Reliability analysis of hydraulic structures considering unit hydrograph uncertainty

Unit hydrographs (UHs), along with design rainfalls, are frequently used to determine the discharge hydrograph for design and evaluation of hydraulic structures. Due to the presence of various uncertainties in its derivation, the resulting UH is inevitably subject to uncertainty. Consequently, the performance of hydraulic structures under the design storm condition is uncertain. This paper integrates the linearly constrained Monte-Carlo simulation with the UH theory and routing techniques to evaluate the reliability of hydraulic structures. The linear constraint is considered because the water volume of each generated design direct runoff hydrograph should be equal to that of the design effective rainfall hyetograph or the water volume of each generated UH must be equal to one inch (or cm) over the watershed. For illustration, the proposed methodology is applied to evaluate the overtopping risk of a hypothetical flood detention reservoir downstream of Tong-Tou watershed in Taiwan.     

A probabilistic framework for floodplain mapping using hydrological modeling and unsteady hydraulic modeling

ABSTRACT

Prediction of design hydrographs is key in floodplain mapping using hydraulic models, which are either steady state or unsteady. The former, which require only an input peak, substantially overestimate the volume of water entering the floodplain compared to the more realistic dynamic case simulated by the unsteady models that require the full hydrograph. Past efforts to account for the uncertainty of boundary conditions using unsteady hydraulic modeling have been based largely on a joint flood frequency–shape analysis, with only a very limited number of studies using hydrological modeling to produce the design hydrographs. This study therefore presents a generic probabilistic framework that couples a hydrological model with an unsteady hydraulic model to estimate the uncertainty of flood characteristics. The framework is demonstrated on the Swannanoa River watershed in North Carolina, USA. Given its flexibility, the framework can be applied to study other sources of uncertainty in other hydrological models and watersheds.     

Nonlinear transformation of unit hydrograph

Unit hydrograph (UH) and its numerous derivatives have been popular for estimation of flood hydrographs. Two major assumptions still overshadow UH applications. One is the linearity and the other is time invariance. In theory, only peak discharge of an equilibrium hydrograph follows linear proportionality to excess rainfall intensity. In trying to relax the linearity constraint, this paper aims to propose a nonlinear way of transforming a given UH to other general hydrographs. The transformation or mapping technique relies on a simple rainfall ratio raised to a power less than unity. The case of nonlinear transformation is illustrated for a number of watershed geometries with either known kinematic wave analytic solutions or observed data. The nonlinear UH approach also relaxes the assumption of constant time base of the UH. The proposed nonlinear UH transformation may thus be viewed as a major step in closing the gap between physically based and traditional UH-based surface runoff simulation approaches.     

A new method for establishing hydrologic fidelity of snow depth measurements based on snowmelt–runoff hydrographs

For snowmelt-driven flood studies, snow water equivalent (SWE) is frequently estimated using snow depth data. Accurate measurements of snow depth are important in providing data for continuous hydrologic simulations of such watersheds. A new hydrologic fidelity metric is proposed in this study to evaluate the potential contribution of particular snow depth datasets to flow characteristics using observed data and hydrologic modeling using the Variable Infiltration Capacity (VIC) model. Data-based hydrologic fidelity of snow depth measurements is defined as a categorical skill score between the snow depth in the watershed and the hydrograph peak or volume at the watershed outlet. Similarly, model-based hydrologic fidelity is defined as a categorical skill score between the model-simulated snow depth and the model-simulated hydrograph peak or volume. The proposed framework is illustrated using the Pecatonica River watershed in the USA, indicating which sites have a higher hydrologic fidelity, which is preferred in hydrologic studies.     

A probabilistic framework to evaluate the uncertainty of design hydrograph: case study of Swannanoa River watershed

ABSTRACT

This study presents a probabilistic framework to evaluate the impact of uncertainty of design rainfall depth and temporal pattern as well as antecedent moisture condition (AMC) on design hydrograph attributes – peak, time to peak, duration and volume, as well as falling and rising limb slopes – using an event-based hydrological model in the Swannanoa River watershed in North Carolina, USA. Of the six hydrograph attributes, falling limb slope is the most sensitive to the aforementioned uncertainties, while duration is the least sensitive. In general, the uncertainty of hydrograph attributes decreases in higher recurrence intervals. Our multivariate analysis revealed that in most of the return periods, AMC is the most important driver for peak, duration and volume, while time to peak and falling limb slope are most influenced by rainfall pattern. In higher return periods, the importance of rainfall depth and pattern increases, while the importance of AMC decreases.     

