Variable power‐law scaling of hillslope Hortonian rainfall–runoff processes

Hydrological studies focused on Hortonian rainfall–run‐off scaling have found that the run‐off depth generally declines with the plot length in power‐law scaling. Both the power‐law proportional coefficient and the scaling exponent show great variability for specific conditions, but why and how they vary remain unclear. In the present study, the scaling of hillslope Hortonian rainfall–run‐off processes is investigated for different rainfall, soil infiltration, and hillslope surface characteristics using the physically based cell‐based rainfall‐infiltration‐run‐off model. The results show that both temporally intermittent and steady rainfalls can result in prominent power‐law scaling at the initial stage of run‐off generation. Then, the magnitude of the power‐law scaling decreases gradually due to the decreasing run‐on effect. The power‐law scaling is most sensitive to the rainfall and soil infiltration parameters. When the ratio of rainfall to infiltration exceeds a critical value, the magnitude of the power‐law scaling tends to decrease notably. For different intermittent rainfall patterns, the power‐law exponent varies in the range of ?1.0 to ?0.113, which shows an approximately logarithmic increasing trend for the proportional coefficient as a function of the run‐off coefficient. The scaling is also sensitive to the surface roughness, soil sealing, slope angle, and hillslope geometry because these factors control the run‐off routing and run‐on infiltration processes. These results provide insights into the variable scaling of the Hortonian rainfall–run‐off process, which are expected to benefit modelling of large‐scale hydrological and ecological processes.     

Improvement of surface run‐off in the hydrological model ParFlow by a scale‐consistent river parameterization

We propose an improvement of the overland‐flow parameterization in a distributed hydrological model, which uses a constant horizontal grid resolution and employs the kinematic wave approximation for both hillslope and river channel flow. The standard parameterization lacks any channel flow characteristics for rivers, which results in reduced river flow velocities for streams narrower than the horizontal grid resolution. Moreover, the surface areas, through which these wider model rivers may exchange water with the subsurface, are larger than the real river channels potentially leading to unrealistic vertical flows. We propose an approximation of the subscale channel flow by scaling Manning's roughness in the kinematic wave formulation via a relationship between river width and grid cell size, following a simplified version of the Barré de Saint‐Venant equations (Manning–Strickler equations). The too large exchange areas between model rivers and the subsurface are compensated by a grid resolution‐dependent scaling of the infiltration/exfiltration rate across river beds. We test both scaling approaches in the integrated hydrological model ParFlow. An empirical relation is used for estimating the true river width from the mean annual discharge. Our simulations show that the scaling of the roughness coefficient and the hydraulic conductivity effectively corrects overland flow velocities calculated on the coarse grid leading to a better representation of flood waves in the river channels.     

A simple model of hillslope response for overland flow generation

This paper deals with the derivation of the hydrological response of a hillslope on the assumption of quick runoff by surface runoff generation. By using the simple non‐linear storage based model, first proposed by Horton, an analytical solution of the overland flow equations over a plane hillslope was derived. This solution establishes a generalization for different flow regimes of Horton's original solution, which is valid for the transitional flow regime only. The solution proposed was compared successfully with that of Horton and, for the turbulent flow regime, to the one derived from kinematic wave theory. This solution can be applied easily to both stationary and non‐stationary rainfall excess events. An analytical solution for the instantaneous response function (IRF) was also derived. Finally, simple expressions to compute peak and time to peak of IRF are proposed. Copyright © 2001 John Wiley & Sons, Ltd.     

Do not only connect: a model of infiltration‐excess overland flow based on simulation

The paper focusses on connectivity in the context of infiltration‐excess overland flow and its integrated response as slope‐base overland flow hydrographs. Overland flow is simulated on a sloping surface with some minor topographic expression and spatially differing infiltration rates. In each cell of a 128 × 128 grid, water from upslope is combined with incident rainfall to generate local overland flow, which is stochastically routed downslope, partitioning the flow between downslope neighbours. Simulations show the evolution of connectivity during simple storms. As a first approximation, total storm runoff is similar everywhere, discharge increasing proportionally with drainage area. Moderate differences in plan topography appear to have only a second‐order impact on hydrograph form and runoff amount. Total storm response is expressed as total runoff, runoff coefficient or total volume infiltrated; each plotted against total storm rainfall, and allowing variations in average gradient, overland flow roughness, infiltration rate and storm duration. A one‐parameter algebraic expression is proposed that fits simulation results for total runoff, has appropriate asymptotic behaviour and responds rationally to the variables tested. Slope length is seen to influence connectivity, expressed as a scale distance that increases with storm magnitude and can be explicitly incorporated into the expression to indicate runoff response to simple events as a function of storm size, storm duration, slope length and gradient. The model has also been applied to a 10‐year rainfall record, using both hourly and daily time steps, and the implications explored for coarser scale models. Initial trails incorporating erosion continuously update topography and suggest that successive storms produce an initial increase in erosion as rilling develops, while runoff totals are only slightly modified. Other factors not yet considered include the dynamics of soil crusting and vegetation growth. Copyright © 2014 John Wiley & Sons, Ltd.     

