水文学原理课件(第十章).

第十章洪水演算(FloodRouting)本章主要内容引言(Introduction)1线性扩散波演算法(Lineardiffusionwaveroutingmethod)2线性特征河长演算法(Linearcharacteristiclengthroutingmethod)3线性运动波演算法(Linearkinematicwaveroutingmethod)4Part1Introduction1、定义(Definition)洪水演算：根据河段上断面出现的洪水过程来推算其下断面洪水过程的方法称洪水演算。2、分类(Classification)具有物理基础的洪水演算法—主要用于河道汇流基于“黑箱子”分析的洪水演算法—主要用于流域汇流Part1Introduction3、具有物理基础的洪水演算法概述(Physically-basedfloodroutingmethod)00()1()fQAMassConservationxtvvvyiiMomentumConservationgtgxx质量守恒动量守恒水力学(),,,,,()dWIOMassConservationdtIOWfIOMomentumConservationtt水文学•水力学方法的关键是如何求解方程式。•水文学方法的关键是如何确定槽蓄方程。Part2Lineardiffusionwaveroutingmethod定解问题的构成(Compositionofsolutionproblems)1入流过程的处理(Processingofinflowhydrograph)2基本解(Basicsolution)3出流过程的计算(Derivationofoutflowhydrograph)4参数的确定方法(Determinationofparameters)5Part2Lineardiffusionwaveroutingmethod2-1定解问题的构成(Compositionofsolutionproblems)洪水波—扩散波（Diffusionwave）初始条件—稳定流（Steadyflow）上边界过程—上断面洪水过程（inflowhydrographatuppersection)下边界条件—半无限长，自由下边界（semi—infinitelong,freelowerboundary）Part2Lineardiffusionwaveroutingmethod2-2Processingofinflowhydrograph(1)简单入流过程(Simpleinflowhydrograph)1t()Hta)单位入流过程(UnitInflowhydrograph)：一直维持1个单位流量的入流过程(例如1m3/s)0010tHtt01taHtata1a0()Ht延迟单位入流Part2Lineardiffusionwaveroutingmethod2-2Processingofinflowhydrographb)单位矩形入流过程(UnitRectangularPulseInput)在单位时间(△t)内维持1个单位流量的入流称之.延迟单位矩形入流00100oatIttata010abtaItatbtb()oaItHtHta(1)简单入流过程(Simpleinflowhydrograph)Part2Lineardiffusionwaveroutingmethod2-2Processingofinflowhydrographc)单位瞬时脉冲入流(UnitinstantaneousPulseInput)时段很短（），强度很大（），但入流总量为有限数（等于1个单位）的入流称之.t0t001ttdtdHttdtHttdt函数：000ttt(1)简单入流过程(Simpleinflowhydrograph)Part2Lineardiffusionwaveroutingmethod2-2Processingofinflowhydrograph(2)入流过程的数学处理(ProcessingofInflowHydrograph)012312011223,,,222IIIIIIIII0101IIt1212IIt()It用柱状图代替光滑的I(t)曲线.用减小△t的方法提高近似精度.第一个矩形：第二个矩形：以此类推。...))3()2(())2()1(())1()(()(...)()()()(231201232312120101tHtHItHtHItHtHItItIItIItIItIPart2Lineardiffusionwaveroutingmethod2-3Basicsolution简单入流的解称为基本解，又称为(河段)汇流曲线(flowconcentrationcurve)。