岩溶流域泉流量的分数阶模型

南京大学学报(自然科学版) ›› 2016, Vol. 52 ›› Issue (3): 490–495.

岩溶流域泉流量的分数阶模型

夏　源1*，姜光辉2，吴吉春3

出版日期:2016-07-02 发布日期:2016-07-02
作者简介:1.桂林理工大学环境科学与工程学院，桂林，541004；
2.中国地质科学院岩溶地质研究所/国土资源部、广西壮族自治区岩溶动力学重点实验室，桂林，541004；
3.南京大学地球科学与工程学院，南京，210023
基金资助:
国家自然科学基金(41302197)，广西自然科学基金(2013GXNSFBA019211)，广西环境污染控制理论与技术重点实验室基金(桂科能1201Z023)

The fractional calculus model for spring’s discharge of karst depression

Xia Yuan1*，Jiang Guanghui2，Wu Jichun3

Online:2016-07-02 Published:2016-07-02
About author:1.College of Environmental Science and Engineering，Guilin University of technology，Guilin，541004，China；
2．Institute of Karst Geology，CAGS/Karst Dynamic Laboratory，MLR&GZAR，Guilin，541004，China；
3．School of Earth Sciences and Engineering，Nanjing University，Nanjing，210023，China

摘要/Abstract

摘要： 根据岩溶流域泉流量与河流流域出口流量过程物理机制的相似性，解释了泉流量对降雨的响应关系．并以稳定分布为基础，将岩溶流域的泉流量衰减公式的衰减核函数进行改进，得到了具有偏态性和拖尾分布的泉流量衰减公式，并推导出了分数阶泉流量衰减方程．当分数阶指数为1时，方程退化为传统的流量方程，当分数阶指数小于1时，该方程描述了泉流量曲线的偏态性和拖尾分布，更具有一般性．为解决分数阶流量方程求解困难，提出了利用傅里叶变换和傅里叶逆变换求衰减核函数的方法．将该模型应用于桂林丫吉岩溶试验场的泉流量模拟，结果表明，新的模型能够模拟出泉流量曲线的偏态性及拖尾分布．

Abstract: The relationship between spring’s discharge of karst depression and rainfall is interpreted according to the similarity between the spring’s discharge and the runoff of a catchment.According to the stable distribution，the attenuation kernel function in the attenuation formula describing the discharge of springs is modified，which results in a novel attenuation equation describing the variation of discharge with skewness and heavy tail.The fractional discharge equation is derived consequently.The novel attenuation equation degenerates to traditional one in the case of the fractional index being 1.If the fractional index is less than 1，the novel attenuation equation describes the discharge of spring with skewness and heavy tail.To deal with the difficulty getting solution from the fractional equation，the Fourier transform and inverse transform are used to obtain the attenuation kernel function.The novel model has been applied to simulate the discharge of spring at Yaji site in Guilin.The result shows the model can simulate the discharge of springs with skewness and heavy tail.

夏　源1*，姜光辉2，吴吉春3. 岩溶流域泉流量的分数阶模型[J]. 南京大学学报(自然科学版), 2016, 52(3): 490–495.

Xia Yuan1*，Jiang Guanghui2，Wu Jichun3. The fractional calculus model for spring’s discharge of karst depression[J]. Journal of Nanjing University(Natural Sciences), 2016, 52(3): 490–495.

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