One‐ and two‐dimensional modelling of overland flow in semiarid shrubland,Jornada basin,New Mexico

Two distributed parameter models, a one‐dimensional (1D) model and a two‐dimensional (2D) model, are developed to simulate overland flow in two small semiarid shrubland watersheds in the Jornada basin, southern New Mexico. The models are event‐based and represent each watershed by an array of 1‐m² cells, in which the cell size is approximately equal to the average area of the shrubs. Each model uses only six parameters, for which values are obtained from field surveys and rainfall simulation experiments. In the 1D model, flow volumes through a fixed network are computed by a simple finite‐difference solution to the 1D kinematic wave equation. In the 2D model, flow directions and volumes are computed by a second‐order predictor–corrector finite‐difference solution to the 2D kinematic wave equation, in which flow routing is implicit and may vary in response to flow conditions. The models are compared in terms of the runoff hydrograph and the spatial distribution of runoff. The simulation results suggest that both the 1D and the 2D models have much to offer as tools for the large‐scale study of overland flow. Because it is based on a fixed flow network, the 1D model is better suited to the study of runoff due to individual rainfall events, whereas the 2D model may, with further development, be used to study both runoff and erosion during multiple rainfall events in which the dynamic nature of the terrain becomes an important consideration. Copyright © 2006 John Wiley & Sons, Ltd.     

A simplified model for estimating field‐scale surface runoff hydrographs

The problem of obtaining field‐scale surface response to rainfall events is complicated by the spatial variability of infiltration characteristics of the soil and rainfall. In this paper, we develop and test a simplified model for generating surface runoff over fields with spatial variation in both rainfall rate and saturated hydraulic conductivities. The model is able to represent the effects of local variation in infiltration, as well as the run‐on effect that controls infiltration of excess water from saturated upstream areas. The effective rainfall excess is routed to the slope outlet using a simplified solution of the kinematic wave approximation. Model results are compared to averaged hydrographs from numerically‐intensive Monte–Carlo simulations for observed and design rainfall events and soil patterns that are typical of Central Italy. The simplified model is found to yield satisfactory results at a relatively small computational expense. A proposal to include a simple channel routing scheme is also presented as a prelude to extend this conceptualization to watershed scales. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of soil‐surface types on the overall runoff of the Tabernas badlands (south‐east Spain): field data and model approaches

The Tabernas desert, an extensive badlands area in Almeria province (south‐east Spain), is characterized by a high variability in soil surface cover and soil properties along with important topographical contrasts giving rise to a wide range of hydrological behaviour. A double approach through field monitoring and modelling has been used to ascertain the influence of soil‐surface variability on the overall hydrological response. Small plots were monitored for 3 years to assess runoff from the different surface types. Data provided by the long‐term monitoring of three small catchments formed by different soil surfaces were used to find out the specific contribution of each soil surface to the catchment runoff. A simple spatially distributed model was built to predict runoff generation based on the infiltration rate of each soil‐surface type (defined as terrain units with the same cover, the same soil type and on the same landform). Plot results prove that the soil surface units within the study area behave differently in terms of hydrological response to natural rainfall. These responses are explained by the types of cover, topographical characteristics and soil properties. When runoff events are simple (with one or two runoff peaks), the modelled hydrographs reproduce the hydrographs observed reasonably well, but in complex events (with several runoff peaks) the adjustment is not as good. The model also shows the influence of the spatial distribution of soil surfaces on the overall runoff, aiding exploration of the spatial hydrological relationships among different landscape units. Copyright © 2002 John Wiley & Sons, Ltd.     