Two‐dimensional continuous simulation of spatiotemporally varied hydrological processes using the time‐area method

Distributed, continuous hydrologic models promote better understanding of hydrology and enable integrated hydrologic analyses by providing a more detailed picture of water transport processes across the varying landscape. However, such models are not widely used in routine modelling practices, due in part to the extensive data input requirements, computational demands, and complexity of routing algorithms. We developed a two‐dimensional continuous hydrologic model, HYSTAR, using a time‐area method within a grid‐based spatial data model with the goal of providing an alternative way to simulate spatiotemporally varied watershed‐scale hydrologic processes. The model calculates the direct runoff hydrograph by coupling a time‐area routing scheme with a dynamic rainfall excess sub‐model implemented here using a modified curve number method with an hourly time step, explicitly considering downstream ‘reinfiltration’ of routed surface runoff. Soil moisture content is determined at each time interval based on a water balance equation, and overland and channel runoff is routed on time‐area maps, representing spatial variation in hydraulic characteristics for each time interval in a storm event. Simulating runoff hydrographs does not depend on unit hydrograph theory or on solution of the Saint Venant equation, yet retains the simplicity of a unit hydrograph approach and the capability of explicitly simulating two‐dimensional flow routing. The model provided acceptable performance in predicting daily and monthly runoff for a 6‐year period for a watershed in Virginia (USA) using readily available geographic information about the watershed landscape. Spatial and temporal variability in simulated effective runoff depth and time area maps dynamically show the areas of the watershed contributing to the direct runoff hydrograph at the outlet over time, consistent with the variable source area overland flow generation mechanism. The model offers a way to simulate watershed processes and runoff hydrographs using the time‐area method, providing a simple, efficient, and sound framework that explicitly represents mechanisms of spatially and temporally varied hydrologic processes. Copyright © 2015 John Wiley & Sons, Ltd.     

A simulation experiment for optimal design hyetograph selection

The aim of this work is to assess the accuracy of literature design hyetographs for the evaluation of peak discharges during flood events. Five design hyetographs are examined in a set of simulations, based upon the following steps: (i) an ideal river basin is defined, characterized by a Beta distribution shaped unit hydrograph (UH); (ii) 1000 years of synthetic rainfall are artificially generated; (iii) a discharge time‐series is obtained from the convolution of the rainfall time‐series and the UH, and the reference T‐years flood is computed from this series; (iv) for the same return period T, the parameters of the intensity–duration–frequency (IDF) curve are estimated from the 1000 years of synthetic rainfall; (v) five design hyetographs are determined from the IDF curves and are convolved with the discrete UH to find the corresponding design hydrographs; (vi) the hydrograph peaks are compared with the reference T‐years flood and the advantages and drawbacks of each of the five approaches are evaluated. The rainfall and UH parameters are varied, and the whole procedure is repeated to assess the sensitivity of results to the system configuration. We found that all design hyetographs produce flood peak estimates that are consistently biased in most of the climatic and hydrologic conditions considered. In particular, significant underestimation of the design flood results from the adoption of any rectangular hyetograph used in the context of the rational formula. In contrast, the Chicago hyetograph tends to overestimate peak flows. In two cases it is sufficient to multiply the result by a constant scaling factor to obtain robust and nearly unbiased estimates of the design floods. Copyright © 2007 John Wiley & Sons, Ltd.     

