为了探究流域气象水文要素间相关性结构及其演化, 采用交叉小波分析、去趋势波动分析( DFA) 、去趋势互相关分析( DCCA) 和去趋势偏互相关分析( DPXA) 对渭河流域 1960- 2015 年的气象水文数据( 年降水量、年蒸发皿蒸发量、年径流深等) 进行了时频域相关性分析和长程相关性分析, 探讨气象水文要素间的相关性结构变化和长程相关性特征。交叉小波分析表明, 研究期内蒸发、降水、径流任意两因子间相关性在不同时频域存在差异, 相关结构上 存在 1~ 2 和 8 a 的相似主导周期, 宏观上降水2径流间多尺度相关结构发生退化, 共振周期减少。长程相关分析表明, 径流、蒸发和降水序列的 Hurst 指数均大于 0.5, 表现出良好的长持续性特征, 当前降水( 径流、蒸发) 会对未来 某一时刻的降水( 径流、蒸发) 产生影响; DCCA 结果表明, 降水-径流间表现出长程相关性, 而降水-蒸发和径流-蒸发 呈长程反相关性, 呈现出不同的长程互相关结构; DPXA 结果表明, 扣除第三因子影响后, 降水-蒸发和径流-蒸发长程相关性发生突变, 从而降水-径流、降水-蒸发和径流2蒸发两两间均呈长程互相关性, 暗示降水、径流和蒸发三者间 长程相关性的互馈特征, 相比于 DCCA 结果, DPXA 的结果显然更具有说服力。透过滑窗分析可发现降水-径流、降水-蒸发之间的长程互相关性在时域上没有发生突变, 未来降水量的可能增加将引起径流量增大, 并间接引起渭河流域受水量制约的蒸发量增大; 径流-蒸发间长程互相关性于 1962 年由长程反相关突变为长程相关, 随后长程相关性持续增强, 标志着渭河流域未来蒸发的变化可能会引发更大的径流波动。

In order to evaluate and investigate the correlation structures of hydro-meteo rological variables in the Wei River basin, the t ime-frequency domain correlation analysis and long-range correlation analysis were carried out by cross wavelet analysis, detrended fluctuat ion analysis ( DFA ) , detrended cross-correlation analysis ( DCCA) , and detrended partial cross-correlation analysis ( DPXA) . The results of cross wavelet analysis show that correlation between precipitation ( P) , panevaporation ( E) , and runoff depth ( R) differ at different time-frequency domain. In terms of correlation structure, there were 122 years and 82 year periods existed in the system co nsisted of P, R, and E. On the macroscale, the multi-scale correlation structures between precipitation and runoff degraded and resonance period were reduced. Long-range correlation analysis showed that the Hurst index of R, E, and P sequences were greater than 0. 5, showing long-term persistence characteristics. The current precipitation ( runoff and evaporation) might have an impact on the pr ecipitation ( runoff and evaporation) at a certain time in the future. The DCCA results show that there was a long-rang ecorrelation between P and R, while an inverse long-range correlation existed between P2E and R2E, showing different cross-correlation structures. The DPXA results show that the long-range correlation change and turn into long-rang ecorrelation, implying the feed-back characterist ics of long-range correlation among P, R, and E. Compared with the results of DCCA, the DPXA was more persuasive. The sliding-window analysis ( 30 years) showed that the long-rang ecorrelation between P2R and P2E did not change in the time domain, and the possible incr ease of precipitation in the future may lead to the increase of runoff and indirectly lead to the incr ease of evapor ation in the Wei River basin. The long-range correlation betwen R2E changed from long-range inverse correlation to long-range correlation in 1962, and then the long-rang ecorrelation continued to increase, indicating that future evaporation changes in the Wei River basin may cause more runoff fluctuations. Therefore, water resources management based on ET control may have a certain significance to increase the av ailable water amount in the Wei River basin.

国家自然科学基金( 51979005) ; 陕西省水利厅科技计划( 2018slkj211) ; 陕西省自然科学基础研究计划( 2020JM2250)