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.     

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.     

The roles of channels and hillslopes in rainfall/run‐off lag times during intense storms in a steep catchment

The response time (lag time) between rainfall input and run‐off output in headwater catchments is a key parameter for flood prediction. Lag times are expected to be controlled by run‐off processes, both on hillslopes and in channels. To demonstrate these effects on peak lag times within a 4.5‐km² catchment, we measured stream water levels at up to 16 channel locations at 1‐min intervals and compared the lag times with topographic indices describing the length and gradient of the hillslope and channel flow path. We captured storm events with a total precipitation of 38–198 mm and maximum hourly precipitation intensity of 9–90 mm/hr. There were positive relationships between lag time and flow path length as well as the ratio of the flow path length and the square root of the gradient of channels for the most intense storms, demonstrating that channel flow paths generally defined the variation in lag times. Topographic analysis showed that hillslope flow path lengths were similar among locations, whereas channel flow path length increased almost one order of magnitude with a 100‐fold increase in catchment area. Thus, the relative importance of hillslope flow path decreased with increasing catchment area. Our results indicate that the variation in lag times is small when hillslopes are sufficiently wet; thus, catchment‐scale variation in lag times can be explained almost entirely by channel processes. Detailed topographic channel information can improve prediction of flood peak timing, whereas hillslopes can be treated as homogeneous during large flood events.     

Understanding the relative role of dispersion mechanisms across basin scales

Different mechanisms are understood to represent the primary sources of the variance of travel time distribution in natural catchments. To quantify the fraction of variance introduced by each component, dispersion coefficients have been earlier defined in the framework of geomorphology-based rainfall-runoff models. In this paper we compare over a wide range of basin sizes and for a variety of runoff conditions the relative role of geomorphological dispersion, related to the heterogeneity of path lengths, and hillslope kinematic dispersion, generated by flow processes within the hillslopes. Unlike previous works, our approach does not focus on a specific study case; instead, we try to generalize results already obtained in previous literature stemming from the definition of a few significant parameters related to the metrics of the catchment and flow dynamics. We further extend this conceptual framework considering the effects of two additional variance-producing processes: the first covers the random variability of hillslope velocities (i.e. of travel times over hillslopes); the second deals with non-uniform production of runoff over the basin (specifically related to drainage density). Results are useful to clarify the role of hillslope kinematic dispersion and define under which conditions it counteracts or reinforces geomorphological dispersion. We show how its sign is ruled by the specific spatial distribution of hillslope lengths within the basin, as well as by flow conditions. Interestingly, while negative in a wide range of cases, kinematic dispersion is expected to become invariantly positive when the variability of hillslope velocity is large.     

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.     

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.     

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.     

Machine learning based identification of dominant controls on runoff dynamics

Hydrological models used for flood prediction in ungauged catchments are commonly fitted to regionally transferred data. The key issue of this procedure is to identify hydrologically similar catchments. Therefore, the dominant controls for the process of interest have to be known. In this study, we applied a new machine learning based approach to identify the catchment characteristics that can be used to identify the active processes controlling runoff dynamics. A random forest (RF) regressor has been trained to estimate the drainage velocity parameters of a geomorphologic instantaneous unit hydrograph (GIUH) in ungauged catchments, based on regionally available data. We analyzed the learning procedure of the algorithm and identified preferred donor catchments for each ungauged catchment. Based on the obtained machine learning results from catchment grouping, a classification scheme for drainage network characteristics has been derived. This classification scheme has been applied in a flood forecasting case study. The results demonstrate that the RF could be trained properly with the selected donor catchments to successfully estimate the required GIUH parameters. Moreover, our results showed that drainage network characteristics can be used to identify the influence of geomorphological dispersion on the dynamics of catchment response.     

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.     

