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WO2022011728A1 - 一种面向遥相关模式的空间自相关聚类方法 - Google Patents

一种面向遥相关模式的空间自相关聚类方法 Download PDF

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WO2022011728A1
WO2022011728A1 PCT/CN2020/103083 CN2020103083W WO2022011728A1 WO 2022011728 A1 WO2022011728 A1 WO 2022011728A1 CN 2020103083 W CN2020103083 W CN 2020103083W WO 2022011728 A1 WO2022011728 A1 WO 2022011728A1
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grid
spatial
rainfall
correlation
telecorrelation
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French (fr)
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赵铜铁钢
陈浩玲
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中山大学
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    • G06F16/906—Clustering; Classification
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
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    • G06F18/23—Clustering techniques
    • G—PHYSICS
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  • the invention relates to the field of meteorology and climatology, and more particularly, to a spatial autocorrelation clustering method oriented to teleconnection patterns.
  • the coefficient itself has a standardized nature, and the commonly used LISA index such as the Moran index, according to the definition described in Chapter 4 of "Quantitative Geography", will be calculated during the calculation process.
  • the variables are standardized, so the obtained results can only reflect the relative distribution of high and low values under the same time and index, and it is difficult to compare the calculation results of different times or indicators horizontally.
  • large-scale meteorological factors often have strong inter-seasonal or inter-annual periodicity, and the teleconnection strengths and patterns in different seasons usually have great differences. Therefore, it is necessary to improve the traditional LISA indicators in order to facilitate the spatial clustering of teleconnection patterns in different seasons and different indicators.
  • a spatial autocorrelation clustering method oriented to telecorrelation patterns including the following steps:
  • step S5 Rearrange the rainfall and meteorological index time series in step S2 to obtain a new rainfall-meteorological index time series, and repeat steps S3-S4 until the preset number of iterations n is reached;
  • the representation method of the distance is the Euclidean distance.
  • the expression method of the weight is the reciprocal of the square of the distance.
  • the observed meteorological index is recorded as:
  • x t is the index value observed in the t year
  • X is the set composed of x t
  • the total number of grids is N
  • i is the grid index.
  • the observed rainfall is:
  • y t,i is the index value observed in grid i in year t
  • Y is the set composed of y t,i.
  • the correlation coefficient between meteorological factors and rainfall is obtained from the X and Y sequences:
  • rx t (ry t ) represents the meteorological factor of the t year, that is, the order of the observed rainfall in the original sequence, and then represents the mean of the sequence rx t (ry t ); the value of r is between -1 and 1, and when the two variables are completely monotonically correlated, the value of r is 1 or -1; for grid i, the calculated
  • the calculation formula of the spatial autocorrelation local index LISAAC is specifically:
  • w i, j r i is the weight for contact with the adjacent grids weight coefficients r j; is the spatially weighted correlation coefficient of adjacent grids of grid i; C i describes the strength of the relationship between ri and its adjacent grids r j ; the weight coefficient in the formula is an important parameter that affects C i.
  • the LISAAC calculation in step S4 uses the correlation coefficient itself and does not perform centralized processing.
  • the inverse distance weight method is used, the distance is calculated by the Euclidean method, and the reciprocal of the square of the distance is used as the distance weight coefficient between the two grids:
  • d(i,j) is the Euclidean distance between the i-th and jth grids; when d(i,j) increases, the influence of the adjacent grid correlation coefficient r j on C i is smaller, usually according to the data
  • the scale presets a distance threshold to reduce the amount of computation.
  • the rearrangement calculation is to directly randomly rearrange the observed rainfall-meteorological index time series of each network.
  • step S6 is specifically:
  • the corresponding null hypothesis is that there is no significant correlation between meteorological indicators and observed rainfall, that is, the teleconnection is not significant; therefore, by randomly arranging the i(j)th grid historical meteorological indicators and rainfall observation recalculated r i (r j), and the corresponding C i; through repeated calculations, the experience of constructing distributions C i H.
  • step S7 is specifically:
  • PP indicates that the r of a grid point and its surrounding grid points are significantly positive;
  • PN indicates that the r of a grid point is positive, but the r value of the surrounding grid is low or negative, and ns represents the grid point.
  • NN last case represents a negative I r r j is negative about;
  • PP and NN indicate the r values having The higher positive spatial correlation indicates the existence of regional clustering; while PN and NN reflect the heterogeneity of the spatial distribution of r.
  • the final grid classification result of the present invention is specifically PP (significant positive telecorrelation grid surrounded by grids with the same sign telecorrelation), PN (outlier value), ns (non-significant grid), NP (abnormal value). value), PP (significant negative telecorrelation grid surrounded by the same sign grid).