如果河段入流为单位入流函数H(t)，则下断面出流为S曲线，又称为单位过程线(UnitHydrograph)如果某河段上断面入流为单位瞬时脉冲入流δ(t)，则河段下断面出流称为瞬时单位线u(0,t)，简写为u(t)如果河段上断面入流为单位矩形入流，则下断面出流称为时段单位线u(△t,t)0()0,,0,tStutdtuttStSttdStutdtPart2Lineardiffusionwaveroutingmethod2-3Basicsolution一般情况下,先求u(0,t)，再求S(t)，最后求u(△t,t)u(0,t)S(t)u(△t,t)Part2Lineardiffusionwaveroutingmethod2-3Basicsolution22(,0)0(0,)()lim(,)0xQQQCtxxQxQttQxt22CQQQCtxx式中、为常数是线性常微分方程（满足叠加性）0(,)(,)tSxtuxtdt应用Laplace变换，容易求得瞬时单位线的表达式为：]4)(exp[41),(22/3txCttxtxuPart2Lineardiffusionwaveroutingmethod2-3Basicsolution若：22(,0)0(0,)()lim(,)0xQQQCtxxQxQtHtQxt1(,)1122222cxxctxctSxterfeerftt(,,)(,)(,)utxtSxtSxtt应用Laplace变换，求得S(t)曲线的表达式：式中—余误差函数(complementaryerrorfunction)()erfPart2Lineardiffusionwaveroutingmethod2-4Derivationofoutflowhydrographt(,)utt01120123,11,()[()(1)][(1)(2)]()()(1)(2)(3)iiiiiItIHtHtIHtHtItIHtIHtIHtIHtIII若式中0120(,)(,)(,)(,2)(,)niiQxtISxtISxttISxttISxtit首先把入流过程离散化(Discretizinginflowhydrograph)用单位矩形入流表示()ItPart2Lineardiffusionwaveroutingmethod2-4Derivationofoutflowhydrograph计算出流量过程的主要步骤：1)确定计算时段△t。2)按在上断面入流过程线上从起涨时刻开始摘取时刻的入流量3)计算时段平均入流量或时段平均入流量的增量。4)按求定的河段的时段单位线或S—曲线，计算出流过程。t0,,2,3,ttt0123,,,,.IIIIPart2Lineardiffusionwaveroutingmethod2-4Derivationofoutflowhydrograph()It01I12I23It()Itt12(,)Iutt()Itt01(,)Iutt()Itt23(,)Iuttt(,)utt现以按u(△t,t)推流为例，说明计算Q(t)-t过程。Part2Lineardiffusionwaveroutingmethod2-4Derivationofoutflowhydrograph()Itt01(,)Iutt()Itt12(,)Iutt()Itt23(,)Iutt()Ot011223()(,)(,)(,)OtIuttIuttIuttt-τ为汇流时间tdtuItQ0),0()()(离散化(Discretization)卷积公式(Convolutionformula)Part2Lineardiffusionwaveroutingmethod2-5Determinationofparameters(1)根据参数的物理公式计算000001,,()22QQdQHCClldAiBiQPart2Lineardiffusionwaveroutingmethod2-5Determinationofparameters~CItQt假定和汇流曲线由2220.0eCCee的和可使达到最小(2)根据实测流量资料确定（试算法）C和()Qt()Qt直到假定的使得推算的与实测足够接近。只要满足方程组：(,,,)cQxtCC和但由于的表达式很复杂，直接解出较困难。0220min(,,,)(,)etcteQxtCQxt最优化方法：Part3Linearcharacteristiclengthroutingmethod描述洪水波运动的基本微分方程式(Basicdifferentialequationsoffloodwavemovement)1汇流曲线的确定(Determinationofflowconcentrationcurve)2参数确定方法(Determinationofparameters)3Part3Linearcharacteristiclengthroutingmethod3-1Basicdifferentialequationsoffloodwavemovement在每个子河段内，满足:每个子河段：Part3Linearcharacteristiclengthroutingmethod3-1Basicdifferentialequationsoffloodwavemovement1212131231232233()()()nnlllllllnlllllllndOdOIOKKKKKKKdtdtdOdOKKKKKKKdtdt先不对每个河段写方程，而对整个河段写方程，则由上式可得：121,,,,nOOO消去所有中间变量得到:12121312322(1)/2()()()nnlllllllnnnnllllndOdOOKKKKKKKdtdtdOKKKKItdtPart3Linearcharacteristiclengthroutingmethod3-1Basicdifferentialequationsoffloodwavemovement12123,()()nnnlllllllnIOdWdtdWdOdOKKKKKKKdtdtdt由可推知：从而Part3