Stormflow generation and flowpath characteristics in an Amazonian rainforest catchment

The Amazon basin covers an area of roughly 7 × 10⁶ km² and encompasses diverse soil – landscape types with potentially differing hydrological behaviour. This study was conducted in the Ultisol landscape of the western Amazon basin in Peru. Processes of stormflow generation were investigated on an event basis in a first‐order rainforest catchment to establish a causal link between soil physical and precipitation characteristics, hillslope flowpaths and stormflow hydrograph attributes. A sharp decrease in soil hydraulic conductivity with depth and high rainfall intensity and frequency favour rapid near‐surface flowpaths, mainly in the form of saturation‐excess overland flow and return flow. The latter results in an almost random occurrence of overland flow, with no obvious topographic control. Hillslope flowpaths do not vary much with respect to the hydrograph attributes time of rise, response time, lag time and centroid lag time. They have the same response time as streamflow, but a somewhat lower time of rise and significantly shorter lag times. The recession constant for hillslope hydrographs is about 10 min, in contrast to the streamflow recession constants of 28, 75 and 149 min. Stormflow generation in this Ultisol rainforest catchment differs strongly from that reported for Oxisol rainforest catchments. These two soilscapes may define a spectrum of possible catchment hydrological behaviour in the Amazon basin. Copyright © 2000 John Wiley & Sons, Ltd.     

Conceptualization of runoff processes using a geographical information system and tracers in a nested mesoscale catchment

Tracer investigations were combined with a geographical information system (GIS) analysis of the 31 km² Girnock catchment (Cairngorm Mountains, Scotland) in order to understand hydrological functioning by identifying dominant runoff sources and estimating mean residence times. The catchment has a complex geology, soil cover and topography. Gran alkalinity was used to demonstrate that catchment geology has a dominant influence on baseflow chemistry, but flow paths originating in acidic horizons in the upper soil profiles controlled stormflow alkalinity. Chemically based hydrograph separations at the catchment scale indicated that ～30% of annual runoff was derived from groundwater sources. Similar contributions (23–36%) were estimated for virtually all major sub‐basins. δ¹⁸O of precipitation (mean: ? 9·4‰; range: ? 16·1 to ? 5·0‰) and stream waters (mean: ? 9·1‰; range: ? 11·6 to ? 7·4‰) were used to assess mean catchment and sub‐basin residence times, which were in the order ～4–6 months. GIS analysis showed that these tracer‐based diagnostic features of catchment functioning were consistent with the landscape organization of the catchment. Soil and HOST (Hydrology of Soil Type) maps indicated that the catchment and individual sub‐basins were dominated by hydrologically responsive soils, such as peats (Histosol), peaty gleys (Histic Gleysols) and rankers (Umbric Leptosols and Histosols). Soil cover (in combination with a topographic index) predicted extensive areas of saturation that probably expand during hydrological events, thus providing a high degree of hydrological connectivity between catchment hillslopes and stream channel network. This was validated by aerial photographic interpretation and groundtruthing. These characteristics of hydrological functioning (i.e. dominance of responsive hydrological pathways and short residence times) dictate that the catchment is sensitive to land use change impacts on the quality and quantity of streamflows. It is suggested that such conceptualization of hydrological functioning using tracer‐validated GIS analysis can play an important role in the sustainable management of river basins. Copyright © 2006 John Wiley & Sons, Ltd.     

A modelling framework for evaluation of the hydrological impacts of nature‐based approaches to flood risk management,with application to in‐channel interventions across a 29‐km2 scale catchment in the United Kingdom

Nature‐based approaches to flood risk management are increasing in popularity. Evidence for the effectiveness at the catchment scale of such spatially distributed upstream measures is inconclusive. However, it also remains an open question whether, under certain conditions, the individual impacts of a collection of flood mitigation interventions could combine to produce a detrimental effect on runoff response. A modelling framework is presented for evaluation of the impacts of hillslope and in‐channel natural flood management interventions. It couples an existing semidistributed hydrological model with a new, spatially explicit, hydraulic channel network routing model. The model is applied to assess a potential flood mitigation scheme in an agricultural catchment in North Yorkshire, United Kingdom, comprising various configurations of a single variety of in‐channel feature. The hydrological model is used to generate subsurface and surface fluxes for a flood event in 2012. The network routing model is then applied to evaluate the response to the addition of up to 59 features. Additional channel and floodplain storage of approximately 70,000 m³ is seen with a reduction of around 11% in peak discharge. Although this might be sufficient to reduce flooding in moderate events, it is inadequate to prevent flooding in the double‐peaked storm of the magnitude that caused damage within the catchment in 2012. Some strategies using features specific to this catchment are suggested in order to improve the attenuation that could be achieved by applying a nature‐based approach.     