Integrating isolated and riparian wetland modules in the PHYSITEL/HYDROTEL modelling platform: model performance and diagnosis

Mathematical modelling is a well‐accepted framework to evaluate the effects of wetlands on stream flow and watershed hydrology in general. Although the integration of wetland modules into a distributed hydrological model represents a cost‐effective way to make this assessment, the added value brought by landscape‐specific modules to a model's ability to replicate basic hydrograph characteristics remains unclear. The objectives of this paper were the following: (i) to present the adaptation of PHYSITEL (a geographic information system) to parameterize isolated and riparian wetlands; (ii) to describe the integration of specific isolated wetland and riparian wetland modules into HYDROTEL, a distributed hydrological model; and (iii) to evaluate the performance of the updated modelling platform with respect to the capacity of replicating various hydrograph characteristics. To achieve this, two sets of simulations were performed (with and without wetland modules), and the added value was assessed at three river segments of the Becancour River watershed, Quebec, Canada, using six general goodness‐of‐fit indicators and 14 water flow criteria. A sensitivity analysis of the wetland module parameters was performed to characterize their impact on stream flows of the modelled watershed. Results of this study indicate the following: (i) integration of specific wetland modules can slightly increase the capacity of HYDROTEL to replicate basic hydrograph characteristics; and (ii) the updated modelling platform allows for the explicit assessment of the impact of wetlands (e.g. typology and location) on watershed hydrology. Copyright © 2015 John Wiley & Sons, Ltd.     

Drainage water temperature as a basis for verifying drainage runoff composition on slopes

Tile drainage water temperatures and discharge rates were measured in five highland watersheds of which most are underlain by acid crystalline rock. One of them, Dehtá?e in the Bohemo‐Moravian highland (Czech Republic), was studied in greater detail. The aim was to evaluate water temperature monitoring as a means of determining the source and pathway of drainage runoff during high‐flow events. Rapid increase in drainage discharge was accompanied by rapid change in water temperature. In winter, the rising limb of the hydrograph was accompanied by a decrease in temperature, and the falling limb was associated with a corresponding temperature increase. In summer, the trends were reversed. These data suggest that the water temperature changes are caused by the fastest component of drainage runoff, water from a precipitation event or snowmelt, which can be separated from the remainder of the hydrograph. Measurements of hydraulic conductivity, soil moisture content, soil temperature, and groundwater table level indicate that the major portion of the event water causing this effect infiltrates in the watershed recharge zone where soils are permeable, enters the weathered bedrock, flows preferentially and rapidly down the slope along disjoint fissures in the bedrock, finally emerging as ascending springs, and is, for the most part, intercepted by the tile drainage systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Assessing urban rainfall-runoff response to stormwater management extent

We report an empirical analysis of the hydrologic response of three small, highly impervious urban watersheds to pulse rainfall events, to assess how traditional stormwater management (SWM) alters urban hydrographs. The watersheds vary in SWM coverage from 3% to 61% and in impervious cover from 45% to 67%. By selecting a set of storm events that involved a single rainfall pulse with >96% of total precipitation delivered in 60 min, we reduced the effect of differences between storms on hydrograph response to isolate characteristic responses attributable to watershed properties. Watershed-average radar rainfall data were used to generate local storm hyetographs for each event in each watershed, thus compensating for the extreme spatial and temporal heterogeneity of short-duration, intense rainfall events. By normalizing discharge values to the discharge peak and centring each hydrograph on the time of peak we were able to visualize the envelope of hydrographs for each group and to generate representative composite hydrographs for comparison across the three watersheds. Despite dramatic differences in the fraction of watershed area draining to SWM features across these three headwater tributaries, we did not find strong evidence that SWM causes significant attenuation of the hydrograph peak. Hydrograph response for the three watersheds is remarkably uniform despite contrasts in SWM, impervious cover and spatial patterns of land cover type. The primary difference in hydrograph response is observed on the recession limb of the hydrograph, and that change appears to be associated with higher storm-total runoff in the watersheds with more area draining to SWM. Our findings contribute more evidence to the work of previous authors suggesting that SWM is less effective at attenuating urban hydrographs than is commonly assumed. Our findings also are consistent with previous work concluding that percent impervious cover may have greater influence on runoff volume than percent SWM coverage.     

