Catena 92 (2012) 216–231

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tRIBS-Erosion: A parsimonious physically-based model for studying catchmenthydro-geomorphic response

Antonio Francipane a,b,⁎, Valeriy Y. Ivanov a, Leonardo V. Noto b, Erkan Istanbulluoglu c,Elisa Arnone b, Rafael L. Bras d

a Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI, USAb Dipartimento di Ingegneria Civile, Ambientale ed Aeronautica, Università di Palermo, Palermo, Italyc Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USAd Department of Civil and Environmental Engineering and Department of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA, USA

⁎ Corresponding author at: Department of Civil anUniversity of Michigan, Ann Arbor, MI, USA.

E-mail address: frantoni@umich.edu (A. Francipane)

0341-8162/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.catena.2011.10.005

a b s t r a c t

a r t i c l e i n f o

Article history:Received 18 March 2011Received in revised form 24 October 2011Accepted 31 October 2011

Keywords:ErosionHydrologic modelingVegetationGeomorphic processes

Our goal is to develop a model capable to discern the response of a watershed to different erosion mecha-nisms. We propose a framework that integrates a geomorphic component into the physically-based andspatially distributed TIN-based Real-time Integrated Basin Simulator (tRIBS) model. The coupled modelsimulates main erosive processes of hillslopes (raindrop impact detachment, overland flow entrainment,and diffusive processes) and channel (erosion and deposition due to the action of water flow). In additionto the spatially distributed, dynamic hydrologic variables, the model computes the sediment transport dis-charge and changes in elevation, which feedback to hydrological dynamics through local changes of terrainslope, aspect, and drainage network configuration. The model was calibrated for the Lucky Hills basin, asemi-arid watershed nested in the Walnut Gulch Experimental Watershed (Arizona, USA). It is demonstratedto be capable of reproducing main runoff and sediment yield events and accumulated volumes over the longterm. The model was also used to study the response of two first-order synthetic basins representative oflandforms dominated by fluvial and diffusive erosion processes to a 100-year long stationary climate. Theanalysis of the resultant slope-contributing area relationships for the two synthetic basins illustrates thatthe model is consistent with assumed principles of behavior and capable of reproducing the main mecha-nisms of erosion.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

The dynamics of sediment production and movement fromsources (hillslopes and highlands) to sinks (lowland channels andwater bodies) have tremendous consequences on the sustainabilityof terrestrial and aquatic environments and have direct impacts onplanning and management of earth resources and human healthrisks. Erosion rates have gone up to unprecedented levels in largeparts of the globe during the past several centuries (Wilkinson andMcElroy, 2007). This increase has been attributed to growing climaticextremes (droughts and floods), urbanization, forest managementpractices, and in particular agricultural expansion. Cultivated landsglobally lose soil at rates in the range of 200–1300 [mm/m2 peryear] which surpass any plausible rate of soil development (Nearinget al., 1999; Pimentel et al., 1995; Wilkinson and McElroy, 2007). Inforested terrain, human activities including road construction, fire

d Environmental Engineering,

.

rights reserved.

suppression, and silvicultural practices have altered the hydrologicalresponse, and combined with wildfires lead to debris flows with mag-nitudes equivalent of hundreds to thousands of years of long-termerosion rates.

Understanding and predicting the basin hydro-geomorphic re-sponse and its relation to landscape morphology and hydrologicalstates is critical for managing soil and water resources under globalchange and for studying the linkages between landforms, climate,and vegetation over geomorphic time scales (Slattery et al., 2002;Wainwright and Thornes, 2003). Process-based research in geomor-phology provides numerous examples that illustrate tight linkagesbetween the landscape form and dominant erosion processes(Ahnert, 1987; Gilbert, 1909; Kirkby, 1985; Kirkby and Chorley,1967), and show how the type and frequency and magnitude of sed-iment fluxes vary across scales of time and space (Benda and Dunne,1997a, 1997b; Bierman et al., 2005; Kirchner et al., 2001; Meyer et al.,2001; Wolman and Miller, 1960). The unique role of river channelsand their morphologies in regulating sediment output from basinsin different climates have also been discussed (Benda and Dunne,1997b; Bull, 1997; Schumm, 1999). These and many other studiesin the geomorphology literature provide invaluable insights for

217A. Francipane et al. / Catena 92 (2012) 216–231

improved predictions of erosion rates and basin sediment yields at arange of scales.

The soil erosion prediction technology arguably started with theUniversal Soil Loss Equation (USLE, Wischmeier and Smith, 1965,1978) that was developed based on over 10,000 plot-years of runoffand erosion measurements on plots of 22.13 m length. The USLEequation relates erosion to a series of indices based on soil properties,conservation practices, vegetation cover condition, local slope, andmean climatology of the area. Because of its simplicity, the USLEequation has been widely used in practice and implemented, withsome modifications, in various numerical models of farm and range-land erosion (Renard et al., 1994; Williams et al., 1984). However,these models only represent sediment transport capacity due to acombination of rainsplash and overland flow erosion, which areassumed to describe processes only at the hillslope scale.

With the pioneering work of Foster and Meyer (1972), erosionmodels began adapting shear stress and stream power based equa-tions developed for sediment transport and erosion for river chan-nels, and applying those at the scale of agricultural and range landsusing various methods for flow routing. Their effort effectivelyextended the scale of erosion modeling from small, rainsplash-dominated field plots to small catchment scales. This idea has led tothe development of more mechanistic erosion models that couplemodels of watershed hydrology (mostly based on infiltration excessrunoff generation) with Foster and Meyer (1972) equations at thefield-scale (100–1000 ha), such as CREAMS (Knisel, 1980) and SWRRB(Williams et al., 1985), and at the basin-scale (>1000 ha), such asANSWERS (Beasley et al., 1980), AGNPS (Young et al., 1989), WEPP(Nearing et al., 1989), CASC2D (Ogden and Heilig, 2001), LISEM (DeRoo et al., 1995), EROSION 3D (Schmidt et al., 1999), and KINEROS(Woolhiser et al., 1990). Digital elevation models were later adaptedby most modeling groups to represent landscape topography andused to route flow and sediment and identify areas of net erosion anddeposition (De Roo, 1998; Morgan and Quinton, 2001).

Most of the aforementioned existing erosion models were devel-oped as short-term decision-making tools for agricultural and range-land management. Two notable limitations of these models are: theylack channel erosion processes, which could account for a significantportion of basin sediment yields; and, with the exception of a fewresearch models (e.g., Mitas et al., 1997), they use a fixed landscapeelevation field represented by a DEM, or cascading planes that collec-tively represent the shape and slope of a basin. As a result, there is nofeedback between erosion processes and the landscape form. Thispresents a critical limitation to model predictions especially for basinswith a well-defined valley network where episodic deposition anderosion events could occur.

At the other end of the spectrum, landscape evolution models(LEMs) were designed to examine the connections between geomor-phic processes and resulting landforms (e.g., Tucker and Bras, 1998;Veneziano and Niemann, 2000; Willgoose et al., 1991), and studythe topographic outcome of erosion-uplift interplay over geologic,millennial time scales (Whipple and Tucker, 2002). Few LEM studiesconcentrated on the role of vegetation (Collins and Bras, 2008;Collins et al., 2004; Istanbulluoglu and Bras, 2005) and subsurfaceflow hydrology (Huang and Niemann, 2006); overall, LEMs oftensimplify or completely disregard the dynamics of environmental vari-ables and hydrology over the time scales of years to decades (Martinand Church, 2004).

