基于ARMA模型的水文序列相依变异分级方法及验证

受自然和人为等因素的影响,水文情势和地理环境不断发生显著变化,不同水文要素形成的水文时间序列常呈现出一定的相依性。为定量研究水文序列中的这种相依现象,本文以自回归滑动平均模型ARMA为例,选取原始水文序列与其相依成分间的相关系数为衡量标准,提出对相依变异强弱程度分级的一种方法。先用公式推导的方式从原理上阐明相关系数与序列的自回归系数和滑动平均系数存在的关系,从而建立相关系数与序列自相关系数的联系,再选择合理阈值作为分级界限,把相关系数划分为5段区间,对应描述5种不同强弱的相依变异程度。分别以较低阶数的ARMA模型为例,通过统计试验验证了以相关系数作为分级指标的合理性。将所提方法分别应用于模拟时间序列和实测水文序列,并结合物理成因从气候变化和人类活动两个方面对实测径流序列的相依变异分级结果进行了分析与验证,结果表明该方法合理可靠。

ARMA model-based classification method of hydrological series dependence variability and its verification

Hydrological processes in many basins and regions worldwide are changing significantly because of the natural and human factors such as continuous global climate change and frequent human activities in recent years. The hydrological time series formed by different hydrological elements often shows certain dependence. This paper takes ARMA model as an example, and selects the correlation coefficient between the original hydrological series and its dependence component as an index. A new classification method for significance evaluation of hydrological dependence variability was proposed to quantitatively study this dependence phenomenon in hydrological series. By deriving the expression of correlation coefficient between the original series and its dependence component, the relationship between correlation coefficient and autocorrelation coefficient is constructed. And then choosing reasonable thresholds of correlation coefficient,this method divides significance degree of dependence into five levels:no,weak,mid,strong,and drastic. The lower order ARMA models were taken as examples,the reasonability of the index used in this method was verified through Monte-Carlo experiments. The proposed method is applied to the simulated time series and the observed hydrological series,and the results of the dependence variability classification for the observed runoff series are analyzed and verified from the aspects of climate change and human activities combined with the physical causes. The results show that the method is reasonable and reliable. Therefore,it is helpful to understand the complex evolution law of hydrological process and quantitatively study the impact of environmental change on hydrological variability.