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

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XIE Ping ，HUO Jingqun ，SANG Yanfang ，WU Linqian ，LI Yaqing ，NIU Jingyi 1
（1. State Key Laboratory of Water Resources and Hydropower Engineering Science，Wuhan University，Wuhan 430072，China；
2. Key Laboratory of Water Cycle and Related Land Surface Processes，Institute of Geographic Sciences and Natural Resources Research，
Chinese Academy of Sciences，Beijing 100101，China）
Abstract： 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 de⁃
pendence. 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 depen⁃
dence 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 autocorre⁃
lation coefficient is constructed. And then choosing reasonable thresholds of correlation coefficient，this meth⁃
od divides significance degree of dependence into five levels：no，weak，mid，strong，and drastic. The low⁃
er order ARMA models were taken as examples，the reasonability of the index used in this method was ver⁃
ified 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 help⁃
ful to understand the complex evolution law of hydrological process and quantitatively study the impact of
environmental change on hydrological variability.
Keywords： auto-regressive moving average model； correlation coefficient； statistical test； classification；
time series；dependence variability
（责任编辑：耿庆斋）
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