Maposa Daniel, Seimela Anna M, Sigauke Caston, Cochran James J
Department of Statistics and Operations Research, University of Limpopo, Private Bag X1106, Sovenga Polokwane, South Africa.
Department of Statistics, University of Venda, Private Bag X5050, Thohoyandou, 0950 South Africa.
Nat Hazards (Dordr). 2021;107(3):2227-2246. doi: 10.1007/s11069-021-04608-w. Epub 2021 Feb 11.
A common problem that arises in extreme value theory when dealing with several variables (such as weather or meteorological) is to find an appropriate method to assess their joint or conditional multivariate extremal dependence behaviour. The method for choosing an appropriate threshold in peaks-over threshold approach is also another problem of endless debate. In this era of climate change and global warming, extreme temperatures accompanied by heat waves and cold waves pose serious economic and health challenges particularly in small economies or developing countries like South Africa. The present study attempts to address these problems, in particular, to deal with and capture dependencies in extreme values of two variables, by applying bivariate conditional extremes modelling with a time-varying threshold to Limpopo province's monthly maximum temperature series. Limpopo and North West provinces are the two hottest provinces in South Africa characterised by heat waves and the present study is carried out in the Limpopo province at Mara, Messina, Polokwane and Thabazimbi meteorological stations for the period 1994-2009. With the aim to model extremal dependence of maximum temperature at these four meteorological stations, two modelling approaches are applied: bivariate conditional extremes model and time-varying threshold. The latter approach was used to capture the climate change effects in the data. The main contribution of this paper is in combining these two approaches in bivariate extremal dependence modelling of maximum temperature extremes in the Limpopo province of South Africa. The findings of the study revealed both significant positive and negative extremal dependence in some pairs of meteorological stations. Among the major findings were the significant strong positive extremal dependence of Thabazimbi on high-temperature values at Mara and the strong negative extremal dependence of Polokwane on high-temperature values at Messina. The findings of this study play an important role in revealing information useful to meteorologists, climatologists, agriculturalists, and planners in the energy sector among others.
在极值理论中，处理多个变量（如天气或气象变量）时出现的一个常见问题是找到一种合适的方法来评估它们的联合或条件多变量极值相依行为。在峰值超过阈值方法中选择合适阈值的方法也是一个无休止争论的问题。在这个气候变化和全球变暖的时代，伴随着热浪和寒潮的极端温度对经济和健康构成了严峻挑战，特别是在像南非这样的小经济体或发展中国家。本研究试图解决这些问题，特别是通过对林波波省的月最高温度序列应用具有时变阈值的二元条件极值建模，来处理和捕捉两个变量极值中的相依关系。林波波省和西北省是南非最热的两个省份，以热浪为特征，本研究在林波波省的马拉、梅西纳、波罗克瓦尼和塔巴津比气象站进行，时间跨度为1994年至2009年。为了对这四个气象站的最高温度极值相依性进行建模，应用了两种建模方法：二元条件极值模型和时变阈值。后一种方法用于捕捉数据中的气候变化影响。本文的主要贡献在于将这两种方法结合起来，用于南非林波波省最高温度极值的二元极值相依性建模。研究结果表明，在一些气象站对中存在显著的正极值相依和负极值相依。主要发现包括塔巴津比对马拉高温值的显著强正极值相依，以及波罗克瓦尼对梅西纳高温值的强负极值相依。本研究的结果在为气象学家、气候学家、农学家以及能源部门规划者等提供有用信息方面发挥了重要作用。
