Configuration of hydrological processes in a steep hillslope through causality analysis of soil moisture measurements

The vertical and lateral profiles of temporal variations in soil moisture are important for understanding the hydrological process along hillside transects. In this study, relationships among measured soil moistures were explored to configure the hydrological contributions of different flowpaths. All the measured soil moistures included a common stochastic structure because rainfall, the hydrometeological driver, is the main factor that determines the soil moisture response feature, and the infiltration process through the topsoil at a shallow depth is also common in all measured soil moisture histories. Therefore, the relationships between the measured series are also affected by both rainfall and topsoil infiltration. The common stochastic structure of the soil moisture series was removed via a prewhitening procedure. A systematic analysis procedure is presented to delineate the exclusive causal relationships among multiple soil moisture measurements. A monitoring system based on multiplexed time domain reflectometry was used to obtain soil moisture time series along two transects on a steep hillslope during the rainy season. The application of the proposed method for monitoring points in two adjacent locations provided 8, 12, 14, and 13, 16, 22 causal relationships for vertical, lateral in parallel, and diagonal directions, respectively, along the two transects. The point‐based contributions of the internal flowpath can be evaluated as the correlation is normalized in the context of inflow and outflow. The hydrological processes in the soil layer, vertical flow, lateral flow, downslope recharge, and return flow were quantified, and the relative importance of each hydrological component was determined to improve our understanding of the hydrological processes along the two transects of the study area. Copyright © 2011 John Wiley & Sons, Ltd.     

Accuracy assessment of optimum interpolation in multichannel precipitation analysis

The accuracy of an optimum interpolation technique in filling missing values in multichannel (or multisite) hydrologic series containing time-coincident data gaps is examined. The applied methodology is based on the maximum entropy method (MEM) of spectral estimation or multivariate autoregressive modeling and heavily depends upon the properties of multichannel prediction error filter (PEF). Six precipitation time series spatially located within a hydrologic basin are used and time-coincident artificial gaps are created in all six series. The performance of the technique is assessed by comparing the filled-in series to the observed and by employing spectral analysis. The results reveal the usefulness of the method in multichannel hydrologic analysis.     

Accuracy assessment of optimum interpolation in multichannel precipitation analysis

The accuracy of an optimum interpolation technique in filling missing values in multichannel (or multisite) hydrologic series containing time-coincident data gaps is examined. The applied methodology is based on the maximum entropy method (MEM) of spectral estimation or multivariate autoregressive modeling and heavily depends upon the properties of multichannel prediction error filter (PEF). Six precipitation time series spatially located within a hydrologic basin are used and time-coincident artificial gaps are created in all six series. The performance of the technique is assessed by comparing the filled-in series to the observed and by employing spectral analysis. The results reveal the usefulness of the method in multichannel hydrologic analysis.     

The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology

This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.     

The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology

This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.     

Development of stochastic dynamic Nash game model for reservoir operation II. The value of players’ information availability and cooperative behaviors

Stochastic dynamic game models can be applied to derive optimal reservoir operation policies by considering interactions among water users and reservoir operator, their preferences, their levels of information availability and cooperative behaviors. The stochastic dynamic game model with perfect information (PSDNG) has been developed by [Ganji A, Khalili D, Karamouz M. Development of stochastic dynamic Nash game model for reservoir operation. I. The symmetric stochastic model with perfect information. Adv Water Resour, this issue]. This paper develops four additional versions of stochastic dynamic game model of water users interactions based on the cooperative behavior and hydrologic information availability of beneficiary sectors of reservoir systems. It is shown that the proposed models are quite capable of providing appropriate reservoir operating policies when compared with alternative operating models, as indicated by several reservoir performance characteristics. Among the proposed models, the selected model by considering cooperative behavior and additional hydrologic information (about the randomness nature of reservoir operation parameters), as exercised by reservoir operator, provides the highest attained level of performance and efficiency. Furthermore, the selected model is more realistic since it also considers actual behavior of water users and reservoir operator in the analysis.     