  • the present invention provides a spatial autocorrelation clustering method oriented to the telecorrelation mode, which improves the calculation of the local Moran index on the basis of the definition of the local Moran index by considering the degree of telecorrelation between each spatial grid unit and the adjacent unit. formula, obtain a new local index LISAAC of spatial autocorrelation, realize the detection of significant positive or negative telecorrelation clustering range, and realize the identification of outliers at the same time. The results are convenient for horizontal comparison of teleconnection degrees in different seasons.
  • Fig. 1 is the schematic flow chart of the method of the present invention
  • Figure 2 shows the spatial distribution of telecorrelation coefficients in four seasons
  • Fig. 3 is the spatial clustering diagram calculated based on the significance level
  • Fig. 4 is a spatial clustering diagram calculated based on the local Moran index
  • Fig. 5 is a spatial clustering diagram based on LISAAC calculation provided by the present invention.
  • Figure 6 is a stacked bar chart of the proportion of each type of grid in four quarters under the three methods.
  • a spatial autocorrelation clustering method for telecorrelation patterns includes the following steps:
  • step S5 Rearrange the rainfall and meteorological index time series in step S2 to obtain a new rainfall-meteorological index time series, and repeat steps S3-S4 until the preset number of iterations n is reached;
  • the representation method of the distance is the Euclidean distance.
  • the expression method of the weight is the reciprocal of the square of the distance.
  • the observed meteorological index is recorded as:
  • x t is the index value observed in the t year
  • X is the set composed of x t
  • the total number of grids is N
  • i is the grid index.
  • the observed rainfall is:
  • y t,i is the index value observed in grid i in year t
  • Y is the set composed of y t,i.
  • the correlation coefficient between meteorological factors and rainfall is obtained from the X and Y sequences:
  • rx t (ry t ) represents the meteorological factor of the t year, that is, the order of the observed rainfall in the original sequence, and then represents the mean of the sequence rx t (ry t ); the value of r is between -1 and 1, and when the two variables are completely monotonically correlated, the value of r is 1 or -1; for grid i, the calculated
  • the calculation formula of the spatial autocorrelation local index LISAAC is specifically:
  • w i, j r i is the weight for contact with the adjacent grids weight coefficients r j; is the spatially weighted correlation coefficient of adjacent grids of grid i; C i describes the strength of the relationship between ri and its adjacent grids r j ; the weight coefficient in the formula is an important parameter that affects C i.
  • the LISAAC calculation in step S4 uses the correlation coefficient itself and does not perform centralized processing.
  • the inverse distance weight method is used, the distance is calculated by the Euclidean method, and the reciprocal of the square of the distance is used as the distance weight coefficient between the two grids:
  • d(i,j) is the Euclidean distance between the i-th and jth grids; when d(i,j) increases, the influence of the adjacent grid correlation coefficient r j on C i is smaller, usually according to the data
  • the scale presets a distance threshold to reduce the amount of computation.
  • the rearrangement calculation is to directly randomly rearrange the observed rainfall-meteorological index time series of each network.
  • step S6 is specifically:
  • the corresponding null hypothesis is that there is no significant correlation between meteorological indicators and observed rainfall, that is, the teleconnection is not significant; therefore, by randomly arranging the i(j)th grid historical meteorological indicators and rainfall observation recalculated r i (r j), and the corresponding C i; through repeated calculations, the experience of constructing distributions C i H.
  • step S7 is specifically:
  • PP positive and positive
  • PN positive and negative
  • ns not significant and the representative grid surrounding meshes r i r j not significant
  • the NP negative positive
  • NN negative
  • I r r j negative about
  • PP and NN indicate the r value has a positive correlation with higher spatial, suggesting the presence of agglomeration zone
  • the PN and NN reflects the heterogeneity of the spatial distribution of r.
  • the final grid classification results of the present invention are specifically PP (significant positive telecorrelation grid surrounded by grids with the same sign telecorrelation), PN (outliers), ns (non-significant grids), NP (outliers), PP (significant negative telecorrelation grid surrounded by the same sign grid).
  • this example illustrates the effect of the method through experiments, using the US climate Prediction Center (CPC) 1982-2010 global seasonal grid precipitation data and Take the indicator as an example, calculate the spatial autocorrelation clustering between El Ni ⁇ o-Southern Oscillation (ENSO) and the global seasonal precipitation telecorrelation pattern, take the significance level ⁇ as 0.10 as an example, calculate LISAAC, and compare the grids without considering the spatial autocorrelation Significance classification results and results calculated using the local Moran index.
  • CPC US climate Prediction Center
  • Fig. 2 shows the spatial distribution of telecorrelation coefficients in winter, spring, summer and autumn in the northern hemisphere (denoted as DJF, MAM, JJA and SON, respectively).
