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.

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 Multivariate Empirical Orthogonal Function-Based Scheme for the Balanced Initial Ensemble Generation of an Ensemble Kalman Filter

The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.

NON-LINEAR DYNAMIC MODEL RETRIEVAL OF SUBTROPICAL HIGH BASED ON EMPIRICAL ORTHOGONAL FUNCTION AND GENETIC ALGORITHM

Aiming at the difficulty of accurately constructing the dynamic model of subtropical high, based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF（empirical orthogonal function） temporal-spatial separation technique, the disassembled EOF time coefficients series were regarded as dynamical model variables, and dynamic system retrieval idea as well as genetic algorithm were introduced to make dynamical model parameters optimization search, then, a reasonable non-linear dynamic model of EOF time-coefficients was established. By dynamic model integral and EOF temporal-spatial components assembly, a mid-/long-term forecast of subtropical high was carried out. The experimental results show that the forecast results of dynamic model are superior to that of general numerical model forecast results. A new modeling idea and forecast technique is presented for diagnosing and forecasting such complicated weathers as subtropical high.

Empirical orthogonal function analysis of short time series of sectional data in the tropical western Pacific

In this paper,some short time series of pnserved data pm sectopm 18°20′N in the tropical western Pacificwere reorganized to give mixed depth-time series,and processed by means of means of empirical orthogonal fonction analysis. It is indicated that the original form of element distribution could be obtained by linear combination of several main canonical distribution functions, and the intrinsic structure of element distribution on a certain section and its variation propertiescould be reveled by canonical distribution function and profiles in corresponding periods.

基于REOF的两种卫星降水产品(IMERG和MSWEP)在金沙江流域降水分区尺度精度评估

高时空分辨率降水产品的精度评估是卫星降水用于水文气象干旱等研究的前提。本研究提出在降水分区尺度下评估IMERG和MSWEP两种卫星降水产品的精度,并与不分区尺度(即流域尺度)进行比较。首先采用旋转经验正交函数(REOF)对金沙江流域(JSB)进行降水分区,通过贡献率得出8个分区较为适合。然后识别降水的空间分布特征,发现2种降水产品都可以很好地捕捉降水呈现出的从上游到下游逐渐增加的趋势。最后在日尺度、降水发生概率和极端降水探测能力3个方面对降水产品在分区尺度和不分区尺度的性能进行评估。结果表明,在日尺度上,MSWEP的精度在多数降水分区优于IMERG,被推荐5次(1、3、6、7和8区),集中在流域的中游。同时流域尺度也推荐MSWEP。在降水事件发生概率方面,MSWEP能再现不同等级降水强度的概率密度分布,但过高估计0.1~1 mm/d降水事件的发生概率;而IMERG过高估计小于0.1 mm/d降水事件的概率。在极端降水探测能力方面,流域尺度的KGE值都是正值,且IMERG优于MSWEP,但分区尺度上,KGE值在部分降水分区中存在负值,表明IMERG和MSWEP均不能很好地探测出该区的极端降水事件。本研究成果表明降水分区尺度是必需的,能够更加精细地评估降水产品。研究结果可为具有类似气候条件的卫星降水评估提供参考。

基于EOF-DBSCAN-GRU的分布式光伏集群出力预测方法研究

提出一种基于EOF-DBSCAN划分集群的改进统计升尺度的光伏集群出力预测建模方法。针对传统统计升尺度方法子集群中光伏电站出力特性不一致问题,通过皮尔逊相关系数和经验正交函数(EOF)优化特征空间,再根据密度聚类模型(DBSCAN)对区域内光伏电站划分集群,从而增强光伏电站聚类后集群出力特性的一致性。针对待预测日权重系数时间序列动态特性的提取、预测问题,提出一种基于动态时间规整(DTW)的相似日选取算法。最后利用循环神经网络(GRU)模型进行光伏电站出力预测。实验表明该集群预测方法的平均误差百分数(MAPE)约为6.33%,均方根误差(RMSE)约为13.93 kW,均方误差(MSE)为194.25 kW,通过实际光伏电站数据证明了所提方法的准确性和有效性。

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。

基于REOF分析的贵州省降水模式识别及变化趋势预测

【目的】为了解贵州省区域降水特点和变化趋势,更好地应对气候变化。【方法】应用旋转经验正交函数分解(REOF)方法,将贵州省1963-2022年降雨场划分为4个区域,并分析了各区域降水特征及其变化趋势。【结果】总体上Ⅰ区、Ⅱ区、Ⅳ区呈减少趋势,Ⅲ区呈增加趋势,变化趋势在1989-2014年之间通过P<0.05的显著性检验,其中Ⅳ区变化趋势在1986年有突变;各区均有35 a的主周期变化,其中Ⅰ区未来5 a为下降周期,Ⅱ区未来9 a为下降周期,Ⅲ区和Ⅳ区未来4 a为下降周期。【结论】贵州省降水有明显的年代际变化,Ⅰ区、Ⅱ区相较于Ⅲ区、Ⅳ区出现极端干旱和强降水事件的概率更大,各区年平均降水量均显示出较为明显的周期性变化特征,未来变化有显著的持续性。

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.

