Bivariate frequency analysis of nonstationary low‐flow series based on the time‐varying copula

Many studies have analysed the nonstationarity in single hydrological variables due to changing environments. Yet, few researches have been done to investigate how the dependence structure between different individual hydrological variables is affected by changing environments. To investigate how the reservoirs have altered the dependence structure between river flows at different locations on the Hanjiang River, a time‐varying copula model, which takes the nonstationarity in the marginal distribution and/or the time variation in dependence structure between different hydrological series into consideration, is presented in this paper to perform a bivariate frequency analysis for the low‐flow series from two neighbouring hydrological gauges. The time‐varying moments model with either time or reservoir index as explanatory variables is applied to build the time‐varying marginal distributions of the two low‐flow series. It's found that both marginal distributions are nonstationary, and the reservoir index yields better performance than the time index in describing the nonstationarities in the marginal distributions. Then, the copula with the dependence parameter expressed as a function of either time or reservoir index is applied to model the variable dependence between the two low‐flow series. The copula with reservoir index as the explanatory variable of the dependence parameter has a better fitting performance than the copula with the constant or the time‐trend dependence parameter. Finally, the effect of the time variation in the joint distribution on three different types of joint return periods (i.e. AND, OR and Kendall) of low flows at two neighbouring hydrological gauges is presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Frequency analysis of nonstationary annual maximum flood series using the time‐varying two‐component mixture distributions

The most popular practice for analysing nonstationarity of flood series is to use a fixed single‐type probability distribution incorporated with the time‐varying moments. However, the type of probability distribution could be both complex because of distinct flood populations and time‐varying under changing environments. To allow the investigation of this complex nature, the time‐varying two‐component mixture distributions (TTMD) method is proposed in this study by considering the time variations of not only the moments of its component distributions but also the weighting coefficients. Having identified the existence of mixed flood populations based on circular statistics, the proposed TTMD was applied to model the annual maximum flood series of two stations in the Weihe River basin, with the model parameters calibrated by the meta‐heuristic maximum likelihood method. The performance of TTMD was evaluated by different diagnostic plots and indexes and compared with stationary single‐type distributions, stationary mixture distributions and time‐varying single‐type distributions. The results highlighted the advantages of TTMD with physically‐based covariates for both stations. Besides, the optimal TTMD models were considered to be capable of settling the issue of nonstationarity and capturing the mixed flood populations satisfactorily. Copyright © 2016 John Wiley & Sons, Ltd.     

A numerical method of moments for solute transport in physically and chemically nonstationary formations: linear equilibrium sorption with random K<Subscript>d</Subscript>

A Lagrangian perturbation method is applied to develop a method of moments for solute flux through a three-dimensional nonstationary flow field. The flow nonstationarity stems from medium nonstationarity and internal and external boundaries of the study domain. The solute flux is described as a space-time process where time refers to the solute flux breakthrough through a control plane (CP) at some distance downstream of the solute source and space refers to the transverse displacement distribution at the CP. The analytically derived moment equations for solute transport in a nonstationarity flow field are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. The developed method is applied to study the effects of heterogeneity and nonstationarity of the hydraulic conductivity and chemical sorption coefficient on solute transport. The study results indicate all these factors will significantly influence the mean and variance of solute flux.     

Flood hydrograph reconstruction from the peak flow value in ephemeral streams using a simplified robust single‐parameter model

Flood hydrographs from ephemeral streams in arid areas provide valuable information for assessing run‐off and groundwater recharge. However, such data are often scarce or incomplete, especially in hyper‐arid regions. The hypothesis of this study was that it is possible to reconstruct a hydrograph of a specific point along an ephemeral stream with the knowledge of only the peak flow rate of a flood event at that point and that this can be done at almost every point along the stream. The feasibility of this approach lies in the shape of the recession stage of the flood hydrograph, which is known to be a repeating phenomenon. The recession stage comes immediately after the peak flow rate, when it begins its decline, and lasts until the flood is extinguished. A general shape of the flood recession stage can be provided. Because the recession stage represents ~80% of the duration of a flood event, it can provide a general idea of the flood hydrograph's shape. A simple model based on geometric progression is suggested to describe the repeating recession stage of a flood. The advantage of the proposed model is that it requires only one parameter: the recession characteristic at a fixed point along the ephemeral stream, termed recession coefficient q. By knowing the recession coefficient of a fixed point and the peak flow rate of a flood event at that point, one can plot the flood hydrograph. A good agreement is shown between the observed and computed values of the recession stage. Copyright © 2016 John Wiley & Sons, Ltd.     

