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.     

FLOOD MODELLING WITH GIS-DERIVED DISTRIBUTED UNIT HYDROGRAPHS

The concept of a spatially distributed unit hydrograph is based on the fact that the unit hydrograph can be derived from the time–area curve of a watershed by the S-curve method. The time–area diagram is a graph of cumulative drainage area contributing to discharge at the watershed outlet within a specified time of travel. Accurate determination of the time–area diagram is made possible by using a GIS. The GIS is used to describe the connectivity of the links in the watershed flow network and to calculate distances and travel times to the watershed outlet for various points within the watershed. Overland flow travel times are calculated by the kinematic wave equation for time to equilibrium; channel flow times are based on the Manning and continuity equations. To account for channel storage, travel times for channel reaches are increased by a percentage depending on the channel reach length and geometry. With GIS capability for rainfall mapping, the assumption of a uniform spatial rainfall distribution is no longer necessary; hence the term, spatially distributed unit hydrograph. An example of the application for the Waiparous Creek in the Alberta Foothills is given. IDRISI is used to develop a simple digital elevation model of the 229 km² watershed, using 1 km × 1 km grid cells. A grid of flow directions is developed and used to create an equivalent channel network. Excess rainfall for each 1 km × 1 km cell is individually computed by the Soil Conservation Service (SCS) runoff curve method and routed through the equivalent channel network to obtain the time–area curve. The derived unit hydrograph gave excellent results in simulating an observed flood hydrograph. The distributed unit hydrograph is no longer a lumped model, since it accounts for internal distribution of rainfall and runoff. It is derived for a watershed without the need for observed rainfall and discharge data, because it is essentially a geomorphoclimatic approach. As such, it allows the derivation of watershed responses (hydrographs) to inputs of various magnitudes, thus eliminating the assumption of proportionality of input and output if needed. The superposition of outputs is retained in simulating flood hydrographs by convolution, since it has been shown that some non-linear systems satisfy the principle of superposition. The distributed unit hydrograph appears to be a very promising rainfall runoff model based on GIS technology.     

Does the incorporation of process conceptualization and tracer data improve the structure and performance of a simple rainfall‐runoff model in a Scottish mesoscale catchment?

A geomorphological instantaneous unit hydrograph (GIUH) rainfall‐runoff model was applied in a 31 km² montane catchment in Scotland. Modelling was based on flow path length distributions derived from a digital terrain model (DTM). The model was applied in two ways; a single landscape unit response based on the DTM alone, and a two‐landscape unit response, which incorporated the distribution of saturated areas derived from field‐validated geographic information system (GIS) analysis based on a DTM and soil maps. This was to test the hypothesis that incorporation of process‐information would enhance the model performance. The model was applied with limited multiple event calibration to produce parameter sets which could be applied to a spectrum of events with contrasting characteristics and antecedent conditions. Gran alkalinity was used as a tracer to provide an additional objective measure for assessing model performance. The models captured the hydrological response dynamics of the catchment reasonably well. In general, the single landscape unit approach produced the best individual model performance statistics, though the two‐landscape unit approach provided a range of models, which bracketed the storm hydrograph response more realistically. There was a tendency to over‐predict the rising limb of the hydrograph, underestimate large storm event peaks and anticipate the hydrograph recession too rapidly. Most of these limitations could be explained by the simplistic assumptions embedded within the GIUH approach. The modelling also gave feasible predictions of stream water chemistry, though these could not be used as a basis for model rejection. Nevertheless, the study suggested that the approach has potential for prediction of hydrological response in ungauged montane headwater basins. Copyright © 2007 John Wiley & Sons, Ltd.     

