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沈铁元, 刘静, 向怡衡, 祁海霞, 殷志远, 王俊超. 2021: 逐时降雨的类条件概率密度分区比较与拟合函数初探. 暴雨灾害, 40(6): 664-674. DOI: 10.3969/j.issn.1004-9045.2021.06.011
引用本文: 沈铁元, 刘静, 向怡衡, 祁海霞, 殷志远, 王俊超. 2021: 逐时降雨的类条件概率密度分区比较与拟合函数初探. 暴雨灾害, 40(6): 664-674. DOI: 10.3969/j.issn.1004-9045.2021.06.011
SHEN Tieyuan, LIU Jin, XIANG Yiheng, Qi Haixia, YIN Zhiyuan, WANG Junchao. 2021: Partition comparison and fitting function of class conditional probability density of hourly rainfall. Torrential Rain and Disasters, 40(6): 664-674. DOI: 10.3969/j.issn.1004-9045.2021.06.011
Citation: SHEN Tieyuan, LIU Jin, XIANG Yiheng, Qi Haixia, YIN Zhiyuan, WANG Junchao. 2021: Partition comparison and fitting function of class conditional probability density of hourly rainfall. Torrential Rain and Disasters, 40(6): 664-674. DOI: 10.3969/j.issn.1004-9045.2021.06.011

逐时降雨的类条件概率密度分区比较与拟合函数初探

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

  • 摘要: 选取六个经纬度长方形区域(在30°N线上四个:雅安附近、鄂西南、江汉平原南部、杭州湾西;南选海南岛、北选郑州附近),把逐时降雨资料细分四十二个等级分别统计三类“类条件概率密度”,并给出了细致的曲线图及形式简单的经验拟合函数。结果显示三类类条件概率密度曲线均是单调凸减函数、在双对数图上曲线均是单调凹减函数,用三参数幂函数的指数函数作为经验拟合函数,能得到好的拟合效果,对所选区与密度函数普适。通过分区比较揭示了雅安“多且强”与海南岛“少而大”的特有降雨结构特征:雅安降雨频次多,第一、二类类条件概率密度在曲线头和尾部比其他分区大,极端短时强降雨多发;海南岛由于强降雨段第一、二类类条件概率密度比其他分区大,纵然其有降雨频率偏低、孤立性小时降雨占比多、逐时连续降雨历时短、第三类类条件概率密度递减快偏态性强等诸多不利因素,但仍致年均降雨量偏大。另外通过比较位置临近的鄂西南山地与江汉平原南部两个分区,探讨了非特殊地形结构下的鄂西南山地对降雨结构的影响,结果表明山地导致降雨频率增加主要是弱降雨的增加,强降雨频率反倒有所减少,山地摩擦阻力对强降水的发生总体上是不利因素,与雅安这类特殊的地形影响迥异。

     

    Abstract: 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.

     

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