扩散模拟型流域地貌汇流模型

扩散模拟型流域地貌汇流模型

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contributed at 2018-12-04

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岳天祥编著
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yue@lreis.ac.cn
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扩散模拟型流域地貌汇流模型

        1)扩散模拟河段:

                  

上式为泛定方程,CD为常数,且:

  式中,为流量;L为距离;t为时间;CD分别为洪水波的波速和扩散系数;为河段上段面的入流过程。当为瞬时脉冲函数时,即为“扩散模拟河段”的响应函数ht),即:

               

        2)三级流域瞬时单位线:

                  

式中,i级河流的平均长度;为初时概率(i级单元面积与全流域面积的比值);为转移概率(注:j级河流的i级河流数与i级河流总数的比值)。

它们均可以写成Horton地貌率理论中河长比,河流分叉比,面积比的函数,即:

             

      3)时段转换:扩散模拟型流域瞬时单位线在应用时,需要经S曲线转化为时段单位线。对三级流域,其瞬时单位线S曲线

           

  式中,

    exp*)为指数函数,erf*)为误差函数,

根据S曲线与时段单位曲线的关系,可求出三级流域的时段单位线:

    

   4)矩法:根据矩的定义,可求出三级流域瞬时单位线的一阶原点矩、二阶中心距分别为:

      

      

  令:,并将入流It)、出流Qt)和瞬时单位线ht)三者间的矩值关系代入上列格式可得:

           

          

式中,分别为出流Qt)和入流It)的一阶原点矩;分别为出流Qt)和入流It)二阶中心矩。

    5)内罚函数法:内罚函数法是一种有约束的最优化方法,用此法估计模型函数CD是,其目标函数和约束条件为:

           

 式中,分别为各离散点的实测流量值和计算流量值;为实测洪峰值;为流域出口断面平均流速最大值;M为本次洪水的计算时段数;r为内罚因子。

 

参考文献:

    谢平,梁瑞驹:扩散模拟型流域地貌汇流模型。地理学报,1997,524

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How to Cite

《资源环境数学模型手册》 (2018). 扩散模拟型流域地貌汇流模型, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/e7eaa53c-3b55-4c8f-b8a9-f91ae04e719b
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Last modifier : 
zhengzhong
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initial contribute: 2018-12-04

Authorship

Affiliation:  
岳天祥编著
Email:  
yue@lreis.ac.cn
Homepage:  
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Last modifier : 
zhengzhong
Last modify time : 
2020-11-09
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