非一致性条件下的年降雨量插补延长方法

Study on interpolation and extrapolation method of annual rainfall under non-consistency condition

为了满足水文水利计算对资料的要求,需要对短系列或不完整的水文资料进行插补延长。然而,在变化环境下,水文系列往往难以满足一致性要求,非一致性条件下采用传统常参数回归方程进行插补延长的适用性面临挑战。针对这一问题,提出采用时变参数回归方程解决非一致性条件下水文资料插补延长问题,并采用梯度下降法求解方程参数。选取纯池站和七步站60 a(1958—2017年)实测年降雨量资料,首先采用Mann-Kendall检验法对资料进行趋势和突变分析,然后分别建立时变参数和常参数线性回归方程,采用梯度下降法求解各方程参数,最后对计算结果进行评价分析。结果表明,在解决非一致性条件下的插补延长问题上,时变参数回归方程明显优于常参数回归方程,且插补延长结果精度较高、合理可靠。

In order to meet the requirement of data in hydrology and water conservancy calculation,it is necessary to interpolate and extrapolate the short or incomplete hydrologic series.However,in the changing environments,the hydrologic series often fails to meet the requirement of consistency,which causes the poor applicability of traditional constant parameter of regression equation for interpolation and extrapolation.Aiming at this problem,the regression equation of time-varying parameter was proposed to solve the interpolation and extrapolation of the hydrologic series under non-stationary condition,and the gradient descent algorithm(GDA)was used to solve the equation parameters.The measured annual rainfall series of Chunchi and Qibu stations in 60 years(1958~2017)were selected.First,the Mann-Kendall test method was used to analyze the trend and mutation of series.Then,the linear regression equations of time-varying and constant parameters were established respectively,and GDA was used to solve the parameters.Finally,the results were evaluated and analyzed.It was concluded that the time-varying parametric regression equation is superior to the constant parametric regression equation in solving the problem of interpolation and extrapolation under non-stationary condition,and the results of the time-varying parametric regression equation are accurate,reasonable and reliable.