A simultaneous analysis of gradual and abrupt changes in Canadian low streamflows

In most studies, trend detection is performed under the assumption of a monotonic trend. However, natural processes and, in particular, hydro‐climatic variables may not conform to this assumption. This study performs a simultaneous evaluation of gradual and abrupt changes in Canadian low streamflows using a modified Mann–Kendall (MK) trend test and a Bayesian multiple change‐point detection model. Statistical analysis, using the whole record of observation (under a monotonic trend assumption), shows that winter and summer low flows are dominated by upward and downward trends, respectively. Overall, about 20% of low flows are characterized by significant trends, where ～80% of detected significant trends are upward (downward) for winter (summer) season. Change‐point analysis shows that over 50% of low‐flow time series experienced at least one abrupt change in mean or in direction of trend, of which ～50% occurred in 1980s with a mode in 1987. Analysis of segmented time series based on a common change‐point date indicates a reduced number of significant trends, which is attributed to first, the change in nonstationarity behaviour of low flows leading to less trend‐type changes in the last few decades; and second, the false detection of trends when the sample data are characterized by shifts in mean. Depending on whether the monotonic trend assumption holds, the on‐site and regional interpretation of results may vary (e.g. winter low flow) or even lead to contradictory conclusions (e.g. summer low flow). Trend analysis of last two decades of streamflows shows that (1) winter low flows are increasing in eastern Canada and southern British Columbia, whereas they are decreasing in western Canada; (2) summer low flows are increasing in central Canada, southern British Columbia and Newfoundland, whereas they are decreasing in Yukon and northern British Columbia and also in eastern Ontario and Quebec. Copyright © 2010 John Wiley & Sons, Ltd.     

Focused Groundwater Controlled Feedbacks into the Hyporheic Zone During Baseflow Recession

Groundwater surface water interaction in the hyporheic zone remains an important challenge for water resources management and ecosystem restoration. In heterogeneous stratified glacial sediments, reach‐scale environments contain an uneven distribution of focused groundwater flow occurring simultaneously with diffusely discharging groundwater. This results in a variation of stream‐aquifer interactions, where focused flow systems are able to temporally dominate exchange processes. The research presented here investigates the direct and indirect influences focused groundwater discharge exerts on the hyporheic zone during baseflow recession. Field results demonstrate that as diffuse sources of groundwater deplete during baseflow recession, focused groundwater discharge remains constant. During baseflow recession the hyporheic zone is unable to expand, while the high nitrate concentration from focused discharge changes the chemistry of the stream. The final result is a higher concentration of nitrate in the hyporheic zone as this altered surface water infiltrates into the subsurface. This indirect coupling of focused groundwater discharge and the hyporheic zone is unaccounted for in hyporheic studies at this time. Results indicate important implications for the potential reduction of agricultural degradation of water quality.     

Drought parameters in relation to truncation levels

Drought parameters, namely the longest duration, largest severity and the intensity have been calculated in relation to the truncation levels ranging from 0 to −0\5 in the standardized domain for the normal, gamma and log‐normal probability distribution functions (PDFs) of the drought variables. The drought variables taken in the investigation are the annual rainfall and runoff time‐series evolving randomly and obeying the Markovian dependence. The analysis showed that the assumption of independence of the drought duration and intensity works well in deriving the expression for drought severity at various truncation levels. An estimate of drought intensity has been realized from the concept of the truncated normal distribution of the standardized form of the time‐series of drought variables in the normalized domain. Furthermore the non‐normality and the dependence in the time‐series have a significant effect on the drought parameters at the truncation levels under consideration. Copyright © 2000 John Wiley & Sons, Ltd.     