Reliability assessment of water structures subject to data scarcity using the SCS-CN model

ABSTRACT

When discharge measurements are not available, design of water structures relies on using frequency analysis of rainfall data and applying a rainfall–runoff model to estimate a hydrograph. The Soil Conservation Service (SCS) method estimates the design hydrograph first through a rainfall–runoff transformation and next by propagating runoff to the basin outlet via the SCS unit hydrograph (UH) method. The method uses two parameters, the Curve Number (CN) and the time of concentration (T_c). However, in data-scarce areas, the calibration of CN and T_c from nearby gauged watersheds is limited and subject to high uncertainties. Therefore, the inherent uncertainty/variability of the SCS parameters may have considerable ramifications on the safety of design. In this research, a reliability approach is used to evaluate the impact of incorporating the uncertainty of CN and T_c in flood design. The sensitivity of the probabilistic outcome against the uncertainty of input parameters is calculated using the First Order Reliability Method (FORM). The results of FORM are compared with the conventional SCS results, taking solely the uncertainty of the rainfall event. The relative importance of the uncertainty of the SCS parameters is also estimated. It is found that the conventional approach, used by many practitioners, might grossly underestimate the risk of failure of water structures, due to neglecting the probabilistic nature of the SCS parameters and especially the Curve Number. The most predominant factors against which the SCS-CN method is highly uncertain are when the average rainfall value is low (less than 20 mm) or its coefficient of variation is not significant (less than 0.5), i.e. when the resulting rainfall at the design return period is low. A case study is presented for Egypt using rainfall data and CN values driven from satellite information, to determine the regions of acceptance of the SCS-CN method.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Efstratiadis     

Indoor imitation experimental study on driving factors of rainfall-runoff process

The driving actions are varied during the rain-fall-runoff process in a catchment. The impacts on therunoff process, caused by human activities or climatechange, can be attributed to two aspects: the charac-teristics of rainfall process and ground pad changes.To clarify their impacts on hydrological cycle is thefoundation of mechanism research of scientific hy-drology. So far, all of the research results, domestic andabroad, indicate that the advances on the understand-ing of hydrologica…     

Precipitation induced stream flow: An event based chemical and isotopic study of a small stream in the Great Plains region of the USA

A small stream in the Great Plains of USA was sampled to understand the streamflow components following intense precipitation and the influence of water storage structures in the drainage basin. Precipitation, stream, ponds, ground-water and soil moisture were sampled for determination of isotopic (D, ¹⁸O) and chemical (Cl, SO₄) composition before and after two intense rain events. Following the first storm event, flow at the downstream locations was generated primarily through shallow subsurface flow and runoff whereas in the headwaters region – where a pond is located in the stream channel – shallow ground-water and pond outflow contributed to the flow. The distinct isotopic signatures of precipitation and the evaporated pond water allowed separation of the event water from the other sources that contributed to the flow. Similarly, variations in the Cl and SO₄ concentrations helped identify the relative contributions of ground-water and soil moisture to the streamflow. The relationship between deuterium excess and Cl or SO₄ content reveals that the early contributions from a rain event to streamflow depend upon the antecedent climatic conditions and the position along the stream channel within the watershed. The design of this study, in which data from several locations within a watershed were collected, shows that in small streams changes in relative contributions from ground water and soil moisture complicate hydrograph separation, with surface-water bodies providing additional complexity. It also demonstrates the usefulness of combined chemical and isotopic methods in hydrologic investigations, especially the utility of the deuterium excess parameter in quantifying the relative contributions of various source components to the stream flow.     

A steepness index unit volume flood hydrograph approach for sub‐daily flow disaggregation

The estimation of sub‐daily flows from daily flood flows is important for many hydrological and hydraulic applications. Flows during flood events often vary significantly within sub‐daily time‐scales, and failure to capture the sub‐daily flood characteristic can result in an underestimation of the instantaneous flood peaks, with possible risk of design failure. It is more common to find a longer record of daily flow series (observed or modelled using daily rainfall series) than sub‐daily flow data. This paper describes a novel approach, known as the steepness index unit volume flood hydrograph approach, for disaggregating daily flood flows into sub‐daily flows that takes advantage of the strong relationship between the standardized instantaneous flood peak and the standardized daily flood hydrograph rising‐limb steepness index. The strength of this relationship, which is considerably stronger than the relationship between the standardized flood peak and the event flood volume, is shown using data from six rivers flowing into the Gippsland Lakes in southeast Australia. The results indicate that the steepness index unit volume flood hydrograph approach can be used to disaggregate modelled daily flood flows satisfactorily, but its reliability is dependent on a model's ability to simulate the standardized daily flood hydrograph rising‐limb steepness index and the event flood volume. Copyright © 2007 John Wiley & Sons, Ltd.     

