基于最小二乘法的绳套型水位流量关系最优定线研究

Optimal Determination of Looped Stage-discharge Relationship by the Least Squres Methods

汛期河道的水位流量关系通常呈绳套型,对其进行高精度的定线是洪水资源实施高效管理的基础。传统的定线方法效率低,误差大,因而本文使用最小二乘法为优化方法,对绳套型水位流量方程进行优化定线。首先,Saint-Venant方程中的迁移惯性项和局地惯性项被去掉以简化方程,附加比降被引入以使方程能够拟合绳套型曲线;然后,简化后的方程通过取对数、多项式展开和幂级数展开被线性化;最后应用最小二乘法估计线性化方程中的参数。对3个案例的应用结果表明,所获得的定线方程能有效拟合观测的水位流量曲线,对拟合结果的偏离符号检验、适线检验和偏离数值检验均符合水文资料整编规范中的定线精度要求,说明将最小二乘法应用于绳套型水位流量曲线的优化定线是有效的。

The stage-discharge in flooding seasons in river channels normally presents a shape of loop, determining it is basic for con- ducting an efficient management of flooding water resources. Traditional ways of determining the looped relationship has such disad- vantages as inefficiency, significant errors, etc. , therefore this paper aims at applying the Least Squares Method （LSM） to optimal determination of the looped stage-discharge relationship. The equation capable of depicting the looped stage-discharge relationship in river channels is obtained based on the original Saint-Venant momentum equation, by identifying the water surface slope as the sum- mation of the channel bottom slope and additional slope of flooding wave. The introduced additional slope item enabled the equation to simulate the looped shape of the stage-discharge relationship. The local and convective inertia items are removed from the original Saint-Venant momentum equation for simplificatiorfs sake. The simplified equation is then linearized by first logarithmized element of the equation, and then polynomial and power series expansions for the steady discharge and additional slope items are conducted. Fi- nally, the LSM is used to estimate the parameters in the linearized equation. The results of the method in 3 cases show that, the re- suiting fitted equation can effectively simulate the observed relation. The biased code test, fitness test and biased value test on the simulation results are conducted. The results show that they completely meet the requirements stipulated in the national standard ＂Code for Hydrologic Data Compilation＂, therefore confirming the effectiveness of applying the LSM to the optimization of the looped stage-discharge relationships.