Investigating mechanisms of stormflow generation by natural tracers and hydrometric data: a small catchment study in the Black Forest,Germany

The importance and interaction of various hydrological pathways and identification of runoff source areas involved in solute transport are still under considerable debate in catchment hydrology. To reveal stormflow generating areas and flow paths, hydrometric behaviour of throughfall, soil water from various depths, runoff, and respective concentrations of the environmental tracers ¹⁸O, Si, K, SO₄ and dissolved organic carbon were monitored for a 14‐week period in a steep headwater catchment in the Black Forest Mountains, Germany. Two stormflow hydrographs were selected and, based on ¹⁸O and Si, chemically separated into three flow components. Their sources were defined using mixing diagrams. Additional information about stormflow generating mechanisms was derived from recession analyses of the basin's complete 5‐year hydrograph record. By providing insight into storage properties and residence times of outflowing reservoirs of the basin, recession analysis proved to be a valuable tool in runoff model conceptualization. Its results agreed well with hydrometric and hydrochemical data. Supported by evaluation of 30 hillslope soil profiles a coherent concept of stormflow generation could be derived: whereas in many steeply sloped basins in the temperate region soil water from hillslopes appears to have an immediate effect on the shape of the stormflow hydrograph, its role at this basin is basically restricted to the recharge of the groundwater reservoir in the near‐channel area. Storm hydrograph peaks appear to be derived from a small direct runoff component supplemented by a fast delivery of baseflow from the groundwater reservoir in the valley bottom. Copyright © 2001 John Wiley & Sons, Ltd.     

Hydrological effects of within-catchment heterogeneity of drainage density

Local drainage density (dd) has been traditionally defined as the inverse of twice the distance one has to walk before encountering a channel. This formalization easily allows to derive raster-based maps of dd extracted straight off from digital elevation model data. Maps of local dd, which are continuous in space, are able to reveal the appearance of strong heterogeneities in the geological and geomorphological properties of natural landscapes across different scales. In this work we employ the information provided by these spatial maps to study the potential effects of the within-catchment variability of dd on the hydrologic response. A simple power law relationship between runoff yield at the local scale and the value of dd has been adopted; the hypothesis is supported by a large number of past empirical observations and modeling. The novel framework proposed (ddRWF) embeds this spatially variable runoff weight in the well-known Rescaled Width Function (RWF) framework, based on the more general geomorphological theory of the hydrologic response. The model is applied to four sub-basins in the Cascade Range Region (Oregon, USA) where strong contrasts in dissection patterns due the underlain geology have been broadly addressed in previous literature. The ddRWF approach is compared with the classic RWF in terms of shape, moments and peak of the simulated hydrograph response. Results hint that the variability of runoff yield due to the heterogeneity of dd (i.e. of hillslope lengths) determines a more rapid concentration of runoff, which implies shorter lag times, larger skewness and higher peak floods, especially in the case hillslope velocity is much smaller than channel velocity. The potential of the proposed framework relies on accounting for spatially variable losses related to geomorphologic heterogeneity in lumped rainfall–runoff models, still keeping the simple and robust structure of the IUH approach.     

