Analytical model for a geomorphological instantaneous unit hydrograph

The rainfall‐runoff modelling of a river basin can be divided into two processes: the production function and the transfer function. The production function determines the proportion of gross rainfall actually involved in the runoff. The transfer function spreads the net rainfall over time and space in the river basin. Such a transfer function can be modelled using the approach of the geomorphological instantaneous unit hydrograph (GIUH). The effectiveness of geomorphological models is actually revealed in rainfall‐runoff modelling, where hydrologic data are desperately lacking, just as in ungauged basins. These models make it possible to forecast the hydrograph shape and runoff variation versus time at the basin outlet. This article is an introduction to a new GIUH model that proves to be simple and analytical. Its geomorphological parameters are easily available on a map or from a digital elevation model. This model is based on general hypotheses on symmetry that provide it with multiscale versatile characteristics. After having validated the model in river basins of very different nature and size, we present an application of this model for rainfall‐runoff modelling. Since parameters are determined relying on real geomorphological data, no calibration is necessary, and it is then possible to carry out rainfall‐runoff simulations in ungauged river basins. Copyright © 2006 John Wiley & Sons, Ltd.     

A model for distributed GIUH‐based flow routing on natural and anthropogenic hillslopes

Attempts to reduce the number of parameters in distributed rainfall–runoff models have not yet resulted in a model that is accurate for both natural and anthropogenic hillslopes. We take on the challenge by proposing a distributed model for overland flow and channel flow based on a combination of a linear response time distribution and the hillslope geomorphologic instantaneous unit hydrograph (GIUH), which can be calculated with only a digital elevation model and a map with field boundaries and channel network as input. The spatial domain is subdivided into representative elementary hillslopes (REHs) for each of which we define geometric and flow velocity parameters and compute the GIUH. The catchment GIUH is given by the sum of all REH responses. While most distributed models only perform well on natural hillslopes, the advantage of our approach is that it can also be applied to modified hillslopes with for example a rectangular drainage network and terrace cultivation. Tests show that the REH‐GIUH approach performs better than classical routing functions (exponential and gamma). Simulations of four virtual hillslopes suggest that peak flow at the catchment outlet is directly related to drainage density. By combining the distributed flow routing model with a lumped‐parameter infiltration model, we were also able to demonstrate that terrace cultivation delays the response time and reduces peak flow in comparison to the same hillslope, but with a natural stream network. The REH‐GIUH approach is a first step in the process of coupling distributed hydrological models to erosion and water quality models at the REH (associated with agricultural management) and at the catchment scale (associated with the evaluation of the environmental impact of human activities). It furthermore provides a basis for the development of models for large catchments and urban or peri‐urban catchments. Copyright © 2013 John Wiley & Sons, Ltd.     

Response time and water origin in a steep nested catchment in the Italian Dolomites

In this study, we investigate the surface flow time of rise in response to rainfall and snowmelt events at different spatial scales and the main sources originating channel runoff and spring water in a steep nested headwater catchment (Rio Vauz, Italian Dolomites), characterized by a marked elevation gradient. We monitored precipitation at different elevations and measured water stage/streamflow at the outlet of two rocky subcatchments of the same size, representative of the upper part of the catchment dominated by outcropping bedrock, at the outlet of a soil‐mantled and vegetated subcatchment of similar size but different morphology, and at the outlet of the main catchment. Hydrometric data are coupled with stable isotopes and electrical conductivity sampled from different water sources during five years, and used as tracers in end‐member mixing analysis, application of two component mixing models and analysis of the slope of the dual‐isotope regression line. Results reveal that times of rise are slightly shorter for the two rocky subcatchments, particularly for snowmelt and mixed rainfall/snowmelt events, compared to the soil‐mantled catchment and the entire Rio Vauz Catchment. The highly‐variable tracer signature of the different water sources reflects the geomorphological and geological complexity of the study area. The principal end‐members for channel runoff and spring water are identified in rainfall and snowmelt, which are the dominant water sources in the rocky upper part of the study catchment, and soil water and shallow groundwater, which play a relevant role in originating baseflow and spring water in the soil‐mantled and vegetated lower part of the catchment. Particularly, snowmelt contributes up to 64 ± 8% to spring water in the concave upper parts of the catchment and up to 62 ± 11% to channel runoff in the lower part of the catchment. These results offer new experimental evidences on how Dolomitic catchments capture and store rain water and meltwater, releasing it through a complex network of surface and subsurface flow pathways, and allow for the construction of a preliminary conceptual model on water transmission in snowmelt‐dominated catchments featuring marked elevation gradients.     