APPLICATION OF UNIT HYDROGRAPH TECHNIQUES TO SOLUTE TRANSPORT IN CATCHMENTS

Current models of solute movement in catchments are based on rainfall–runoff models and are consequently biased towards processes which determine the magnitude and timing of water flux. It is shown here that the instantaneous unit hydrograph (IUH), or runoff response function, obtained from a hydrograph is fundamentally different from the residence time distribution which governs the response to solutes/tracers. Using hydrometric and tracer data obtained from a small (25 ha) catchment in the humid tropics a modification of the IUH technique is demonstrated which also allows approximate modelling of the tracer data. New features of the modified conceptual model are identified with known hillslope processes.     

Use of Groundwater Levels with the PULSE Analytical Model

The PULSE analytical model, which calculates daily groundwater discharge on the basis of user‐specified recharge, was originally developed for calibration using streamflow data. This article describes a model application in which groundwater level data constitute the primary control on model input. As a test case, data were analyzed from a small basin in central Pennsylvania in which extensive groundwater level data are available. The timing and intensity of daily water‐level rises are used to ascertain temporal distribution of recharge, and the simulated groundwater discharge hydrograph has shape features that are similar to the streamflow hydrograph. This article does not include details about calibration, but some steps are illustrated and general procedures are described for calibration in specific hydrologic studies. The PULSE model can be used to assess results of fully automated base flow methods and can be used to define groundwater recharge and discharge at a relatively small time scale.     

Uncertainty estimates for surface runoff models

A lower bound for variance in surface runoff modelling estimates is advanced. The bound is derived using a linear unit hydrograph approach which utilizes a discretization of the catchment into an arbitrary number of subareas, a linear routing technique for channel flow effects, a variable effective rainfall distribution over the catchment, and calibration parameter distributions developed in correlating rainfall-runoff data by the model. The uncertainty bound reflects the dominating influence of the unknown rainfall distribution over the catchment and is expressed as a distribution function that can be reduced only by supplying additional rainfall-runoff data. It is recommended that this uncertainty distribution in modelling results be included in flood control design studies in order to incorporate a prescribed level of confidence in flood protection facilities.     

A multi-objective calibration approach using in-situ soil moisture data for improved hydrological simulation of the Prairies

ABSTRACT

Traditionally, hydrological models are only calibrated to reproduce streamflow regime without considering other hydrological state variables, such as soil moisture and evapotranspiration. Limited studies have been performed on constraining the model parameters, despite the fact that the presence of a large number of parameters may provide large degree of freedom, resulting in equifinality and poor model performance. In this study, a multi-objective optimization approach is adopted, and both streamflow and soil moisture data are calibrated simultaneously for an experimental study basin in the Saskatchewan Prairies in western Canada. The results of this study show that the multi-objective calibration improves model fidelity compared to the single objective calibration. Moreover, the study demonstrates that single objective calibration performed against only streamflow can fairly mimic the streamflow hydrograph but does not yield realistic estimation of other fluxes such as evapotranspiration and soil moisture (especially in deeper soil layers).     

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.     

On the relationship between flood and contributing area

Although it is well known that the vast majority of the time only a portion of any watershed contributes run‐off to the outlet, this extent is rarely documented. Also, the power law form of the streamflow and contributing area (Q‐A_c) relationship has been known for a half century, but it is uncommon for it to be quantified, and time series of contributing area extensive enough to calculate its frequency distribution are almost non‐existent. Data from the Canadian Prairies, where there are extensive estimates of contributing area during the median annual flood, imply that the power law coefficient for any Q‐A_c curve is a function of flow magnitude and return period. These data also suggest that regional flood frequency curves are a construct of Q‐A_c curves from individual basins. This paper will discuss research that attempted to reproduce the Q‐A_c curves for the La Salle River Watershed with a semidistributed numerical hydrological model, MESH‐PDMROF. The model simulated streamflow reasonably well (Nash Sutcliffe values = 0.62) compared with published examples of comparable models applied in the region. Estimates of the coefficient and exponent of the Q‐A_c power law function ranged from 0.08–0.14 and 0.9–1.12, respectively. These exponent values were lower than those of regional flood frequency curves and support the theory that regional flood frequency curves are a construct of Q‐A_c curves. Simulations of the area contributing to the median annual flood were lower (0.3) than those derived from independent topographic analysis (0.9) described in earlier literature though there is uncertainty in both these estimates. This uncertainty was extended across the flood frequency distribution and may be too large to definitively verify the study hypothesis.     

