加约束正交多项式在水位流量关系拟合中的应用

Application of orthogonal polynomials with constraints to fitting of stage-discharge relation

水位流量关系 (Z～ Q)拟合是水文资料电算整编的基础。任一断面的 Z～ Q关系受其上下游河段综合水力条件的影响 ,常在其水位变幅内水力条件多变 ,以一种线型 (函数 )拟合不能满足精度要求。文章考虑生产实际中常见的测站控制条件 ,在普通正交多项式中增加约束条件 ,实现分段拟合及通过某一固定点的 Z～ Q关系拟合 ,导出不同约束条件下正交多项式系数求解算式。经安徽省皖南山区十余个断面近 60个站年资料验证 ,拟合精度大有改善 ,此模型已在生产中作为常规方法使用。

Fitting of stage-discharge relation (Z～Q) is foundational to hydrologic data processing by computer. Cross-section stage-discharge relation (Z～Q) are usually influenced by the whole hydraulic conditions of upstream and downstream, and the hydraulic conditions in fluctuation range of the stage are so changeable that fitting of one curve form can not be necessarily precise. This paper deduces orthogonal polynomials coefficient calculation formula under different constraint conditions, with consideration of normal station control conditions in practice and the constraint conditions in common orthogonal polynomials that can be used to realize a coincidence with separated segments and certain Z～Q point. Through fitting with the annual data obtained from more than ten cross-sections at nearly sixty stations located in the southern mountainous area of Anhui province, the accuracy of the presented method has been improved very much. The pattern has now been used as an ordinary method in practice.