At the intermediate time scales, decadal to centennial, memory inbasin hydrology (soil moisture, subsurface, and groundwater flow),geomorphology (e.g., drainage patterns), and vegetation can affectthewatershed geomorphic response (e.g., Greenway, 1987). Many ob-servational studies underscore the importance of accurate representa-tion of basin hydrological response in predicting sediment fluxes: dueto a strong nonlinear dependence of sediment entrainment and trans-port on runoff discharge, inaccuracies in runoff prediction can have an

amplified influence on predicted erosion (Bennet, 1974; Rojas andWoolhiser, 2000; Wainwright and Parsons, 1998). Only few LEMsoperating at the intermediate time scales have been adapted to inte-grate a more sophisticated representation of hydrological processes(Hancock et al., 2011). For example, a grid-based model of Coulthardet al. (2002, 2005), CAESAR, introduced a topography-driven, quasi-steady-state description of the hydrological response. Operating ata fine spatial scale, the model has the capability to include effects ofdifferent vegetation covers and soil types.

Climatic extremes (both floods and droughts) have increasedsignificantly in the past century (Seager et al., 2007). Future climatepredictions further suggest even more extreme climates in someparts of the globe (Bates et al., 2008; Christensen et al., 2007). Predic-tion of erosion rates in transient climate conditions will require real-istic representations of the coupled geomorphic, hydrologic, andecologic responses that are relevant to the time and space scales ofa river basin. The objective of this study is to present a frameworkthat seamlessly integrates a geomorphic component to a hydrologicmodel. The framework is formulated to be suitable for addressingthe coupled response both at the short-term and intermediate timescales, i.e., hours to sub-millennial time intervals. The hydrologicmodel is the physically-based, spatially distributed TIN-based Real-time Integrated Basin Simulator (tRIBS) (Ivanov et al., 2004a). Thegeomorphic component is mainly based on CHILD, the Channel-Hillslope Integrated Landscape Development model (Tucker et al.,2001a). Model calibration has been carried out using streamflow, sed-iment yield, and meteorological data for the Lucky Hills basin, a semi-arid watershed nested in the Walnut Gulch Experimental Watershed(Arizona, USA).

The paper is organized as follows. Section 1 provides a brief intro-duction of the main aspects concerning the modeling of soil erosion.Section 2 describes the new geomorphic component embedded intothe tRIBS model. Section 3 introduces the Lucky Hills basin and de-scribes the data used for the model calibration (Section 4). Section 5presents a first application to two synthetic domains and its results,which are discussed in Section 6.

2. Model formulation

2.1. Overview of hydrological model

This paper presents an integration of a geomorphic componentinto an existing spatially-distributed physically-based hydrologicalmodel, the TIN (Triangulated Irregular Network)-based Real-timeIntegrated Basin Simulator, tRIBS (Ivanov et al., 2004a, 2004b). tRIBSreproduces essential hydrologic processes over complex topographyof a river basin. The model explicitly considers spatial variability inprecipitation fields and land-surface descriptors and the correspond-ing moisture dynamics. The model stresses the role of topography inlateral soil moisture redistribution by accounting for the effects ofheterogeneous and anisotropic soil. It has been recently used asframework to develop a simulation of rainfall-triggered landslides(Arnone et al., 2011). A brief outline of the implemented processparameterizations is described in the following.

1) For simulating the precipitation interception, the Rutter canopywater balance model (Rutter et al., 1971, 1975) is used at thehourly time step. Canopy water dynamics are formulated to bespecies dependent, such that model parameters vary for differentvegetation types.

2) Surface energy budget is simulated at each computational elementat the hourly scale; shortwave and longwave radiation componentsare obtained accounting for a geographic location, time of year, as-pect and slope of the element surface, and atmospheric conditions(e.g., Bras, 1990). The Penman–Monteith equation (Monteith,1965; Penman, 1948), the gradient method (Entekhabi, 2000), and

218 A. Francipane et al. / Catena 92 (2012) 216–231

the force-restore (Hu and Islam, 1995; Lin, 1980) methods are usedto estimate the latent, sensible, and ground heat fluxes at the landsurface. An optimum surface temperature is sought that leads tothe energy balance closure. A species-dependent parameterizationof stomatal conductance allows for diurnal variation of transpirationflux.

3) Latent heat flux is partitioned into evaporation from wet canopy,vegetation transpiration, and bare soil evaporation; the lattertwo are limited by available moisture in the soil zone, dependingon vegetation fractional coverage of an element and canopy state.

4) For simulating the process of infiltration (minute resolution), anassumption of gravity-dominated flow in a sloped, vertically het-erogeneous, anisotropic soil is used. The evolution of the wettingand top fronts in an element may lead to unsaturated, perched,surface, and completely saturated states. The unsaturated andthe saturated zones are coupled, accounting for the interaction ofthe moving infiltration front with a variable water table. Topogra-phy and soil control the magnitude of the lateral moisture transferin the unsaturated zone. Continuous soil moisture permits han-dling both storm and interstorm periods, thus allowing long-term simulations over a range of hydrometeorological forcings.

5) For computing the groundwater dynamics, a model based on theBoussinesq's equation under the Dupuit–Forcheimer assumptionsis used, allowing for a lateral water redistribution in the saturatedzone and its dynamic interactions with the unsaturated zone. Thelateral exchanges between contiguous elements are calculated byusing the depth-averaged aquifer transmissivity, the flow widthand the local water table slope.

6) A snowpack dynamic model has been recently added (Rinehartet al., 2008) that permits the simulation of energy and mass bud-gets of snow-covered areas.

7) Runoff generation is made possible via four mechanisms: saturationexcess (Dunne and Black, 1970), infiltration excess (Horton, 1933;Loague et al., 2010), perched subsurface stormflow (Weyman,1970), and groundwater exfiltration (Hursh and Brater, 1941). Therunoff is obtained by tracking the infiltration fronts, water tablefluctuations, and lateral moisture fluxes in the unsaturated and sat-urated zones. The runoff computed in subsurface module at theminute scale is used as input to the geomorphic model.

In order to represent basin characteristics, the model uses amultiple-resolution approach based on a TIN. The primary motivationfor the using TINs is the multiple resolutions offered by the irregularlyspaced nodes. This offers a flexible computational structure that re-duces the number of computational elements without a significantloss of information (Vivoni et al., 2004) and translates to computa-tional savings. Another advantage is that linear features can be pre-cisely preserved in the mesh which allows mimicking of terrainbreaklines, stream networks, and boundaries between heterogeneousregions. The computational elements of the coupled model are re-gions derived as the dual representation of the triangular mesh,i.e., in the form of Voronoi cells. Basin hydrological response can besimulated at very fine temporal (minutes to hour) and spatial(10–100 m) resolutions. Further details of model computationalbasis, structure, and descriptions of process parameterizations arepresented in Ivanov et al. (2004a). A discussion of the model perfor-mance for mid-sized basins is provided in Ivanov et al. (2004b).

2.2. Coupling of hydrological and geomorphic dynamics

tRIBS calculates physical processes such as interception, infiltra-tion, evapotranspiration as well as runoff using the Voronoi polygonnetwork (VPN). It is assumed that Voronoi-based quantities thatserve as input to the geomorphic model, i.e., precipitation, through-fall, canopy drainage (Section 2.3), and runoff rates (Section 2.4)are uniformly distributed inside each Voronoi cell. Possible subgrid

variability of fluxes is implemented by using “mosaic” areal fractionsof, for example, vegetation, throughfall, and bare soil (Section 2.3).