UNIT HYDROGRAPH DERIVED FROM A SPATIALLY DISTRIBUTED VELOCITY FIELD

A unit hydrograph model is proposed in which the watershed is decomposed into subareas which are individual cells or zones of neighbouring cells. The unit hydrograph is found for each subarea and the response at the outlet to excess rainfall on each subarea is summed to produce the watershed runoff hydrograph. The cell to cell flow path to the watershed outlet is determined from a digital elevation model. A constant flow velocity is assigned to each cell and the time lag between subarea input and response at the watershed outlet is found by integrating the flow time along the path from the subarea to the outlet. The response function for a subarea is modelled as a lagged linear reservoir in which the flow time is equal to the sum of a time of translation and an average residence time in the reservoir. It is shown that the assumption of a spatially varying, but time-invariant, velocity field underlying this model produces a linear system model for all subareas whose outputs can be summed in the manner indicated. An example application is presented for the 8.70 km² Severn watershed at Plynlimon in Wales using a 50 m digital elevation model in which the cell velocity is calculated by modifying an average watershed velocity according to the terrain slope and the drainage area of each cell. The resulting model reasonably reproduces the observed unit hydrograph.     

GEOMORPHOLOGICAL TRANSFER FUNCTION CALCULATED FROM DIGITAL ELEVATION MODELS FOR DISTRIBUTED HYDROLOGICAL MODELLING

Recently, several attempts have been made to relate the hydrological response of a catchment to its morphological and topographical features using different hypotheses to model the effect of the drainage network. Several transfer functions were developed and some of these are based on the theory of a linear model, the geomorphological unit hydrograph. The aim of this paper is to present a methodology to automatically identify the transfer function, using digital elevation models for applications in distributed hydrological modelling. The transfer function proposed herein is based on the Hayami approximation solution of the diffusive wave equation especially adapted for the routing hydrograph through a channel network. The Gardon d’Anduze basin, southern France, was retained for applications. Digital elevation models were used to extract the channel network and divide the basin into subcatchments. Each subcatchment produces, at its own outlet, an impulse response which is routed to the outlet of the whole catchment using the diffusive wave model described by two parameters: celerity and diffusivity functions of geometrical characteristics of the channel network. Firstly, a geomorphological unit hydrograph obtained by routing a homogeneous effective rainfall was compared with the unit hydrograph identified by a lumped model scheme, then the distributed model was applied to take into account the spatial variability of effective rainfall in the catchment. Results show that this new method seems to be adapted for distributed hydrological modelling; it enables identification of a transfer function response for each hydrological unit, here subcatchments, and then simulation of the contribution of each unit to the hydrograph at the outlet. © 1997 by John Wiley & Sons, Ltd.     

Hydrograph separation using tracers and digital filters to quantify runoff components in a semi‐arid mesoscale catchment

Chemical hydrograph separation using electrical conductivity and digital filters is applied to quantify runoff components in the 1,640 km² semi‐arid Kaap River catchment and its subcatchments in South Africa. A rich data set of weekly to monthly water quality data ranging from 1978 to 2012 (450 to 940 samples per site) was analysed at 4 sampling locations in the catchment. The data were routinely collected by South Africa's national Department of Water and Sanitation, using standard sampling procedures. Chemical hydrograph separation using electrical conductivity (EC) as a tracer was used as reference and a recursive digital filter was then calibrated for the catchment. Results of the two‐component hydrograph separation indicate the dominance of baseflow in the low flow regime, with a contribution of about 90% of total flow; however, during the wet season, baseflow accounts for 50% of total flow. The digital filter parameters were very sensitive and required calibration, using chemical hydrograph separation as a reference. Calibrated baseflow estimates ranged from 40% of total flow at the catchment outlet to 70% in the tributaries. The study demonstrates that routinely monitored water quality data, especially EC, can be used as a meaningful tracer, which could also aid in the calibration of a digital filter method and reduce uncertainty of estimated flow components. This information enhances our understanding of how baseflow is generated and contributed to streamflow throughout the year, which can aid in quantification of environmental flows, as well as to better parameterize hydrological models used for water resources planning and management. Baseflow estimates can also be useful for groundwater and water quality management.     

