Climatic changes as a natural phenomenon are usually multivariate phenomena that are influenced by various factors and have a kind of heterogeneity. Examining these phenomena in a comprehensive, single and homogeneous manner, especially in multivariate mode, can lead to completely misleading results. In many practical problems, identifying the appropriate model for the possible distribution of climate changes is of particular importance. Because climate changes, as a natural phenomenon, are usually multi-variable phenomena that are influenced by various factors and have a kind of heterogeneity. Investigating these phenomena in a comprehensive, unified and homogeneous manner, especially in multivariate mode, can lead to completely misleading results. In general, the probability distribution of multivariate random data is more complicated compared to their univariate state due to the nonlinear dependence between random variables. One of the ways to solve this problem is the use of detailed functions, which has been the focus of researchers in recent years. Due to its high flexibility, the application and use of detailed function is a very useful tool in most scientific fields, including medicine, agriculture, meteorology, marketing, management, etc. The theory of detailed functions as the basis of this science was presented by Sklar (1956). Detailed functions are a powerful tool for constructing multivariate distribution functions based on one-dimensional marginal distribution functions. In fact, detailed functions describe the type and how the variables are related. show. Detailed functions express the non-parametric and dependence features of distribution functions of random variables well. Detailed functions can be used in risk measurement problems. Because, in quantitative risk problems, the role dependence structure It plays an important role and with the knowledge of the dependence structure, a measure of risk can be obtained with the help of the detailed function.Therefore, the probability distribution of multivariate random data is more complicated compared to their univariate state due to the nonlinear dependence between random variables. One of the ways to solve this problem is the use of detailed functions. In this article, using detailed functions, a combined analytical model between temperature and precipitation was presented in the prediction of climate changes in Ilam city. The results showed that the performance of the joint functions were close to each other and among the examined joint functions, the Legamble-Barnett joint was more suitable for modeling the dependence of rainfall and temperature at Ilam station. These results have been analyzed based on the comparison of the dependence sizes between the original data and the simulated data for 1000 samples. The results showed that the performance of all five FGM, Clayton, GB, NC and AMH joint functions are close to each other, but considering that among the five joint functions examined, only Gumbel Barnett (GB) joint has the ability to model negative dependencies. , so it was chosen as a suitable detailed function to model the dependence of rainfall and temperature in Ilam city station. The simulated data also showed that there is a consistency between the original temperature and precipitation data of Ilam city by detailed functions with Sperman's correlation coefficient. Sani Khani et al. (2013) used Frank's joint to model their climate data. In the only study conducted regarding the simultaneous modeling of climate variables using detailed functions, we can refer to the studies of Scholzel and Friedrich (2008), who investigated the relationship between precipitation and wind speed on a daily scale from a simple model based on detailed functions. . In their studies, Scholzel and Friedrich (2008) used a wide range of joint functions, including Archimedesian, semi-elliptical and normal joint functions, to model precipitation and wind speed in two stations, Postdam and Berlin, in Germany. The results indicated the acceptable performance of detailed functions in the investigated range and introduced detailed functions as practical and useful tools in climatology studies.

By using the combined distribution of temperature and precipitation of Ilam city, important information about the data can be obtained. This possibility is very useful in critical conditions of global warming and how to manage the effects of global warming and be safe from this phenomenon. By using the detailed function and marginal distribution functions, it is easy to obtain the probabilities and other information about the temperature and precipitation of Ilam city and the relationship between the two factors. Conditional distribution functions can also be determined by using Gamble-Barnett detail and based on them, the probability of how one factor changes against the controlled changes of another factor can be discussed.