Investigating hydrologic responses to spatio‐temporal characteristics of storms using a Dynamic Moving Storm generator

A synthetic storm generator—Dynamic Moving Storm (DMS)—is developed in this study to represent spatio‐temporal variabilities of rainfall and storm movement in synthetic storms. Using an urban watershed as the testbed, the authors investigate the hydrologic responses to the DMS parameters and their interactions. In order to reveal the complex nature of rainfall–run‐off processes, previously simplified assumptions are relaxed in this study regarding (a) temporal variability of rainfall intensity and (b) time‐invariant flow velocity in channel routing. The results of this study demonstrate the significant contribution of storm moving velocity to the variation of peak discharge based on a global sensitivity analysis. Furthermore, a pairwise sensitivity analysis is conducted to elucidate not only the patterns in individual contributions from parameters to hydrologic responses but also their interactions with storm moving velocity. The intricacies of peak discharges resulting from sensitivity analyses are then dissected into independent hydrologic metrics, that is, run‐off volume and standard deviation of run‐off timings, for deeper insights. It is confirmed that peak discharge is increased when storms travel downstream along the main channel at the speed that corresponds to a temporal superposition of run‐off. Spatial concentration of catchment rainfall is found to be a critical linkage through which characteristics of moving storms affect peak discharges. In addition, altering peak timing of rainfall intensity in conjunction with storm movement results in varied storm core locations in the channel network, which further changes the flow attenuation effects from channel routing. For future directions, the DMS generator will be embedded in a stochastic modelling framework and applied in rainfall/flow frequency analysis.     

Nonlinear multivariate rainfall–stage model for large wetland systems

Wetland restoration is often measured by how close the spatial and temporal water level (stage) patterns are to the pre-drainage conditions. Driven by rainfall, such multivariate conditions are governed by nonstationary, nonlinear, and nonGaussian processes and are often simulated by physically based distributed models which are difficult to run in real time due to extensive data requirements. The objective of this study is to provide the wetland restorationists with a real time rainfall–stage modeling tool of simpler input structure and capability to recognize the wetland system complexity. A dynamic multivariate Nonlinear AutoRegressive network with eXogenous inputs (NARX) combined with Principal Component Analysis (PCA) was developed. An implementation procedure was proposed and an application to Florida Everglade’s wetland systems was presented. Inputs to the model are time lagged rainfall, evapotranspiration and previously simulated stages. Data locations, preliminary time lag selection, spatial and temporal nonstationarity are identified through exploratory data analysis. PCA was used to eliminate input variable interdependence and to reduce the problem dimensions by more than 90% while retaining more than 80% of the process variance. A structured approach to select optimal time lags and network parameters was provided. NARX model results were compared to those of the linear Multivariate AutoRegressive model with eXogenous inputs. While one step ahead prediction shows comparable results, recursive prediction by NARX is far more superior to that of the linear model. Also, NARX testing under drastically different climatic conditions from those used in the development demonstrates a very good and robust performance. Driven by net rainfall, NARX exhibited robust stage prediction with an overall Efficiency Coefficient of 88%, Mean Square Error less than 0.004 m², a standard error less than 0.06 m, a bias close to zero and normal probability plots show that the errors are close to normal distributions.     

Time series and stochastic analyses to study the hydrodynamic characteristics of karstic aquifers

The regional study of hydrodynamic characteristics of karstic aquifers is challenging because of the great variety of lithology and the structural complexity found in carbonate formations. In order to improve this situation, a combined approach of time series and stochastic analyses was adopted to assess the hydrodynamic behaviour of the karstic aquifers. To achieve this, daily flow rates of 20 springs were taken from the 11 most significant aquifer units of the Basque Country. The results demonstrate the presence of memory effects, which modulated the input rainfall for short‐, medium‐ and long‐term storage capacity, resulting in hydrodynamic properties such as system memory, response time and mean delay between input and output. They reflect the storage and the manner in which these are filled and emptied, thus indicating the karstification of the aquifer. Likewise, the hydrodynamic and hydraulic classification obtained from the stochastic analysis provides a complementary approach to characterize the hydraulic behaviour of the studied karstic aquifers. The discussed examples indicate that this approach provides an excellent method to research hydrological karst systems. It is also shown that the use of hydrologic time series, alone, does not lead to a satisfactory classification of the hydrodynamic characteristics. Therefore, the general approach to hydrological regionalization in karst areas should take into account the structural complexity, heterogeneity of the lithology and the degree of karstification. Only in this case will the regionalization be physically founded, leading to a regional understanding of the hydrodynamic characteristics and flow conditions in a karst aquifer. Copyright © 2009 John Wiley & Sons, Ltd.     

