Partition comparison and fitting function of class conditional probability density of hourly rainfall

Six latitude-longitude rectangular regions were selected (Four is on the 30°N line: around Ya'an, in the southwest of Hubei, in the souther of Jianghan Plain, west Hangzhou Bay.Others are Hainan Island and around Zhengzhou, one is in its south and another is in its north). The hourly rainfall data are subdivided into 42 grades and three kinds of "class-conditional probability density" are counted respectively. Its detailed curve graph and empirical fitting function which is in the simple form were given.The three kinds of conditional probability density curves are monotonic convex decreasing functions. Using the exponential function of three-parameter power function as the empirical fitting function, we can get a good fitting, which is universal to six sub-regions and the three kinds of class conditional probability density function. The results show that the frequency of rainfall in Ya'an is high, the first and second kinds of class conditional probability density are higher than that in other regions at the head and tail of the curve, indicating that the extreme short-term heavy rainfall occurs frequently. Due to the fact that the first and second kinds of class conditional probability density of heavy rainfall in Hainan Island are larger than that in other regions, the annual average rainfall is still larger even though there are many negative factors, such as low rainfall frequency, more isolated hourly rainfall, short duration of hourly continuous rainfall, fast decline of the third type of conditional probability density and strong skewness. In addition, by comparing the adjacent mountainous areas of Southwest Hubei and the Southern Jianghan Plain, the influence of the mountainous areas of Southwest Hubei on the rainfall structure is discussed. The increase of rainfall frequency caused by mountainous areas is mainly the increase of weak rainfall, but the weakly decrease of heavy rainfall frequency, so the mountain friction when there is no special terrain structure is negative factor for the occurrence of heavy rainfall.