Analysis of the regional spectral properties in northwestern South China Sea based on an empirical orthogonal function

This study presents an analysis of the spectral characteristics of remote sensing reflectance(Rrs)in northwestern South China Sea based on the in situ optical and water quality data for August 2018.Rrswas initially divided into four classes,classes A to D,using the max-classification algorithm,and the spectral properties of whole Rrs were characterized using the empirical orthogonal function(EOF)analysis.Subsequently,the dominant factors in each EOF mode were determined.The results indicated that more than 95%of the variances of Rrs are partly driven by the back-scattering characteristics of the suspended matter.The initial two EOF modes were well correlated with the total suspended matter and back-scattering coefficient.Furthermore,the first EOF modes of the four classes of Rrs(A-D Rrs-EOF1)significantly contributed to the total variances of each Rrs class.In addition,the correlation coefficients between the amplitude factors of class A-D Rrs-EOF1 and the variances of the relevant water quality and optical parameters were better than those of the unclassified ones.The spectral shape of class ARrs-EOF1 was governed by the absorption characteristic of chlorophyll a and colored dissolved organic matter(CDOM).The spectral shape of class B Rrs-EOF1 was governed by the absorption characteristic of CDOM since it exhibited a high correlation with the absorption coefficient of CDOM(ag(λ)),whereas the spectral shape of class C Rrs-EOF1 was governed by the back-scattering characteristics but not affected by the suspended matter.The spectral shape of class D Rrs-EOF1 exhibited a relatively good correlation with all the water quality parameters,which played a significant role in deciding its spectral shape.

A NEW ONE-STEP BAND-LIMITED EXTRAPOLATION PROCEDURE USING EMPIRICAL ORTHOGONAL FUNCTIONS

A one-step band-limited extrapolation procedure is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed scheme is to expand the known signal segment based on a band-limited basis function set and then to generate a set of Empirical Orthogonal Functions (EOF’s) adaptively from the sample values of the band-limited function set. Simulation results indicate that, in addi- tion to the attractive adaptive feature, this scheme also appears to guarantee a smooth result for inexact data, thus suggesting the robustness of the proposed procedure.

基于REOF的不同量级降雨侵蚀力时空变化——以重庆市为例

研究重庆市不同地理分区内各量级降雨侵蚀力的时空变化特征,为该地区进行更加精准的区域性水土流失防治工作提供理论依据。选取1981-2020年重庆市31个站点逐日降雨数据,利用旋转经验正交函数(Rotated Empirical Orthogonal Function,REOF)对降雨侵蚀力进行地理分区,并结合R/S、5年滑动平均、Mann-Kendall检验等方法,分析各分区不同量级降雨侵蚀力时空变化。结果表明:①重庆市降雨侵蚀力可分为6个地理区域(Ⅰ-Ⅵ区);②重庆市多年平均降雨侵蚀力为5784.04 MJ·mm/(hm^(2)·h·a),不同降雨侵蚀力从大到小依次为:大雨、暴雨、中雨、大暴雨;③大雨侵蚀力在Ⅰ-Ⅲ区和Ⅴ-Ⅵ区占主导优势,暴雨侵蚀力在Ⅳ区占主导优势。各分区中,中雨、大雨及暴雨侵蚀力主要集中在5-9月,大暴雨侵蚀力集中在6-8月;④各区不同量级降雨侵蚀力年际变化从小到大依次为:中雨、大雨、暴雨、大暴雨;同一量级降雨侵蚀力的整体变化趋势均不显著;Hurst指数表明,中雨侵蚀力在Ⅰ和Ⅴ区、大雨侵蚀力在Ⅱ和Ⅴ区、大暴雨侵蚀力在Ⅰ和Ⅲ区呈强持续上升趋势;⑤中雨、大雨及大暴雨侵蚀力在渝东南、渝东北占主导优势,暴雨侵蚀力在渝西以及重庆中部占主导优势,且Ⅰ区酉阳和秀山、Ⅱ区开州、Ⅲ区北碚和铜梁、Ⅳ区璧山和永川、Ⅴ区巫溪和云阳及Ⅵ区忠县是不同量级降雨侵蚀力的高峰中心。通过对重庆各分区不同量级降雨侵蚀力的分析,明确了可能引起土壤侵蚀的主要雨型、高发时期和潜在风险较高的地区,可为区域水土流失动态监测和水土保持措施的合理制定提供参考。