Modelling the bulk flow of a bedrock‐constrained,multi‐channel reach of the Mekong River,Siphandone, southern Laos

The general nature of bulk flow within bedrock single‐channel reaches has been considered by several studies recently. However, the flow structure of a bedrock‐constrained, large river with a multiple channel network has not been investigated previously. The multiple channel network of the Siphandone wetlands in Laos, a section of the Mekong River, was modelled using a steady one‐dimensional hydraulic model. The river network is characterized by a spatially‐varying channel‐form leading to significant changes in the bulk flow properties between and along the channels. The challenge to model the bulk flow in such a remote region was the lack of ideal boundary conditions. The flow models considered both low flow, high inbank and overbank flows and were calibrated using SPOT satellite sensor imagery and limited field data concerning water levels. The application of the model highlighted flow characteristics of a large multi‐channel network and also further indicated the field data that would be required to properly characterize the flow field empirically. Important results included the observation that adjacent channels within the network had different water surface slopes for the same moments in time; thus calibration data for modelling similar systems needs to account for these significant local differences. Further, the in‐channel hydraulic roughness coefficient strongly varied from one cross‐section to the next (Manning's ‘n’ range: 0·01 to 0·10). These differences were amplified during low flow but persisted in muted form during high discharges. Copyright © 2012 John Wiley & Sons, Ltd.     

Implications of decadal to century scale glacio‐hydrological change for water resources of the Hood River basin,OR, USA

In glacier‐fed rivers, melting of glacier ice sustains streamflow during the driest times of the year, especially during drought years. Anthropogenic and ecologic systems that rely on this glacial buffering of low flows are vulnerable to glacier recession as temperatures rise. We demonstrate the evolution of glacier melt contribution in watershed hydrology over the course of a 184‐year period from 1916 to 2099 through the application of a coupled hydrological and glacier dynamics model to the Hood River basin in Northwest Oregon, USA. We performed continuous simulations of glaciological processes (mass accumulation and ablation, lateral flow of ice and heat conduction through supra‐glacial debris), which are directly linked with seasonal snow dynamics as well as other key hydrologic processes (e.g. evapotranspiration and subsurface flow). Our simulations show that historically, the contribution of glacier melt to basin water supply was up to 79% at upland water management locations. We also show that supraglacial debris cover on the Hood River glaciers modulates the rate of glacier recession and progression of dry season flow at upland stream locations with debris‐covered glaciers. Our model results indicate that dry season (July to September) discharge sourced from glacier melt started to decline early in the 21st century following glacier recession that started early in the 20th century. Changes in climate over the course of the current century will lead to 14–63% (18–78%) reductions in dry season discharge across the basin for IPCC emission pathway RCP4.5 (RCP8.5). The largest losses will be at upland drainage locations of water diversions that were dominated historically by glacier melt and seasonal snowmelt. The contribution of glacier melt varies greatly not only in space but also in time. It displays a strong decadal scale fluctuations that are super‐imposed on the effects of a long‐term climatic warming trend. This decadal variability results in reversals in trends in glacier melt, which underscore the importance of long‐time series of glacio‐hydrologic analyses for evaluating the hydrological response to glacier recession. Copyright © 2016 John Wiley & Sons, Ltd.     

Long‐term variations and temporal scaling of hydroclimatic time series with focus on the German part of the Elbe River Basin

Long‐term variations and temporal scaling of mean monthly time series of river flow, precipitation, temperature, relative humidity, air pressure, duration of bright sunshine, degree of cloud cover, short wave radiation, wind speed and potential evaporation within or in vicinity of the German part of the Elbe River Basin are analyzed. Statistically significant correlations between the 2–15 year scale‐averaged wavelet spectra of the hydroclimatic variables and the North Atlantic Oscillation‐ and Arctic Oscillation index are found which suggests that such long‐term patterns in hydroclimatic time series are externally forced. The Hurst parameter estimates (H) based on the Detrended Fluctuation Analysis (DFA) indicate persistence for discharge, precipitation, wind speed, air pressure and the degree of cloud cover, all having an annual cycle and a broad low‐frequency distribution. Also, DFA H parameter estimates are higher for discharge than for precipitation. The major long‐term quasi‐periodic variability modes of precipitation detected using Singular Spectrum Analysis coincide with those detected in the discharge time series. Upon subtraction of these low‐frequency quasi‐periodic modes, the DFA H parameter estimates suggest absence of the persistence for both precipitation and discharge. Copyright © 2013 John Wiley & Sons, Ltd.     