Nonlinear bacterial load‐streamflow response on a marine beach

Bacterial concentration (Escherichia coli) is used as the key indicator for marine beach water quality in Hong Kong. For beaches receiving streamflow from unsewered catchments, water quality is mainly affected by local nonpoint source pollution and is highly dependent on the bacterial load contributed from the catchment. As most of these catchments are ungauged, the bacterial load is generally unknown. In this study, streamflow and the associated bacterial load contributed from an unsewered catchment to a marine beach, Big Wave Bay, are simulated using a modelling approach. The physically based distributed hydrological model, MIKE‐SHE, and the empirical watershed water quality model (Hydrological Simulation Program – Fortran) are used to simulate streamflow and daily‐averaged E. coli concentration/load, respectively. The total daily derived loads predicted by the model during calibration (June–July 2007) and validation (July–October 2008) periods agree well with empirical validation data, with a percentage difference of 3 and 2%, respectively. The simulation results show a nonlinear relationship between E. coli load and rainfall/streamflow and reveal a source limiting nature of nonpoint source pollution. The derived load is further used as an independent variable in a multiple linear regression (MLR) model to predict daily beach water quality. When compared with the MLR models based solely on hydrometeorological input variables (e.g. rainfall and salinity), the new model based on bacterial load predicts much more realistic E. coli concentrations during rainstorms. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Book Review

Abstract

The instantaneous unit hydrograph (IUH) of a watershed is the result of one instantaneous unit of rainfall excess distributed uniformly over the watershed. Although the geomorphological characteristics of the basin remain relatively constant, the variable characteristics of storms cause variations in the shape of the resulting hydrographs. It is, therefore, inadequate to use one typical IUH to represent the hydrological response generated from any specific storm. In this study, a variable IUH was derived that directly reflects the time-varying rainfall intensity during storms. The rainfall intensity used to generate the variable IUH at time t is the mean rainfall intensity occurring from the time t—T _c to t in which T _c is the watershed time of concentration. Hydrological records from three watersheds in Taiwan were used to demonstrate the applicability of the proposed model. The results show that better simulations can be obtained by using the proposed model than by using the conventional unit hydrograph method, especially for concentrated rainstorm cases.     

On-line estimation of unit hydrographs using the wavelet-based LMS algorithm / Estimation en ligne des hydrogrammes unitaires grâce à l'algorithme des moindres carrés moyens à base d'ondelettes

Abstract

This study applies the discrete wavelet transform (DWT) to decompose the unit hydrograph, thereby generating parsimonious reparameterizations of the unit hydrograph. A model compression method is then employed to significantly compress the unit hydrograph requiring that fewer coefficients be estimated. Moreover, a wavelet-based linearly constrained least mean squares (WLCLMS) algorithm is also used to estimate on-line the wavelet coefficients of the unit hydrograph. The updated wavelet coefficients of the unit hydrograph, convoluted with effective rainfall input in the wavelet domain, allow for accurate prediction of one-step-ahead runoff in the time domain. The proposed approach allows the unit hydrographs to vary in time and accurately predicts runoff from a basin in Taiwan, thus making it highly promising for flood forecasting.     

