参考作物蒸腾量的多重分形特性分析

分析ET(Evapotranspiration,参考作物蒸腾量)的动力学特性,有助于进行中长期需水量的分析与预测。将多重分形特性分析方法应用于1978-2007年间30 a汉江流域3个典型站点(钟祥、天门、武汉)的参考作物ET时间序列。结果表明,逐日参考作物ET序列不仅具有不规则的高频振荡的特征,而且还具有明显的分形行为;在不同时间宽度(日、旬、月)下,逐日参考作物ET序列的多重分形特征最强。进一步的分析结果表明,序列中脉动引起的波动相关性和极端事件引起的胖尾概率等都是引起多重分形特征形成的原因。结合趋势转折分析方法发现:不同时间阶段内的多重分形特征显著;但在不同的时间段内,多重分形谱和局部分维宽度等都受到了极端事件的影响,且影响幅度与所处流域内的位置有关。     

黄河上游月径流序列多尺度特性分析

采用Hilbert-Huang变换(HHT)方法对黄河上游贵德站、小川站和兰州站的天然月径流序列进行分析,分解得到不同尺度下的固有模态函数,然后结合重标度极差(R/S)分析法分析了各阶模态函数及天然月径流量,得到Hurst指数和分维数,并对河川径流序列的波动周期性、分形特征、趋势性进行了分析。结果表明:黄河上游1929—1997年的天然月径流具有1 a以下、1.6 a、2～3 a、5～8 a、15～32 a的波动周期和自相似性及反持续的长程相关性。     

大坝变形实测数据的多重分形特征解析方法

为更好地分析大坝变形实测数据的波动特征进而评价变形的整体性态,以某混凝土重力坝的实测数据为凭,将多重分形理论应用于大坝变形性态分析中,利用MF-DFA、MV-MFDFA和A-MFDFA解析变形性态的多重分形特征及其非对称性。结果表明,无论是多测点或单测点,实测序列均具有明显的多重分形特征,并且这种多重分形特征具有明显的非对称特性;实测序列从多测点到单测点、从整体波动到局部趋势均表现出良好的记忆性和长程相关性特征,在水位等大波动因素的影响下,该坝坝顶水平位移发展良好,大坝整体状态稳定。     

MF-DFA在大坝安全监测序列分析和整体性态识别中的应用

为更好地分析监测序列的波动特征进而识别大坝整体性态演变规律,将多重分形消除趋势波动分析(MF-DFA)方法应用到大坝监测序列分析,并以一混凝土坝垂线监测序列为例,通过单个测点、环境量的长程相关性和多重分形特征分析及3个不同坝段测点比较,结果表明:坝体变形序列具有较强的多重分形特征,大波动受温度和库水位的周期性变化影响,小波动则受水位的频繁涨落控制;同时,溢流坝段和挡水坝段又因其环境荷载条件和工作机理不同波动特征略有差异;总体看,变形序列受环境量控制,大坝整体性态正常。实例分析结果表明MF-DFA可以从局部和整体两个层面评价大坝的工作性态及其演变规律。     

河道水沙变化过程的多重分形研究——以长江重庆河段为例

河道水沙变化过程具有非线性特征,基于长江寸滩站、朱沱站和嘉陵江北碚站(简称"三站")1955-2011年的水文资料,应用多重分形消除趋势波动分析法(MF-DFA方法),研究长江重庆河段水沙变化过程的多重分形特征。结果表明:三站日流量和日输沙率序列具有多重分形特征,该多重分形特征是由序列的长程相关性引起的;日流量序列的奇异谱呈右钩状曲线,小涨落的影响在序列中占优势,日输沙率序列的奇异谱对称,大小涨落的标度行为在序列中基本一致;水沙时序变化的复杂程度可用多重分形谱宽Δα表征,且日输沙率序列的Δα相对较大,变化更为复杂;不同时段水沙序列的谱曲线形状存在较大差异,丰水丰沙时序的谱曲线较宽,顶部较圆滑,Δα较大,枯水枯沙时序的谱曲线较窄,顶部较尖锐,Δα较小。     

