Extended Abstract

Scale Parameter10090807060504030rainy day after a dry orwet precedingrainy day after a dryprecedingrainy day after a wetpreceding20Fig.1. The Illustration of the test catchment andthe locations of 5 stations in the test area. (1,2, 3, 4and5represent for Xixian, Fuyang,Shangqiu, Huaian and Lianyungang rain gaugesite, and the black triangle represents thehydrographic station, representatively.).100 1 2 3 4 5 6 7 8Shape Parameter*10Fig 2. The scatter of shape parameterand scale parameter of gammadistribution of daily precipitation overHuaihe basin.stochastic process of precipitation could be described by a dual variable, that is, ((J n-1 ,X n ), n = 1, 2, 3 ... ...), where J represent the nth day is a rainy day (daily precipitation >0 mm) as J equal 1, and it represent the nth day is not a rainy day as J equal 0. X n isthe precipitation of the nth day. The dual variable (J n-1 , X n ) express that the probabilitydistribution of the nth day’s precipitation is related to whether the (n - 1)th day is rainy.The gamma distribution density function is shown in Equation (1). The completegamma function is shown in Equation (2) ( Gregory et al., 2007)1 x 1 xifi( x) ( ) exp t 1i( i)i i i …… (1) , ( i ) e t dt0 ……(2)Where x > 0, α i , β i > 0, i = 0, 1, 2. That is correspond to the unconditional rainydays, rainy day which has a dry preceding day (J n-1 = 0, J n = 1) and rainy day whichhas a wet preceding day (J n-1 = 1, J n = 1) separately. The samples of rainy days of 158sites in the Huaihe basin are investigated according to these three types, and both therainy day which has a dry preceding day and the one has a wet preceding day areconditional rainy days. The shape parameter α i and the scale parameter β i , as wellas thex i and2s i, are estimated by the maximum likelihood estimation(Gregory etx 2 2al., 2007), that is, , s . Finally, the probability density function f i (x) iscalculated in a certain interval according to the formula (1) and (2).3.Result3.1 The parameter analysis of the unconditional and conditional rainy days-423-