间的平衡约束关系。理想试验结果表明 ,GRAPeS 3DVAR能够正确地反映多变量之间相互作用关系 ,收敛迅速 ,分析结果合理     

多普勒雷达风场信息变分同化的试验研究

文中试验研究了一个在三维变分框架中直接同化多普勒天气雷达信息,获取雷达覆盖范围内大气风场的技术方案。径向风速是多普勒天气雷达数据中可直接被三维变分同化系统用来反演大气风场的唯一信息。由于风矢量有二或三个分量,径向风速作为风矢量的一个分量,不能为反演风矢量提供足够的信息。如果三维变分同化系统仅仅同化径向风速,所存在的不确定性将可能会给所反演的风场带来错误。文中提出的方案,不仅同化雷达径向风速,还同化雷达回波的移动信息,其关键是将雷达回波强度时空变化转换成一个新的雷达观测变量———雷达“视风速”。由于“视风速”是包含风场信息的变量,这在三维变分同化系统中增加了风场探测信息。通过联合利用“视风速”和径向风速,由单一径向风速确定风矢量所带来的不确定性可以被克服。使用中国气象科学研究院数值预报研究中心开发的三维变分同化系统(GRAPES-3Dvar)和广东省新一代天气雷达的监测资料进行了实例试验,结果表明本技术方案能够对获取大气系统结构是有用和有效的,也可用于形成模式初始场,这对中尺度天气预报是有作用的。     

GRAPES非静力数值预报模式的三维变分资料同化系统的发展

为了减少分析变量与模式状态变量之间的插值误差,改善业务预报模式的初值质量,在GRAPES等压面三维变分资料同化系统的基础上,研究发展了针对GRAPES区域模式的非静力模式变量三维变分资料同化系统(GRAPES m3DVAR).该资料同化系统的垂直坐标及其分析变量的水平分布格式、垂直跳点方案与GRAPES预报模式保持完全一致.由于垂直坐标的变化和非静力关系,m3DVAR分析系统中设计了求解动力学约束方程的新方案.通过有效的高精度数学方案,避免了地形追随坐标下平衡方程的非线性项造成的复杂计算,有效解决了非静力平衡条件下求解平衡方程中非线性项的切线性方程和伴随方程引起的困难.重新构造各种观测算子,并考虑了质量场和风场之间的平衡约束关系、背景误差协方差结构,实现对探空、地面资料、船舶报等常规观测的同化.理想单点试验和实际资料的多变量资料同化分析结果表明,非静力模式变量三维变分资料同化系统能够正确地描写多变量之间的相互作用以及物理约束关系,分析结果合理,能够有效减少原等压面三维变分资料同化系统的分析与模式变量之间需要相互插值、变换产生的误差,在一定程度上提高了分析场质量,对预报模式的初值具有一定改善.     

GRAPES全球三维变分同化系统--基本设计方案与理想试验

中国气象局数值预报研究中心开发了一个全球和区域统一框架的格点三维变分资料同化系统(GRAPES3D-Var).作者给出全球版本的方案设计,采用单点观测试验检验方案设计的合理性和正确性.全球方案选择流函数、速度势、非平衡高度和相对湿度作为分析求解的控制变量,用线性平衡方程作为质量场和风场的动力约束,通过预调方法解决背景误差协方差矩阵阶数过大和难以求逆的问题,其中垂直变换和物理变换以及观测算子设计等方面与区域方案相同,但预调的水平变换采用球谐函数谱滤波表示背景误差协方差的水平相关模型,避免了递归滤波在高纬和极区因相关尺度过大无法实施的问题.另外,设计了一个使极区插值和差分计算完全闭合的网格以及相应的算法,解决了极点分析问题.单点观测理想试验结果表明,GRAPES 3D-Var系统能够合理给出全球任何地区的分析.     

