کاربرد توابع مفصل در مدل سازی دما و بارش سالانه استان خوزستان

Temperature variations have a very strong impact on ecosystems and pose many challenges for economic, social and agricultural developments. According to reports from the Intergovernmental Panel on Climate Change (IPCC) in the 20th century, the global temperature could rise by about 0.4 to 0.8 degrees Celsius. By the way, forecasts with six different scenarios showed that the temperature rise may reach 1.8 to 4 degrees Celsius at the end of the 21st century. Researches indicated that despite uncertainties in climate forecasts, the increase in temperature caused by human activities is bound to result in sudden and irreversible changes in the global water cycle. It has been confirmed in several studies that the temperature changes affect the precipitation parameter. Finding the relationship between the marginal distributions of the various variables to understand the laws governing these dependencies can be very effective in recognition of the observed hydrological events. Therefore, the assumption of independence between the variables can cause doubt in the accuracy of the results, so using bivariate data analysis methods could be very helpful. Due to the correlation between different hydrological parameters, the use of methods that can take into account the interdependence of variables and jointly model them could gain more reliable accuracy. In this regard, the lack of studies is strongly observed, thus the purpose of this research is to use copula functions in simultaneous modeling of annual precipitation and temperature in Khuzestan province.
Copulas are multivariate distribution functions which their one-dimensional margins are uniform in (0, 1). Sklar (1959) introduced the theory of the copula function and showed how univariate distribution functions could be interconnected using this method to create multivariate distribution functions. An important advantage of copula functions is that they allow the transfer of multivariate functions from to . For this purpose, the marginal functions of each variable are calculated and the copula function is construct using the dependency structure between the parameters. Therefore, it presents a full description of inner dependency structure In other words, the Sklar’s theorem claims that the dependency structure explained by copula function when the inner dependency among the variables is considered and univariate marginal distributions are calculated. The copula functions are made up of many families, including the Archimedean copulas. Archimedean copulas have been used in various fields of science such as economics, environmental studies and hydrological events due to their specific mathematical explicit formula. Many copulas do not have explicit formula, and this poses many challenges to their application. Applications of multivariate techniques for frequency analysis of hydrological parameters can be very useful and provide more reliable results. The most important part of using copulas is calculating the copula parameter. Many methods have been developed for this purpose. Ultra-innovative optimization algorithms can be very useful.In this study, four different copula functions (including, Ali - Mikhail – Haq, Clayton, Frank and Farlie- Gumbel- Morgenstern) were used for multivariate analysis of annual precipitation and temperature in Khuzestan province. In order to select the suitable copula function for forming the bivariate distribution, after fitting the suitable marginal distribution on every variables and estimating the distribution parameters, seven copula function used to link the marginal functions and the dependency parameter of every copula function was estimated by WOA method. Finally, the best fitted copula function was selected by comparing the CDF values of every copula function with corresponding values obtained from empirical copula. For selecting the best copula function, the Cramér–von Mises (Sn) and Normalized Root Mean Square Error (NRMSE) criteria were used.
Copula is a flexible approach for constructing joint distribution with different types of marginal distributions. Indeed, the copula is a function which links univariate marginal distributions to construct a bivariate or multivariate distribution function. In this study, the annual precipitation and temperature in Khuzestan province during 1988-2018 were investigated, using copula functions. For this purpose, six synoptic stations were selected because of their sufficient statistics, including: Dezful, Ahvaz, Ramhormoz, Mahshahr, Abadan and Masjed Soleiman. In the next step, nine different distribution functions were fitted on considered series and the best fitted distributions was selected for studid stations. After specifying the marginal distributions, four different copula functions (including: Ali- Mikhail- Haq, Clayton, Frank and Farlie- Gumbel- Morgenstern) were used for constructing multivariate frequency analysis of temperature and rainfall series. The most important part of applying multivariate functions is to determine the coefficient of copula function. Thus for this purpose, the Whale Optimization Algorithm (WOA) was used. After determining the coefficients of the copula functions, the joint distributions were constructed. The results showed that for the precipitation and temperature series of the Abadan, Dezful, Mahshahr and Masjed Soleiman stations Clayton function, and in other stations the Frank function had the best accuracy.