ROTATED COMPLEX EMPIRICAL ORTHOGONAL FUNCTION(RCEOF)ANALYSIS:THEORY AND EXAMPLES—PART I

In this paper,a new diagnostic method,the rotated complex empirical orthogonal function (RCEOF)analysis is developed.The general principle and the mathematical foundation of RCEOF are discussed.

ROTATED COMPLEX EMPIRICAL ORTHOGONAL FUNCTION(RCEOF)ANALYSIS—PART Ⅱ:THEORY AND EXAMPLES

The numerical solving and the program designing of the rotated complex empirical orthogonal function(RCEOF)are discussed.Some examples of RCEOF are also presented.

Feature analysis of stratospheric wind and temperature fields over the Antigua site by rocket data

The wind and temperature fields at 20 to 55 km above the Antigua launch site(17°N,61°W)were analyzed by using sounding rocket data published by the research organization on Stratosphere-Troposphere Processes and their Role in Climate(SPARC).The results showed distinct variations in the wind and temperature fields at different heights from the 1960s to the 1990s.The overall zonal wind speed showed a significant increasing trend with the year,and the overall change in meridional wind speed showed a falling trend from 1976 to 1990,whereas the temperature field showed a significant cooling trend from 1964 to 1990.The times the trends mutated varied at different levels.By taking the altitudes at 20,35,and 50 km as representatives,we found that the zonal wind speed trend had mutated in 1988,1986,and 1986,respectively;that the meridional wind speed trend had mutated in 1990,1986,and 1990,respectively;and that the temperature trend had mutated separately in 1977,1973,and 1967,respectively.Characteristics of the periodic wind and temperature field variations at different heights were also analyzed,and obvious differences were found in time scale variations across the different layers.The zonal and meridional wind fields were basically characterized as having a significant periodic variation of 5 years across the three layers,and each level was characterized as having a periodic variation of less than 5 years.Temperature field variation at the three levels was basically characterized as occurring in 10-year and 5-year cycles.

基于REOF分析的山东省年降水区域特征及趋势分析

[目的]探究山东省不同气候分区年降水量的时空特征,为该地区气候分析、防灾减灾提供更加区域性的参考依据。[方法]根据山东省95个国家地面气象观测站1991—2020年降水年值数据,首先对山东省年降水场进行气候分区,然后通过相关统计方法分析各分区降水的时空变化特征。[结果](1)山东省各降水模态降水偏少的年份更多,降水偏多的年份降水强度更大,年代际变化均较为明显,但各模态降水偏多偏少的年份分布及强度变化有所不同。(2)山东省年降水量大致由东南向西北递减,年降水场划分为东南沿海区(Ⅰ区)、西北平原区(Ⅱ区)和中部山地区(Ⅲ区)3个区域,各降水分区年降水均呈不显著增加趋势,趋势率各不相同,突变均不明显。(3)山东省各降水分区年降水量均具有较为明显的周期性特征,东南沿海区年降水场存在2个较为明显的能量中心,中心尺度均为2~3 a,未来变化具有强持续性;西北平原区年降水场存在3个较为明显的能量中心,中心尺度分别为5~7 a, 3 a和2~3 a,未来变化具有持续性;中部山地区年降水场存在2个较为明显的能量中心,中心尺度分别为2~3 a, 6 a,未来变化具有强持续性。[结论]山东省降水偏少的年份更多,降水偏多的年份降水强度更大,年降水场大致可分为3个分区,各分区年降水量均呈不显著增加趋势,均具有较为明显的周期性特征,且未来变化均具有持续性。

Space-time objective decomposition of vortex equations and mechanism analysis of subtropical high abnormal activities