基于EOF和LSTM的广西月降水量预测模型研究

针对夏季降水天气过程具有时间相关性和非线性变化的特点,以及现有预报方法未能充分获取月降水量的本质特征而造成的建模因子处理和预报建模困难等问题,提出了一种以自然正交展开(EOF)与深度学习长短期记忆神经网络(LSTM)相结合的月降水量预测模型。以广西81个气象观测站7月降水量为预报研究对象,对81站7月降水量作EOF计算,选取累积方差贡献超过76%的前7个主分量作为预报分量,再利用LSTM模型建立月降水量的深度学习预测模型,以1960—2016年81站7月降水量为建模样本,2017—2022年为独立样本进行建模研究。结果表明,在相同的预报建模样本和相同的预报因子条件下,新建立的预测模型比线性逐步回归预报方法有更高的预报能力,显示了对非线性月降水量预测问题的适用性。由于LSTM模型隐层里引入了存储单元状态和门结构,使得网络能够保留长期的状态,更适合于处理和预测时间序列中间隔和延迟相对较长的重要问题。

基于EOF的淮河流域潜在蒸散发时空演变特征研究

[目的]揭示流域潜在蒸散发(ET_(0))时空演变规律,阐明淮河流域ET_(0)变化的主要原因,为淮河流域水资源管理、干旱评估及农业用水评估和规划等提供参考研究。[方法]基于淮河流域内及其周边29个气象站点1960—2020年逐日实测气象数据,采用Penman-Monteith公式、Mann-Kendall法研究了ET_(0)的基本变化趋势,并运用经验正交函数分解法(EOF)分解了流域各站点组成的ET_(0)矩阵,得到流域年和四季ET_(0)气象场的时空分布结构,通过分析典型分布模态对应的时间系数揭示了流域ET_(0)气象场的变化规律。[结果]流域年ET_(0)多年均值为858.4 mm,除春季外,其他三季和年ET_(0)均呈下降趋势。流域年ET_(0)整体以同增同减、流域西北和东南区域反相变化两种空间分布模态为主,其中,模态一以1980年为界,有从“全流域高ET_(0)”的空间分布形式转变为“全流域低ET_(0)”的显著变化趋势;模态二也有从“西北ET_(0)偏高东南ET_(0)偏低”向“西北ET_(0)偏低东南ET_(0)偏高”的显著变化趋势。流域四季ET_(0)整体以同增同减的空间分布为主,流域年ET_(0)空间分布模态的转变主要是由夏季ET_(0)的空间模态转变造成的。[结论]淮河流域ET_(0)时空变化存在明显的季节和区域性差异,夏季ET_(0)对年ET_(0)的变化贡献率最大,显著减少的日照时数和风速是导致流域存在“蒸发悖论”的主要原因,未来可针对性地加强夏季蒸散发的实际观测和研究。

云南区域性暴雨过程时空变化特征

针对中国气象局发布的《区域性重要过程(暴雨)监测和评价业务规定》确定了云南本地化区域性暴雨过程识别阈值,经灾害数据检验客观有效。进一步应用气候趋势分析、M-K检验、小波分析、EOF分析及REOF分析等方法研究了1961—2022年云南区域性暴雨过程的时空分布特征。结果表明:云南历次区域性暴雨过程综合强度波动较大,年平均综合强度呈减小趋势,但不显著,月平均综合强度呈波动分布,峰值出现在1月,雨季各旬平均综合强度变化较小。云南区域性暴雨过程年均4次,1977年以后呈减少趋势,但不显著,没有明显突变点,2008—2022年过程频次有6~8 a周期,但不稳定,云南区域性暴雨过程夏季最多,冬季最少,6月中旬至8月下旬过程数约占全年近7成。云南区域性暴雨过程呈南多北少分布,北部边缘虽然频次较少,但过程降水强度较大。云南区域性暴雨过程呈现全省大部一致型、东北-西南反向型及南北反向型等5个主要模态,进一步可分为5个典型区,即南区、西区、中东部区、北区及西北区,过去62 a,南区、西区和中东部区波动较大,变化趋势不明显,北区平稳少变,西北区前期以偏少为主,后期增加明显。