基于ICEEMDAN-MFDFA的广东日降水序列的多重分形特征

【目的】降水时间序列是典型的非平稳、非线性时间序列，在全球变暖的背景下呈现出明显的复杂波动特征。通过全面考察广东日降水序列的分形特征，为有效应对区域水旱灾害风险提供参考。【方法】引入改进的自适应噪声完全集合经验模态分解(ICEEMDAN)方法改善传统多重分形去趋势波动分析(MFDFA)方法在去趋势过程中的不足，利用ICEEMDAN-MFDFA方法得到1973—2021年广东日降水序列的多重分形结果。【结果】结果显示：广东日降水序列具有复杂的多重分形特征，多重分形谱表现为右偏、左勾状，Hurst指数小于0.5;各项多重分形谱参数呈现阶段性上下波动特征，谱宽、不对称指数、谱端高差和Holder指数的极值分别达到1.00、-0.72、1.01和0.12;降水序列的多重分形谱宽与谱端高差、不对称指数与Holder指数两两之间有着密切的联系。【结论】结果表明：降水序列内部演变的波动行为具有长程相关性，表现为反持续性；日降水对小幅度的局部气候波动较敏感，且有增大的趋势；当降水复杂性越强时对应着日降水增大的态势越明显，当多重分形谱的右偏程度越弱时其精细结构越丰富；与传统方法相比，ICEEMDAN-M...     

变化环境下流域气象水文要素的相关性演化

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。     

不同时间尺度径流的多重分形特征解析

径流时间序列的变化过程呈现出复杂的非线性特征,分形是非线性时间序列的典型特点。以锦江流域为例,研究了1967年～2018年的年、月尺度平均流量时间序列的多重分形结构特征。分析结果表明,锦江流域过去52年的年、月尺度的平均流量均表现出明显的多重分形特征。其中,年平均流量的波动幅度最小,月平均流量中9月平均流量序列的波动幅度较大,即9月平均流量表现出强烈的多重分形特征;锦江流域10月平均流量波动行为的混乱程度和奇异性最低,而11月平均流量波动行为的混乱程度和奇异性最高。研究说明锦江流域年、月平均流量时间序列具有较为复杂的混乱特性,可为锦江流域年、月平均流量的复杂性规律的解析提供依据。     

基于DFA的长江上游径流演化标度特性研究

针对河川径流时序所具有的非线性与非平稳性特征,运用消除趋势波动分析法（Detrended Fluctuation Analysis,DFA）对长江上游控制性水文站-宜昌站1878～2001年的月均流量时序的演化特征进行了研究,以揭示该流域河川径流的长程相关性及其内在规律性。结果表明：长江上游河川径流时序波动具有长程相关性,且其标度指数具有显著的区域性,即在短时间尺度上具有强烈的正持续性,在长时间尺度上具有强烈的负持续性,且其正持续性至多可持续19个月,显示了长江上游流域产汇流系统演化具有复杂的物理机制     

基于DFA的长江上游径流演化 标度特性研究

针对河川径流时序所具有的非线性与非平稳性特征,运用消除趋势波动分析法（Detrended Fluctuation Analysis,DFA）对长江上游控制性水文站—宜昌站1878～2001年的月均流量时序的演化特征进行了研究,以揭示该流域河川径流的长程相关性及其内在规律性。结果表明：长江上游河川径流时序波动具有长程相关性,且其标度指数具有显著的区域性,即在短时间尺度上具有强烈的正持续性,在长时间尺度上具有强烈的负持续性,且其正持续性至多可持续19个月,显示了长江上游流域产汇流系统演化具有复杂的物理机制。     

Multiscaling Analysis of Monthly Runoff Series Using Improved MF-DFA Approach

An improved multifractal detrended fluctuation analysis(MF-DFA) method is applied to analyze the long-term monthly runoff records of a hydrological station in the Yangtze River with seasonal trend eliminated, through which the long-range correlation and the multifractal characteristics have been found. The multifractal spectrum has been fitted by a generalized expression of the multiplicative cascade model, and the results show that the monthly runoff series has strong multifractal characteristics. Comparing the results for the original runoff series with those of shuffled and surrogate series, it concludes that the multifractal characteristics of the monthly runoff time series is due to the broadness of both the probability density function and long-range correlation, and the broadness of the probability density function is dominant.     