Investigation of changes in characteristics of hydrological time series by Bayesian methods

A review of literature reveals the inadequacy of Intervention analysis and spectrum based methods to adequately quantify changes in hydrologic times series. A Bayesian method is used to investigate the statistical significance of observed changes in hydrologic times series and the results are reported herein. The Bayesian method is superior to the previous methods.     

基于迭代PCA的GPS时间序列震后形变估计方法和应用

GPS时间序列的震后形变分析对于研究区域震后形变机制和岩石圈流变学特性以及维持国际动态地球参考框架具有重要意义.本文在现有参数估计方法的基础上,提出兼顾震后形变衰减特征空间相关性和整体建模的"迭代PCA参数估计方法",并利用模拟数据证实了新方法可以获取更稳健可靠的震后形变、同震形变和震间速度参数.最后,以37个新西兰GPS连续站坐标时间序列为例,利用迭代PCA方法提取了2016年11月13日Kaikoura地震共性的震后形变时间演化过程和各站点的震后形变,并定量分析了震后形变对地表速度的影响.结果表明各站的震后形变在时间域上以衰减常数τ为4天的对数模型持续松弛;空间域上南岛北东部和北岛最南部震后形变较大,其中,最大震后形变点为cmbl站,截至2017年6月10日NEU方向累计的震后形变分别达到107mm,135mm和187mm,地表速度分别达到133.58mm·a-1,112.05mm·a-1和175.58mm·a-1,仍高于稳定的震间速度.     

Multivariate analysis of soil moisture history for a hillslope

In this study, the spatial distribution of measured soil moisture was analyzed on the platform of multivariate modeling. Soil moisture time series for two seasons were selected and used for analysis to reveal similarities and differences in soil moisture responses for a few rainfall events. The development of a soil moisture transport process that considers the representative element volume and uncertainty of soil media provides the hydrological basis for time series modeling. The systematic procedure of Box–Jenkins with noise modeling was used to delineate the final models for all monitoring points. The physical basis of mass balance and the continuity in inflow contribution, as well as statistical criteria, were used in the model selection procedure. Heuristic approaches provide the spatial distribution of selected models along the transect of a hillside. Comparative analysis for two different depths and seasons provide an understanding of the variation in soil moisture transfer processes at the hillslope scale. Differences in soil moisture models for both depths and seasons are associated with eco-hydrological processes. The relationships between distributed topographic features and modeling results were explored to configure dominant hydrological processes for each season.     

Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach

Abstract

Hydrological models are commonly used to perform real-time runoff forecasting for flood warning. Their application requires catchment characteristics and precipitation series that are not always available. An alternative approach is nonparametric modelling based only on runoff series. However, the following questions arise: Can nonparametric models show reliable forecasting? Can they perform as reliably as hydrological models? We performed probabilistic forecasting one, two and three hours ahead for a runoff series, with the aim of ascribing a probability density function to predicted discharge using time series analysis based on stochastic dynamics theory. The derived dynamic terms were compared to a hydrological model, LARSIM. Our procedure was able to forecast within 95% confidence interval 1-, 2- and 3-h ahead discharge probability functions with about 1.40 m³/s of range and relative errors (%) in the range [–30; 30]. The LARSIM model and the best nonparametric approaches gave similar results, but the range of relative errors was larger for the nonparametric approaches.

Editor D. Koutsoyiannis; Associate editor K. Hamed

Citation Costa, A.C., Bronstert, A. and Kneis, D., 2012. Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach. Hydrological Sciences Journal, 57 (1), 10–25.     