The VPN-based, locally produced runoff follows edges of a water-shed TIN in accordance with pre-determined drainage directions(boundaries between Voronoi regions serve as interfaces betweenadjoining cells, see also Section 2.5). Unlike many other erosionmodels used in practice, the presented framework explicitly evolveslandscape elevations through time (see Section 2.5), presenting adynamic feedback loop between hydrology and geomorphology. Forexample, changes in elevation will impact local slopes, which maylead to formation of a different drainage graph and thus a differentpattern of flow accumulation in a basin; locally modified site expo-sure (i.e., aspect) will imply changes in surface irradiance and there-fore energy and latent heat partition; deepening of gullies may resultin stronger connection of groundwater dynamics to surface processes,etc. Currently, runoff is assumed to propagate downstream withinthe step of 1 h, which limits the scale of application of the model toheadwater basins.

Using hydrological quantities averaged at the hourly scale asinput, the geomorphic component formulates flux equations of rain-fall detachment and sheet erosion entrainment combined with thecontinuity of mass to compute sediment dynamics across the land-scape. The rate of change in landscape elevations, ∂z/∂t, is predictedby the smaller of local erosion capacity or divergence of sedimentflux (i.e., the excess sediment transport capacity, Tucker andSlingerland, 1997; Tucker et al., 2001b):

∂z∂t ¼ −Min Dc;∇qs½ �; ð1Þ

where Min is the minimum operator, Dc [L/T] is the detachment/entrainment capacity (i.e., this work describes sediment detach-ment by rainfall and entrainment by flowing water), qs [L3/T] isthe sediment load of overland flow and ∇ is the divergence opera-tor, i.e., the sum of incoming sediment flux minus the sedimenttransport capacity, qt, at a given location. The term Dc representsa combination of the sediment detached due to raindrop impact(rainsplash) and the sediment entrained in the sheet overlandflow. In the application of this equation, similar to runoff, sedimentis routed on a cell-by-cell basis using the steepest descend flowdirection. Detached/entrained sediment of an upstream Voronoielement (or multiple elements) enters a downstream cell and isused in calculating the divergence of the sediment flux. In a continu-ous application of the geomorphic model to a watershed domain thathas a spatially variable structure of hydrological states, the trans-ported sediment accumulates or moves downstream and landscapeelevations consequently change as a result of these processes(Section 2.5). The exact geomorphological functionality introducedin the geomorphic model by considering the two mechanisms, de-tachment by raindrop impact and entrainment by sheet flow erosion,is presented in the following.

2.3. Raindrop impact detachment

Raindrops break cohesive bonds between soil particles detachingthem from soil and making them available for transport. This phe-nomenon is influenced by rainfall and soil characteristics, groundand canopy cover, and water flow depth over soil. In order to developmodel with the properties of parsimony and robustness, a well-testedapproach is implemented here, as compared to more complex ap-proaches that have only been tested for idealized conditions (e.g.,Kinnell, 2005; 2006). In particular, the conceptual approach ofWicks and Bathurst (1996) is used to assess the rate of soil detach-ment by raindrop, DR [M L−2 T−1]:

DR ¼ krFw CRMR þ CDMD½ �; ð2Þ

219A. Francipane et al. / Catena 92 (2012) 216–231

where kr [J−1] is the raindrop soil erodibility and Fw is the shield effectof surface water. Rain action is split between the action due to the di-rect raindrop impact and the effect of leaf drip. The termsMR [M2T−3]and MD [M2T−3] are the rainfall squared momentum and the leaf dripsquared momentum, respectively (Salles et al., 2000; Styczen andHogh-Schmidt, 1988), which cause the splash of the soil particlesinto the air. The variables CR and CD are weighted areal fractionsthat quantify the direct raindrop and leaf drip impacts on rainsplashdetachment respectively.

The fraction CR is modeled according to:

CR ¼ 1–Cp

� �1−Vð Þ þ pV½ �; ð3Þ

where Cp is the fraction of the Voronoi cell protected against droperosion, V is the vegetative fraction of a Voronoi cell, and p is thethroughfall coefficient for the vegetation fraction, i.e., the fraction ofrainfall over canopy not intercepted by vegetation. In Eq. (3), theterms (1−Cp) (1−V) and (1−Cp) pV represent the splash erosionin the bare soil and in the vegetated soil fraction of the Voronoi cell,respectively.

The fraction CD is modeled according to:

CD ¼ Fl 1–Cp

� �1−pð ÞV ; ð4Þ

where Fl [0÷1] is the fraction of rainfall intercepted by canopy,(1−p), that reaches the soil in the form of leaf drip. The variable Flis defined as the fraction Dl/D (Fig. 1), where Dl is the interceptionloss due to leaf dripping and D is the total canopy drainage (Ivanovet al., 2004a). The remaining fraction of rainfall intercepted bythe canopy can be split into the canopy storage component, that isreturned back to the atmosphere as evaporation, and water that canreach the soil as stemflow in a fraction equal to Fs [0÷1], anddefined as Ds/D (Fig. 1), where Ds is the loss due to stemflow. The frac-tions Fl and Fs thus represent Voronoi area subject to canopy drainagecomponent, where no erosion takes place in the fraction Fs (Fig. 1). Forfurther details the reader is referred to Appendix A and Francipane(2010).

2.4. Overland and channel transport and deposition

The model uses the shear stress-based formulations for the en-trainment and transport of sediment by runoff discharge (Nearinget al., 1999; Yang, 1996), making no distinction between overlandflow and channel flow as the form of the shear-stress based formula-tions for both cases are nearly identical. This assumption is consistentwith field observations that in most landscapes overland flow oftenquickly forms rills once an entrainment threshold is exceeded. Inaddition, at the size of elements typically used in simulations, it is

Fig. 1. A conceptual diagram of the partition of a computational cell subject to splasherosion.

difficult to distinguish rills from overland flow features. No subgridparameterization to represent rill erosion is used at this time. There-fore we calculate flow per unit width of a Voronoi edge, which morerealistically represents overland flow according to the acceptedassumption of sheet flow.

The effective boundary shear stress, τ [M/LT2], is calculatedaccording to the well known power function of local discharge andslope:

τ ¼ ktqmbSnb ; ð5Þ

where q [L3/LT] is the local discharge per unit width of Voronoi edge(for any given Voronoi cell, it is obtained by summing the outfluxesof topographically upstream elements that contribute to that cell fol-lowing the surface topographic gradient divided by the width), S [rad]is the local slope, mb and nb are empirical parameters (Istanbulluogluet al., 2004; Willgoose et al., 1991). Assuming locally uniform overlandflow conditions and using Manning's equation for the flow velocity,mb

and nb are equal to 0.6 and 0.7, respectively (Tucker et al., 2001a). Thevariable kt [ML−2 T−2] depends on the Manning's coefficient n throughthe expression (Istanbulluoglu et al., 2005; Simons and Senturk, 1977;Tucker et al., 2001b):

kt ¼ρwgn

1:5s

ns þ nvð Þ0:9 ; ð6Þ

where ρw is the water density [M/L3], g is the acceleration of gravity[L/T2], ns is the Manning's roughness coefficient for soil, and nv isthe Manning's roughness coefficient for vegetation calculated follow-ing Istanbulluoglu et al. (2005):

nv ¼ nvRVVR

� �ω; ð7Þ

where nvR and VR are the Manning's roughness coefficient and thevegetation fraction for a reference cover condition of a selected vege-tation type, respectively, and ω is a parameter. The variables VR and ωhere are assumed to be equal to 0.95 and 0.5, respectively for under-story vegetation such as grass or shrub Istanbulluoglu et al. (2005).Eq. (6) assumes site roughness n to be composed of two componentsrelated to the bare soil and vegetated fractions. The addition of vege-tation roughness in the numerator as an additive term implies thepartitioning of total shear stress on the bare soil: as nv increases, τwould reduce as a result of vegetation taking up a higher fraction ofthe total shear stress. For a detailed formulation, see Istanbulluogluand Bras (2005). The spatial variation of ns and nv inside the domaincan therefore be taken into account (Fig. 2).