A comparison of high‐resolution specific conductance‐based end‐member mixing analysis and a graphical method for baseflow separation of four streams in hydrologically challenging agricultural watersheds

Quantifying the relative contributions of different sources of water to a stream hydrograph is important for understanding the hydrology and water quality dynamics of a given watershed. To compare the performance of two methods of hydrograph separation, a graphical program [baseflow index (BFI)] and an end‐member mixing analysis that used high‐resolution specific conductance measurements (SC‐EMMA) were used to estimate daily and average long‐term slowflow additions of water to four small, primarily agricultural streams with different dominant sources of water (natural groundwater, overland flow, subsurface drain outflow, and groundwater from irrigation). Because the result of hydrograph separation by SC‐EMMA is strongly related to the choice of slowflow and fastflow end‐member values, a sensitivity analysis was conducted based on the various approaches reported in the literature to inform the selection of end‐members. There were substantial discrepancies among the BFI and SC‐EMMA, and neither method produced reasonable results for all four streams. Streams that had a small difference in the SC of slowflow compared with fastflow or did not have a monotonic relationship between streamflow and stream SC posed a challenge to the SC‐EMMA method. The utility of the graphical BFI program was limited in the stream that had only gradual changes in streamflow. The results of this comparison suggest that the two methods may be quantifying different sources of water. Even though both methods are easy to apply, they should be applied with consideration of the streamflow and/or SC characteristics of a stream, especially where anthropogenic water sources (irrigation and subsurface drainage) are present. Copyright © 2014 John Wiley & Sons, Ltd.     

Determination of unit hydrographs by multiple storm analysis

This paper discusses the derivation of a unit hydrograph by multiple storm analysis using least squares methods. Variations of least squares method was generalized using the framework of weighted ridge analysis. The paper also shows two theorems to support using multi-storm analysis to derive UH. In addition, an issue was addressed on the scaling effect in the conventional multi-storm analysis which could create potential bias toward large storms in deriving a multi-storm UH. For that, a simple scaling procedure was proposed to reduce such potential bias problem. Numerical investigations were conducted to examine the performance of the scaling procedure by comparing with the conventional multi-storm analysis (without scaling) and the HEC-1 weighing procedures. Based on various performance criteria using a total of 39 storms from three watersheds, the proposed scaling procedure was found to produce a quite desirable UH.     

Determination of runoff components using path analysis and isotopic measurements in a glacier‐covered alpine catchment (upper Hailuogou Valley) in southwest China

Monitoring of stable water isotopes (δ¹⁸O and δ²H) at the watershed scales can improve our understanding of complex hydrology and hydroclimatology of the watershed, especially in remote regions. Previous studies that used tracers for hydrograph separation are largely based on end‐member mixing approach (EMMA), but one drawback of this approach is that at least two independent tracers are required for multi‐component separation. Here we introduce a new approach—path analysis, in combination with isotopic measurements to investigate the runoff generation in a glacier‐covered alpine catchment (upper Hailuogou Valley) in southwest China. This newly developed method can not only provide a multi‐component hydrograph separation with the aid of only one tracer but also determine the direct and indirect influence of sources on streamflow. Path analysis show that the majority of streamflow is dominated by ice/snow meltwater that represents about 63–78% of the total discharge, whereas precipitation and groundwater contribute approximately 19–39% and 2–4% of the streamflow discharge, respectively. These results are in good agreement with those derived from EMMA (using ¹⁸O and Cl^? as tracers), corroborating that our proposed approach is successful in hydrograph separation of the catchment. This approach may provide new opportunities for the hydrograph separation of catchment with sparse data and be of interest to catchment hydrologists who seek to understand the behaviour of hydrologic systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Drifting runoff periodicity during the 20th century due to changing surface water volume

