{"title":"Analysing Maximum Monthly Temperatures in South Africa for 45 years Using Functional Data Analysis","authors":"Mapitsi Rangata, Sonali Das, Montaz Ali","doi":"10.47654/v24y2020i3p1-27","DOIUrl":null,"url":null,"abstract":"The paper uses Functional Data Analysis (FDA) to explore space and time variation of monthly maximum temperature data of 16 locations in South Africa for the period 1965 - 2010 at intervals of 5 years. We explore monthly maximum temperature variation by first representing data using the B-spline basis functions. Thereafter registration of the smooth temperature curves was performed. This data was then subjected to analysis using phase-plane plots which revealed the constant shifting of energy over the years analysed. We next applied functional Principal Component Analysis (fPCA) to reduce the dimension of maximum temperature curves by identifying the maximum variation without loss of relevant information, which revealed that the first functional PCA explains mostly summer variation while the second functional PCA explains winter variation. We next explored the functional data using functional clustering using K-means to reveal the spatial location of maximum temperature clusters across the country, which revealed that maximum temperature clusters were not consistent over the 45 years of data analysed, and that the cluster points within a cluster were not necessarily always spatially adjacent. The overall analysis has displayed that maximum temperature clusters have not been static across the country over time. To the best of our knowledge, this the first instance of performing in-depth analysis of maximum temperature data for 16 locations in South Africa using various FDA methods.","PeriodicalId":38875,"journal":{"name":"Advances in Decision Sciences","volume":"24 1","pages":"1-27"},"PeriodicalIF":0.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Decision Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47654/v24y2020i3p1-27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Decision Sciences","Score":null,"Total":0}
引用次数: 2
Abstract
The paper uses Functional Data Analysis (FDA) to explore space and time variation of monthly maximum temperature data of 16 locations in South Africa for the period 1965 - 2010 at intervals of 5 years. We explore monthly maximum temperature variation by first representing data using the B-spline basis functions. Thereafter registration of the smooth temperature curves was performed. This data was then subjected to analysis using phase-plane plots which revealed the constant shifting of energy over the years analysed. We next applied functional Principal Component Analysis (fPCA) to reduce the dimension of maximum temperature curves by identifying the maximum variation without loss of relevant information, which revealed that the first functional PCA explains mostly summer variation while the second functional PCA explains winter variation. We next explored the functional data using functional clustering using K-means to reveal the spatial location of maximum temperature clusters across the country, which revealed that maximum temperature clusters were not consistent over the 45 years of data analysed, and that the cluster points within a cluster were not necessarily always spatially adjacent. The overall analysis has displayed that maximum temperature clusters have not been static across the country over time. To the best of our knowledge, this the first instance of performing in-depth analysis of maximum temperature data for 16 locations in South Africa using various FDA methods.
本文采用功能数据分析(Functional Data Analysis, FDA)方法,对南非16个地点1965—2010年逐月最高气温数据进行了以5年为间隔的时空变化分析。我们通过首先使用b样条基函数表示数据来探索月最高温度变化。然后进行光滑温度曲线的配准。然后使用相平面图对这些数据进行分析,这些图揭示了所分析的年份中能量的不断变化。利用功能主成分分析(functional Principal Component Analysis, fPCA)在不丢失相关信息的情况下,通过识别最大变化来降低最高温度曲线的维数,结果表明,第一个功能主成分分析可以解释夏季变化,而第二个功能主成分分析可以解释冬季变化。接下来,我们利用K-means的功能聚类方法对功能数据进行了探索,揭示了全国最高温度集群的空间位置,结果表明,在45年的数据分析中,最高温度集群并不一致,集群内的集群点不一定总是空间相邻。总体分析显示,随着时间的推移,全国各地的最高温度集群并不是一成不变的。据我们所知,这是第一次使用各种FDA方法对南非16个地点的最高温度数据进行深入分析。