Frequency analyses of annual extreme rainfall series from 5 min to 24 h

The parameter estimation methods of (1) moments, (2) maximum‐likelihood, (3) probability‐weighted moments (PWM) and (4) self‐determined PWM are applied to the probability distributions of Gumbel, general extreme values, three‐parameter log‐normal (LN3), Pearson‐3 and log‐Pearson‐3. The special method of computing parameters so as to make the sample skewness coefficient zero is also applied to LN3, and hence, altogether 21 candidate distributions resulted. The parameters of these distributions are computed first by original sample series of 14 successive‐duration annual extreme rainfalls recorded at a rain‐gauging station. Next, the parameters are scaled by first‐degree semi‐log or log‐log polynomial regressions versus rainfall durations from 5 to 1440 min (24 h). Those distributions satisfying the divergence criterion for frequency curves are selected as potential distributions, whose better‐fit ones are determined by a conjunctive evaluation of three goodness‐of‐fit tests. Frequency tables, frequency curves and intensity–duration–frequency curves are the outcome. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigating the linkage between streamflow recession rates and channel network contraction in a mesoscale catchment in New York state

The rate of recession (dQ/dt) in a given time interval has long been plotted in log–log space against the concurrent mean discharge (Q_avg). Recent interpretations of these dQ/dt–Q_avg plots have sought to look at curves for individual events instead of the data cloud from all the data points together. These individual recession curves have been observed to have near‐constant slope but to have varying intercepts, features hypothesized to possibly be explained by the nature of the contraction of the active channel network during recession. For a steep, 150‐ha forested catchment in central New York state with an 8.8‐km channel network, changes in the active channel network were mapped between April and November 2013. Streamflow recession occurred in a matter of days, but changes in the active channel network occurred over a matter of weeks. Thus, in this catchment, it does not appear that channel contraction directly controls recession. Additionally, field observations indicate that dry down did not occur in a spatially organized, sequential way such that the upper end of higher‐order streams dried first. Instead, the location of groundwater seeps, in part, controlled the active portion of the channel network. Consistent with the presence of different types of flow contributing zones, the paper presents a conceptual model that consists of multiple parallel reservoirs of varying drainage rate and varying degrees of recharge at different times of the year. This conceptual model is able to reproduce a slope of 2 and a seasonal shift in intercept typical of individual recession curves. Copyright © 2015 John Wiley & Sons, Ltd.     

Probability prediction of peak break‐up water level through vine copulas

Prediction of the peak break‐up water level, which is the maximum instantaneous stage during ice break‐up, is desirable to allow effective ice flood mitigation, but traditional hydrologic flood routing techniques are not efficient in addressing the large uncertainties caused by numerous factors driving the peak break‐up water level. This research provides a probability prediction framework based on vine copulas. The predictor variables of the peak break‐up water level are first chosen, the pair copula structure is then constructed by using vine copulas, the conditional density distribution function is derived to perform a probability prediction, and the peak break‐up water level value can then be estimated from the conditional density distribution function given the conditional probability and fixed values of the predictor variables. This approach is exemplified using data from 1957 to 2005 for the Toudaoguai and Sanhuhekou stations, which are located in the Inner Mongolia Reach of the Yellow River, and the calibration and validation periods are divided at 1986. The mean curve of the peak break‐up water level estimated from the conditional distribution function can capture the tendency of the observed series at both the Toudaoguai and Sanhuhekou stations, and more than 90% of the observed values fall within the 90% prediction uncertainty bands, which are approximately twice the standard deviation of the observed series. The probability prediction results for the validation period are consistent with those for the calibration period when the nonstationarity of the marginal distributions for the Sanhuhekou station are considered. Compared with multiple linear regression results, the uncertainty bands from the conditional distribution function are much narrower; moreover, the conditional distribution function is more capable of addressing the nonstationarity of predictor variables, and the conclusions are confirmed by jackknife analysis. Scenario predictions for cases in which the peak break‐up water level is likely to be higher than the bankfull water level can also be conducted based on the conditional distribution function, with good performance for the two stations.     