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.     

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.     

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.     

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.     

A physically based distributed subsurface–surface flow dynamics model for forested mountainous catchments

This study was designed to develop a physically based hydrological model to describe the hydrological processes within forested mountainous river basins. The model describes the relationships between hydrological fluxes and catchment characteristics that are influenced by topography and land cover. Hydrological processes representative of temperate basins in steep terrain that are incorporated in the model include intercepted rainfall, evaporation, transpiration, infiltration into macropores, partitioning between preferential flow and soil matrix flow, percolation, capillary rise, surface flow (saturation‐excess and return flow), subsurface flow (preferential subsurface flow and baseflow) and spatial water‐table dynamics. The soil–vegetation–atmosphere transfer scheme used was the single‐layer Penman–Monteith model, although a two‐layer model was also provided. The catchment characteristics include topography (elevation, topographic indices), slope and contributing area, where a digital elevation model provided flow direction on the steepest gradient flow path. The hydrological fluxes and catchment characteristics are modelled based on the variable source‐area concept, which defines the dynamics of the watershed response. Flow generated on land for each sub‐basin is routed to the river channel by a kinematic wave model. In the river channel, the combined flows from sub‐basins are routed by the Muskingum–Cunge model to the river outlet; these comprise inputs to the river downstream. The model was applied to the Hikimi river basin in Japan. Spatial decadal values of the normalized difference vegetation index and leaf area index were used for the yearly simulations. Results were satisfactory, as indicated by model efficiency criteria, and analysis showed that the rainfall input is not representative of the orographic lifting induced rainfall in the mountainous Hikimi river basin. Also, a simple representation of the effects of preferential flow within the soil matrix flow has a slight significance for soil moisture status, but is insignificant for river flow estimations. Copyright © 2005 John Wiley & Sons, Ltd.     

A hillslope-based hydrological model using catchment area and width functions

Abstract

A flow-interval hillslope discretization scheme is proposed for catchment hydrological modelling. By this scheme, a two-dimensional catchment is simplified into a one-dimensional cascade of flow intervals linked by the main stream. Each flow interval comprises a set of parallel hillslopes. The hillslope is the fundamental computational unit in the hydrological model providing lateral inflow to the main stream. The size of hillslope is determined by the catchment area and width functions. Catchment runoff is the total of hillslope responses through the river routing. Tests in four Japanese catchments showed that the model performed well on simulating the overall water balance, general flow pattern, and daily and hourly hydrographs of a whole catchment, as well as simultaneous simulation in different subcatchments. Characteristics of catchment hydrological responses and model applicability are discussed.     

Effects of hillslope dynamics and network geometry on the scaling properties of the hydrologic response

This paper investigates the specific contributions of river network geomorphology, hillslope flow dynamics and channel routing to the scaling behavior of the hydrologic response as function of drainage area. Scaling relationships emerged from the observations of geomorphological and hydrological data and were reproduced in previous works through mathematical models, for both idealized self-similar networks and natural basins. Recent literature highlighted that scale invariance of hydrological quantities depends not only on the metrics of the drainage catchment but also on effective flow routing. In this study we employ a geomorphological width function scheme to test the simple scaling hypothesis adopting more realistic dynamic conditions than in previous approaches, specifically taking into account the role of hillslopes. The analysis is based on the derivation of the characteristic distributions of path lengths and travel times, inferred from DEM processing and measurements of rainfall and runoff data. The study area is located in the Tiber River region (central Italy).Results indicate that, while scaling properties clearly emerge when the hydrologic response is defined on the basis of the sole geomorphology, scale invariance is broken when less idealized flow dynamics are taken into account. Lack of scaling appears in particular as a consequence of the catchment to catchment variability of hillslope velocities.     