A spatially distributed Clark’s unit hydrograph based hybrid hydrologic model (Distributed-Clark)

ABSTRACT

A hybrid hydrologic model (Distributed-Clark), which is a lumped conceptual and distributed feature model, was developed based on the combined concept of Clark’s unit hydrograph and its spatial decomposition methods, incorporating refined spatially variable flow dynamics to implement hydrological simulation for spatially distributed rainfall–runoff flow. In Distributed-Clark, the Soil Conservation Service (SCS) curve number method is utilized to estimate spatially distributed runoff depth and a set of separated unit hydrographs is used for runoff routing to obtain a direct runoff flow hydrograph. Case studies (four watersheds in the central part of the USA) using spatially distributed (Thiessen polygon-based) rainfall data of storm events were used to evaluate the model performance. Results demonstrate relatively good fit to observed streamflow, with a Nash-Sutcliffe efficiency (E_NS) of 0.84 and coefficient of determination (R²) of 0.86, as well as a better fit in comparison with outputs of spatially averaged rainfall data simulations for two models including HEC-HMS.     

The role of hydrograph indices in parameter estimation of rainfall–runoff models

A reliable prediction of hydrologic models, among other things, requires a set of plausible parameters that correspond with physiographic properties of the basin. This study proposes a parameter estimation approach, which is based on extracting, through hydrograph diagnoses, information in the form of indices that carry intrinsic properties of a basin. This concept is demonstrated by introducing two indices that describe the shape of a streamflow hydrograph in an integrated manner. Nineteen mid‐size (223–4790 km²) perennial headwater basins with a long record of streamflow data were selected to evaluate the ability of these indices to capture basin response characteristics. An examination of the utility of the proposed indices in parameter estimation is conducted for a five‐parameter hydrologic model using data from the Leaf River, located in Fort Collins, Mississippi. It is shown that constraining the parameter estimation by selecting only those parameters that result in model output which maintains the indices as found in the historical data can improve the reliability of model predictions. These improvements were manifested in (a) improvement of the prediction of low and high flow, (b) improvement of the overall total biases, and (c) maintenance of the hydrograph's shape for both long‐term and short‐term predictions. Copyright © 2005 John Wiley & Sons, Ltd.     

The influence of elevation error on the morphometrics of channel networks extracted from DEMs and the implications for hydrological modelling

Stream network morphometrics have been used frequently in environmental applications and are embedded in several hydrological models. This is because channel network geometry partly controls the runoff response of a basin. Network indices are often measured from channels that are mapped from digital elevation models (DEMs) using automated procedures. Simulations were used in this paper to study the influence of elevation error on the reliability of estimates of several common morphometrics, including stream order, the bifurcation, length, area and slope ratios, stream magnitude, network diameter, the flood magnitude and timing parameters of the geomorphological instantaneous unit hydrograph (GIUH) and the network width function. DEMs of three UK basins, ranging from high to low relief, were used for the analyses. The findings showed that moderate elevation error (RMSE of 1·8 m) can result in significant uncertainty in DEM‐mapped network morphometrics and that this uncertainty can be expressed in complex ways. For example, estimates of the bifurcation, length and area ratios and the flood magnitude and timing parameters of the GIUH each displayed multimodal frequency distributions, i.e. two or more estimated values were highly likely. Furthermore, these preferential estimates were wide ranging relative to the ranges typically observed for these indices. The wide‐ranging estimates of the two GIUH parameters represented significant uncertainty in the shape of the unit hydrograph. Stream magnitude, network diameter and the network width function were found to be highly sensitive to elevation error because of the difficulty in mapping low‐magnitude links. Uncertainties in the width function were found to increase with distance from outlet, implying that hydrological models that use network width contain greater uncertainty in the shape of the falling limb of the hydrograph. In light of these findings, care should be exercised when interpreting the results of analyses based on DEM‐mapped stream networks. Copyright © 2007 John Wiley & Sons, Ltd.