  • the grid itself only significant correlation coefficient based on the classification, the grid may be classified as P, ns and N, i.e., n-r i, the grid is not significant and negative r i.
  • Figure 3 presents the results of classifying grids according to the significance of the correlation coefficients regardless of the spatial relationship.
  • the spatial distribution map of the classification grid shows that there are many areas where rainfall is significantly affected by ENSO.
  • This method of directly using grid saliency classification can effectively reflect the saliency of the grid itself, but it cannot reflect the above-mentioned spatial information, that is, are some scattered grids a spatial outlier? Are there significant spatial correlations for such large-scale teleconnections that appear in spatial blocks?
  • the local Moran exponent is further calculated.
  • the formula for calculating the local Moran index is as follows:
  • the null hypothesis for the local Moran index r i adjacent points randomly distributed The significance of I i is therefore tested by the reference distribution obtained by randomly permuting r j.
  • the grid can be classified according to the quantiles I ⁇ /2 and I 1- ⁇ /2 as follows:
  • the local Moran exponent is given relative to The degree of high (low) is high, and the classification results are HH (high and high), HL (high and low), ns (not significant), LH (low and high) and LL (low and low).
  • HH indicates that a grid and other surrounding grids have high r values
  • HL indicates that a grid has higher r but lower surrounding points.
  • LH and LL are the exact opposite.
  • HH and LL indicated a high positive spatial correlation, indicating that there was regional similarity, while LH and HL indicated that there was a strong negative spatial correlation, that is, regional heterogeneity.
  • Fig. 4 shows the result of classifying the grid according to the local Moran index I considering the spatial relationship.
  • the local Moran exponent is considered in the calculation due to Compared with the global average value of each season, the spatial agglomeration results of high and low values are given in the spatial classification diagram.
  • the local Moran index indicates that there is a strong heterogeneity in the teleconnection relationship in some regions. For example, some positive teleconnections appeared in the central part of South America in spring, and the surrounding teleconnections were dominated by negative teleconnections.
  • FIG. 5 the calculation result of the local spatial autocorrelation index provided by the LISAAC provided by the present invention is shown in FIG. 5 . Similar to Figure 3, several major regions of spatially teleconnected agglomeration can be seen, such as the southern United States to northern Mexico, northern South America, East Africa, South Africa, western Australia, and Southeast Asia in winter. At the same time, LISAAC also showed some "anomalous" areas, such as small PN areas along the Peruvian coast of Peru and Ecuador.
  • the positive teleconnection effect here is mainly due to the abnormal warming of the eastern Pacific Ocean in El Ni ⁇ o years, which makes the Walker circulation in the equatorial Pacific move in normal years, and the convection center moves to the central and eastern Pacific Ocean, resulting in abnormally increased rainfall on the west coast of South America.
  • this movement of the convection center caused the eastern part of South America to become an abnormal airflow sinking area.
  • due to the increase of the sea temperature in the eastern Pacific the sea temperature gradient along the coast of Colombia decreased, so the rainfall in the northern part of South America was abnormally low.
  • the LISAAC classification results can well identify the spatial relationship between this negative telecorrelation effect and a small number of positive correlation effects. In Figure 3, however, the spatial heterogeneity of this PN along the coast of Ecuador and Peru in winter is not reflected.
  • Figure 6 shows the classification grid proportions calculated by the three methods respectively.
  • Fig. 6a is the grid classification calculated by LISAAC provided by the present invention. It can be clearly seen that although studies have shown that seasonal rainfall in most regions of the world is affected by different degrees of ENSO teleconnection, most grids show insignificant teleconnection. Factors such as snowmelt, soil moisture, and topography may, on the one hand, be due to weak ENSO signals in these regions or the season itself. In addition, it can be seen that the proportion of positive teleconnection in summer is lower than that of the other three seasons. On the contrary, the proportion of negative teleconnection is relatively higher.
  • Moran index classification can effectively identify the spatial characteristics of teleconnection, it is difficult to distinguish whether there is a significant teleconnection effect.