Precipitation Complexity Measurement Using Multifractal Spectra Empirical Mode Decomposition Detrended Fluctuation Analysis

The stability of current methods of complexity measurement are generally Inefficient. In this study, multifractal spectra (MFS) analysis, which depends on empirical mode decomposition detrended fluctuation analysis (EMD–DFA), was used to measure the complexity of the monthly precipitation series from 1964 to 2013 (50 years) of 11 districts in Harbin, Heilongjiang Province, China. By comparing the anti-noise capability of MFS–EMD–DFA with that of conventional complexity measurement approaches, such as sample entropy, Lempel–Ziv complexity, and approx mate entropy, it was established that MFS–EMD–DFA has greater robustness in anti-noise jamming, and thus it could be applied more widely. The precipitation series complexity strength map of the 11 regions was drawn using a geographical information system. This study analyzed the correlation between precipitation and some meteorological factors and then ranked their strengths. The results showed that many meteorological factors have strong connections with the regional precipitation series in the study area. This study provided a solid foundation for further extraction of hydrological information in Harbin and proposed a new method for complexity analysis. The novel MFS–EMD–DFA approach could also be applied to the analysis of multifractal characteristics as well as complexity measurement in various other disciplines.     

The effects of extremes and temporal scale on multifractal properties of river flow time series

For accurate forecasting of extreme events in rivers, streamflow time series with sub‐daily temporal resolution (1–6 hour) are preferable, but discharge time series for long rivers are usually available at daily or monthly resolution. In this study, the scaling properties of hourly and daily streamflow time series were measured. As an innovation, the effects of extreme values on the multifractal behavior of these series were evaluated. Interestingly, both hourly and daily discharge records led to nearly identical scaling trends and identical crossover times. Daily and hourly discharge time series appeared to be non‐stationary when the timescale ranged from 75 to 366 days. Otherwise, the signals may be considered stationary time series. In addition, the results indicated that the extreme values strongly contribute to the multifractality of the series. The width of singularity spectra decreased considerably when the extreme events were removed from both hourly and daily discharge records.     

The Research of Monthly Discharge Predictor-corrector Model Based on Wavelet Decomposition

Based on wavelet analysis theory, a wavelet predictor-corrector model is developed for the simulation and prediction of monthly discharge time series. In this model, the non-stationary time series of monthly discharge is decomposed into an approximated time series and several stationary detail time series according to the principle of wavelet decomposition. Each one of the decomposed time series is predicted, respectively, through the ARMA model for stationary time series. Then the correction procedure is conducted for the sum of the prediction results. Taking the monthly discharge at Yichang station of Yangtse River as an example, the monthly discharge is simulated by using ARMA model, seasonal ARIMA model, BP artificial neural network model and the wavelet predictor-corrector model proposed in this article, respectively. And the effect of decomposition scale for the wavelet predictor-corrector model is also discussed. It is shown that the wavelet predictor-corrector model has higher prediction accuracy than the some other models and the decomposition scale has no obvious effect on the prediction for monthly discharge time series in the example.     