Rainfall intensity affects runoff responses in a semi-arid catchment

The source and hydrochemical makeup of a stream reflects the connectivity between rainfall, groundwater, the stream, and is reflected to water quantity and quality of the catchment. However, in a semi-arid, thick, loess covered catchment, temporal variation of stream source and event associated behaviours are lesser known. Thus, the isotopic and chemical hydrographs in a widely distributed, deep loess, semi-arid catchment of the northern Chinese Loess Plateau were characterized to determine the source and hydrochemical behaviours of the stream during intra-rainfall events. Rainfall and streamflow were sampled during six hydrologic events coupled with measurements of stream baseflow and groundwater. The deuterium isotope (²H), major ions (Cl⁻, SO₄²⁻, NO₃⁻, Ca²⁺, K⁺, Mg²⁺, and Na⁺) were evaluated in water samples obtained during rainfall events. Temporal variation of ²H and Cl⁻ measured in the groundwater and stream baseflow prior to rainfall was similar; however, the isotope compositions of the streamflow fluctuated significantly and responded quickly to rainfall events, likely due to an infiltration excess, overland dominated surface runoff during torrential rainfall events. Time source separation using ²H demonstrated greater than 72% on average, the stream composition was event water during torrential rainfall events, with the proportion increasing with rainfall intensity. Solutes concentrations in the stream had loglinear relationships with stream discharge, with an outling anomaly with an example of an intra-rainfall event on Oct. 24, 2015. Stream Cl⁻ behaved nonconservative during rainfall events, temporal variation of Cl⁻ indicated a flush and washout at the onset of small rainfall events, a dilution but still high concentration pattern in high discharge and old water dominated in regression flow period. This study indicates rainfall intensity affects runoff responses in a semi-arid catchment, and the stored water in the thick, loess covered areas was less connected with stream runoff. Solute transport may threaten water quality in the area, requiring further analysis of the performance of the eco-restoration project.     

A two‐dimensional model of hydraulic performance of stormwater infiltration systems

Stormwater infiltration systems are a popular method for urban stormwater control. They are often designed using an assumption of one‐dimensional saturated outflow, although this is not very accurate for many typical designs where two‐dimensional (2D) flows into unsaturated soils occur. Available 2D variably saturated flow models are not commonly used for design because of their complexity and difficulties with the required boundary conditions. A purpose‐built stormwater infiltration system model was thus developed for the simulation of 2D flow from a porous storage. The model combines a soil moisture–based model for unsaturated soils with a ponded storage model and uses a wetting front‐tracking approach for saturated flows. The model represents the main physical processes while minimizing input data requirements. The model was calibrated and validated using data from laboratory 2D stormwater infiltration trench experiments. Calibrations were undertaken using five different combinations of calibration data to examine calibration data requirements. It was found that storage water levels could be satisfactorily predicted using parameters calibrated with either data from laboratory soils tests or observed water level data, whereas the prediction of soil moistures was improved through the addition of observed soil moisture data to the calibration data set. Copyright © 2012 John Wiley & Sons, Ltd.     

Predicting saturation‐excess runoff distribution with a lumped hillslope model: SWAT‐HS

Saturation‐excess runoff is the major runoff mechanism in humid well‐vegetated areas where infiltration rates often exceed rainfall intensity. Although the Soil and Water Assessment Tool (SWAT) is one of the most widely used models, it predicts runoff based mainly on soil and land use characteristics, and is implicitly an infiltration‐excess runoff type of model. Previous attempts to incorporate the saturation‐excess runoff mechanism in SWAT fell short due to the inability to distribute water from one hydrological response unit to another. This paper introduces a modified version of SWAT, referred to as SWAT‐Hillslope (SWAT‐HS). This modification improves the simulation of saturation‐excess runoff by redefining hydrological response units based on wetness classes and by introducing a surface aquifer with the ability to route interflow from “drier” to “wetter” wetness classes. Mathematically, the surface aquifer is a nonlinear reservoir that generates rapid subsurface stormflow as the water table in the surface aquifer rises. The SWAT‐HS model was tested in the Town Brook watershed in the upper reaches of the West Branch Delaware River in the Catskill region of New York, USA. SWAT‐HS predicted discharge well with a Nash‐Sutcliffe Efficiency of 0.68 and 0.87 for daily and monthly time steps. Compared to the original SWAT model, SWAT‐HS predicted less surface runoff and groundwater flow and more lateral flow. The saturated areas predicted by SWAT‐HS were concentrated in locations with a high topographic index and were in agreement with field observations. With the incorporation of topographic characteristics and the addition of the surface aquifer, SWAT‐HS improved streamflow simulation and gave a good representation of saturated areas on the dates that measurements were available. SWAT‐HS is expected to improve water quality model predictions where the location of the surface runoff matters.     