INFLUENCE OF THE DRAINAGE NETWORK IDENTIFICATION METHOD ON GEOMORPHOLOGICAL PROPERTIES AND HYDROLOGICAL RESPONSE

The influence of the method of identification of the drainage network on its geomorphological characteristics and on its hydrological response is analysed. Blue lines, photo-interpreted networks and networks generated from digital elevation models (DEMs) by an automatic algorithm are compared with field observations for two small alpine catchments. The comparisons are carried out in quantitative terms by using several geomorphological indices and functions and by calculating the hydrological response of the networks as represented by their geomorphologic instantaneous unit hydrograph (GIUH). The results show that the effect of the identification method on the geomorphological indices and on the hydrological response is significant, and that the threshold area for channel initiation is not constant. Moreover, the available data show a poor correlation between local slope and threshold area. Finally, the influence of the threshold area on the shape of the GIUH is larger when the residence time on the hillslopes is of the same order as the residence time in the network. In the opposite case, the variability of the flow velocity along the network seems to play an important role. © 1997 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.     

Assessment of flooding in urbanized ungauged basins: a case study in the Upper Tiber area,Italy

The reliability of a procedure for investigation of flooding into an ungauged river reach close to an urban area is investigated. The approach is based on the application of a semi‐distributed rainfall–runoff model for a gauged basin, including the flood‐prone area, and that furnishes the inlet flow conditions for a two‐dimensional hydraulic model, whose computational domain is the urban area. The flood event, which occurred in October 1998 in the Upper Tiber river basin and caused significant damage in the town of Pieve S. Stefano, was used to test the approach. The built‐up area, often inundated, is included in the gauged basin of the Montedoglio dam (275 km²), for which the rainfall–runoff model was adapted and calibrated through three flood events without over‐bank flow. With the selected set of parameters, the hydrological model was found reasonably accurate in simulating the discharge hydrograph of the three events, whereas the flood event of October 1998 was simulated poorly, with an error in peak discharge and time to peak of −58% and 20%, respectively. This discrepancy was ascribed to the combined effect of the rainfall spatial variability and a partial obstruction of the bridge located in Pieve S. Stefano. In fact, taking account of the last hypothesis, the hydraulic model reproduced with a fair accuracy the observed flooded urban area. Moreover, incorporating into the hydrological model the flow resulting from a sudden cleaning of the obstruction, which was simulated by a ‘shock‐capturing’ one‐dimensional hydraulic model, the discharge hydrograph at the basin outlet was well represented if the rainfall was supposed to have occurred in the region near the main channel. This was simulated by reducing considerably the dynamic parameter, the lag time, of the instantaneous unit hydrograph for each homogeneous element into which the basin is divided. The error in peak discharge and time to peak decreased by a few percent. A sensitivity analysis of both the flooding volume involved in the shock wave and the lag time showed that this latter parameter requires a careful evaluation. Moreover, the analysis of the hydrograph peak prediction due to error in rainfall input showed that the error in peak discharge was lower than that of the same input error quantity. Therefore, the obtained results allowed us to support the hypothesis on the causes which triggered the complex event occurring in October 1998, and pointed out that the proposed procedure can be conveniently adopted for flood risk evaluation in ungauged river basins where a built‐up area is located. The need for a more detailed analysis regarding the processes of runoff generation and flood routing is also highlighted. Copyright © 2005 John Wiley & Sons, Ltd.     

