Synthetic design hydrographs for ungauged catchments: a comparison of regionalization methods

Design flood estimates for a given return period are required in both gauged and ungauged catchments for hydraulic design and risk assessments. Contrary to classical design estimates, synthetic design hydrographs provide not only information on the peak magnitude of events but also on the corresponding hydrograph volumes together with the hydrograph shapes. In this study, we tested different regionalization approaches to transfer parameters of synthetic design hydrographs from gauged to ungauged catchments. These approaches include classical regionalization methods such as linear regression techniques, spatial methods, and methods based on the formation of homogeneous regions. In addition to these classical approaches, we tested nonlinear regression models not commonly used in hydrological regionalization studies, such as random forest, bagging, and boosting. We found that parameters related to the magnitude of the design event can be regionalized well using both linear and nonlinear regression techniques using catchment area, length of the main channel, maximum precipitation intensity, and relief energy as explanatory variables. The hydrograph shape, however, was found to be more difficult to regionalize due to its high variability within a catchment. Such variability might be better represented by looking at flood-type specific synthetic design hydrographs.     

Climate variability,snow, and physiographic controls on storm hydrographs in small forested basins,western Cascades,Oregon

Large floods are often attributed to the melting of snow during a rain event. This study tested how climate variability, snowpack presence, and basin physiography were related to storm hydrograph shape in three small (<1 km²) basins with old‐growth forest in western Oregon. Relationships between hydrograph characteristics and precipitation were tested for approximately 800 storms over a nearly 30‐year period. Analyses controlled for (1) snowpack presence/absence, (2) antecedent soil moisture, and (3) hillslope length and gradient. For small storms (<150 mm precipitation), controlling for precipitation, the presence of a snowpack on near‐saturated soil increased the threshold of precipitation before hydrograph rise, extended the start lag, centroid lag, and duration of storm hydrographs, and increased the peak discharge. The presence of a snowpack on near‐saturated soil sped up and steepened storm hydrographs in a basin with short steep slopes, but delayed storm hydrographs in basins with longer or more gentle slopes. Hydrographs of the largest events, which were extreme regional rain and rain‐on‐snow floods, were not sensitive to landform characteristics or snowpack presence/absence. Although the presence of a snowpack did not increase peak discharge in small, forested basins during large storms, it had contrasting effects on storm timing in small basins, potentially synchronizing small basin contributions to the larger basin hydrograph during large rain‐on‐snow events. By altering the relative timing of hydrographs, snowpack melting could produce extreme floods from precipitation events whose size is not extreme. Further work is needed to examine effects of canopy openings, snowpack, and climate warming on extreme rain‐on‐snow floods at the large basin scale. Copyright © 2008 John Wiley & Sons, Ltd.     

Using hysteretic behaviour and hydrograph classification to identify hydrological function across the “hillslope–depression–stream” continuum in a karst catchment

In cockpit karst landscapes, fluxes from upland areas contribute large volumes of water to low-lying depressions and stream flow. Hydrograph hysteresis and similarity between monitoring sites is important for understanding the space–time variability of hydrologic responses across the “hillslope–depression–stream” continuum. In this study, the hysteretic feature of hydrographs was assessed by characterizing the loop-like relationships between responses at upstream sites relative to subsurface discharge at the outlet of a small karst catchment. A classification of hydrograph responses based on the multi-scale smoothing Kernel -derived distance classifies the hydrograph responses on the basis of similarities between hillslope and depression sites, and those at the catchment outlet. Results demonstrate that the temporal and spatial variability of hydrograph hysteresis and similarity between hillslope flow and outlet stream flow can be explained by the local heterogeneity of depression aquifer. Large depression storage deficits emerging in the highly heterogeneous aquifer produce strong hysteresis and multiple relationships of upstream hydrographs relative to the outlet subsurface discharge. In contrast, when depression storage deficits are filled during consecutive rainfall events, depression hydrographs at the high permeability sites are almost synchronous or exhibit a monotonous function with the hydrographs at the outlet. This reduced hydrograph hysteresis enhances preferential flow paths in fractured rocks and conduits that can accelerate the hillslope flow to the outlet. Therefore, classification of hydrograph similarities between any upstream sites and the catchment outlet can help to identify the dominant hydrological functions in the heterogeneous karst catchment.     