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Abstract

一种面向遥相关模式的空间自相关聚类方法，其通过考虑每一个空间网格单元与相邻单元遥相关的相关程度，在局部Moran指数定义的基础上，采用相关系数原始数值而不作中心化处理，从而改进局部Moran指数计算公式，得到新的空间自相关局部指标LISAAC，实现显著正或负遥相关集聚范围的探测，同时实现异常值(即显著正值区域中出现不显著或负值网格，显著负值区域中出现不显著或正值网格)的识别。该方法能根据遥相关系数本身的标准化性质，实现对不同类型遥相关的空间聚类，结果便于对不同季节的遥相关程度进行横向对比。

Description

一种面向遥相关模式的空间自相关聚类方法 技术领域
本发明涉及气象与气候学领域，更具体的，涉及一种面向遥相关模式的空间自相关聚类方法。
背景技术
大尺度的气象因子与全球各地降水异常的相互关系一直受到人们的重视，利用相关的气象因子指标和各地月或季节尺度降水的相关系数，可以量化这种遥相关作用的强度和模式。然而在实际计算中，相邻区域的降水往往并非独立，而是存在较强的相关关系。为了探测这种空间上的自相关性，往往采用空间自相关局部指标(LISA)进行空间自相关分析，探测变量是否存在空间格局的有关信息。然而对于以相关系数衡量的遥相关模式而言，系数本身已经具有标准化的性质，而常用的LISA指标如Moran指数，根据《计量地理学》第四章中所描述的定义，其计算过程中将对变量进行标准化处理，因此所得结果只能反映在同一时间及指标下，相对的高值和低值分布，而难以对不同时间或指标的计算结果进行横向对比。而大尺度气象因子往往具有较强的季节间或年际周期性，不同季节下的遥相关强度和模式通常具有较大的差别。因此，有必要对传统的LISA指标进行改进，以便于对不同季节、不同指标下遥相关模式的空间聚类模式。
发明内容
本发明为解决传统的LISA指标得到的结果只能反映在同一时间及指标下，相对的高值和低值分布，而难以对不同时间或指标的计算结果进行横向对比的技术缺陷，提供一种面向遥相关模式的空间自相关聚类方法。
为实现以上发明目的，而采用的技术手段是：
一种面向遥相关模式的空间自相关聚类方法，包括以下步骤：
S1：获取研究区域空间网格坐标信息，依据坐标信息计算空间权重矩阵；
S2：获取研究区域网格尺度降雨数据及相同时间范围的大尺度气象因子指标，得到降雨-气象指标时间序列；
S3：依据所获得的降雨-气象指标时间序列，逐网格计算降雨-气象指标相关系数 r；
S4：根据相关系数r及空间权重矩阵，计算逐网格的空间自相关局部指标LISAAC；
S5：重排步骤S2中的降雨及气象指标时间序列，获得新的降雨-气象指标时间序列，重复执行步骤S3-S4，直到达到预设的迭代次数n；
S6：根据步骤S4得到的n组随机LISAAC，构建参考经验分布H；
S7：根据观测LISAAC、观测相关系数r以及经验分布H，得到在指定显著性水平下各网格的分类结果。
其中，在所述步骤S1的空间权重矩阵计算中，距离的表示方法为欧几里得距离。
其中，在所述步骤S1的空间权重矩阵计算中，权重的表示方法为距离平方的倒数。
其中，在所述步骤S2中，记观测的气象指标为：
X＝[x t]
其中，x t为第t年观测到的指标数值，X为x t组成的集合；记网格总数为N，以i为网格索引，类似地，记观测降雨为：
Y＝[y t,i]
其中，y t,i为第t年在网格i观测到的指标数值，Y为y t,i组成的集合。
其中，在所述步骤S3中，对于给定的网格i，由X和Y序列得到气象因子和降雨之间的相关系数：
Figure PCTCN2020103083-appb-000001
式中，rx t(ry t)代表第t年气象因子，即观测降雨在原始序列中的排序，而
Figure PCTCN2020103083-appb-000002
则代表序列rx t(ry t)的均值；r的值介于-1与1之间，当两个变量完全单调相关时，r的值为1或-1；对于网格i，所计算的相关系数可记为r i，由此可得到相关系数组成的集合R＝[r i]。
其中，在所述步骤S4中，所述空间自相关局部指标LISAAC的计算公式具体为：
Figure PCTCN2020103083-appb-000003
其中，w i,j是用于将r i与邻近网格r j进行联系的权重系数；
Figure PCTCN2020103083-appb-000004
为网格i邻近网格的空间加权相关系数；C i描述r i和其邻近网格r j之间的关系的强度；式中的权重系数是影响C i的重要参数。
上述方案中，所述步骤S4的LISAAC计算采用相关系数本身不作中心化处理。
其中，为了使权重系数随距离增大而衰减，采用反距离权重法，以欧几里得法计算距离，并以该距离的平方的倒数作为两网格之间的距离权重系数：
Figure PCTCN2020103083-appb-000005