DISTRIBUTED RAINFALL–RUNOFF MODEL INCORPORATING CHANNEL EXTENSION AND GRIDDED DIGITAL MAPS

Models based on gridded maps provide a simple and flexible way of modelling hydrological processes at the catchment scale. Such a model is described for humid temperate regions where no regional aquifer is present. The catchment is represented by a grid of 50 × 50 m interconnected cells. These are characterized by the depth and porosity of the soil layer, the slope and direction of drainage, the possible presence of a stretch of river and the presence or absence of forest canopy. Three types of hydrological processes are modelled: throughflow (described by a modified version of Darcy's law); channel flow (described by Manning's equation); and the interception–evaporation process as dependent on the presence or absence of forest canopy. The model predicts the hydrograph at the catchment outlet and the location of rivers in the catchment. These are compared with the observed river network, thus providing an additional means of assessing the model. © 1997 by John Wiley & Sons, Ltd.     

MODELLING RAINFALL-RUNOFF FROM LARGE CATCHMENT TO BASIN SCALE: THE GOULBURN VALLEY,VICTORIA

A lumped parameter dynamic rainfall-runoff model, IHACRES, is applied to the large upland area (more than 4500 km²) of the Goulburn Valley Basin, Victoria, Australia to predict streamflow under different climatic conditions. This paper presents the first evaluation of a rainfall–runoff model at large catchment scale, which is comprehensive in terms of the number of catchments investigated and the number of calibration and simulation periods used. The basin is subdivided into 12 catchments (from 100 to 700 km²), each of which is calibrated separately. High values of model efficiency and low bias are consistently obtained for different calibration sub-periods for all catchments in the basin. Simulation or so-called validation tests are used to select the best models for each catchment. This allows simulation of the water regime during long historical (approximately 90 year) periods when only climatological (rainfall and temperature) data were available. This procedure is extremely important for the estimation of the effect of climate variability and of the possible impact of climate change on the hydrological regime in the region and, in particular, for supporting irrigation management of the basin. Analysis of a composite catchment (2417 km²) and its five separate subcatchments indicates that the information content in the rainfall–streamflow data is independent of catchment size. Dynamic modelling of the daily water balance at the macroscale is limited principally by the adequacy of the precipitation gauging network. When a good estimate of areal precipitation is available for a catchment, it is not necessary to consider subcatchment-scale variability for modelling if the only interest is the daily discharge and evaporation losses from the catchment.     

Impact of the spatial distribution of imperviousness on the hydrologic response of an urbanizing basin

An event‐based model is used to investigate the impact of the spatial distribution of imperviousness on the hydrologic response of a basin characterized by an urban land use. The impact of the spatial distribution of imperviousness is investigated by accounting for its location within the basin when estimating the generated runoff and the hydrologic response. The event model accounts for infiltration and saturation excess; the excess runoff is routed to the outlet using a geomorphologic unit hydrograph. To represent the spatial distribution of rainfall and imperviousness, radar and remotely derived data are used, respectively. To estimate model parameters and analyse their behaviour, a split sample test and parameter sensitivity analysis are performed. From the analysis of parameters, we found the impervious cover tends to increase the sensitivity and storm dependency of channel routing parameters. The calibrated event model is used to investigate the impact of the imperviousness gradient by estimating and comparing hydrographs at internal locations in the basin. From this comparison, we found the urban land use and the spatial variability of rainfall can produce bigger increases in the peak flows of less impervious areas than the most urbanized ones in the basin. To examine the impacts of the imperviousness pattern, scenarios typifying extreme cases of sprawl type and clustered development are used while accounting for the uncertainty in parameters and the initial condition. These scenarios show that the imperviousness pattern can produce significant changes in the response at the main outlet and at locations internal to the overall watershed. Overall, the results indicate the imperviousness pattern can be an influential factor in shaping the hydrologic response of an urbanizing basin. Copyright © 2010 John Wiley & Sons, Ltd.