Unit hydrograph estimation with multiple events and prior information: I. Theory and a computer program

Abstract

The method of regularization for estimating unit hydrographs is expanded to allow the inclusion of prior information about the unit hydrograph shape. This may give smooth estimates without any loss in volume. The method is illustrated with prior information from a regression on catchment characteristics and with catchment lag determined from the data. A computer program to implement the method is given together with a sample calculation.     

Runoff estimation for an ungauged catchment using geomorphological instantaneous unit hydrograph (GIUH) models

A geomorphological instantaneous unit hydrograph (GIUH) is derived from the geomorphological characteristics of a catchment and it is related to the parameters of the Clark instantaneous unit hydrograph (IUH) model as well as the Nash IUH model for deriving its complete shape. The developed GIUH based Clark and Nash models are applied for simulation of the direct surface run‐off (DSRO) hydrographs for ten rainfall‐runoff events of the Ajay catchment up to the Sarath gauging site of eastern India. The geomorphological characteristics of the Ajay catchment are evaluated using the GIS package, Integrated Land and Water Information System (ILWIS). The performances of the GIUH based Clark and Nash models in simulating the DSRO hydrographs are compared with the Clark IUH model option of HEC‐1 package and the Nash IUH model, using some commonly used objective functions. The DSRO hydrographs are computed with reasonable accuracy by the GIUH based Clark and Nash models, which simulate the DSRO hydrographs of the catchment considering it to be ungauged. Inter comparison of the performances of the GIUH based Clark and Nash models shows that the DSRO hydrographs are estimated with comparable accuracy by both the models. Copyright © 2007 John Wiley & Sons, Ltd.     

Storm‐event rainfall–runoff modelling approach for ungauged sites in Taiwan

This work develops a top‐down modelling approach for storm‐event rainfall–runoff model calibration at unmeasured sites in Taiwan. Twenty‐six storm events occurring in seven sub‐catchments in the Kao‐Ping River provided the analytical data set. Regional formulas for three important features of a streamflow hydrograph, i.e. time to peak, peak flow, and total runoff volume, were developed via the characteristics of storm event and catchment using multivariate regression analysis. Validation of the regional formulas demonstrates that they reasonably predict the three features of a streamflow hydrograph at ungauged sites. All of the sub‐catchments in the study area were then adopted as ungauged areas, and the three streamflow hydrograph features were calculated by the regional formulas and substituted into the fuzzy multi‐objective function for rainfall–runoff model calibration. Calibration results show that the proposed approach can effectively simulate the streamflow hydrographs at the ungauged sites. The simulated hydrographs more closely resemble observed hydrographs than hydrographs synthesized using the Soil Conservation Service (SCS) dimensionless unit hydrograph method, a conventional method for hydrograph estimation at ungauged sites in Taiwan. Copyright © 2008 John Wiley & Sons, Ltd.     

Application of Gibbs’ model to urban drainage networks: a case study in southwestern Chicago,USA

Hydrologic analysis of urban drainage networks often encounters a number of issues, including data acquisition and preparation for modelling, which can be costly and time‐consuming processes. Moreover, it can get more challenging with missing data and complex loops inside networks. In this article, Gibbs’ model is applied to urban drainage networks to investigate the possibility of replacing an actual existing urban drainage network in terms of the shape and peak flow of the hydrographs at the outlet. The characteristic network configuration is given as a value of a parameter β of Gibbs’ model. Instead of the actual network, stochastic networks from Monte‐Carlo simulation are utilized to obtain a synthetic width function from the generated networks, and runoff hydrographs are estimated based on it. The results show that the synthetic width function and the resulting hydrographs obtained from the networks simulated by Gibbs’ model are close to those from the actual network. The result also shows that even the behaviour of a looped network can be approximated by equivalent dendritic networks generated by Gibbs’ model. The applicability of a stochastic network model in urban catchment implies a complement to modelling approaches in case of data unavailability. Moreover, the network property (β) is utilized not only to estimate the discharge hydrograph of a catchment but also as a key link to evaluate the effect from rainstorm movement in urban catchments. Copyright © 2012 John Wiley & Sons, Ltd.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Direct estimation of catchment response time parameters in medium to large catchments using observed streamflow data