Fourier and wavelet analyses were used to reveal the dominant trends and coherence of a more than one‐century‐long time series of precipitation and discharge in several watersheds in Sweden, two of which were subjected to hydropower and intensive agriculture. During the 20th century, there was a gradual, significant drift of the dominant discharge periodicity in agricultural watersheds. This study shows that the steepness of the Fourier spectrum of runoff from the May to October period each year increased gradually during the century, which suggests a more predictable intra‐annual runoff pattern (more apart from white‐noise). In the agricultural watershed, the coherence spectrum of precipitation and runoff is generally high with a consistent white‐noise relationship for precipitation during the 20th century, indicating that precipitation is not controlling the drift of the discharge spectrum. In the hydropower regulated watershed, there was a sudden decrease of the discharge spectrum slope when regulation commenced in the 1920s. This study develops a new theory in which the runoff spectrum is related to the hydraulic and hydro‐morphological characteristics of the watershed. Using this theory, we explain the changes in runoff spectra in the two watersheds by the anthropogenic change in surface water volume and, hence, changes in kinematic wave celerity and water transit times. The reduced water volume in the agricultural watershed would also contribute to decreasing evaporation, which could explain a slightly increasing mean discharge during the 20th century despite the fact that precipitation was statistically constant in the area. Copyright © 2010 John Wiley & Sons, Ltd.     

Design hydrograph estimation in small and ungauged watersheds: continuous simulation method versus event‐based approach

The proper assessment of design hydrographs and their main properties (peak, volume and duration) in small and ungauged basins is a key point of many hydrological applications. In general, two types of methods can be used to evaluate the design hydrograph: one approach is based on the statistics of storm events, while the other relies on continuously simulating rainfall‐runoff time series. In the first class of methods, the design hydrograph is obtained by applying a rainfall‐runoff model to a design hyetograph that synthesises the storm event. In the second approach, the design hydrograph is quantified by analysing long synthetic runoff time series that are obtained by transforming synthetic rainfall sequences through a rainfall‐runoff model. These simulation‐based procedures overcome some of the unrealistic hypotheses which characterize the event‐based approaches. In this paper, a simulation experiment is carried out to examine the differences between the two types of methods in terms of the design hydrograph's peak, volume and duration. The results conclude that the continuous simulation methods are preferable because the event‐based approaches tend to underestimate the hydrograph's volume and duration. Copyright © 2011 John Wiley & Sons, Ltd.     

Experimental evaluation of the effect of storm movement on peak discharge

The hypothesis that downstream moving storms with storm length less than watershed length(L_s/L< 1.0) magnify the peak discharges as indicated by kinematic-wave models in previous studies was evaluated in an analysis of the dimensionless peak discharge and dimensionless storm velocity.Previously unpublished experimental data collected for a V-shaped watershed in the Watershed Experimentation System(WES) at the University of Illinois at Urbana-Champaign,were used in comparison with the simulation results of a kinematic-wave model.It is found that downstream moving storms with L_s/L < 1.0 increase the peak discharges to a limited extent compared to stationary storms,and the kinematic-wave model overstates the increase in the peak flows resulting from downstream moving storms with L_s/L < 1.0.To evaluate the importance of the backwater effects in the experimental watershed,the accuracy of kinematic-wave and dynamic-wave models for the simulation of surface runoff resulting from upstream and downstream moving storms was evaluated utilizing the same experimental data.The kinematic-wave model simulates the upstream moving storms pretty well,i.e.Nash-Sutcliffe coefficient of model fit efficiency equal to 0.948 and 0.831 for storms lengths equal to and not equal to the watershed length,respectively.Whereas,the kinematic wave model substantially overestimates the peak discharge of downstream moving storms,and yields generally poorer fits than for upstream moving storm,i.e.NSE equal to 0.867 and 0.674 for storms with lengths equal to and not equal to the watershed length,respectively.The dynamic-wave model simulates the downstream moving storms pretty well,i.e.NSE equal to 0.843 and 0.879 for storms with lengths equal to and not equal to the watershed length,respectively,indicating backwater significantly affects runoff for even this simple experimental watershed.Considering that storm movement did not substantially magnify peak discharge,the assumption of stationary storms made in standard hydrologic design seems reasonable and adequate.