应用雷达回波强度资料反演大气云微物理量

文中利用三维变分原理 ,由多普勒天气雷达回波强度反演模式大气的雨水混合比 qr,分析变量 qr 的确定取决于对目标函数的极小化计算 ,目标函数由分析变量 qr 与 qr 的背景场之差 ,以及由分析变量演算的大气回波强度与雷达观测的回波强度之差构成。采用所谓的NMC方法求取模式变量的背景场误差协方差矩阵 ,采用二阶自回归型相关函数确定空间水平变换中的递归滤波系数以适用于反映积云结构的小尺度空间。通过理想数值试验 ,验证了变分同化系统和结果的合理性 ,由敏感性试验说明了雷达观测的回波强度随机误差对于反演的qr 值有一定的影响。对 2 0 0 2年 6月 19日安徽省马鞍山市一次多普勒雷达实际观测数据的个例试验表明 ,经过变分同化反演后的积云尺度模式大气的 qr 场与观测的雷达回波图像的细节相吻合。     

GRAPES集合卡尔曼滤波资料同化系统Ⅰ:系统设计及初步试验

集合卡尔曼滤波资料同化方法,可以用集合样本统计出随天气形势变化的误差协方差,是当前资料同化领域的研究热点。主要介绍了GRAPES集合卡尔曼滤波资料同化系统的设计以及初步的试验结果。针对集合卡尔曼滤波同化实际观测资料难以实施的问题,采用成批观测同化的顺序同化方法进行多变量的集合卡尔曼滤波同化;为了滤除有限集合数造成的误差相关噪音和缓解求逆矩阵不满秩的问题,在水平和垂直方向都采用了Schur滤波;建立了与GRAPES预报模式的垂直坐标和预报变量一致的模式面集合卡尔曼滤波系统;集合样本的生成考虑了模式变量的空间相关和模式变量之间的相关,通过利用三维变分分析中的控制变量变换得到模式变量扰动场。通过比较GRAPES集合卡尔曼滤波资料同化系统和GRAPES区域三维变分资料同化系统的单点观测资料同化分析结果,对比背景误差相关系数的分布,验证了GRAPES集合卡尔曼滤波系统的正确性。此外,同化区域探空观测资料试验结果表明,GRAPES集合卡尔曼滤波资料同化系统能够得到合理的分析,并且具有实际运行能力。对分析结果进行12h预报表明,GRAPES集合卡尔曼滤波资料同化系统的分析协调性不如三维变分资料同化系统。     

GRAPES-3DVar高阶递归滤波方案及其初步试验

背景误差协方差矩阵B及其逆的求解是三维变分同化研究的核心问题之一.在GRAPES区域三维变分同化系统(GRAPES-3Dvar)中背景误差协方差矩阵的水平变换部分,假定各向同性并进行递归滤波运算.原有方案中采用一阶递归滤波器,但收敛不够迅速,每次循环同化时需滤波10次才能使目标函数收敛.根据Purser等2003年的研...     

三维变分同化雷达视风速的改进方案及其数值试验

用雨滴末速度改进了万齐林等2005年提出的一种直接同化多普勒雷达径向风和回波强度时空变化所包含的风场信息——视风速的变分同化方法。通过理论推导和尺度分析发现,中尺度系统中雨滴末速度具有较大的量级,故该项在雷达回波守恒方程中起着重要作用。在原方案的基础上考虑雨滴末速度的影响,可以避免云团的局地增长作用对视风速的干扰,视风速能更准确地表示雷达回波的平流信息。台风风神的雷达观测资料分析表明,改进方案计算的视风速分布紧密、有规则,能较好地表现台风云系内的中尺度辐合辐散结构。运用中国气象科学研究院研发的三维变分同化系统(GRAPES-3D-Var)进行了一组模拟观测试验表明,改进方案的水平风场增量和位势高度增量都与模拟观测减自由积分的差值场相似,呈偶极型环流,径向风的垂直变化也得到明显改进。改进的视风速与径向风共同反演出的大气水平风场更准确。原方案的模拟观测试验则不能表现出以上特征。使用改进方案同化广州雷达观测资料后,敏感性试验的初始场中台风的中心位置与实况观测更接近,初始风场的气旋性环流更明显。敏感性试验模拟的6h降水分布与实况观测更相似,降水中心强度较小,但优于控制试验。     

包含“开关”变量的MM5四维变分资料同化系统

数值模式中的湿物理过程对于模拟各种尺度的天气现象非常重要,但它会使得模式方程的状态变量不连续,这种不连续在模式程序中表现为“开关”变量。本文对包括Kuo降水参数化方案的非静力中尺度数值模式MM5的四维变分资料同化系统进行研究,利用对实际降水的模拟,比较详细地讨论了有关的“开关”变量以及切向线性化和伴随问题。结果表明：对于一个离散的数值模式,保持“开关”变量与基态一致,用伴随码方法构造的伴随模式计算的梯度值能够为最小化过程提供较好的下降方向;Kuo方案中对流每隔一个积分步的交替发生并不影响目标函数最小化的收敛速度;“开关”变量的存在也不影响将风、温度、气压和比湿结合起来同化对MM5降水预报准确性的提高。     