To analyze the dynamic mechanism of unusual activities of the subtropical high, the space-time varible separation of the partial differential vortex equations is carried out with Galerkin methods based on the heat force and the whirl movement dissipation effect. Aiming at the subjective and man-made conventional method of choice in the space basis functions, we propose to combine the empirical orthogonal function （EOF） analysis with the genetic algorithm to inverse the space basis functions from the actual sequence of fields. A group of trigonometric functions are chosen as a generalized space basis function. With the least-squares error of the basis function and EOF typical fields, and with the complete orthogonality of basis functions, we can get the dual-bound function. A genetic algorithm is then introduced to carry out surface fitting and coefficient optimization of the basis function. As a result, the objective and reasonable constant differential equation of the subtropical high is obtained by inversion. Finally, based on the obtained nonlinear dynamics model, the dynamic behavior and mechanism of the subtropical high is analyzed and discussed under the influence of heat force. We find that solar radiation and zonal differences in land and sea are important factors impacting the potential field and flow field changes of the subtropical areas. These factors lead to strength changes of the subtropical high and medium-term advance/retreat activities. The former is a gradual change, while the latter shows more break characteristics. Meaningful results are obtained in the analysis.

COMPARATIVE ANALYSIS OF VARIOUS DATA OF AIR-SEA TEMPERATURE DIFFERENCE AND ITS VARIATION ACROSS SOUTH CHINA SEA IN THE PAST 35 YEARS

Using the International Comprehensive Ocean-Atmosphere Data Set(ICOADS) and ERA-Interim data, spatial distributions of air-sea temperature difference(ASTD) in the South China Sea(SCS) for the past 35 years are compared,and variations of spatial and temporal distributions of ASTD in this region are addressed using empirical orthogonal function decomposition and wavelet analysis methods. The results indicate that both ICOADS and ERA-Interim data can reflect actual distribution characteristics of ASTD in the SCS, but values of ASTD from the ERA-Interim data are smaller than those of the ICOADS data in the same region. In addition, the ASTD characteristics from the ERA-Interim data are not obvious inshore. A seesaw-type, north-south distribution of ASTD is dominant in the SCS; i.e., a positive peak in the south is associated with a negative peak in the north in November, and a negative peak in the south is accompanied by a positive peak in the north during April and May. Interannual ASTD variations in summer or autumn are decreasing. There is a seesaw-type distribution of ASTD between Beibu Bay and most of the SCS in summer, and the center of large values is in the Nansha Islands area in autumn. The ASTD in the SCS has a strong quasi-3a oscillation period in all seasons, and a quasi-11 a period in winter and spring. The ASTD is positively correlated with the Nio3.4 index in summer and autumn but negatively correlated in spring and winter.

Statistical analysis of surface hydrography and circulation variations in northern South China Sea

To study the variations in surface hydrography and circulation in northern South China Sea (NSCS), rotated empirical orthogonal function (REOF) and extended associate pattern analysis (EAPA) are used with daily sea surface salinity (SSS), sea surface temperature (SST) and sea surface height (SSH) datasets cover- ing 1 126 days from American Navy Experimental Real-Time East Asian Seas Ocean Nowcast System in this paper. Results show that in summer, the SCS Diluted Water Expansion (SDWE) is the most dominant factor con- trolling SSS variations in the NSCS. The remarkable SDWE usually begins in early July, reaches its maximum in middle August and weakens in late September. In summer flourishing period, its low saline core is just limited between 21°N and 22°N because of strong surface anomalous anticyclonic circulation in the NSCS. In early or late stage, the anomalous anticyclonic circulation becomes weak or turns into cyclonic one, thus the weak SCS diluted water can disperse. And its influence on the SSS variations has obviously decreased. The Kuroshio intrusion is the second controlling factor, and it has the almost opposite seasonal or intraseasonal oscillations and spatial charac- teristics to the SDWE. Winter Kuroshio Intrusion (WKI) begins in early November and lasts about three months. Intraseasonal Kuroshio Intrusion (IKI) takes place at any seasons. The westward Ekman transport produced by the north anomaly of East Asia Monsoon (EAM) pushes warmer and more saline seawater into the NSCS through the Bashi Strait and seems to decide the intensity of seasonal and intraseasonal Kuroshio intrusions.