In single‐event deterministic design flood estimation methods, estimates of the peak discharge are based on a single and representative catchment response time parameter. In small catchments, a simplified convolution process between a single‐observed hyetograph and hydrograph is generally used to estimate time parameters such as the time to peak (T_P), time of concentration (T_C), and lag time (T_L) to reflect the “observed” catchment response time. However, such simplification is neither practical nor applicable in medium to large heterogeneous catchments, where antecedent moisture from previous rainfall events and spatially non‐uniform rainfall hyetographs can result in multi‐peaked hydrographs. In addition, the paucity of rainfall data at sub‐daily timescales further limits the reliable estimation of catchment responses using observed hyetographs and hydrographs at these catchment scales. This paper presents the development of a new and consistent approach to estimate catchment response times, expressed as the time to peak (T_Px) obtained directly from observed streamflow data. The relationships between catchment response time parameters and conceptualised triangular‐shaped hydrograph approximations and linear catchment response functions are investigated in four climatologically regions of South Africa. Flood event characteristics using primary streamflow data from 74 flow‐gauging stations were extracted and analysed to derive unique relationships between peak discharge, baseflow, direct runoff, and catchment response time in terms of T_Px. The T_Px parameters are estimated from observed streamflow data using three different methods: (a) duration of total net rise of a multipeaked hydrograph, (b) triangular‐shaped direct runoff hydrograph approximations, and (c) linear catchment response functions. The results show that for design hydrology and for the derivation of empirical equations to estimate catchment response times in ungauged catchments, the catchment T_Px should be estimated from both the use of an average catchment T_Px value computed using either Methods (a) or (b) and a linear catchment response function as used in Method (c). The use of the different methods in combination is not only practical but is also objective and has consistent results.     

Hybrid method to update the design flood shape for spillway operation in a dam: case study of the Huites Dam,Mexico

To design and review the operation of spillways, it is necessary to estimate design hydrographs, considering their peak flow, shape and volume. A hybrid method is proposed that combines the shape of the design hydrograph obtained with the UNAM Institute of Engineering Method (UNAMIIM) with the peak flow and volume calculated from a bivariate method. This hybrid method is applied to historical data of the Huites Dam, Sinaloa, Mexico. The goal is to estimate return periods for the maximum discharge flows (that account for the damage caused downstream) and the maximum levels reached in the dam (measure of the hydrological dam safety) corresponding to a given spillway and its management policy. Therefore, to validate the method, the results obtained by the flood routing of the 50-year hydrograph are compared with those obtained by the flood routing of the three largest historical floods. Both maximum flow and elevation were in the range of values observed within 37.5–75 years corresponding to the length of the historical record.     

An approach to hydrograph classification

The stream hydrograph is an integration of spatial and temporal variations in water input, storage and transfer processes within a catchment. For glacier basins in particular, inferences concerning catchment‐scale processes have been developed from the varying form and magnitude of the diurnal hydrograph in the proglacial river. To date, however, such classifications of proglacial diurnal hydrographs have developed in a relatively subjective manner. This paper develops an objective approach to the classification of diurnal discharge hydrograph ‘shape’ and ‘magnitude’ using a combination of principal components analysis and cluster analysis applied to proglacial discharge time‐series and to diurnal bulk flow indices. The procedure is applied to discharge time‐series from two different glacier basins and four separate ablation seasons representing a gradient of increasing hydrological perturbation as a result of (i) variable water inputs generated by rainstorm activity and (ii) variable location and response of hydrological stores through a systematic decrease in catchment glacierized area. The potential of the technique for application in non‐glacial hydrological contexts is discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

Using stochastic state‐space modelling to specify and reduce hydrograph error

A Bayesian post‐processor is used to generate a representation of the likely hydrograph forecast flow error distribution using raingauge and radar input to a stochastic catchment model and its deterministic equivalent. A hydrograph ensemble is so constructed. Experiments are analysed using the model applied to the River Croal in north‐west England. It is found that for rainfall input to the model having errors less than 3mm h^?1, corresponding to about a 15% error in peak flow, the stochastic model outperforms the deterministic model. The range of hydrographs associated with the different model simulations and the measured hydrographs are compared. The significant improvement possible using a stochastic approach is demonstrated for a specific case study, although the mean hydrograph derived using the stochastic model has an error range associated with it. Copyright © 2007 John Wiley & Sons, Ltd.     