A network‐index‐based version of TOPMODEL for use with high‐resolution digital topographic data

This paper describes the preliminary development of a network‐index approach to modify and to extend the classic TOPMODEL. Application of the basic Beven and Kirkby form of TOPMODEL to high‐resolution (2·0 m) laser altimetric data (based upon the UK Environment Agency's light detection and ranging (LIDAR) system) to a 13·8 km² catchment in an upland environment identified many saturated areas that remained unconnected from the drainage network even during an extreme flood event. This is shown to be a particular problem with using high‐resolution topographic data, especially over large appreciable areas. To deal with the hydrological consequences of disconnected areas, we present a simple network index modification in which saturated areas are only considered to contribute when the topographic index indicates continuous saturation through the length of a flow path to the point where the path becomes a stream. This is combined with an enhanced method for dealing with the problem of pits and hollows, which is shown to become more acute with higher resolution topographic data. The paper concludes by noting the implications of the research as presented for both methodological and substantive research that is currently under way. Copyright © 2004 John Wiley & Sons, Ltd.     

Infiltration,runoff and sediment production in blanket peat catchments: implications of field rainfall simulation experiments

Blanket peat covers the headwaters of many major European rivers. Runoff production in upland blanket peat catchments is flashy with large flood peaks and short lag times; there is minimal baseflow. Little is known about the exact processes of infiltration and runoff generation within these upland headwaters. This paper presents results from a set of rainfall simulation experiments performed on the blanket peat moorland of the North Pennines, UK. Rainfall was simulated at low intensities (3–12 mm h^?1), typical of natural rainfall, on bare and vegetated peat surfaces. Runoff response shows that infiltration rate increases with rainfall intensity; the use of low‐intensity rainfall therefore allows a more realistic evaluation of infiltration rates and flow processes than previous studies. Overland flow is shown to be common on both vegetated and bare peat surfaces although surface cover does exert some control. Most runoff is produced within the top few centimetres of the peat and runoff response decreases rapidly with depth. Little vertical percolation takes place to depths greater than 10 cm owing to the saturation of the peat mass. This study provides evidence that the quickflow response of upland blanket peat catchments is a result of saturation‐excess overland flow generation. Rainfall–runoff response from small plots varies with season. Following warm, dry weather, rainfall tends to infiltrate more readily into blanket peat, not just initially but to the extent that steady‐state surface runoff rates are reduced and more flow takes place within the peat, albeit at shallow depth. Sediment erosion from bare peat plots tends to be supply limited. Seasonal weather conditions may affect this in that after a warm, dry spell, surface desiccation allows sediment erosion to become transport limited. Copyright © 2002 John Wiley & Sons, Ltd.     

The importance of surface controls on overland flow connectivity in semi‐arid environments: results from a numerical experimental approach

In semi‐arid environments, the characteristics of the land surface determine how rainfall is transformed into surface runoff and influences how this runoff moves from the hillslopes into river channels. Whether or not water reaches the river channel is determined by the hydrological connectivity. This paper uses a numerical experiment‐based approach to systematically assess the effects of slope length, gradient, flow path convergence, infiltration rates and vegetation patterns on the generation and connectivity of runoff. The experiments were performed with the Connectivity of Runoff Model, 2D version distributed, physically based, hydrological model. The experiments presented are set within a semi‐arid environment, characteristic of south‐eastern Spain, which is subject to low frequency high rainfall intensity storm events. As a result, the dominant hydrological processes are infiltration excess runoff generation and surface flow dynamics. The results from the modelling experiments demonstrate that three surface factors are important in determining the form of the discharge hydrograph: the slope length, the slope gradient and the infiltration characteristics at the hillslope‐channel connection. These factors are all related to the time required for generated runoff to reach an efficient flow channel, because once in this channel, the transmission losses significantly decrease. Because these factors are distributed across the landscape, they have a fundamental role in controlling the landscape hydrological response to storm events. Copyright © 2013 John Wiley & Sons, Ltd.     