Retrieval and analysis of sea surface air temperature and relative humidity

Air temperature and relative humidity have been the main parameters of meteorology study. In the past data could be obtained from in-situ observations, but the observations are local and sparse, especially over ocean. Now we can get them from satellites, yet it is hard to estimate them from sat- ellites directly so far. This paper presents a new method to retrieve monthly averaged sea air temper- ature （SAT） and relative humidity （RH） near sea surface from satellite data with artificial neural networks （ANN）. Compared with the observations in Pacific and Atlantic, the root mean square （RMS） and the correlation between the estimated SAT and the observations are about 0.91 ~C and 0.99, respectively. The RMS and the correlation of RH are about 3.73% and 0.65, respectively. Compared with the multiple regression method, the ANN methodology is more powerful in building nonlinear relations in this research. Thus the global monthly average SAT and RH are retrieved from the fixed ANN network from July 1987 to May 2004. In general the annual average SAT shows the increasing trend in recent 18 years. The abnormality of SAT is decomposed with the empirical or- thogonal function （EOF）. The leading three EOFs could explain 84% of the total variation. EOF1 （76.1%） presents the seasonal change of the SAT abnormality. EOF2 （4.6%） is mainly related with ENSO. EOF3 （3.3%） shows some new interesting phenomena appearing in the three main currents in Pacific, Atlantic and Indian Ocean.

浅水声速剖面用经验正交函数(EOF)表示的可行性研究

本文研究利用经验正交函数（ＥＯＦ）及少量参数以近似表示实测浅水声速剖面的方法，研究了 样本数，不同浅水域的样本和算法的关系，并得出结论：一定区域的浅水声速剖面，以经验正交函数 （ＥＯＦ）近似表示，仍可以达到较好的精度。这对于声场层析及被动定位问题有着很重要的意义。

EOF/PCA诊断气象变量场问题的新探讨

进一步论证了经验正交函数 /主分量分析 (EOF PCA)在气象变量场诊断中的物理内涵 ,证明基于EOF PCA的R型和Q型展开 ,可描述为气象变量场主要振荡型分解和主要空间分布型分解两种方案。前者表明 ,气象变量场的准周期振荡可分解为各主分量的周期振荡 ,它们各自等价于不同网格点 (或站点 )以其载荷为权重的迭加周期振荡 ,因此 ,气象变量场准周期振荡可视为来自不同周期源 (网格点或站点 )的准周期振荡逐层叠加的结果 ;后者表明 ,气象变量场的水平空间分布可视为各种主要空间分布型的叠加 ,而Q型展开才是对各种主要空间分布型的正交分解。由此深化了EOF PCA气象变量场诊断的物理内涵。

东、黄海海表面温度季节内变化特征的EOF分析

基于1998—2004年的TRMM/TMI卫星遥感海面温度(SST)数据,在初步分析东、黄海SST的季节分布特征的基础上,采用EOF方法分析了SST的季节内变化特征,进而对SST季节内变化的可能机制进行了探讨。EOF分析获得的前4个模态的累积方差贡献率为57.07%,其结果基本反映了东、黄海SST变化的主要物理过程。其中,EOF的第一模态的方差贡献率占30.17%,其空间模态揭示了以东海北部为中心的、整个海域SST变化趋于一致的特征,这一模态的显著变化周期为6.3周;第二模态的方差贡献率占14.36%,其空间模态呈现东南海域与西北海域SST的反相变化趋势,显著变化周期为8.7周和10.6周;第三模态的方差贡献率占7.02%,其空间SST变率最大的区域位于黄海海域,显著变化周期为6.8,8.7,10.2周等;第四模态的方差贡献率占5.52%,其空间SST变率最大的区域位于东、黄海近海,显著变化周期为6.8周。东、黄海SST季节内变化与此海区大气中的季节内振荡是紧密相关的。