Fig. 2. A conceptual diagram representing a possible model of spatial variability ofManning's roughness coefficient as assumed in the model framework.

220 A. Francipane et al. / Catena 92 (2012) 216–231

The flow entrainment capacity, DD [L/T], is calculated as:

DD ¼ kb τ−τcð ÞPb ; ð8Þ

where kb is the soil erosion efficiency coefficient [L/T (ML−1 T−2)pb],τc [M/LT2] is a threshold stress for particle entrainment (i.e., “the crit-ical shear stress”), and pb is an empirical parameter equal to 2.3(Nearing et al., 1999).

The transport capacity, DT [L3/T], is calculated as:

DT ¼ Wkf τ−τcð ÞPf ; ð9Þ

where W [L] is the channel width, considered to be equal to the widthof Voronoi edge (Tucker et al., 2001b, Fig. 7), pf is a parameter equal to2.5, and kf is a coefficient considered for the transport of a single sed-iment size-fraction and calculated using the following expression(Simon and Senturk, 1977; Yalin, 1977):

kf ¼ kk

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffig s−1ð Þd3

qρwg s−1ð Þd½ �Pf ; ð10Þ

where s is the ratio of sediment density to water density (taken as2.65) and d is the dominant grain size [L], often taken as d50, i.e., thediameter corresponding to the 50% value of the granulometric distri-bution curve, and kk is a calibration coefficient. The values of kk arereported to be in the range of 4–40 in different studies (Yalin, 1977).

2.5. Computational steps

An outline of a numerical procedure for the solution of Eq. (1)as implemented in the model is presented below. Similar to locallyproduced runoff (Ivanov et al., 2004a), eroded material is assumedto follow the TIN edges in accordance with the consecutive drainagedirections. The boundaries between Voronoi regions define the inter-faces between adjoining cells. When a mass moves into a neighboringcell, the length of a given interface is used as the width in the fluxcomputation (Ivanov et al., 2004a; Tucker et al., 2001a, 2001b). Bothrunoff and sediment are assumed to propagate downstream withinthe step of 1 h, limiting the scale of application of the model to head-water basins.

Calculation starts at the Voronoi cell with the highest elevationand proceeds downstream to the basin outlet cell:

1. For each computational element the rate of soil detachment byraindrop DR and the entrainment capacity rate DD are calculatedusing Eqs. (2) and (8), respectively.

2. The transport capacity rate DT is calculated with Eq. (9).3. For each cell a potential rate of transport-limited erosion is calcu-

lated using the control volume approach. The continuity of mass

equation can be written for any cell i as∂zi∂t ¼ 1

1−ηð Þ∂DT=W

∂x ,

where η is the bed sediment porosity and zi is the elevation at

node location i. Assuming∂z∂t≈

ΔzΔt

, Δz is solved using the forward

differencing in time:

Δzi;potΔt

¼ 11−η

∑mj qs;j

� �−DT;i

Λ i; ð11Þ

where qs is the incoming sediment flux for the cell i, m is thenumber of upstream nodes that flow directly to node i and Λi isthe Voronoi area of node i. The resulting elevation change, Δzi,pot,corresponds to the potential change. It is evaluated for each cell.

4. For each cell, the rate of detachment/entrainment-limited erosionis calculated based on the sum of rates DR and DD. This gives the

maximum rate of sediment,Δzi;avaΔt

, that can be removed from the

cell, conditioned by the local soil erodibility and the actual shearstress, even under infinite transport capacity. The potential rateof detachment/entrainment-limited erosion is:

Δzi;avaΔt

¼ − DR

ρsþ DD

� �; ð12Þ

where ρs [M/L3] is the soil density. Δzi, ava is always smaller thanzero.

5. Finally the two rates are compared with the following logicalstatements:

a. If Δzi,pot>0, then a deposition occurs and Δz=Δzi,pot;b. If Δzi, avabΔzi,potb0 (erosion), then Δzi=Δzi,pot and a transport-

limited erosion occurs;c. If Δzi,potbΔzi,avab0 (erosion), then Δzi=Δzi,ava and a detachment/

entrainment-limited erosion occurs.d. In the event that |Δzi,pot|>|Δzi,ava|, the transport capacity

rate of the flow is not at the maximum value (i.e., detachment/entrainment-limited) and upon calculation of the actual amountof erosion/deposition in the cell, the outgoing sediment fluxfrom the cell into a downstream cell is re-defined as

DT;i ¼ ∑mj¼1qs;j

� �−Λ i 1−ηð ÞΔzi;ava

Δt: ð13Þ

6. At the hourly scale, the model updates the elevation of each Voro-noi element and re-computes slopes, azimuthal aspects, flow di-rections, and drainage areas of the entire VPN, as well as re-sortsnodes following the topography-dictated network order. The latteris determined based on local maximum surface slopes (Ivanovet al., 2004a) and thus leads to a continuously updated drainagepattern. An update of all of the above terrain elements contributesto feedback from geomorphic processes of erosion and depositionto the watershed hydrological dynamics.

3. Lucky Hills watershed description and data

Data used in this study were collected in the Lucky Hills watershed#103, which is nested within the Walnut Gulch Experimental Water-shed (WGEW) in southeastern Arizona, USA (31° 43′ N, 110° 41′ W)(Renard et al., 1993). The watershed, located near the town ofTombstone, is approximately 3.7 ha (0.037 km2) in size and its eleva-tion is between 1364 and 1375 m above sea level (Fig. 3). Averageannual precipitation is approximately 300 mm, 70% of which fallsduring the summer monsoon between the months of July andSeptember (Tiscareno-Lopez, 1991); much of the remaining precipi-tation is concentrated in the winter months of December throughFebruary (Nichols et al., 2002). The typical storms tend to be verylocalized and of short duration. The mean annual temperature is18 °C with the average monthly maximum temperatures of 35 °Cin June, and the average monthly minimum temperatures of 2 °Cin December. Vegetation in the area is dominated by desert shruband semi-arid rangeland plants. The dominant vegetation types areCreosote bush (Larrea tridentada, shrub) at 2 to 5 m spacing (26%cover), and Whitethorn (Acacia constricta, shrub), with lesser popula-tions of Desert Zinnia (Zinnia acerosa, shrub), Tarbush (Flourensiacernua, shrub), and Black Grama (Bouteloua eriopoda, grass). LargerCreosote shrubs are about 1 m tall and can be characterized by a spa-tially averaged leaf-area index value of 0.4 (Flerchinger et al., 1998).Canopy cover during the rainy season is approximately 25%. Approx-imately 50% of the ground area is covered with rock, an alluvial out-wash consisting predominantly of gravel and cobble sized material,and the remaining 25% is bare soil. The dominant soil type is the

Fig. 3. The digital elevation model (DEM) of the Lucky Hills watershed and locations of measurement points. The grid resolution is 10 m×10 m. The basin morphology features of aknick-point type of drop (~10 m) near the center of the domain.

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McNeal Gravelly Sandy Loam (60% sand, 25% silt, and 15% clay) withapproximately 25% of rock fragments in the surface layer. The rockcontent of the soil profile is 28% by volume between 0 and 5 cm andthen decreases with depth (Hymer et al., 2000). Table 1 reports asummary of the principal characteristics of the watershed (Nearinget al., 2005).