基于星载SAR数据和模式资料的海面风场变分融合方法研究

为实现合成孔径雷达数据与数值预报模式资料融合,提高海面风场精度和业务化运用水平,提出了一种基于星载SAR数据与模式资料的变分融合方法。其研究思路是采用二维连续小波变换提取SAR图像中高精度风条纹风向,结合地球物理模型函数求解海面风场的经向分量和纬向分量,然后采用Kriging插值方法将数值预报模式风速插值到SAR海面风场覆盖区域,得到SAR风速观测算子,由此构建SAR风场与模式风场融合的代价函数,并采用变分方法求解分析风场,最终得到融合后的海面风场结果。仿真分析结果表明,变分融合后的海面风速和风向结果更接近于理想值,尤其在SAR海面风场覆盖区域更为明显。选取ENVISAT/ASAR资料和与其时空匹配的欧洲中期天气预报中心模式风场资料开展实例验证,结果表明融合后的海面风场结果比模式风场更加接近于浮标观测结果。     

Implementation of CMA-GFS 3D-Var System on the Yin-Yang Grid

The global three-dimensional variational (3D-Var) data assimilation is implemented on a new quasi-uniform overset (Yin-Yang) grid on sphere. As a quasi-uniform spherical grid, it covers the sphere by overlapping two perpendicularly oriented grid components which is nothing but low latitude region of the usual latitude-longitude grid. Based on this characteristic of the Yin-Yang grid, it enables us to implement the regional 3D-Var system efficiently and accurately on the Yin or Yang component grid, respectively. The global analysis could update directly from the regional analysis since they have the same configurations like the precondition of eigenvalue decomposition for vertical direction, recursive filtering for horizontal direction, minimization method and observation operator and so on. However, the balance equation and vector wind are needed to be paid more attention on the Yin grid analysis due to its coordinate transformation. How to spread the observation information near the boundary of Yin and Yang grid is a key to the 3D- Var analysis. Extending double the horizontal correlation length distance in the overset boundary of Yin and Yang grid has successfully solved the problem. The results show that the analysis on the Yin-Yang grid is reasonable and similar to the result on the latitude-longitude (LAT-LON) grid. This paper provides a promising strategy for the development of a 3D-Var global system for overset grids.     

三维变分和物理初始化方法相结合同化多普勒雷达资料的试验研究

以美国新近研发的天气研究预报模式(WRF)配置的三维变分(3D-Var)同化系统WRF 3D-Var为平台,结合物理初始化方法(Physical Initialization,简称PI)来同化多普勒雷达径向风和回波强度观测资料.其基本做法是首先用物理初始化方法由雷达回波资料估计出比湿、云水混合比和垂直速度,然后用估计的比湿和云水混合比对模式的相应变量进行调整,最后再将估计出的垂直速度作为一种新的观测类型添加到现有的WRF 3D-Var目标函数中,同时以WRF 3D-Var提供的方法直接同化径向风.针对2002年6月19日的一次强对流性降水过程和2003年7月5日的一次梅雨锋暴雨过程进行了一组同化多普勒雷达径向风和回波资料的试验研究.同化结果表明:分析变量的增量场和观测的雷达回波有很好的对应关系.在雷达回波区,有正的比湿增量、云水含量增量和垂直速度增量,并且水平风增量在此辐合;在没有雷达回波的地方有负的垂直速度增量.预报结果表明,调整云水含量对降水预报改善不明显,调整比湿对降水预报改进明显,直接用物理初始化估计出的垂直速度替代模式的初始垂直速度,对降水预报改进不明显,但以新的方案同化雷达资料能有效地缩短模式的起转时间(spin-up time),明显改进短时降水预报.     

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.     

The Regularized WSM6 Microphysical Scheme and Its Validation in WRF 4D-Var

A cold cloud assimilation scheme was developed that fully considers the water substances, i.e., water vapor, cloud water, rain, ice, snow, and graupel, based on the single-moment WSM6 microphysical scheme and four-dimensional variational(4D-Var) data assimilation in the Weather Research and Forecasting data assimilation(WRFDA) system. The verification of the regularized WSM6 and its tangent linearity model(TLM) and adjoint mode model(ADM) was proven successful. Two groups of single observation a...     