式中d(i,j)为第i和j各网格之间的欧式距离；当d(i,j)增大，邻近网格相关系数r j对C i的影响越小，通常根据数据尺度预设距离阈值以减少计算量。
其中，在所述步骤S5中，所述重排计算为直接随机重排每个网络的观测降雨-气象指标时间序列。
其中，所述步骤S6具体为：
判断遥相关的空间聚类显著性，其对应原假设为气象指标与观测降雨不存在显著的相关性，即遥相关不显著；因此，通过随机排列第i(j)个网格历史气象指标和观测降雨序列，重新计算r i(r j)，及相应的C i；通过多次重复计算，构建C i的参考经验分布H。
其中，所述步骤S7具体为：
依据参考经验分布H，获得观测C i对应的p i值，以表示原假设为真时的强度,根据观测r i和相应的p i值，计算得到网格i的分类：
Figure PCTCN2020103083-appb-000006
式中PP表示某一网格点和其周围网格点的r都显著为正；PN表示某一网格的r为正，但其周围网格的r值偏低或为负，ns代表网格r i及其周围网格r j均不显著；NP代表负r i被正的r j围绕；最后一种情况NN表示的是负r i被负r j围绕；PP和NN表示r值具有较高的空间正相关性，提示存在区域集聚；而PN和NN则反映了r的空间分布存在异质性。
上述方案中，本发明最后的网格分类结果具体为PP(显著正遥相关网格被相同符号遥相关的网格围绕)、PN(异常值)、ns(不显著网格)、NP(异常值)、PP(显著负遥相关网格被相同符号网格围绕)。
与现有技术相比，本发明技术方案的有益效果是：
本发明提供的一种面向遥相关模式的空间自相关聚类方法，通过考虑每一个空间网格单元与相邻单元遥相关的相关程度，在局部Moran指数定义的基础上，改进局部Moran指数计算公式，得到新的空间自相关局部指标LISAAC，实现显著正或负遥相关集聚范围的探测，同时实现异常值的识别，能根据遥相关系数本身的标准化性质，实现对不同类型遥相关的空间聚类，结果便于对不同季节的遥相关程度进行横向对比。
附图说明
图1为本发明所述方法的流程示意图；
图2为四个季节下遥相关系数空间分布图；
图3为基于显著性水平计算得到的空间聚类图；
图4为基于局部Moran指数计算所得空间聚类图；
图5为基于本发明提供的LISAAC计算所得空间聚类图；
图6为三种方法下四个季度各类型网格占比堆叠柱状图。
具体实施方式
附图仅用于示例性说明，不能理解为对本专利的限制；
为了更好说明本实施例，附图某些部件会有省略、放大或缩小，并不代表实际产品的尺寸；
对于本领域技术人员来说，附图中某些公知结构及其说明可能省略是可以理解的。
下面结合附图和实施例对本发明的技术方案做进一步的说明。
实施例1
如图1所示，一种面向遥相关模式的空间自相关聚类方法，包括以下步骤：
S1：获取研究区域空间网格坐标信息，依据坐标信息计算空间权重矩阵；
S2：获取研究区域网格尺度降雨数据及相同时间范围的大尺度气象因子指标，得到降雨-气象指标时间序列；
S3：依据所获得的降雨-气象指标时间序列，逐网格计算降雨-气象指标相关系数r；
S4：根据相关系数r及空间权重矩阵，计算逐网格的空间自相关局部指标LISAAC；
S5：重排步骤S2中的降雨及气象指标时间序列，获得新的降雨-气象指标时间序列，重复执行步骤S3-S4，直到达到预设的迭代次数n；
S6：根据步骤S4得到的n组随机LISAAC，构建参考经验分布H；
S7：根据观测LISAAC、观测相关系数r以及经验分布H，得到在指定显著性水平下各网格的分类结果。
更具体的，在所述步骤S1的空间权重矩阵计算中，距离的表示方法为欧几里得距离。
更具体的，在所述步骤S1的空间权重矩阵计算中，权重的表示方法为距离平方的倒数。
更具体的，在所述步骤S2中，记观测的气象指标为：
X＝[x t]
其中，x t为第t年观测到的指标数值，X为x t组成的集合；记网格总数为N，以i为网格索引，类似地，记观测降雨为：
Y＝[y t,i]
其中，y t,i为第t年在网格i观测到的指标数值，Y为y t,i组成的集合。
更具体的，在所述步骤S3中，对于给定的网格i，由X和Y序列得到气象因子和降雨之间的相关系数：
Figure PCTCN2020103083-appb-000007
式中，rx t(ry t)代表第t年气象因子，即观测降雨在原始序列中的排序，而
Figure PCTCN2020103083-appb-000008
则代表序列rx t(ry t)的均值；r的值介于-1与1之间，当两个变量完全单调 相关时，r的值为1或-1；对于网格i，所计算的相关系数可记为r i，由此可得到相关系数组成的集合R＝[r i]。
更具体的，在所述步骤S4中，所述空间自相关局部指标LISAAC的计算公式具体为：
Figure PCTCN2020103083-appb-000009
其中，w i,j是用于将r i与邻近网格r j进行联系的权重系数；
Figure PCTCN2020103083-appb-000010