The basin morphology consists of a knick-point type drop (~10 m)in the middle of the flow path (Fig. 3). Runoff and sediment aremeasured with calibrated, Santa-Rita type supercritical flumes andtraversing slot sediment samplers at the outlet of the watershed.Sediment is sampled by an automatic traversing slot sampler, whichtakes a depth-integrated sample at specified time intervals within aflow event (Renard et al., 1986). Runoff and sediment yield resultalmost exclusively from convective storms during the summer sea-son. Event runoff and sediment discharge from 1999 to 2009 werecollected at the location FL103 (Fig. 3). Rainfall data from 1999 to2009 were collected at the rain gage RG83, which is located insidethe watershed (Fig. 3). The rain gage RG83 is a part of dense networkof weighing-type recording rain gages used to capture the temporaland spatial variability of precipitation inside the Walnut Gulch water-shed. Goodrich et al. (2008) describe the instrumentation and long-term precipitation database. Data were downloaded at http://www.tucson.ars.ag.gov/dap/.

4. Model setup and calibration

An essential component in evaluating reliability of hydrologicaland geomorphic models is validation against observed data. Histori-cally, the model performance has been measured through compari-sons with discharge and sediment yield time series at thecatchment outlet (Flanagan et al., 1998; Ivanov et al., 2004a). Therehave been only few examples of model validation based on the

Table 1Characteristics of the Lucky Hills basin.

Characteristic Lucky Hills watershed

Area [km2] 0.037Annual rainfall [mm] 300Land use/plant community Shrub dominated rangelandPlant cover [%] 25%Soil type Gravelly sandy loam

interior catchment information because of the typical lack of informa-tion and the limitations of most models to use such information(Houser et al., 1998; Ivanov et al., 2004a, 2004b; Refsgaard, 1997;Senarath et al., 2000).

4.1. Data

Climate, hydrology, digital elevation model (DEM), and land usedata necessary for calibrating the model, were collected for theLucky Hills watershed #103 (Nearing et al., 2005). The calibrationperiod extends from mid-July, 1999, to mid-August, 2009.

Rainfall is assumed to be uniformly distributed over the entirebasin. Data for the rain gage RG83 (Fig. 3) were used. Original rainfalldata collected at the resolution of 1 min were aggregated to 15-minute resolution data (Fig. 4). Fig. 4 also illustrates average dailycycles of other climatic data used in simulations and collected at anhourly time step from a flux tower near the Lucky Hills basin (stationBREB in Fig. 3). They were assumed to be representative for the entirebasin area as well. Finally, runoff volumes and sediment yield for eachevent occurred during the calibration period were observed at theoutlet section FL103 (Fig. 3) of the watershed.

Spatially uniform soil and land use characteristics were assumed,i.e., the vegetation fraction, v, the saturation soil moisture contentθs, the residual soil moisture content, θr, the saturated hydraulicconductivity, Ks, and the conductivity decay parameter, f. The soilhydraulic parameter values were inferred from measurements ofSchaap and Shouse (2004). Some of these parameters were subse-quently calibrated as described in the following and in Francipane(2010).

4.2. Spatial–temporal scales of calibration

Since the Lucky Hills watershed is small (3.7 ha) and has nonested gages, calibration was carried out for the entire basin areausing data for the outlet FL103 (Fig. 3). Manual streamflow and sedi-ment yield calibration were carried out. It was a stepwise approachthat included the analysis of a number of variables considered atdifferent spatial and temporal scales.

According to Yapo et al. (1996), when the objective of a geomor-phological model is to study the landscape morphology over thetime scales of hundreds of years, it is important to ensure that themodel reproduces correctly the runoff and sediment yield volumes

Fig. 4. Characteristics of climate at the Lucky Hills site in terms of the empirical probability density function (pdf) of rainfall measured at the rain gage #83 and average diurnalcycles of meteorological variables, as inferred from data observed at the Bowen Ratio Energy Balance (BREB) location. The integration period is 1999 to 2009.

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at large and continuous scales, rather than only at the event scale.Yapo et al. (1996) suggest that a calibration period of at least8 years is needed to produce results that are independent of theselected period. Calibration over a 10-year period (mid-July, 1999 tomid-August, 2009) was carried out in this study. A previous calibra-tion effort of the model at the event scale was done by Arnone et al.(2008).

4.3. Calibration

The approach used in calibration targeted satisfactory model per-formance over the long-term rather than over short-term time scales.Two metrics of the system were used in calibration in a sequentialmode: streamflow and sediment yield.

4.3.1. StreamflowRunoff regime of the Lucky Hills watershed is typical of many

semiarid regions where channels are dry for most time of the year.

Fig. 5. Observations and results of model calibration for the Lucky Hills site: (a) accumulatoutlet and presented for the period starting in mid-July, 1999, and ending in mid-August, 2

Typically, runoff occurs as a result of intense thunderstorm rainfall,the flood peak arrives very quickly after the start of generation, andrunoff duration is short (Keppel and Renard, 1962). It is primarilyproduced by the infiltration-excess component (Chorley, 1978).tRIBS can reproduce such a mechanism, if hydrometeorological con-ditions are conducive to runoff generation. The initial water tableposition, which affects the initial soil moisture by capillary rise, hasbeen arbitrarily set to the depth of 50 m. This assumption is consis-tent with observations of very deep groundwater in the region.

In this study, the calibration of the model was carried out withrespect to several parameters, such as Ks, θs, θr, and f. These are themost sensitive model parameters (Ivanov et al., 2004b). The masscurves of observed and simulated runoff volumes for the entire simu-lation period are shown in Fig. 5(a). The model is capable of reprodu-cing main runoff events, even though capturing each individual eventaccurately may be problematic in some instances. As Fig. 5(a) shows,over the long-term, the fit between the observed and simulated accu-mulated volumes is “good”, according to the criteria provided by

ed runoff; (b) accumulated sediment yield. Both variables were simulated at the basin009.

Table 2Overall statistics of runoff computed at the daily scale (1999–2009).

Statistic Symbol Value

Correlation coefficient Rr2 0.795

Nash–Sutcliffe coefficient Er 0.697Mass balance error Mr 5.26%

Table 3Overall statistics of sediment yield computed at the daily scale (2001–2009).

Statistic Symbol Value

Correlation coefficient Rs2 0.622

Nash–Sutcliffe coefficient Es 0.535Mass balance error Ms 3.39%

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Moriasi et al. (2007) (see Table 2 for values of the correlation coeffi-cient, Rr2, and the Nash–Sutcliffe efficiency coefficient, Er, Tobin andBennett (2009)). The mass balance error,Mr, suggests that on averagethe observed volume is slightly overestimated by the model (Table 2).

4.3.2. Sediment yieldThe calibration of the sediment production/deposition model was

carried out after the calibration of hydrological dynamics. Overall,the following parameters were adjusted during calibration: the soilerodibility coefficient, kb, the critical shear stress, θc, the Manning'sroughness coefficient for the soil, ns, and the Manning's roughnesscoefficient for a vegetation of reference, nvR.

Some of the most sensitive parameters are related to the formula-tion of shear stress exerted by sheet flow on soil. Tiscareno-Lopezet al. (1994) define the effective shear stress, τf, acting on the baresoil surface as a fraction of the total shear stress, τ, due to shear stresspartitioning between soil and vegetation:

τf ¼ τtnv

ns þ nv

� �0:5: ð14Þ

The value of ns can be related to the median sediment diameter,d50, using empirical relationships that have the following generalform (Yen, 1992)

ns ¼ k⋅dp50; ð15Þ

where k is a constant, considered to be equal to 0.0474 for sandy soils(Yen, 1992), and p is reported to be equal to 1/6. Considering d50 to bewithin the range of 0. 5 mm and 50 mm, typical of sand and gravel, ns

Table 4tRIBS land use parameters and their values used in this study.