Solute transport by surface runoff from low‐angle slopes: theory and application

The removal of chemicals in solution by overland flow from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface‐mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of depression storage capacity on overland‐flow generation for rough horizontal surfaces: water transfer distance and scaling

Overland‐flow triggering on rough surfaces was investigated using an understanding‐oriented model. The model was based on conditioned‐walker technique and developed to simulate and analyse the evolution of puddle connection on numerically generated rough surfaces. The percolation theory gave a theoretical framework to formalize model outputs and to study overland‐flow scaling. Overland‐flow triggering appeared consistent with a percolation process. A scale‐change exponent was suggested. New insights based on the concept of transfer distance of water were emphasized. Transfer distance enabled us to analyse the water redistribution inside a field and helped to define rainfall efficiency when infiltration occurred. Copyright © 2002 John Wiley & Sons, Ltd.     

Conceptual rainfall–runoff model with a two‐parameter,infinite characteristic time transfer function

A two‐parameter transfer function with an infinite characteristic time is proposed for conceptual rainfall–runoff models. The large time behaviour of the unit response is an inverse power function of time. The infinite characteristic time allows long‐term memory effects to be accounted for. Such effects are observed in mountainous and karst catchments. The governing equation of the model is a fractional differential equation in the limit of long times. Although linear, the proposed transfer function yields discharge signals that can usually be obtained only using non‐linear models. The model is applied successfully to two catchments, the Dud Koshi mountainous catchment in the Himalayas and the Durzon karst catchment in France. It compares favourably to the linear, non‐linear single reservoir models and to the GR4J model. With a single reservoir and a single transfer function, the model is capable of reproducing hysteretic behaviours identified as typical of long‐term memory effects. Computational efficiency is enhanced by approximating the infinite characteristic time transfer function with a sum of simpler, exponential transfer functions. This amounts to partitioning the reservoir into several linear sub‐reservoirs, the output discharges of which are easy to compute. An efficient partitioning strategy is presented to facilitate the practical implementation of the model. Copyright © 2015 John Wiley & Sons, Ltd.     

A depth‐averaged two‐phase model for debris flows over erodible beds

Mass exchange between debris flow and the bed plays a vital role in debris flow dynamics. Here a depth‐averaged two‐phase model is proposed for debris flows over erodible beds. Compared to previous depth‐averaged two‐phase models, the present model features a physical step forward by explicitly incorporating the mass exchange between the flow and the bed. A widely used closure model in fluvial hydraulics is employed to estimate the mass exchange between the debris flow and the bed, and an existing relationship for bed entrainment rate is introduced for comparison. Also, two distinct closure models for the bed shear stresses are evaluated. One uses the Coulomb friction law and Manning's equation to determine the solid and fluid resistances respectively, while the other employs an analytically derived formula for the solid phase and the mixing length approach for the fluid phase. A well‐balanced numerical algorithm is applied to solve the governing equations of the model. The present model is first shown to reproduce average sediment concentrations in steady and uniform debris flows over saturated bed as compared to an existing formula underpinned by experimental datasets. Then, it is demonstrated to perform rather well as compared to the full set of USGS large‐scale experimental debris flows over erodible beds, in producing debris flow depth, front location and bed deformation. The effects of initial conditions on debris flow mass and momentum gain are resolved by the present model, which explicitly demonstrates the roles of the wetness, porosity and volume of bed sediments in affecting the flow. By virtue of extended modeling cases, the present model produces debris flow efficiency that, as revealed by existing observations and empirical relations, increases with initial volume, which is enhanced by mass gain from the bed. Copyright © 2017 John Wiley & Sons, Ltd.     

The hydrology of inland valleys in the sub‐humid zone of West Africa: rainfall‐runoff processes in the M'bé experimental watershed

Inland valleys with wet lowlands are an important water source for farming communities in the sub‐humid zone of West Africa. An inland valley and surrounding contributing watershed area located in the sub‐humid zone near M'bé in central Côte d'Ivoire was instrumented to study surface runoff and base flow mechanisms. Four flumes at different distances down the main stream and more than 100 piezometers were installed. Measurements were taken during two rainfall seasons in 1998 and 1999. Under initial wet conditions, a typical single‐peak hydrograph was observed. Under low antecedent moisture conditions, however, runoff was characterized by a double‐peaked hydrograph. The first peak, which occurred during the storm, was caused by rain falling on the saturated valley bottom. The second peak was delayed by minutes to hours from the first peak and consisted of rain flowing via the subsurface of the hydromorphic zone that surrounds the valley bottom. The duration of the delay was a function of the water table depth in the hydromorphic zone before the storm. The volume of the second peak constituted the largest portion of the stream flow. Copyright © 2003 John Wiley & Sons, Ltd.