Evaluation of the impact of observations on blended sea surface winds in a two-dimensional variational scheme using degrees of freedom

This paper presents an evaluation of the observational impacts on blended sea surface winds from a two-dimensional variational data assimilation (2D-Var) scheme. We begin by briefly introducing the analysis sensitivity with respect to observations in variational data assimilation systems and its relationship with the degrees of freedom for signal (DFS), and then the DFS concept is applied to the 2D-Var sea surface wind blending scheme. Two methods, a priori and a posteriori, are used to estimate the DFS of the zonal (u) and meridional (v) components of winds in the 2D-Var blending scheme. The a posteriori method can obtain almost the same results as the a priori method. Because only by-products of the blending scheme are used for the a posteriori method, the computation time is reduced significantly. The magnitude of the DFS is critically related to the observational and background error statistics. Changing the observational and background error variances can affect the DFS value. Because the observation error variances are assumed to be uniform, the observational influence at each observational location is related to the background error variance, and the observations located at the place where there are larger background error variances have larger influences. The average observational influence of u and v with respect to the analysis is about 40%, implying that the background influence with respect to the analysis is about 60%.     

中尺度WRF数值模式系统本地化业务试验

利用中尺度WRF数值模式及WRF三维变分同化系统,在对比试验的基础上,选取了适合本地的积云过程、微物理过程和辐射过程的方案组合;选择了NCEP/GFS作为模式的背景场;统计计算了以云南为中心的区域背景误差协方差并替换了三维变分同化系统中原有的背景误差协方差;同时,考虑模式底层高度与地面观测站高度的差异,进行了地面资料地形订正.通过上述试验研究,建立了本地化的中尺度WRF数值预报业务系统,该系统能较好地刻画本地下垫面的动力和热力状况,预报能力有明显改善.     

同化多普勒雷达风资料的两种方法比较

以美国新近研发的天气研究预报模式(WRF)配置的三维变分同化系统WRF 3D-Var为平台,比较了两种不同的同化多普勒雷达径向风资料的方法。一种是WRF 3D-Var系统现有的径向风资料直接同化方法;另一种是首先用两步变分法由多普勒资料反演出水平风,再同化反演风场。针对2003年7月4~5日的一次淮河暴雨过程进行的同化试验结果表明,同化了雷达风资料后得到的水平风场包含了更多的中尺度特征;从降水预报评分和预报的雷达回波来看,两种方法都能够明显改进降水预报,这种正作用能维持6 h左右;相对而言,同化反演的水平风场的效果略优于直接同化雷达径向风的效果。     

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.     

Variational data assimilation in the tropics using precipitation data part I: Column model

Summary This paper describes initial effort in the development of a four-dimensional variational data assimilation (4D-Var) in the tropics using precipitation data derived from remote sensing. The method of 4D-Var using precipitation data is formulated, and modifications to the parameterization schemes of moist processes to remove zeroth-order discontinuities are described. Variational data assimilation experiments are carried out using a column model to investigate the problems caused by discontinuities in parameterization schemes and assess the impact of assimilating precipitation data in the tropics.It is found that variational data assimilation with discontinuous parameterization schemes exhibits large fluctuations during the minimization process, slow convergence rates, and large analysis errors. The fluctuations become much more serious when precipitation data is assimilated. Precipitation data is very useful to estimate divergence in the tropics, provided that the temporal resolution of the data is sufficiently high. However, its impact on the analysis of temperature and moisture is not clear in the column model assimilation experiments, possibly due to the absence of horizontal advection.     

Use of incremental analysis updates in 4D-Var data assimilation

The four-dimensional variational(4D-Var) data assimilation systems used in most operational and research centers use initial condition increments as control variables and adjust initial increments to find optimal analysis solutions. This approach may sometimes create discontinuities in analysis fields and produce undesirable spin ups and spin downs. This study explores using incremental analysis updates(IAU) in 4D-Var to reduce the analysis discontinuities. IAU-based 4D-Var has almost the same mathematical formula as conventional 4D-Var if the initial condition increments are replaced with time-integrated increments as control variables.The IAU technique was implemented in the NASA/GSFC 4D-Var prototype and compared against a control run without IAU. The results showed that the initial precipitation spikes were removed and that other discontinuities were also reduced,especially for the analysis of surface temperature.