Effects of irrigation withdrawals on streamflows in a karst environment: lower Flint River Basin,Georgia, USA

Extensive implementation of centre pivot irrigation systems occurred between 1970 and 1980 in the lower Flint River Basin (FRB) of southwestern Georgia, USA. Groundwater within this karstic system is in direct hydraulic connection with regional streams, many of which are incised through the overburden into underlying limestone. We used long‐term U.S. Geological Survey gaging station data to evaluate multiple flow metrics of two tributaries (Ichawaynochaway Creek and Spring Creek) in the lower FRB to determine the extent of changes in stream behaviour since irrigation practices intensified. We compared pre‐ and post‐irrigation flow duration curves, 1‐, 7‐, and 14‐day minimum flows, and 8‐day (seasonal) and annual baseflow recession slopes, in addition to evaluating regional climate data to determine whether significant differences existed between the pre‐ and post‐irrigation periods. Our results showed significant changes in low‐flow durations in the post‐irrigation record for both gages, including a decrease by an order of magnitude for 98% exceedance flows at Spring Creek. Both gages indicated significant reductions in 1‐, 7‐, and 14‐day low flows. Eight‐day baseflow recession curves (within early summer months) and annual baseflow recession curves became significantly steeper during the post‐irrigation period for Ichawaynochaway Creek. We also found that a significant relationship existed between winter and summer minimum flows in both streams in the pre‐irrigation period which was disrupted in post‐irrigation years. Regional climate data for the study period revealed no significant changes in rainfall totals or frequency of drought; however, there was evidence for a shift in seasonal rainfall patterns. Copyright © 2011 John Wiley & Sons, Ltd.     

A model for daily flows of intermittent streams

A stochastic model for synthetic data generation is not available in the literature for daily flows of intermittent streams. Such a model is required in the planning and operation of structures on an intermittent stream for purposes where short time flow fluctuations are important. In this study a model is developed for such a case. The model consists of four steps: determination of the days on which flow occurs, determination of the days on which a flow increment occurs, determination of the magnitude of the flow increment, and calculation of the flow decrement on days when the flow is reduced. The first two steps are modelled by a three‐state Markov chain. In the third step, flow increments on the rising limb of the hydrograph are assumed to be gamma distributed. In the last step an exponential recession is used with two different coefficients. Parameters of the model are estimated from the observed daily stream flow data for each month of the year. The model is applied to a daily flow series of 35 years' length. It is seen that the model can preserve the short‐term characteristics (the ascension and recession curves and peaks) of the hydrograph in addition to the long‐term characteristics (mean, variance, skewness, lag‐one and higher lag autocorrelation coefficients, and zero flow percentage). The number of parameters of the model can be decreased by fitting Fourier series to their annual variation. Copyright © 2000 John Wiley & Sons, Ltd.     

大气边界层湍流的动力非平稳性的验证

首次用验证时间序列中是否存在动力非平稳性的一种简单图示方法——space time index法来分析大气边界层湍流的动力平稳性特征.本文以取自淮河流域和威斯康星森林下垫面条件下的三维高精度风速和温度、湿度湍流脉动资料对大气边界层湍流的平稳性特征进行了分析.结果表明space time index方法能有效地检验大气边界层湍流信号中是否存在动力平稳性.另外,均匀下垫面条件（水稻田）及复杂下垫面条件（森林）下的大气边界层湍流信号中几乎都存在动力非平稳性,大气湍流动力学非平稳性可能是边界层湍流信号相当普遍具有的一种特性.大气边界层湍流中的间歇性和相干结构使得其非平稳性图形的特征不同于一般时间序列非平稳性图形的“V”型特征;森林下垫面条件下的湍流信号比相对均匀下垫面（水稻田）下的湍流信号更有组织性,相干结构更强.     