台湾以东海域声速剖面序列的EOF分析

利用了4 a的Argo剖面序列,通过经验正交函数（EOF）分析,得出了台湾以东海域声速垂直结构的时空变化特征。EOF拟合声速剖面的精度与选取的模态数有关,合成剖面时包含的模态数越多,精度越高;前3-6个模态反映了海区声速结构的主要变化,累积方差贡献率可达89.4%-96.6%。第1模态描述了声速在垂直方向上的同相变化,具有年周期,峰值和谷值分别出现在夏季和冬季;第2模态描述了声速在近表层与次表层和主跃层的反相变化。第1、2模态的共同作用是声速垂直结构差异的主导因素,使近表层声速的季节性变化较大,而主跃层的变化相对较小;而第3模态及更高阶的模态对声速剖面的调制作用在物理意义上并不明显。

利用EOF相空间分析东亚梅雨旱涝长期过程的初步研究

利用非线性动力学中的相空间概念，分析了梅雨旱涝３～５年循环的长期过程。对全球热带 ８５０ ｈＰａ的纬向风场距平所作的 ＥＯＦ，第 １特征向量显示Ｔ Ｗａｌｋｅｒ环流异常在赤道球圈上的分布；第２特征向量主要显示热带一副热带之间的环流异常的经向分布。在第１时间系数和第２时间系数所定义的二维相空间中，由相轨线分析，得到梅雨涝年主要集中于第２象限，而旱年则相对多在第４象限。说明梅雨旱涝年际变异的主导模态和热带大气环流的主要特征向量有着密切的关联。它们显示了以３～５年时间尺度的大气环流演变的长期特征性过程。

一次暴雨过程的EOF分析

在用21层η坐标细网格模式对1998年7月21-22日发生在武汉地区的一次持续性特大暴雨过程数值模拟的基础上，利用较高时空分辨的模式输出结果对暴雨过程做经验正交函数分解（EOF分析）尝试。结果表明：EOF第1主分量的空间分布代表典型的暴雨环境背景场的低值系统；EOF第2主分量的空间分布与人字形切变线（西部为冷式切变，东部为暖式切变）相联系，是影响这次暴雨的重要形势场；利用相轨线分析方法发现，暴雨过程中EOF第1主分量和EOF第2主分量的时间系数在暴雨临近阶段，两者正相关，激发暴雨，在暴雨后期两者负相关，促使这次暴雨趋于减弱结束。

EOF分解与Kalman滤波相结合的副高位势场数值预报优化

用经验正交分解和Kalman滤波相结合的方法,建立了夏季500hPa位势高度场数值预报误差修正模型,以改进副高数值预报效果,提高副高预报准确率。首先用经验正交分解(EOF)方法将T106数值预报500hpa位势高度场分解为彼此正交的空间结构模态和相应的时间系数的线性组合,随后选取前15个模态的时间系数(其方差贡献98．7％)序列,分别建立了各自的Kalman(卡尔曼)滤波模型,最后用优化出的时间系数与相应的空间结构场进行EOF重构,进而得到修正后的副高位势预报场。修正后的位势场与原始的数值预报场的对比结果表明,该修正模型可对副高数值预报误差进行有效修正,优化后的预报效果较原始数值预报场有明显改进提高。

非均匀站网EOFs展开的失真性及其修正

从理论上证明，非均匀站网ＥＯＦｓ展开有不同程度的失真。在同等条件下，均匀站网与非均匀站网ＥＯＦｓ展开结果有明显差异．提出了一种附加面积权重的修正方案用以弥补非均匀站网ＥＯＦｓ展开的失真现象。实例计算表明，中国气温场（１６０站）经修正ＥＯＦｓ展开后，其气温变化主分量趋势与特征能更加客观地揭示中国地区增暖效应的局地差异。

南海夏季风爆发的EOF分析

本文利用 1983～ 1992年的NCEP资料 ,对南海夏季风爆发做经验正交函数分解 ,分析了主要模态的时空变换特征。结果表明 :太阳辐射北移 ,是南海夏季风爆发的最重要的因素。南海夏季风爆发前后 ,在典型季风区 85 0hPa上东西风有一次重大调整。南半球中高纬西风带槽脊振幅的增强和北半球副热带系统经向环流的加大是南海夏季风爆发的重要原因。西太平洋副高的迅速减弱东撤 ,导致南海夏季风的爆发。