Predicting and forecasting flow discharge at sites receiving significant lateral inflow

Two models, one linear and one non‐linear, were employed for the prediction of flow discharge hydrographs at sites receiving significant lateral inflow. The linear model is based on a rating curve and permits a quick estimation of flow at a downstream site. The non‐linear model is based on a multilayer feed‐forward back propagation (FFBP) artificial neural network (ANN) and uses flow‐stage data measured at the upstream and downstream stations. ANN predicted the real‐time storm hydrographs satisfactorily and better than did the linear model. The results of sensitivity analysis indicated that when the lateral inflow contribution to the channel reach was insignificant, ANN, using only the flow‐stage data at the upstream station, satisfactorily predicted the hydrograph at the downstream station. The prediction error of ANN increases exponentially with the difference between the peak discharge used in training and that used in testing. ANN was also employed for flood forecasting and was compared with the modified Muskingum model (MMM). For a 4‐h lead time, MMM forecasts the floods reliably but could not be applied to reaches for lead times greater than the wave travel time. Although ANN and MMM had comparable performances for an 8‐h lead time, ANN is capable of forecasting floods with lead times longer than the wave travel time. Copyright © 2007 John Wiley & Sons, Ltd.     

Quantifying peakflow attenuation/amplification in a karst river using the diffusive wave model with lateral flow

The aim of this paper is to quantify peakflow attenuation and/or amplification in a river, investigating lateral flow from the intermediate catchment during floods. This is a challenge for the study of the hydrological response of permeable/intermittent streams, and our contribution refers to a modelling framework based on the inverse problem for the diffusive wave model applied in a karst catchment. Knowing the upstream and downstream hydrographs on a reach between two stations, we can model the lateral one, given information on the hydrological processes involved in the intermediate catchment. The model is applied to 33 flood events in the karst reach of the Iton River in French Normandy where peakflow attenuation is observed. The monitored zone consists of a succession of losing and gaining reaches controlled by strong surface‐water/groundwater (SW/GW) interactions. Our results show that despite a high baseflow increase in the reach, peakflow is attenuated. Model application shows that the intensity of lateral outflow for the flood component is linked to upstream discharge. A combination of river loss and overbank flow for highest floods is proposed for explaining the relationships. Our approach differentiates the role of outflow (river loss and overbank flow) and that of wave diffusion on peakflow attenuation. Based on several sets of model parameterization, diffusion is the main attenuation process for most cases, despite high river losses of up to several m³/s (half of peakflow for some parameterization strategies). Finally, this framework gives new insight into the SW/GW interactions during floods in karst basins, and more globally in basins characterized by disconnected river‐aquifer systems.     

A new baseflow separation method based on analytical solutions of the Horton infiltration capacity curve

The separation of baseflow is an important issue in hydrology. The objective of this paper is to develop a new baseflow separation method based on the Horton infiltration capacity curve. For this purpose, the mathematical expressions of three parameters for the Horton infiltration capacity curve were derived in terms of rainfall and runoff data, and the lag time of the effective rainfall in the unsaturated zone and the groundwater flow routing equation are also presented. With these equations, the baseflow hydrographs at the outlet of the basin can be separated. The flow chart of the proposed method for baseflow hydrograph separation is given. Three recent baseflow separation methods, i.e. digital filter, non‐linear reservoir and the Boussinesq equation, were chosen as parallel schemes to compare with the proposed method. Rainfall‐runoff data from four watersheds located in different climatic regions in China were selected and used as case studies. Test and application results indicate that the proposed baseflow hydrograph separation method is in accordance with the hydrological physical process. The proposed method is comparable with current available methods and reduces some of the subjective aspects for the rising limb of the baseflow hydrograph, and it is useful for unit hydrograph analysis and for the study of the rainfall‐runoff relationship. Copyright © 2006 John Wiley & Sons, Ltd.     

