A novel approach for modelling pattern and spatial dependence structures between climate variables by combining mixture models with copula models

Abstract

Spatiotemporal dependence structures play a pivotal role in understanding the meteorological characteristics of a basin or subbasin. This further affects the hydrological conditions and, consequently, will provide misleading results if these structures are not taken into account properly. In this study, we modelled the spatial dependence structure of three climate variables, maximum and minimum temperature and precipitation, throughout the Monsoon‐dominated zone of Pakistan. For temperature, six meteorological stations have been considered, for precipitation we used the results of four meteorological stations. For modelling the dependence structure between temperature and precipitation at multiple sites, we utilized C‐Vine, D‐Vine and student t‐copula models. For temperature, multivariate mixture normal distributions, and for precipitation, the gamma distribution, have been used as marginals under the copula models. The models were calibrated by utilizing the 20 years daily data from 1981 to 2000, and for validation, we used the data for 10‐year period from 2001 to 2010. The simulations were performed for each variable separately, conditioned on spatial neighbours. A comparison was made between the different copula models, on the basis of observational and simulated patterns and spatial dependence structures, the performance was evaluated for the validation period. The results show that all copula models performed well; however, there are subtle differences between them. The copula models captured the patterns and spatial dependence structures between climate variables, however, the t‐copula showed poor performance in reproducing the dependence structure with respect to magnitude. It was observed that important statistics of observed data have been closely approximated except a few maximum values for maximum temperature and minimum values for minimum temperature. Probability density functions of simulated data follow closely the pattern of observational data. These methods can be combined with statistical downscaling models to improve their performance, particularly in modelling the dependence structure between climate variables at multiple sites.

Minimum temperature mapping with spatial copula interpolation

“…When we examine the January 2017 minimum temperature prediction maps obtained by both methods, we see that copula prediction maps have more detail over the area and gave better results in extrapolation. The obtained results are in accordance with those of Alidoost et al (2018), Khan et al (2019), andDzupire et al (2020). Alidoost et al (2018) showed that spatial copulas with covariates outperform kriging predictions.…”

“…Alidoost et al (2018) showed that spatial copulas with covariates outperform kriging predictions. Khan et al (2019) showed that using C-Vine, D-Vine, and t-copula models resulted into accurate predictions of daily maximum and minimum temperature and precipitation. They found that copulas were good at capturing the spatial dependence structure between climatic variables.…”

Performance evaluation of Standardized Copula‐based Drought Index with Reconnaissance Drought Index and Standardized Precipitation Temperature Index using severity–duration frequency curves over Balochistan, Pakistan

“…It can efficiently be used in case of high correlation and even if different probability distributions for the variables exist to jointly simulate the drought variables (Salvadori and De Michele, 2010). Hence copula modelling has an advantage over traditional multivariate distributions that it can be used for similar as well as different probability distributions of the variables and existing high correlation in several fields (e.g., Shiau, 2006; Lee and Cook, 2019; Yu et al ., 2020; Bazrafshan et al ., 2020; Khan et al ., 2020; Deng and Liang, 2021; Ullah and Akbar, 2021a; 2021b). In literature, copula models have also been effectively used in the development of new multivariate indices or in combing the results of existing indices (e.g., Kavianpour et al ., 2018; Van de Vyver and Van den Bergh, 2018; Wang et al ., 2020; Won et al ., 2020; Amjad et al ., 2022).…”

A spatial copula interpolation in a random field with application in air pollution data

“…They (Khan et al. 2020 ) apply regular (C- and D-) Vine copula and the Student t-copula to explore the structure of spatial dependence of different climate variables, for instance, precipitation, and air temperature. A combination of extreme value models like the Generalized Pareto Distribution (GPD) with copulas (Masseran and Hussain 2020 ) illustrate a dependence between and a set of four major pollutant variables, namely, CO, NO , SO , and O .…”