斯里兰卡极端降水时空演变特征及趋势预测

斯里兰卡是中国“一带一路”倡议的重要节点国家,极端降水对当地社会经济威胁较大,极易引发灾害。选取当地10个气象站2008—2020年的逐日降水资料,基于RClimDex模型计算斯里兰卡6个极端降水指标,利用经验正交函数分析、Morlet小波分析和重标极差法(R/S分析)等,分析极端降水事件的时空演变特征。结果表明:极端降水指数在时间分布上,除持续干旱指数(CDD)呈减少趋势外,其他各指数均为上升趋势;极端降水指数空间差异表现为北部沿海平原地带的极端降水强度高于南部沿海平原,拉特纳普勒市以西地区为斯里兰卡降水事件的多发区;极端降水指数周期性明显,绝大多数极端降水指数以6~7 a为第一主周期。R/S分析表明当地极端降水事件未来持续可能性较大。研究成果可为斯里兰卡极端气候预测、生态环境保护、防灾减灾工作等提供决策支持。

Modeling the global ionospheric total electron content with empirical orthogonal function analysis

In the present work we model the global ionospheric total electron content (TEC) with the analysis of empirical orthogonal functions (EOF). The obtained statistical eigen modes, which makeup the modeled TEC, consist of two factors: the eigen vectors mapping TEC patterns at latitude and longitude (or local time LT), and the corresponding coefficients displaying the TEC variations in different time scales, i.e., the solar cycle, the yearly (annual and semiannual) and the diurnal universal time variations. It is found that the EOF analysis can separate the TEC variations into chief processes and the first two modes illustrate the most of the ionospheric climate properties. The first mode contains both the semiannual component which shows the semiannual ionospheric anomaly and the annual component which shows the annual or non-seasonal ionospheric anomaly. The second mode contains mainly the annual component and shows the normal seasonal ionospheric variation at most latitudes and local time sectors. The annual component in the second mode also manifests seasonal anomaly of the ionosphere at higher mid-latitudes around noontime. It is concluded that the EOF analysis, as a statistical eigen mode method, is resultful in analyzing the ionospheric climatology hence can be used to construct the empirical model for the ionospheric climatology.

基于相对湿润指数的浙江省茶叶气象干旱特征分析

【目的】研究浙江省茶叶气象干旱的演变规律,为茶叶安全生产优化布局提供科学依据。【方法】利用浙江省68个地面气象观测站50 a(1971—2020年)的逐日气温、降水量、日照时数等数据,基于相对湿润指数、正交经验函数和小波分析法等分析浙江省茶叶气象干旱的时空分布规律。【结果】浙江省茶叶生产夏季干旱的强度和发生频率高于秋季,且均呈现西高东低的分布,中西部尤其金衢盆地的干旱强度和频率为全省最强,浙北地区次之,沿海地区最小。茶叶夏季干旱站次比呈逐年下降的趋势,秋季则呈现先升后降的趋势,2000年以后夏秋两季出现极端大范围茶叶气象干旱的年份增多。茶叶夏季和秋季干旱强度的正交经验函数第一模态表现为全省变化一致性,第二模态中沿海局部地区和内陆呈反相位变化,夏秋两季干旱强度的主模态时间序列分别存在2-6、2-4、6-10 a的振荡周期。【结论】浙江省在夏季和秋季出现茶叶气象干旱的频率在下降,但出现极端干旱的概率在增加,应重点加强茶叶主产区干旱监测预警能力建设,提升防旱抗旱能力。

青海省多年地表感热通量的时空变化特征

选取青海省35个气象站观测数据,基于CHEN-WENG感热系数方案,计算了1980—2017年青海省地表感热通量。利用小波分析、Mann-Kendall突变检验和经验正交函数法(Empirical Orthogonal Function,EOF),对感热通量的时空变化特征及其影响因子进行分析。结果表明:(1)1980年以来,青海省全年和各季节感热通量总体上均呈上升趋势,并具有28 a的主周期和约18 a的副周期,冬季的周期变化较为复杂;(2)全年和各季节感热通量与地气温差存在显著相关性,2004—2017年受地气温差增大的影响上升;(3)全年、春季和秋季感热通量与风速存在显著相关性,1980—2004年受风速减小的影响感热通量下降;(4)夏季降水与感热通量呈显著负相关;(5)从空间上看,全年以及春季感热通量呈现出显著的东西分异,秋、冬季表现出一定程度的南北分异。

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。

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。