Hydrodynamic derivation of a variable parameter Muskingum method: 2. Verification

Abstract

The hydrodynamic derivation of a variable parameter Muskingum method and its solution procedure for estimating a routed hydrograph were presented in Part I of this series (Perumal, 1994a). In this paper, the limitations of the method, the criterion for its applicability and its accuracy are discussed based on the assumptions used. The method is verified by routing a given hypothetical inflow hydrograph through uniform rectangular cross-section channels and comparing the results with the corresponding numerical solutions of the St. Venant equations. The stage hydrographs as computed by the method are also compared with the corresponding St. Venant solutions. It is demonstrated that the method closely reproduces the St. Venant solutions for the discharge and stage hydrographs subject to the compliance of the assumptions of the method by the routing process.     

Real‐time monitoring and estimation of the discharge of flash floods in a steep mountain catchment

Synchronously and accurately estimating the flood discharges and dynamic changes in the fluid density is essential for hydraulic analysis and forecasting of flash floods, as well as for risk assessment. However, such information is rare for steep mountain catchments, especially in regions that are hotspots for earthquakes. Therefore, six hydrological monitoring sites were established in the main stream and tributaries of the 78.3‐km² Longxi River catchment, an affected region of the Wenchuan earthquake region in China. Direct real‐time monitoring equipment was installed to measure the flow depths, velocities, and fluid total pressures of the flood hydrographs. On the basis of field measurements, real‐time mean cross‐sectional velocities during the flood hydrographs could be derived from easily obtainable parameters: cross‐sectional maximum velocities and the calibrated dimensionless parameter K_h . Real‐time discharges were determined on the basis of a noncontact method to establish the effective rating curves of this mountainous stream, ranging from 1.46 to 386.34 m³/s with the root mean square errors of ≤10.22 m³/s. Compared with the traditional point‐velocity method and empirical Manning's formula, the proposed noncontact method was reliable and safe for monitoring whole flood hydrographs. Additionally, the real‐time fluid density during the flood hydrographs was calculated on the basis of the direct monitoring parameters for fluid total pressures and water depths. During the flood hydrograph, transient flow behaviour with higher fluid density generally occurred downstream during the flood peak periods when the flow was in the supercritical flow regime. The observed behaviour greatly increased the threat of damage to infrastructure and human life near the river. Thus, it is important to accurately estimate flood discharge and identify for fluid densities so that people at risk from an impending flash flood are given reliable, advanced warning.     

Coupled modeling of rainfall-induced floods and sediment transport at the catchment scale

Rainfall-induced floods may trigger intense sediment transport on erodible catchments, especially on the Loess Plateau in China, which in turn modifies the floods. However, the role of sediment transport in modifying floods has to date remained poorly understood. Concurrently, traditional hydrodynamic models for rainfall-induced floods typically ignore sediment transport, which may lead to inaccurate results for highly erodible catchments. Here, a two-dimensional (2D) coupled shallow water hydro-sediment-morphodynamic (SHSM) model, based on the Finite Volume Method on unstructured meshes and parallel computing, is proposed and applied to simulate rainfall-induced floods in the Zhidan catchment on the Loess Plateau, Shaanxi Province, China. For six historical floods of return periods up to 2 years, the numerical results compare well with observations of discharge hydrographs at the catchment outlet. The computed runoff-sediment yield relation is quantitatively reasonable as compared with other catchments under similar geographical conditions. It is revealed that neglecting sediment transport leads to underestimation of peak discharge of the flood by 14%–45%, whilst its effect on the timing of the peak discharge varies for different flood events. For 18 design floods with return periods of 10–500 years, sediment transport may lead to higher peak discharge by around 9%–15%. The temporal pattern of concentrated rainfall in a short period may lead to a larger exponent value of the power function for the runoff-sediment yield relation. The current finding leads us to propose that incorporating sediment transport in rainfall-induced flood modeling is warranted. The SHSM model is applicable to flood and sediment modeling at the catchment scale in support of risk management and water and soil management.