Information and complexity measures applied to observed and simulated soil moisture time series

Abstract

Time series of soil moisture-related parameters provide important insights into the functioning of soil water systems. Analysis of patterns within such time series has been used in several studies. The objective of this work was to compare patterns in observed and simulated soil moisture contents to understand whether modelling leads to a substantial loss of information or complexity. The time series were observed at four plots in sandy soils within the USDA-ARS OPE3 experimental watershed, for a year; precipitation and evapotranspiration (ET) were measured and estimated, respectively, and used for soil water flow simulation with the HYDRUS-1D software. The information content measures are the metric entropy and the mean information gain, and complexity measures are the fluctuation complexity and the effective measure complexity. These measures were computed based on the binary encoding of soil moisture time series, and used probabilities of patterns, i.e. probabilities of joint or sequential appearance of symbol sequences. The information content of daily soil moisture time series was much smaller than that of rainfall data, and had higher complexity, indicating that soil worked essentially as an information filter. Information content and complexity decreased and increased with depth, respectively, demonstrating the increase in the information filtering action of soil. The information measures of simulated soil moisture content were close to those of the measurements, indicating the successful simulation of patterns in the data. The spatial variability of the information measures for simulated soil moisture content at all depths was less pronounced than the one of measured time series. Compared with precipitation and estimated ET, soil moisture time series had more structure and less randomness in this work. The information measures can provide useful complementary knowledge about model performance and patterns in observation and modelling results.

Citation Pan, F., Pachepsky, Y. A., Guber, A. K., & Hill, R. L. (2011) Information and complexity measures applied to observed and simulated soil moisture time series. Hydrol. Sci. J. 56(6), 1027–1039.     

Matched block bootstrap for resampling multiseason hydrologic time series

A nonparametric method for resampling multiseason hydrologic time series is presented. It is based on the idea of rank matching, for simulating univariate time series with strong and/or long‐range dependence. The rank matching rule suggests concatenating with higher likelihood those blocks that match at their ends. In the proposed method, termed ‘multiseason matched block bootstrap’, nonoverlapping within‐year blocks of hydrologic data (formed from the observed time series) are conditionally resampled using the rank matching rule. The effectiveness of the method in recovering various statistical attributes, including the dependence structure from finite samples generated from a known population, is demonstrated through a two‐level hypothetical Monte Carlo simulation experiment. The method offers enough flexibility to the modeller and is shown to be appropriate for modelling hydrologic data that display strong dependence, nonlinearity and/or multimodality in the time series depicting the hydrologic process. The method is shown to be more efficient than the nonparametric ‘k‐nearest neighbor bootstrap’ method in simulating the monthly streamflows that exhibit a complex dependence structure and bimodal marginal probability density. Even with short block sizes, this bootstrap method is able to predict the drought characteristics reasonably accurately. Copyright © 2005 John Wiley & Sons, Ltd.     

云南GNSS时间序列共模分量提取分析

针对共模分量的精确获取问题,以2011—2018年云南31个GNSS连续站垂向时间序列为基础,选用区域叠加法和主成分分析法,提取得到共模分量的主要成分,对比分析了这两种方法的效果。结果表明:(1)由于云南垂向非线性运动空间一致性较好(测站间相关系数平均值为0.88),两种方法得到的共模分量较为一致;(2)两种方法提取得到的共模分量与全球水文负荷和大气负荷模型给出的位移时间序列接近(相关系数均为0.9),说明共模分量的主要成分为地表负荷变化引发的地壳垂向非构造运动;(3)共模分量不能用周期模型完全表示,还包含了年际间的运动差异等信息;(4)两种方法的空间滤波效果非常接近(WRMS减速比平均值都为0.70),测站的空间滤波效果与测站间相关系数呈显著的正相关。由于区域叠加法对测站数据完整率要求相对较低,因此建议当测站较少或者数据缺失较多时,采用区域叠加法;在测站较多且数据完整率较高时,建议采用主成分分析法。     