Impacts of upland open drains upon runoff generation: a numerical assessment of catchment‐scale impacts

Shallow upland drains, grips, have been hypothesized as responsible for increased downstream flow magnitudes. Observations provide counterfactual evidence, often relating to the difficulty of inferring conclusions from statistical correlation and paired catchment comparisons, and the complexity of designing field experiments to test grip impacts at the catchment scale. Drainage should provide drier antecedent moisture conditions, providing more storage at the start of an event; however, grips have higher flow velocities than overland flow, thus potentially delivering flow more rapidly to the drainage network. We develop and apply a model for assessing the impacts of grips on flow hydrographs. The model was calibrated on the gripped case, and then the gripped case was compared with the intact case by removing all grips. This comparison showed that even given parameter uncertainty, the intact case had significantly higher flood peaks and lower baseflows, mirroring field observations of the hydrological response of intact peat. The simulations suggest that this is because delivery effects may not translate into catchment‐scale impacts for three reasons. First, in our case, the proportions of flow path lengths that were hillslope were not changed significantly by gripping. Second, the structure of the grip network as compared with the structure of the drainage basin mitigated against grip‐related increases in the concentration of runoff in the drainage network, although it did marginally reduce the mean timing of that concentration at the catchment outlet. Third, the effect of the latter upon downstream flow magnitudes can only be assessed by reference to the peak timing of other tributary basins, emphasizing that drain effects are both relative and scale dependent. However, given the importance of hillslope flow paths, we show that if upland drainage causes significant changes in surface roughness on hillslopes, then critical and important feedbacks may impact upon the speed of hydrological response. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical simulation of the impact of sediment supply and streamflow variations on channel grain sizes and Chinook salmon habitat in mountain drainage networks

Climatically driven changes in streamflow and hillslope sediment supply could potentially alter stream surface grain size distribution patterns and thereby impact habitat for a number of threatened and endangered in‐stream fish species. Relatively little is known about hydrograph (shape, peak flow) influence or the relative importance of chronic and episodic hillslope inputs on channel conditions. To better understand these external drivers, we calculated sediment routing through a gravel‐bedded river network using a one‐dimensional (1D) bedload transport model. We calculated changes in grain sizes and estimated Chinook salmon habitat suitability caused by a dry year and an extreme flood hydrograph, and chronic (diffusive, overland flow) or pulse (landslide, debris flow) hillslope sediment supplies. To obtain accurate channel conditions, a relatively high reference Shields stress, representative of steep mountain streams, was needed. An extreme event flood without any hillslope sediment inputs caused widespread bed coarsening and a decrease in aquatic habitat. Chronic sediment input combined with this hydrograph eliminated any changes in grain size and habitat, although when combined with a dry year flow, caused systematic bed fining. The influence of a given hydrograph therefore highly depends on the hillslope sediment supply. Regardless of the flow hydrograph or sediment pulse timing, grain size distribution or location, pulse sediment inputs did not cause widespread grain size changes despite being 100 times the total chronic input volume. Widespread and continuous hillslope sediment inputs may influence channel grain sizes and aquatic habitat more than a single discrete sediment pulse. Depending on the magnitudes of flow hydrograph and sediment supply alterations, climate change may induce no differences in grain sizes or very dramatic changes with significant consequences for long‐term sustainability. Copyright © 2013 John Wiley & Sons, Ltd.     

The introduction of runoff routing into large-scale hydrological models

Two alternative schemes are presented that are appropriate for the representation of runoff routing in large-scale grid-based hydrological models and atmospheric general circulation models (AGCMs). The first scheme characterizes routing processes as a single conceptual store. The second scheme, developed by Naden (1992), uses the normalized network width function to characterize the channel network form and a linear solution to the convective diffusion equation of one-dimensional flow to characterize the routing effect of a single channel. Both schemes are applied to the Severn catchment at the daily time-scale for the period 1981 to 1990 using a grid resolution of 40 km. Comparable results were obtained using both schemes (efficiencies were of the order of 80% in both cases). A combined model using a conceptual reservoir to represent hillslope routing and the network-based scheme to represent channel routing was developed to investigate the relative roles of hillslope and channel routing at the catchment scale. The application of this model demonstrated the important role of hillslope routing in reproducing the low frequency component of the catchment response. However, in terms of goodness-of-fit there was little to choose between the three schemes. Consequently, it is recommended that additional a priori knowledge of the routing processes should be used to condition the choice of model structure. © 1997 John Wiley & Sons, Ltd.