为网格i邻近网格的空间加权相关系数；C i描述r i和其邻近网格r j之间的关系的强度；式中的权重系数是影响C i的重要参数。
在具体实施过程中，所述步骤S4的LISAAC计算采用相关系数本身不作中心化处理。
更具体的，为了使权重系数随距离增大而衰减，采用反距离权重法，以欧几里得法计算距离，并以该距离的平方的倒数作为两网格之间的距离权重系数：
Figure PCTCN2020103083-appb-000011
式中d(i,j)为第i和j各网格之间的欧式距离；当d(i,j)增大，邻近网格相关系数r j对C i的影响越小，通常根据数据尺度预设距离阈值以减少计算量。
更具体的，在所述步骤S5中，所述重排计算为直接随机重排每个网络的观测降雨-气象指标时间序列。
更具体的，所述步骤S6具体为：
判断遥相关的空间聚类显著性，其对应原假设为气象指标与观测降雨不存在显著的相关性，即遥相关不显著；因此，通过随机排列第i(j)个网格历史气象指标和观测降雨序列，重新计算r i(r j)，及相应的C i；通过多次重复计算，构建C i的参考经验分布H。
更具体的，所述步骤S7具体为：
依据参考经验分布H，获得观测C i对应的p i值，以表示原假设为真时的强度,根据观测r i和相应的p i值，计算得到网格i的分类：
Figure PCTCN2020103083-appb-000012
式中PP(正正)表示某一网格点和其周围网格点的r都显著为正；PN(正负)表示某一网格的r为正，但其周围网格的r值偏低或为负，ns(不显著)代表网格r i及其周围网格r j均不显著；NP(负正)代表负r i被正的r j围绕；最后一种情况NN(负负)表示的是负r i被负r j围绕；PP和NN表示r值具有较高的空间正相关性，提示存在区域集聚；而PN和NN则反映了r的空间分布存在异质性。
在具体实施过程中，本发明最后的网格分类结果具体为PP(显著正遥相关网格被相同符号遥相关的网格围绕)、PN(异常值)、ns(不显著网格)、NP(异常值)、PP(显著负遥相关网格被相同符号网格围绕)。
实施例2
更具体的，在实施例1的基础上，本实施例通过实验对方法的效果进行说明，以美国气候预测中心(CPC)1982-2010全球季节网格降水数据及
Figure PCTCN2020103083-appb-000013
指标为例，计算厄尔尼诺-南方涛动(ENSO)与全球季节降水遥相关模式的空间自相关聚类，以显著性水平α为0.10为例，计算LISAAC，同时对比不考虑空间自相关的网格显著性分类结果和采用局部Moran指数计算的结果。
如图2所示，图2给出了北半球冬、春、夏和秋季(分别表示为DJF、MAM、JJA和SON)下遥相关系数空间分布图。若不考虑空间自相关关系，仅以网格本身相关系数的显著性为分类依据，网格可分类为P、ns和N，即正r i、不显著网格和负r i。图3给出了不考虑空间关系，根据相关系数显著性对网格进行分类的结果。分类网格空间分布图显示出多处降雨明显受ENSO影响的区域，例如，冬季美国南部到墨西哥北部区域，南美北部区域，南非、东非、东南亚以及澳大利亚西部都有较大面积的区域受到不同程度和形式的ENSO影响。类似的，在春、夏及秋季，分类图都能有效反映出集聚的遥相关模式。然而，相比于一些遥相关连续分布且覆盖面积较大的区域，从分类图可以看到，在一些区域(尤其是高纬度地区)，P和N网格的分布较为零散；此外，一些相邻较近的区域，同时出现 了P和N两种类型的网格。这种直接用网格显著性分类的方法，能够有效反映网格本身的显著性，但无法反映上述提到的空间信息，即：一些零散出现的网格是否是空间上的异常值？这种空间上成块出现的大面积遥相关是否具有显著的空间相关性？
为了量化遥相关的这种空间信息，进一步计算局部Moran指数。局部Moran指数的计算公式如下：
Figure PCTCN2020103083-appb-000014
不同于本发明提出的LISAAC，局部Moran指数的原假设为r i邻近点随机分布。因此I i的显著性通过随机排列r j得到的参考分布检验。类似的，给定显著性水平α，根据分位数I α/2和I 1-α/2可以对网格进行如下分类：
Figure PCTCN2020103083-appb-000015
和LISAAC相比，局部Moran指数给出的是相对于
Figure PCTCN2020103083-appb-000016
的高(低)程度，钦此分类结果为HH(高高)、HL(高低)、ns(不显著)、LH(低高)和LL(低低)。HH表示某一网格和其它周围网格的r值均较高，HL表示某一网格的r较高但周围点较低。LH和LL正好相反。HH和LL表明具有较高的空间正相关，表示存在区域的相似性，而LH和HL表示存在较强的空间负相关，即具有区域异质性。
在具体实施过程中，图4给出了考虑空间关系、根据局部Moran指数I对网格进行分类的结果。局部Moran指数由于在计算中考虑了