Climate‐informed low‐flow frequency analysis using nonstationary modelling

Stationarity is often assumed for frequency analysis of low flows in water resources management and planning. However, many studies have shown that flow characteristics, particularly the frequency spectrum of extreme hydrologic events, were modified by climate change and human activities. Thus, the conventional frequency analysis that fails to consider the nonstationary characteristics may lead to costly design. The analysis presented in this paper was based on the more than 100 years of daily flow data from the Yichang gauging station 44 km downstream of the Three Gorges Dam. The Mann–Kendall trend test under the scaling hypothesis showed that the annual low flows had a significant monotonic trend, whereas an abrupt change point was identified in 1936 by the Pettitt test. The climate‐informed low‐flow frequency analysis and the divided and combined method were employed to account for the impacts from related climate variables and nonstationarities in annual low flows. Without prior knowledge of the probability density function for the gauging station, six distribution functions including the generalized extreme values (GEV), Pearson Type III, Gumbel, Gamma, Lognormal and Weibull distributions have been tested to find the best fit, in which the local likelihood method is used to estimate the parameters. Analyses show that GEV had the best fit for the observed low flows. This study has also shown that the climate‐informed low‐flow frequency analysis is able to exploit the link between climate indices and low flows, which would account for the dynamic feature for reservoir management and provide more accurate and reliable designs for infrastructure and water supply. Copyright © 2014 John Wiley & Sons, Ltd.     

Hydrological responses to conservation practices in a catchment of the Loess Plateau,China

Since the late 1950s a series of soil conservation practices have been implemented in the Loess Plateau. It is important to assess the impact of these practices on hydrology at the catchment scale. The Jialuhe River catchment, a tributary of the Yellow River, with a drainage area of 1117 km² in the Loess Plateau, was chosen to investigate the hydrological responses to conservation practices. Parametric and non‐parametric Mann–Kendall tests were utilized to detect trends in hydrological variables or their residuals. Relationships between precipitation and hydrological variables were developed to remove the impact of precipitation variability. Significant linear decreasing trends in annual surface runoff and baseflow were identified during the treated period from 1967 to 1989, and the rate of reduction was 1·30 and 0·48 mm/year, respectively. As result, mean annual surface runoff and baseflow decreased by 32% over the period of 1967 to 1989. Seasonal runoff also decreased during the treated period with the greatest reduction occurring in summer and the smallest reduction in winter. The response of high and low daily flow to conservation practices was greater than average flows. Copyright © 2004 John Wiley & Sons, Ltd.     

Spectral‐temporal characterization of riverflow variability in England and Wales for the period 1865–2002

We have investigated riverflow variability in England and Wales by examining the reconstructed monthly discharge time series from fifteen catchments in these regions for the period 1865–2002. The riverflow fluctuations exhibit a strong annual cycle. The flow in the annual cycle is found to be intermittent, with the degree of intermittency varying from one catchment to another. An intermittent flow is characterized by bursts of high discharge separated by intervals with low or no discharge. By applying a continuous wavelet transform to the time series, we have identified the occurrence of intermittency in the annual cycle. The riverflow activity is also found to exhibit variations at interannual and quasi‐decadal time scales. These variations may be linked to large‐scale climatic processes such as the North Atlantic Oscillation (NAO). We have used the kurtosis of the probability density functions of the various time series as a measure of the degree of intermittency. An intermittent flow is characterized by a peaked (super‐Gaussian) probability density function with kurtosis in excess of 3. A higher value of kurtosis signifies a higher degree of intermittency. Intermittent fluctuations are more difficult to predict accurately than persistent oscillations, i.e., those lasting continuously over a long time interval. Copyright © 2009 John Wiley & Sons, Ltd.