Analysis of seismic dynamical systems

A procedure is presented for the analysis of complex stationary time series for which the Fourier power spectra reveals broadband noise or broadened pulses. We first determine the Hurst exponent from which we may know whether the time series under study is mainly random or if the data points present correlations. If the data are correlated, a chaotic analysis will reveal whether they may be interpreted as a low dimensional nonlinear system (defined by a low correlation dimension and a finite and positive Kolmogorov entropy and largest positive Lyapunov exponent) or as a stochastic process. We have studied three kind of temporal series: inter-event time series of infrasonic pulses recorded at Stromboli volcano, and, S-coda waves and microseisms, that have been recorded at the eastern Pyrenees. Results show that microseisms and Coda waves can be modeled as a low dimensional deterministic system, Correlation dimensions 2.3, 3.2, respectively. At the contrary infrasonic has resulted stochastic. This chaotic character can be attributed to the medium properties. Coda waves with scattering through a fractal distribution of scatters or to multiple reflection inside resonators (for example sedimentary basins) and microseisms as a propagation of wave guide of variable cross section which have the same temporal characteristics as a nonlinear forced oscillator.     

Discrete wavelet‐based trend identification in hydrologic time series

Trend identification is a substantial issue in hydrologic series analysis, but it is also a difficult task in practice due to the confusing concept of trend and disadvantages of methods. In this article, an improved definition of trend was given as follows: ‘a trend is the deterministic component in the analysed data and corresponds to the biggest temporal scale on the condition of giving the concerned temporal scale’. It emphasizes the intrinsic and deterministic properties of trend, can clearly distinguish trend from periodicities and points out the prerequisite of the concerned temporal scale only by giving which the trend has its specific meaning. Correspondingly, the discrete wavelet‐based method for trend identification was improved. Differing from those methods used presently, the improved method is to identify trend by comparing the energy difference between hydrologic data and noise, and it can simultaneously separate periodicities and noise. Furthermore, the improved method can quantitatively estimate the statistical significance of the identified trend by using proper confidence interval. Analyses of both synthetic and observed series indicated the identical power of the improved method as the Mann–Kendall test in assessing the statistical significance of the trend in hydrologic data, and by using the former, the identified trend can adaptively reflect the nonlinear and nonstationary variability of hydrologic data. Besides, the results also showed the influences of three key factors (wavelet choice, decomposition level choice and noise content) on discrete wavelet‐based trend identification; hence, they should be carefully considered in practice. Copyright © 2012 John Wiley & Sons, Ltd.     

Simulation of historical temperatures using a multi‐site,multivariate block resampling algorithm with perturbation

Stochastic weather generators have evolved as tools for creating long time series of synthetic meteorological data at a site for risk assessments in hydrologic and agricultural applications. Recently, their use has been extended as downscaling tools for climate change impact assessments. Non‐parametric weather generators, which typically use a K‐nearest neighbour (K‐NN) resampling approach, require no statistical assumptions about probability distributions of variables and can be easily applied for multi‐site use. Two characteristics of traditional K‐NN models result from resampling daily values: (1) temporal correlation structure of daily temperatures may be lost, and (2) no values less than or exceeding historical observations can be simulated. Temporal correlation in simulated temperature data is important for hydrologic applications. Temperature is a major driver of many processes within the hydrologic cycle (for example, evaporation, snow melt, etc.) that may affect flood levels. As such, a new methodology for simulation of climate data using the K‐NN approach is presented (named KnnCAD Version 4). A block resampling scheme is introduced along with perturbation of the reshuffled daily temperature data to create 675 years of synthetic historical daily temperatures for the Upper Thames River basin in Ontario, Canada. The updated KnnCAD model is shown to adequately reproduce observed monthly temperature characteristics as well as temporal and spatial correlations while simulating reasonable values which can exceed the range of observations. Copyright © 2012 John Wiley & Sons, Ltd.     

基于时间序列相似性匹配算法的地震预测研究

把匹配抽象时间序列相似性的方法引入到地震预报的应用中,结合大量地震历史源数据,在地震领域的专家经验知识和相关成果基础上,提出了一种简化的抽象时间序列匹配模型。该模型在对海量数据进行预处理筛选的基础上再进行时间相似性匹配,增加了横向和纵向多方位地区和多方位时间段的匹配,不同时间差和阈值的匹配,并通过大量实验对该模型进行了反复验证,同时对我国地震频繁地区近几十年的地震历史数据进行了相似性匹配实验分析,取得了可信度较高的实验结果,实验结果验证了所给时间序列相似性匹配控制策略的有效性、实用性以及算法的优越性。