Figure PCTCN2020103083-appb-000017
的作用，空间分类图中给出了相比于各季节的全球平均值，偏高值和偏低值空间集聚结果。相比于直接根据网格自身显著性分类，局部Moran指数提示部分区域的遥相关关系存在较强的异质性。例如春季南美洲中部出现的部分正遥相关关系，其周围遥相关以 负的遥相关为主。这些特殊的遥相关关系，有可能是由于观测误差导致的，也有可能来自当地地形如高山、土壤湿度、冰川融雪等其它气象因子产生的影响。这些特殊的关系正是研究季节降水的重要因子，局部Moran指数有效提供了这种识别这种关系的方法。然而，由于局部Moran指数计算过程中的标准化处理，使得计算结果考虑目标季节的全局平均值
Figure PCTCN2020103083-appb-000018
这就导致四个季节的结果无法横向比较。如图4中夏季南美呈现出大面积遥相关作用，这种遥相关具有很强的空间相似性(只有少量的异常值出现在西南-东北两块集聚区域交界处)，局部Moran指数很好的描述出了这种空间集聚现象。而由图2的相关系数分布图可以看到，对比冬季，虽然具有较好的空间相似性，但事实上夏季的这种遥相关作用整体的幅度都偏小，且相关系数不显著的网格也被划分为HH和LL。而图4无法体现这种整体幅度的变化以及网格本身相关系数的显著性。
为了同时量化遥相关的空间自相关特征以及遥相关幅度，利用本发明提供的LISAAC局部空间自相关指标计算结果如图5所示。类似于图3，图中可以看到空间上呈现遥相关集聚的几个主要区域，如冬季美国南部到墨西哥北部、南美北部、东非、南非、澳大利亚西部和东南亚。同时，LISAAC也显示出一些“异常”区域，例如秘鲁和厄瓜多尔秘鲁沿岸出现的小块PN区域。此处的正遥相关作用主要源于东太平洋在厄尔尼诺年异常增温，使赤道太平洋正常年份的沃克环流发生移动，对流中心移动到中、东太平洋，使得南美洲西岸的降雨异常增多。而这种对流中心移动同时导致南美东部变为气流异常下沉区，同时由于东太平洋海温的增高，导致哥伦比亚沿岸海温梯度降低，因此南美北部降雨异常偏少。而LISAAC的分类结果可以很好的识别出这种负遥相关作用和少量的正相关作用之间的空间关系。而在图3中，冬季厄瓜多尔秘鲁沿岸的这种PN的空间异质现象并没有得到体现。
图6分别给出了采用三种方法计算的分类网格占比。其中图6a为利用本发明提供的LISAAC计算的网格分类。可以明显看到，虽然研究表明全球大部分区域季节降雨受到不同程度的ENSO遥相关作用，但大部分网格显示出不显著的遥相关作用，一方面可能是由于这种遥相关作用受到其它气象因素如融雪、土壤湿度和地形等的影响，一方面可能是由于ENSO信号在这些区域或季节本身偏弱。此外可以看到，夏季正遥相关作用所占网格比例低于其它三个季节，相反的，其负遥相关作用占比相对更高。相比而言，如果不考虑网格的空间信息，仅仅按照 遥相关的显著性对网格进行分类，可以得到类似的结果(图6b)，即不显著遥相关作用占比最高。但是，一些特殊的空间异质性现象在图6b中无法得到体现，如冬季南美洲西部沿岸的正遥相关作用，以及加拿大到美国北部出现的正相关作用。最后，图6c给出的局部Moran指数结果仅考虑了空间相关作用，而忽略遥相关本身的显著性，因此出现了和图6a-b截然不同的结果：不显著的网格占比在四个季节中都偏少。这是因为局部Moran指数考虑的是相比于全局的平均值的高低程度，且原假设不是遥相关是否显著，而是变量在空间上是否随机分布。因此，利用Moran指数进行分类虽然能够有效识别遥相关的空间特征，却难以区别显著的遥相关作用是否存在。
以上实验结果表明，本发明考虑了相关系数本身的标准化性质，同时结合变量的空间信息，实现对不同类型遥相关的空间聚类，结果便于对不同季节的遥相关程度进行横向对比。
附图中描述位置关系的用语仅用于示例性说明，不能理解为对本专利的限制；
显然，本发明的上述实施例仅仅是为清楚地说明本发明所作的举例，而并非是对本发明的实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式的变化或变动。这里无需也无法对所有的实施方式予以穷举。凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明权利要求的保护范围之内。

Claims (10)

  1. 一种面向遥相关模式的空间自相关聚类方法，其特征在于，包括以下步骤：
    S1：获取研究区域空间网格坐标信息，依据坐标信息计算空间权重矩阵；
    S2：获取研究区域网格尺度降雨数据及相同时间范围的大尺度气象因子指标，得到降雨-气象指标时间序列；
    S3：依据所获得的降雨-气象指标时间序列，逐网格计算降雨-气象指标相关系数r；
    S4：根据相关系数r及空间权重矩阵，计算逐网格的空间自相关局部指标LISAAC；
    S5：重排步骤S2中的降雨及气象指标时间序列，获得新的降雨-气象指标时间序列，重复执行步骤S3-S4，直到达到预设的迭代次数n；
