Singular points of the polarization tensor

The problem to compute the magnetic field above the chromosphere using data of the vector = B _t/Bt that gives the projected field direction can be solved with different approximations. The field of direction vectors is, however, not the only field accessible to observations. The Stokes parameters, which are components of the radiation tensor, can be measured at each point of the image plane. The directions of the eigenvectors of the radiation tensor define two mutually orthogonal systems of integral curves in the image plane. These families of curves have singular points, which are generally of different type than those of the vector field. When the morphology of H chromospheric fibrils are used to infer the topology of the magnetic field, a similar problem is met, suggesting that singular points should also be present there.     

东亚地区春冬季与夏季大气环流异常相互关系的研究

利用1951~2000年共50年的北半球500 hPa月平均高度距平场资料和奇异值分解技术（SVD），重点对东亚地区季节间大气环流异常的相互关系进行了初步探讨。结果表明，东亚地区季节间大气环流异常存在着较为密切的关联，并且这种明显的非同步联系具有时空相关显著的特点，尤其是夏季大气环流异常与其前冬和前春大气环流异常的联系更为密切。当前冬和前春北半球东亚大槽和北美大槽及蒙古高压偏强（或偏弱），极涡偏弱（或偏强），中高纬度盛行经向环流（或纬向环流），以及低纬和热带地区高度正距平（或负距平）明显时，则对应于夏季东亚地区西太平洋副高和鄂霍次克海阻高强度偏强（或偏弱），位置偏南（或偏北），贝加尔湖阻高强度也偏强（或偏弱），但位置偏西（或偏东）的大尺度环流形势出现。当春季北半球大气环流具有上述特点以及夏季鄂霍次克海阻高和西太平洋副高强度偏强（或偏弱），位置偏南（或偏北），且极涡较弱（较强）时，则东亚地区秋季大气环流对应于蒙古高压加强（或较弱），西太平洋副高减弱（或加强），并向南和向东移动（或移动较慢），极涡向南扩散（或扩散减弱），大气环流向冬季过渡加快（或减慢）。另外，大气环流异常还具有一定的持续性特征。     

奇异值分解和奇异交叉谱分析方法在华北夏季降水诊断中的应用

利用1965~2000年华北5省市及相邻省73个地面观测站逐月平均降水场及北半球500 hPa高度场、北太平洋海温场资料, 采用奇异值分解 (SVD)、奇异交叉谱 (SCSA) 分析方法, 将华北夏季降水场分别与1月北半球500 hPa高度场、冬季北太平洋海温场进行了诊断分析, 得出奇异向量分布型及相互作用的耦合周期信号。在对前4对奇异向量的分析中发现, 华北夏季降水全区域为正距平时与1月北半球500 hPa高度场PNA遥相关型关系非常密切。ENSO对华北夏季降水的影响确实存在, 但华北夏季降水全区域为正距平时与冬季北太平洋ENSO关系并不明显。同时还找出了华北降水与北半球500 hPa高度、北太平洋海温场相互作用的关键区。在华北各型降水与高度场、海温场关键区相互作用的耦合周期中, 前者以准2~7年振荡为主; 后者则周期较长, 最短周期仍为准2年振荡, 最长周期为准10~11年振荡。以上结论为进一步研究华北夏季降水短期气候预测方法, 提供了参考依据。     

GRAPES全球奇异向量方法改进及试验分析

基于总能量模的奇异向量扰动常用于构造集合预报的初始条件。以建立GRAPES（Global and Regional Assimilation PrEdiction System）全球集合预报系统为目的,基于前期研发的GRAPES全球模式奇异向量方法,在GRAPES全球切线性模式和伴随模式2.0版的框架下,开展了引入线性化边界层方案来改善奇异向量结构,并提高奇异向量计算效率的研究。通过连续试验,从奇异向量的扰动能量结构、扰动能量谱及扰动空间分布等方面,综合分析改进GRAPES全球奇异向量的结构及演变特征。试验结果表明,改进后的GRAPES奇异向量方法有效抑制了之前扰动能量在近地面层不合理的快速增长,同时,奇异向量最优扰动的结构更客观地体现了中高纬度区域大气初始条件中的斜压不稳定扰动及其演变,如在初始时刻奇异向量扰动能量主要位于对流层中层,并呈现出随高度向西倾斜的大气斜压特征;经过线性化演变,扰动能量向较大水平尺度转移,并在垂直结构上表现出向对流层高层上传及向对流层低层下传的特征等。针对GRAPES奇异向量迭代求解中伴随模式计算耗时为主的情况,改进伴随模式中广义共轭余差方案的调用方式,并采用大内存存储法来提高其计算效率,进而将奇异向量总计算时间缩短了25%。总之,改进后的GRAPES奇异向量方法,可应用于构建面向业务应用的GRAPES全球集合预报系统。      

Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications

It is well known that high-leverage observations significantly affect the estimation of parameters. In geodetic literature, mainly redundancy numbers are used for the detection of single high-leverage observations or of single redundant observations. In this paper a further objective method for the detection of groups of important and less important (and thus redundant) observations is developed. In addition, the parameters which are predominantly affected by these groups of observations are identified. This method thus complements other diagnostics tools, such as, e.g., multiple row diagnostics methods as described in statistical literature (see, e.g., Belsley et al. in Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York, 1980). The method proposed in this paper is based on geometric aspects of adjustment theory and uses the singular value decomposition of the design matrix of an adjustment problem together with cluster analysis methods for regression diagnostics. It can be applied to any geodetic adjustment problem and can be used for the detection of (groups of) observations that significantly affect the estimated parameters or that are of negligible impact. One of the advantages of the proposed method is the improvement of the reliability of observation plans and thus the reduction of the impact of individual observations (and outliers) on the estimated parameters. This is of particular importance for the very long baseline interferometry technique which serves as an application example of the regression diagnostics tool.     

统一方差分量估计公式

本文提出了一种适用于协方差阵奇异或非奇异、设计阵列满秩或降秩时的方差分量估计方法;其公式推导简单,形式统一,不需解线性方程组,同时可保证迭代计算方差分量的非负要求。作为特例还和Helmert法及MINQUE法作了比较。最后讨论了用真误差进行方差分量估计的计算公式,并给出了一个测距误差分析的实例。     

基于奇异谱分析的南方涛动指数短期气候预测试验

The Southern Oscillation Index (SOI) time series is analyzed by means of the singular spectrum analysis (SSA) method with 60-month window length. Two major oscillatory pairs are found in the series whose pe riods are quasi-four and quasi-two years respectively. The auto-regressive model, which is developed on the basis of the Maximum Entropy Spectrum Analy sis, is fitted to each of the 9 leading components including the oscillatory pairs. The prediction of SOI with the 36-month lead is obtained from the reconstruction of these extrapolated series. Correlation coefficient between predicted series and 5 months running mean of observed series is up to 0.8. The model can successfully predict the peak and duration of the strong ENSO event from 1997 to 1998. It＇s also shown that the proper choice of reconstructed components is the key to improve the model prediction.     

SVD方法在气象场诊断分析中的普适性

本文首次从理论上推导证明两个气象场的奇异值分解（ＳＶＤ）在气象场时空分布耦合信号的诊断分析中具有普适性。结果表明，两个场的ＳＶＤ求解准则不同于典型相关分析（ＣＣＡ），且ＣＣＡ模型可视为ＳＶＤ之特例，尤其当各个场经ＰＣＡ滤波后，其ＣＣＡ完全与ＳＶＤ等价。ＳＶＤ分析的结果不但可完全代替ＣＣＡ，且计算更简便，所得耦合信号的物理解释更清晰，特别适合于大尺度气象场的遥相关型研究。     

集成奇异谱分析和自回归滑动平均预测日本近海海平面变化

本文从日本沿岸选取了28个验潮站及联测的GPS站,利用奇异谱分析（Singular Spectrum Analysis,SSA）和SSA+自回归滑动平均（Auto Regression Moving Average,ARMA）方法预测了2014—2018年的近海海平面变化和地壳垂直变化.并用同时段的验潮及GPS的实际测量值进行验证,结果显示,SSA+ARMA预测的相对海平面精度为0.0357~0.0607 m,地壳垂直运动的精度为0.0049~0.0077 m,绝对海平面的精度为0.0433~0.0683 m,且三者SSA+ARMA的预测结果均优于只用SSA预测的结果.在此基础上本文利用SSA+ARMA预测了日本沿岸2019—2023年的近海绝对海平面变化,结果显示,2019—2023年的平均海面高较往年（2014—2018）升高0.0353 m,2003—2023年绝对海平面的变化率为0.0039 m·a^-1,预测结果较为理想.     

Improvement of Nakamura technique by singular spectrum analysis

In this work we investigate the application of the Singular Spectrum Analysis to improve Nakamura Technique. The SSA has a wide and multidisciplinary range of applications; it allows a time series to be decomposed into different components, e.g. the signal itself, as well as various noise components, which can be subsequently removed from the data. Removal of the minor component of the data can lead to significant improvements in the identification of the system. In this paper the use of SSA Technique allows to optimize the signal to noise ratio before computing the classical Nakamura spectral ratios. A number of typical applications are also presented.