Parameter Description

0 ID1 s Canopy storage2 b Interception coefficient3 p Free throughfall coefficient4 S Canopy capacity5 K Drainage coefficient6 g Drainage exponent parameter7 a Albedo8 Hv Vegetation height9 Kt Optical transmission coefficient10 rs Reference canopy stomatal resistance11 v Vegetation fraction12 Cr % of bare soil protected against drop erosion13 Kr Soil erodibility coefficient14 Fl Drip coefficient15 nvR Manning's roughness coefficient for a reference vege

L = from literature; C = from calibration.

can be assumed ranging between 0.013 and 0.03 m−1/3/s. Ranges ofvegetation roughness, nv, can be estimated from the lookup tablesof the Manning's roughness coefficient n (= ns+nv) for overlandflow for a variety of land use conditions (Engman, 1986; Woolhiseret al., 1990). For a typical range of n, for medium to dense brush, nvcan be assumed to be between 0.03 and 0.05 m−1/3/s. In this study,values of kb and pb provided by Nearing et al., (1999) were used asthe initial values in the entrainment capacity Eq. (8) when calibrationwas carried out for the Lucky Hills basin.

Accumulated sediment yield volumes for the entire simulationperiod are shown in Fig. 5(b). The model is capable of reproducingmain events but, as can be seen in the figure, for some, it does notreproduce the volumes perfectly. Fig. 5(b) also shows that the fit be-tween the observed and simulated data is acceptable and representa-tive of the long-term process. The Rs

2 and Es indicate that the fit is“satisfactory” to “good” (Table 3) for daily values, according to the cri-teria provided by Moriasi et al. (2007). The mass balance error, Ms,suggests that on average the observed sediment yield is slightly over-estimated by the model (Table 3).

Tables 4 and 5 list all of the tRIBS model parameters and their re-spective values for the land use and soil types. Tables show both theoriginal values, obtained from either field surveys or literature, andthe calibrated values. All of the calibrated parameter values fall withinthe range typical of the study area, as inferred from previous studies.

5. Response of a catchment to different morphologies andpredominant mechanisms of erosion

5.1. Geomorphic initialization conditions

The patterns of erosion and deposition in the landscape are largelycontrolled by the topographic structure and the frequency and mag-nitude of rainfall events. The performance of the model was furtherexamined for two synthetic catchments with different hillslope andchannel characteristics. The basins had been previously constructedwith the CHILD landscape evolution model (Tucker et al., 2001a)using either fluvial erosion or diffusive transport (e.g., soil creep), aspredominant geomorphic processes. To simulate these two domainsin CHILD, only the hillslope transport component was altered. Allelse being equal, using a smaller hillslope transport coefficient leadsto longer channels and smaller and steeper hillslopes (Fig. 6), whileusing a higher hillslope transport coefficient leads to smaller channelsand longer and gentler hillslopes (Fig. 7). These domains, first used inan ecohydrological study by Ivanov et al. (2008b), are of rectangularshape with an outlet in the southwest corner. In the following, thetwo synthetic basins will be referred to as the “concave”, CV, and

Initial values Source Final values

1 mm L –

0.2 L –

0.35 L –

1 mm L –

0.18 mm/h L –

3.9 mm−1 L –

0.22 L –

0.46 L –

0.7 L –

200 s/m L –

0.5 L –

0.1 L –

20 J−1 L –

0 L –

tation type 0.05 m−1/3 s−1 C 0.041 m−1/3 s−1

Table 5tRIBS soil parameters and their values used in this study.

Parameter Description Initial values Source Final values

0 ID1 Ks Saturated hydraulic conductivity 32.81 mm/h C 19.0 mm/h2 θs Soil moisture at saturation 0.46 C 0.393 θr Residual soil moisture 0.0429 C 0.04634 λ0 Pore-size distribution index 0.3813 L –

5 ψb Air entry bubbling pressure −63 mm L –

6 f Conductivity decay parameter 0.032 mm−1 L –

7 As Anisotropy ratio for saturated zone 1 L –

8 Au Anisotropy ratio for unsaturated zone 1 L –

9 n Porosity 0.46 L –

10 ks Volumetric heat conductivity 0.214 J/m s K L –

11 Cs Soil heat capacity 1,209,573 J/m3K L –

12 cs Soil cohesion parameter 1.706 N/m2 L –

13 cr Root cohesion parameter 1000 N/m2 L –

14 φ Soil internal friction angle 20° L –

16 Kb Erodibility coefficient 3.77E−08 m/s(kg m−1 s−2) C 9.33E−08 m/s(kg m−1 s−2)pb

17 θc Critical shear stress 1.5 Pa C 4.1 Pa18 kk Coefficient kk to calculate kf 20 L –

19 kd Diffusive coefficient 3.17E−10 m2/s L –

20 ns Manning's roughness coefficient for soil 0.025 m−1/3/s C 0.05 m−1/3/s21 d Dominant grain size 0.0005 m L –

L = from literature; C = from calibration.

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“convex”, CX, domains, respectively. In total, 2,400 computational el-ements are used to represent each of the synthetic topographies thatcover a wide range of slope magnitudes and aspects. The dimensionsof the basic computational element, the hexagonal Voronoi element,are approximately 40 m×40 m.

The dominant forms of sediment transport process for the two ba-sins can be inferred from the slope–contributing area (S–A) diagram(Fig. 8) (Yetemen et al., 2010). They characterize the initializationstates of these watersheds for simulations carried out in this study.Specifically, two characteristic regions can be identified: region Iwith a positive S–A gradient that corresponds to hillslopes withlower drainage areas where diffusive erosion is predominant; regionII is mainly dominated by the fluvial transport (Yetemen et al.,2010). In region II, channels appear to be identical but longer in thefluvial-erosion dominated domain (CV) than in the diffusion–erosiondominated domain (CX). The steepest slopes in the landscapes arelocated at the transition between regions I and II, where diffusiveprocesses give way to fluvial erosion, marking the location of the val-ley head. According to the S–A relation in the figure, valleys begin

Fig. 6. A map of vegetation fractional cover overl

with a smaller contributing area (the location is indicated by a grayvertical line) in the CV basin and with a higher contributing area(the location is indicated by a black vertical line) in the CX basin.

5.2. Objectives and design of experiments

Long-term simulations were designed using the CV and CX do-mains as geomorphic initializations. The objective was to test themodel at larger, first-order catchment scale as well as assess the dis-criminative power of the model with respect to predominant geo-morphic processes that are characteristic of these geometries. Thesame parameter values obtained in the calibration for the LuckyHills basin were used, except for the soil erodibility (see the formula-tion of entrainment capacity (8) and Tables 4 and 5). Specifically, thesynthetic domains were developed for climatic conditions (in termsof precipitation) nearly identical to that of the Lucky Hills site; how-ever, a smaller erodibility was used. When the erodibility parameterobtained in the calibration was used in the model, the erosion re-sponse of these domains was very strong and leads to widespread

aid on surface topography of the CV domain.

Fig. 7. A map of vegetation fractional cover overlaid on surface topography of the CX domain.

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erosion, indicating non-equilibrium conditions. In order to alleviatethis effect of initial conditions, a smaller erodibility value consistentwith the one used previously in the CHILD model was used.