    S6：根据步骤S4得到的n组随机LISAAC，构建参考经验分布H；
    S7：根据观测LISAAC、观测相关系数r以及经验分布H，得到在指定显著性水平下各网格的分类结果。
  2. 根据权利要求1所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，在所述步骤S1的空间权重矩阵计算中，距离的表示方法为欧几里得距离。
  3. 根据权利要求1所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，在所述步骤S1的空间权重矩阵计算中，权重的表示方法为距离平方的倒数。
  4. 根据权利要求1所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，在所述步骤S2中，记观测的气象指标为：
    X＝[x t]
    其中，x t为第t年观测到的指标数值，X为x t组成的集合；记网格总数为N，以i为网格索引，类似地，记观测降雨为：
    Y＝[y t,i]
    其中，y t,i为第t年在网格i观测到的指标数值，Y为y t,i组成的集合。
  5. 根据权利要求4所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，在所述步骤S3中，对于给定的网格i，由X和Y序列得到气象因子和 降雨之间的相关系数：
    Figure PCTCN2020103083-appb-100001
    式中，rx t(ry t)代表第t年气象因子，即观测降雨在原始序列中的排序，而
    Figure PCTCN2020103083-appb-100002
    则代表序列rx t(ry t)的均值；r的值介于-1与1之间，当两个变量完全单调相关时，r的值为1或-1；对于网格i，所计算的相关系数可记为r i，由此可得到相关系数组成的集合R＝[r i]。
  6. 根据权利要求5所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，在所述步骤S4中，所述空间自相关局部指标LISAAC的计算公式具体为：
    Figure PCTCN2020103083-appb-100003
    其中，w i,j是用于将r i与邻近网格r j进行联系的权重系数；
    Figure PCTCN2020103083-appb-100004
    为网格i邻近网格的空间加权相关系数；C i描述r i和其邻近网格r j之间的关系的强度；式中的权重系数是影响C i的重要参数。
  7. 根据权利要求6所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，为了使权重系数随距离增大而衰减，采用反距离权重法，以欧几里得法计算距离，并以该距离的平方的倒数作为两网格之间的距离权重系数：
    Figure PCTCN2020103083-appb-100005
    式中d(i,j)为第i和j各网格之间的欧式距离；当d(i,j)增大，邻近网格相关系数r j对C i的影响越小，通常根据数据尺度预设距离阈值以减少计算量。
  8. 根据权利要求7所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，在所述步骤S5中，所述重排计算为直接随机重排每个网络的观测降雨-气象指标时间序列。
  9. 根据权利要求7所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，所述步骤S6具体为：
    判断遥相关的空间聚类显著性，其对应原假设为气象指标与观测降雨不存在显著的相关性，即遥相关不显著；因此，通过随机排列第i(j)个网格历史气象指标和观测降雨序列，重新计算r i(r j)，及相应的C i；通过多次重复计算，构建C i的参考经验分布H。
  10. 根据权利要求9所述的一种面向遥相关模式的空间自相关聚类方法，其特征在于，所述步骤S7具体为：
    依据参考经验分布H，获得观测C i对应的p i值，以表示原假设为真时的强度,根据观测r i和相应的p i值，计算得到网格i的分类：
    Figure PCTCN2020103083-appb-100006
    式中PP表示某一网格点和其周围网格点的r都显著为正；PN表示某一网格的r为正，但其周围网格的r值偏低或为负，ns代表网格r i及其周围网格r j均不显著；NP代表负r i被正的r j围绕；最后一种情况NN表示的是负r i被负r j围绕；PP和NN表示r值具有较高的空间正相关性，提示存在区域集聚；而PN和NN则反映了r的空间分布存在异质性。
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