Emotional ANN (EANN) and Wavelet-ANN (WANN) Approaches for Markovian and Seasonal Based Modeling of Rainfall-Runoff Process

The hydrological time series have three principle components (autoregressive, seasonality and trend) and the performance of the models is strongly related to the nature of these components. The current research examines the accuracy of two Artificial Neural Network (ANN) based approaches for rainfall-runoff (r-r) modeling of two catchments with different geomorphological conditions at monthly and daily time scales. The techniques proposed here are hybrid wavelet-ANN (WANN) model, as a multi-resolution forecasting tool and Emotional Artificial Neural Network (EANN) (a new generation of ANN based models) which serves artificial emotional factors as well as classic bias and weights parameters. The obtained results for monthly modeling show that WANN could perform better than the simple feed forward neural network (FFNN) model up to 40% and 35% in terms of verification and training efficiency criteria due to significant seasonality involved in the monthly time series of the process. On the other hand, the obtained results for daily modeling via FFNN and EANN, both as Markovian models, indicates the superiority of EANN over FFNN because of EANN capability to better learning of extraordinary and extreme conditions of the process in the training phase.     

Volterra模型在月径流预测中的应用研究

水文过程的月均径流序列存在着较明显的低维混沌特性,利用Volterra模型可以较好的预测低维混沌序列。引入低维混沌动力系统相空间坐标重构的Volterra自适应预测模型,对多年月均径流序列采用二阶Volterra自适应滤波器进行预测。以大渡河石棉站33年的月径流量为例进行验证,预测相对误差<10%的天数为73.3%,相对误差<20%的天数为90.0%,与人工神经网络预测结果对比表明该方法具有较满意的准确率。     

基于混沌的小凌河流域月降水时间序列分析

小凌河流域是辽宁省西部地区较大的河流之一,近年来降水量的减少是影响该流域水资源开发利用的重要因素。本文以小凌河流域的典型测站-锦州水文站1951—2012年的月降水时间序列为例,采用混沌理论中的C-C法确定时间序列的延迟时间间隔,重构嵌入相空间,并利用G-P算法计算该序列的关联维数,结果表明,小凌河流域月降水时间序列存在明显的混沌特性。同时,采用主分量分析法予以验证。从而为进一步建立月降水预测模型奠定了基础。     

基于ASWPD-BO-GRU的月径流量预测模型

为提高月径流量预测精度,并针对传统分解集成径流预测模型错误使用未来数据的问题,提出并建立了基于自适应小波包分解（ASWPD）和贝叶斯优化（BO）的门控循环单元（GRU）月径流量预测模型（ASWPD-BO-GRU）。首先,利用ASWPD对原始月径流量时间序列进行分解,在不使用未来数据的前提下得到4个相对规律的分解子序列,以降低预测难度;然后,利用BO优选分解后的子序列对应的GRU模型超参数;最终,对每个子序列进行预测,将预测结果相加重组得出月径流量预测结果。将提出并建立的模型应用于黑河流域莺落峡水文站月径流量预测中,并与GRU、BO-GRU、WPD-BO-GRU模型（基于传统分解思想对原始月径流量时间序列整体进行分解的预测模型）的预测结果进行对比。结果表明：ASWPD-BO-GRU模型的纳什效率系数（NSE）为0.89,在实例应用中预测精度最高,说明ASWPD-BO-GRU模型在正确分解的前提下具有较高的预测精度和更强的泛化能力。     

Analysis of Irrigation Water Use Efficiency Based on the Chaos Features of a Rainfall Time Series

The chaos theory is used to analyze the mechanism behind the response of irrigation water use efficiency (IWUE) to rainfall in irrigation districts of the Heilongjiang Province in China. The Lyapunov exponent and correlation dimension of the monthly rainfall time series of eight large- and medium-sized irrigation districts are calculated, and the correlations between IWUE and certain factors are analyzed. The results indicate that the monthly rainfall time series of each district sample exhibits chaotic characteristics, and high correlations exist between IWUE and the chaos features of the monthly rainfall time series. Furthermore, the scale of the irrigation district has some correlations with IWUE. The research results show that the difference in the temporal distribution of rainfall and the difference in the scale of an irrigation district both impact IWUE. This study provides a theoretical basis for improving the usage efficiency of water resources in the irrigation districts of Heilongjiang Province and for increasing the IWUE.