Note that the model can distinguish the influence of vegetation onboth overland flow and rainsplash erosion. In order to assure a morerealistic effect of vegetation cover on the geomorphic dynamics ofthe two synthetic basins “placed” in a semiarid setting, a 30-yearlong average spatial distribution of vegetation cover fraction wasobtained with the tRIBS+VEGGIE model (Ivanov et al., 2008a,2008b). tRIBS+VEGGIE had been previously calibrated for theLucky Hills site, so as to ensure the distribution of biomass consistentwith the basin morphology and climate. Fig. 9 shows the time seriesof simulated soil moisture, as well as simulated and observed leafarea index (LAI) and biomass at the site. Figs. 6 and 7 illustrate thesimulated distributions. The CV domain exhibits the spatial variationof vegetation with a fractional cover ranging between ~36% and~44%. The CX domain has a vegetation fractional cover in the rangeof ~41.5÷44% over the entire domain. North facing hillslopes exhibithigher values of vegetation fractional cover for both domains. Suchspatial patterns can be attributed to the local effects of shortwave ir-radiance and rainfall (Ivanov et al., 2008b). Vegetation initialized in

Fig. 8. Slope as a function of surface contributing area for the diffus

this fashion was considered to be constant throughout the entire sim-ulation period and not prone to the effect of erosion, i.e., vegetationfraction remained constant in time.

In order to robustly infer the metrics of local dynamics charac-terizing predominant geomorphic processes (such as local ero-sion/deposition rates), a long-term simulation is required since itwould allow filtering out the effects of individual geomorphicevents. However, observational records with data suitable for forc-ing a hydrological model are typically short. A scenario of climateforcing at the computationally feasible, intermediate time scale of100 years was therefore generated using the Advanced WEatherGENerator (AWE-GEN, Fatichi, 2010; Fatichi et al., 2011), anhourly-scale weather generator capable of reproducing low andhigh frequency characteristics of hydro-climatic variables (e.g., pre-cipitation, air temperature, solar radiation, cloud cover, relativehumidity, vapor pressure, wind speed, and atmospheric pressure)and their essential statistical properties. The climate scenario wasbased on meteorological variables observed at the Tucson airportover the period of 1960–2000. The generated realization assumesstationary climate corresponding to the observational period (see

ion-erosion (CX) and fluvial-erosion (CV) dominated domains.

Fig. 9. Calibration of tRIBS+VEGGIE for the Lucky Hills basin. The figure shows the time series of simulated soil moisture (top panel), leaf area index (LAI), and biomass for theperiod of 1997–2008. “MODIS” refers to the inferences of LAI based on data from the Moderate Resolution Imaging Spectroradiometer. The circle point at the bottom plot refersto the actual observations in the Lucky Hills basin (the data were obtained at http://www.tucson.ars.ag.gov/dap/).

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Fatichi et al., 2011 for details). Fig. 10 shows the statistics of thegenerated climate scenario.

5.3. Results

Using the generated climate, the developed model was run for100 years and erosion patterns were compared for the two basins.The net change in the landscape elevations of the two simulateddomains was inferred as the difference between the elevation at thebeginning and the end (i.e., after 100 years) of the simulations(Figs. 11 and 12). Positive values indicate net erosion, while negativevalues indicate deposition. Fig. 11 shows erosion activity mainly con-centrated in the stream network of the CV domain. This agrees with

Fig. 10. A statistical representation of the 100-year scenario of stationary climate simulatedcipitation interannual variability (top), the probability of exceedance of hourly rainfall (midspeed, incoming longwave, and shortwave fluxes.

the more heterogeneous terrain of the initial state of the basinthat was obtained by emphasizing fluvial erosion as the predominantprocess. The CX domain shows higher erosion activity in the hill-slopes (Fig. 12). The erosion rates that can be inferred from Figs. 11and 12 are consistent with the values reported in literature (Jha andPaudelb, 2010). They range between 0 and ~0.15 mm/year of deposi-tion and between 0 and ~0.40 mm/year of erosion for the fluvial-erosion dominated domain (CV); between 0 and ~0.58 mm/year ofdeposition and between 0 and ~0.60 mm/year of erosion for thediffusion-erosion dominated domain (CX). Following the classifica-tion of Table 6 (Jha and Paudelb, 2010), almost 85% of the CX domaincan be characterized by “very low” and “very high” erosion rates, withthe remaining part of the basin corresponding to “low” to “high”

with the Advanced WEather GENerator (AWE-GEN) model of Fatichi et al. (2011): pre-dle row, left subplot), and the diurnal cycles of air temperature, relative humidity, wind

Fig. 11. A map of changes in elevation after 100 years of simulation for the CV domain. Positive values indicate erosion, while negative values illustrate deposition.

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erosion; almost 95% of the CV domain can be described by “verylow” erosion, with the remaining 5% equally attributed to “low” and“moderate” erosion rates. Only few locations in the CV domain arecharacterized by “high” and “very high” erosion.

The net effects of different erosive patterns are illustrated inFig. 13. The figure shows the net change in elevation with respect toslope (left panel) and contributing area (right panel) for each compu-tational element of the domain. The contributing area that corre-sponds to the maximum slope magnitude in the S–A plot (Fig. 8)designates the location of the channel head. Such locations can beidentified in Fig. 13. Considering the values of contributing areawhere valleys begin (Fig. 8), it is possible to identify regions dominat-ed either by diffusive processes (I) or by fluvial erosion (II) (Fig. 13).Hillslope erosion is always lower with respect to erosion in thestream network. Despite the smaller range of slopes, the CX domainexhibits a higher range of surface elevation changes. This indicatesan evident dependence of erosion on slope (Fig. 13, left panel), typicalof catchments with a strong diffusive component. On the contrary,

Fig. 12. A map of changes in elevation after 100 years of simulation for the CX doma

the CV domain has a low variability of elevation changes correspond-ing to higher slope magnitudes, which signifies a low dependence oferosion on diffusive mechanism. The same behavior is reflected inFig. 13 (right panel). The CX domain exhibits a higher variability oferosion in the region I, as compared to the CV domain, and bothbasins exhibit an almost log–log linear relationship of elevationchange with contributing area for region II. One may notice thatthe region I exhibits different values of changes in elevation for thesame value of slope in the CX domain case (e.g., red rectangle inFig. 13, left panel) and contributing area (e.g., red rectangle inFig. 13, right panel). This could be related to the influence of slopeand aspect on the spatial distribution of vegetation in the basin(Fig. 7) and opens an interesting question about the influence of veg-etation on the spatial distribution of erosion activity. Such inferences,however, are beyond of the scope of this study.

The difference in initialization conditions and predominant ero-sion mechanisms affects the simulation results in terms of sedimentyield. After 100 years of simulation, the CX domain leads to a

in. Positive values indicate erosion, while negative values illustrate deposition.

Table 6Mean annual erosion rates classes (Jha and Paudelb, 2010).

No. Erosion rate[mm/year]

Erosion risk class CV CX[%] [%]

1 b0.037 Very low 95.4 51.62 0.037–0.074 Low 2.60 4.103 0.074–0.185 Moderate 1.84 5.604 0.185–0.370 High 0.08 4.205 >0.370 Very high 0.08 34.5

Fig. 14. Cumulative sediment yield at the outlet locations for the CV and CX domains.

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sediment yield that is about 20÷25% higher than that of the CV do-main (Fig. 14). The higher sediment yield of the CX domain is likelya sign of the transient diffusive activity over the hillslopes thatmakes a larger amount of sediment available for transport.

6. Summary

A coupled hydro-geomorphic modeling approach to catchmentevolution is presented in this study. The model integrates an existingphysically-based, spatially-distributed hydrological model TIN-basedReal-time Integrated Basin Simulator with the geomorphic function-ality of a landscape evolution model. Besides hydrological processes,the coupled model simulates essential erosive processes of hillslopes,such as detachment due to raindrop impact and entrainment due tooverland sheet flow, as well as channel processes, i.e., erosion and de-position due to the action of channelized flow. This work introduces anumber of novel features, as compared to the current generation oferosion and landscape evolution models. They are summarized inthe following.

