A novel Approach for Modelling Pattern ...

Spatio‐temporal dependence structures play a pivotal role in understanding the meteorological characteristics of a basin or sub‐basin. 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 modeled the spatial dependence structure of three climate variables, maximum, 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 twenty years daily data from 1981–2000, and for validation we used the data for ten year period from 2001–2010. The simulations were performed for each variable separately, conditioned on spatial neighbors. 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 modeling the dependence structure between climate variables at multiple sites.