اﺳﺘﺨﺮاج ﺗﻮاﺑﻊ ﺗﻮزﯾﻊ اﺣﺘﻤﺎﻻﺗﯽ ﺗﻮأم ﻣﺸﺨﺼﻪﻫﺎي ﺑﺎرش ﺑﺎ اﺳﺘﻔﺎده از ﺳﺎﺧﺘﺎر درﺧﺘﯽ دي- واﯾﻦ ﭼﻬﺎرﺑﻌﺪي

Extraction of joint probabilistic distribution functions of characteristics of precipitation using a four-dimensional D-vine tree structure

ﺗﺤﻠﯿﻞ ﻓﺮاواﻧﯽ ﭼﻨﺪ ﻣﺘﻐﯿﺮه ﭘﺪﯾﺪه ﻫﺎي ﻫﯿﺪروﻟﻮژﯾﮑﯽ، ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ واﺑﺴﺘﮕﯽ ﺑﯿﻦ ﻣﺸﺨﺼﻪﻫﺎي اﺳﺎﺳﯽ اﯾﻦ ﭘﺪﯾﺪهﻫﺎ ، ﻣﻨﺠﺮ ﺑﻪ ﺗﺨﻤﯿﻦ دﻗﯿﻖﺗﺮ آﻧﻬﺎ ﺧﻮاﻫﺪ ﺷﺪ. ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ اﻧﻌﻄﺎفﭘﺬﯾﺮي ﺑﺎﻻﯾﯽ ﮐﻪ ﻣﻔﺼﻞﻫﺎي درﺧﺘﯽ واﯾﻦ در ﻣﺴﺎﺋﻞ ﺑﺎ اﺑﻌﺎد ﺑﺎﻻﺗﺮ از دو اراﺋﻪ دادهاﻧﺪ، در اﯾﻦ ﻣﻄﺎﻟﻌﻪ از ﺗﺎﺑﻊ ﻣﻔﺼﻞ دي- واﯾﻦ ﺟﻬﺖ ﺗﻌﯿﯿﻦ ﺗﺎﺑﻊ ﺗﻮزﯾﻊ اﺣﺘﻤﺎﻻﺗﯽ ﺗﻮأم ﭼﻬﺎرﺑﻌﺪي ﻣﺸﺨﺼﻪﻫﺎي ﻣﻬﻢ روﯾﺪادﻫﺎي ﺑﺎرش اﯾﺴﺘﮕﺎه ﺳﺮﯾﻤﻮﻧﺎ واﻗﻊ در ﮐﺸﻮر اﯾﺘﺎﻟﯿﺎ ﺷﺎﻣﻞ ﺑﯿﺸﯿﻨﻪ ﺷﺪت ﺑﺎرشM) (، ﻋﻤﻖ ﮐﻞ ﺑﺎرش )(R، ﻣﺪت زﻣﺎن دوره ﻣﺮطﻮب )(Lو ﻣﺪت دوره ﺧﺸﮏ )D( اﺳﺘﻔﺎده ﺷﺪه اﺳﺖ. ﺑﺪﯾﻦ ﻣﻨﻈﻮر، در اﺑﺘﺪا ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﻌﻨﯽداري واﺑﺴﺘﮕﯽ ﺑﯿﻦ ﻣﺸﺨﺼﻪﻫﺎي ﻣﻬﻢ روﯾﺪادﻫﺎي ﺑﺎرش و ﻫﻤﭽﻨﯿﻦ ﺑﺎ اﺳﺘﻔﺎده از ﺟﺎﯾﮕﺸﺖ آﻧﻬﺎ ﺳﺎﺧﺘﺎرﻫﺎي ﻣﻨﺘﺨﺐ درﺧﺘﯽ دي-واﯾﻦ ﺣﺎﺻﻞ ﮔﺮدﯾﺪ. ﭘﺲ از ﺑﺮازش ﻣﻔﺼﻞﻫﺎي ﻣﺨﺘﻠﻒ ﺧﺎﻧﻮادهﻫﺎي ارﺷﻤﯿﺪﺳﯽ و ﺑﯿﻀﻮي ﺑﺮ ﺟﻔﺖ- ﻣﻔﺼﻞﻫﺎي ﻫﺮ ﯾﮏ از ﺳﺎﺧﺘﺎرﻫﺎي درﺧﺘﯽ دي-واﯾﻦ، ﻣﻨﺎﺳﺐﺗﺮﯾﻦ ﺧﺎﻧﻮادهﻫﺎي ﻣﻔﺼﻞ ﺟﻬﺖ ﺑﺮازش ﺑﺮ ﺟﻔﺖ- ﻣﻔﺼﻞﻫﺎي ﻫﺮﯾﮏ از ﺳﺎﺧﺘﺎرﻫﺎي دي- واﯾﻦ ﺑﻮاﺳﻄﻪ ﻣﻌﯿﺎرﻫﺎي ﺣﺪاﮐﺜﺮ ﻟﻮگ درﺳﺖ-ﻧﻤﺎﺋﯽ ، اﻃﻼﻋﺎت آﮐﺎﺋﯿﮑﻪ )AIC( و اﻃﻼﻋﺎت ﺑﯿﺰﯾﻦ )BIC( ﺗﻌﯿﯿﻦ ﮔﺮدﯾﺪﻧﺪ . ﺳﭙﺲ ﺑﻪ ﻣﻨﻈﻮر ارزﯾﺎﺑﯽ دﻗﺖ ﺗﻮاﺑﻊ ﺗﻮزﯾﻊ اﺣﺘﻤﺎﻻﺗﯽ ﺗﻮأم ﭼﻬﺎرﺑﻌﺪي ﻣﺸﺨﺼﻪﻫﺎي ﻣﻬﻢ روﯾﺪادﻫﺎي ﺑﺎرش، ﺗﻮاﺑﻊ ﻣﺬﮐﻮر ﺑﺎ ﻣﻔﺼﻞ ﭼﻬﺎرﺑﻌﺪي ﺗﺠﺮﺑﯽ ﻣﻘﺎﯾﺴﻪ ﮔﺮدﯾﺪﻧﺪ. در ﻧﻬﺎﯾﺖ ﺳﺎﺧﺘﺎر دي- واﯾﻦ ﭼﻬﺎر ﺑﻌﺪي M-R-D-L ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﯿﺰان ﻣﻌﯿﺎرﻫﺎي ارزﯾﺎﺑﯽ RMSE= 0/031 ،R2= 0/991، و 0/024=MAE، و روش ﮔﺮاﻓﯿﮑﯽ ﺑﻌﻨﻮان ﻣﻨﺎﺳﺐﺗﺮﯾﻦ ﺳﺎﺧﺘﺎر ﺟﻬﺖ ﺗﻌﯿﯿﻦ ﺗﺎﺑﻊ ﺗﻮزﯾﻊ ﺗﻮأم ﻣﺸﺨﺼﻪ ﻫﺎي ﻣﻬﻢ ﺑﺎرش در اﯾﺴﺘﮕﺎه ﺳﺮﯾﻤﻮﻧﺎ اﻧﺘﺨﺎب ﮔﺮدﯾﺪ.

Multivariate frequency analysis of hydrological phenomena by considering the dependence between the basic characteristics of these phenomena will lead to more their accurate estimation. Due to the high flexibility provided by vine tree copulas in problems with dimension greater than two. In this study the D-vine function is used to determine the four-dimensional probabilistic distribution function of main characteristics of the precipitation events of Cremona station in Italy (including maximum rainfall intensity, total rainfall depth, duration of wet period and dry period). First, due to the significant dependence between the main characteristics of precipitation events and also using their permutation, D-vine tree structures were obtained. After fitting the various Archimedean and elliptical copula families to the pair-copulas of each D-vine tree structure, the most suitable copula families were determined for fitting the pair-copulas of each D-vine structure by the maximum log-likelihood, Akaike (AIC) and Bayesian Information Criterion (BIC). Then, in order to evaluate the accuracy of the four-dimensional probabilistic distribution functions of the important characteristics of precipitation events, the mentioned functions were compared with the corresponding four-dimensional empirical copulas. Finally, the M-R-D-L four-dimensional D-vine structure according to the evaluation criteria of R2 = 0.991, RMSE = 0.031, and MAE = 0.024, was selected as the most appropriate structure for constructing of the joint distribution function of main characteristics of precipitation in Cremona station