• Although a proper description of hydrology, in particular, the runoffgeneration process, is crucial for estimating erosion/geomorphicresponse of a catchment, most erosion and landscape evolutionmodels use over-simplified representations of hydrology. Themodel developed in this study enhances the traditional, discipline-focused approach of geomorphic simulation by merging it with afully transient description of hydrological processes. The modelhas the capacity to improve predictability of the coupled hydro-geomorphic response associated with climate and environmentalchange.

• The representation of dynamic feedbacks between local erosion andelevation change in numerical models has been shown to improve

Fig. 13. Relationships between the change in elevation and slope (left pa

erosion and deposition predictions. While this coupled phenome-non is represented in most landscape evolution models, suchmodels are typically developed to address long-term landscapedevelopment questions, implying a number of simplifications.These involve coarse time steps with underlying gross integrationof hydrological dynamics, an assumption of uniform rainfall rates,simplifications of environmental variability of land-surface proper-ties, and limited capabilities of predicting the influence of geomor-phic change on the watershed hydrologic response. The finetemporal and spatial resolutions allowing one to properly capturethe consequences of complex rainfall events over heterogeneoussurface, as well as the capability to incorporate geomorphic feed-backs into a hydrological simulation through changing elevation,slope, aspect, and drainage pattern, represent a unique feature ofthe developed framework. This is an important step towards, forexample, modeling future climate consequences in soil and waterresources management.

• From a technical perspective, the coupled model uses variablemesh resolution associated with TINs, which are not frequentlyemployed in geoscience modeling. Both advantages and disadvan-tages of TINs have been discussed in numerous previous publica-tions (e.g., Tucker et al., 2001a; Vivoni et al., 2004, amongothers). For example, TINs offer the flexibility in representingterrain and soil/landuse variability, terrain breaklines, stream net-works, and boundaries between heterogeneous regions but featuremore cumbersome ways of storing representation information and

nel) and the change in elevation and contributing area (right panel).

Table A.1Values of the rainfall soil erodibility coefficient, kr.

Data source Mean kr coefficient [J−1]

Clay Siltclay

Silty clayloam

Silt Siltloam

Loam Sandyloam

Sand

Meyer and Harmon(1984)

19.0 18.2 16.2 29.8 39.8 28.2 32.0

Morgan (1985) 30.0Bradford et al. (1987) 73.5 22.2 25.7 37.6 34.4 62.4Verhaegen (1987) 24.7 23.4 30.0

Table A.2The values of α and β coefficients as a function of rainfall intensity I (Wicks and Bathurst,1996).

Rainfall intensity I [mm/h] α β

0≤ Ib10 2.69×10−8 1.689610≤ Ib50 3.75×10−8 1.554550≤ Ib100 6.12×10−8 1.4242100≤ Ib250 11.75×10−8 1.2821

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mapping procedures, such as precipitation mapping on VPN. With-in the framework of the presented model, using a TIN presentsinteresting possibilities of dynamic re-meshing based on hydrolog-ic and geomorphic dynamics, which might lead to further compu-tational savings.

With an increased number of processes described in the coupledmodel, one apparent drawback is that the computational efficiencybecomes much lower than that of the existing erosion and landscapeevolution models. For example, while sub-millennium (hundreds ofyears) simulation time scales are feasible in a serial implementationwith a modern-era personal computer, carrying out multi-millennialruns will require the capabilities of a parallelized architecture (e.g.,Vivoni et al., 2011) and high-performance computing facilities.

The presented model was calibrated for the Lucky Hills basin, asub-basin of the Walnut Gulch Experimental Watershed (Arizona,USA). The calibration procedure demonstrates a good capability ofthe model to reproduce main runoff events and the accumulatedstreamflow and sediment yield volumes over a long-term period.While the observed and simulated volumes do not perfectly matchfor every individual event, the fit over the long period is good andconsistent in terms of temporal dynamics. The model thus representsa potentially robust tool for long-term assessments of change ofgeomorphic dynamics as a result of land use alterations in headwaterbasins, climate or vegetation change.

Two synthetic basins characterized by different morphologicalcharacteristics and initially generated so as to illustrate the predomi-nance of different erosion mechanisms (fluvial and diffusive) wereused in the evaluation simulations for a 100-year period of stationaryclimate. The changes in surface elevation demonstrate a consistentperformance of the model, which is capable of identifying regionsdominated by diffusive processes and fluvial erosion. These are alsoconfirmed based on an analysis of the “change in elevation” vs.slope and contributing area diagrams.

The model application to the case study and to the synthetic do-mains has highlighted the following aspects:

• The developed model parsimoniously reproduces essential processesthat regulate the phenomena of erosion and deposition; the modelperformance is consistent with assumed principles of behavior.

• The case study simulations are consistent with values reported inliterature in terms of mean annual soil erosion rates; the fluvial ero-sion is the more efficient geomorphic process for the consideredenvironment.

• The model is capable of differentiating between stream networkand hillslopes and reproduces the relevant geomorphic processes,i.e., fluvial and diffusive erosion, when applied to first-order catch-ments developed under these conditions.

• The model can parsimoniously mimic the effect of vegetation onerosion.

Furthermore, the results obtained in simulations suggest a topo-graphically differential effect (i.e., the dependence on site aspectand slope) of vegetation on erosion activity in a semiarid environ-ment. In order to address these preliminary inferences, further effortswill enhance the model by introducing modeling of ecological pro-cesses that mimics growth and death of vegetation with erosion/deposition events.

Acknowledgment

Prof. Bras acknowledges the support of the National Science Foun-dation, grant EAR-0962253. Collaborative Research: Co-Organizationof River Basin Geomorphology and Vegetation. Valeriy Ivanov waspartially supported by NSF Grant 0911444. Erkan Istanbulluoglu waspartially supported by NSF EAR-0963858. Leonardo V. Noto was

partially supported by CNR-Short Term Mobility Program and byCORI2006-UNIPA.

Appendix A

A.1. Soil erodibility coefficient, kr

The values of soil erodibility coefficient, kr [J−1], can be found inliterature as a function of soil texture (Table A.1).

A.2. Shield effect of surface water, Fw

The shield effect factor, Fw, is evaluated as a function of the surfacewater depth h [L] and the median raindrop diameter Dm [L] asfollows:

Fw ¼ exp 1−h=Dmð Þ; if h > Dm1; if h > Dm

:

�

The median raindrop diameter Dm is based on an empirical rela-tionship of Laws and Parson (1943): Dm=a·Ic, where a=0.00124and c=0.182 are the empirical coefficients.

A.3. Leaf drip squared momentum, MR

The term MR can be expressed as a function of rainfall intensityI [L/T]:

MR ¼ α ⋅ Iβ :

Using the Marshall and Palmer (1948) drop-size distribution, thevalues of the two coefficients were found through a regression forfour different rainfall intensity ranges, as shown in Table A.2 (Wicksand Bathurst, 1996):

A.4. Leaf drip squared momentum, MD

The momentum MD can be calculated as:

MD ¼vρπD3

d6

� �2⋅ F l⋅D

πD3D

6

;

230 A. Francipane et al. / Catena 92 (2012) 216–231

where v [L/T] is the raindrop velocity estimated with an approxima-tion of Epema and Riezebos (1983), ρ [M/L3] is the density of water,Dd [L] is the leaf drip diameter (typically assumed to be 5–6 mm), Flis the canopy drainage fraction that reaches soil as leaf drip, and D[L/T] is the total canopy drainage (Ivanov et al., 2004a).

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