On the dynamics of soil moisture, vegetation, and erosion: …€¦ · Implications of climate variability and change Erkan Istanbulluoglu1 and Rafael L. Bras2 Received 17 March 2005;

On the dynamics of soil moisture, vegetation, and erosion:

Implications of climate variability and change

Erkan Istanbulluoglu1 and Rafael L. Bras2

Received 17 March 2005; revised 13 February 2006; accepted 28 February 2006; published 21 June 2006.

[1] We couple a shear-stress-dependent fluvial erosion and sediment transport rule withstochastic models of ecohydrological soil moisture and vegetation dynamics. Rainfall issimulated by the Poisson rectangular pulses rainfall model with three parameters:mean rainfall intensity, duration, and interstorm period. These parameters are related tomean annual precipitation on the basis of published data. The model is used to investigatethe sensitivity of grass cover and erosion potential to drought length, changes in stormfrequency under fixed mean seasonal rainfall, and variations in mean annualprecipitation. Three fundamental factors, amount of precipitation, storm frequency, andsoil type, are predicted to control the system response. Variation in storm frequencyis predicted to have a significant influence on sediment transport capacity because of itsinfluence on vegetation dynamics. Our results predict soil loss potential to be moresensitive to a reduction in storm frequency (under fixed mean annual precipitation) inhumid ecosystems than in arid and semiarid regions. The well-known dependencebetween mean annual sediment yields and precipitation (e.g., Langbein and Schumm,1958) is reproduced by the model. Numerical experiments using different soil typesunderscore the importance of soil texture in controlling the magnitude and shape of suchdependence. Coupling abiotic and biotic Earth surface processes under randomclimatic forcing is the salient aspect of our approach, opening new avenues for research inthe emerging field of complex climate-soil-vegetation-landscape dynamics.

Citation: Istanbulluoglu, E., and R. L. Bras (2006), On the dynamics of soil moisture, vegetation, and erosion: Implications of

climate variability and change, Water Resour. Res., 42, W06418, doi:10.1029/2005WR004113.

1. Introduction

[2] In water limited ecosystems spatial and temporalvegetation dynamics are predominantly controlled by soilwater availability, driven by climate and modulated bylandscape morphology. Vegetation in turn regulates basinwater balance, soil moisture dynamics [Eagleson, 2002;Rodriguez-Iturbe and Porporato, 2004], as well as the formand tempo of erosion and landscape evolution [Collins etal., 2004; Istanbulluoglu and Bras, 2005].[3] Basin topography and soils are recognized among the

most critical controls of the hydrological response and theresulting spatial organization of terrestrial vegetation pat-terns [e.g., Wierenga et al., 1987; Florinsky and Kuryakova,1996; Coblentz and Riiters, 2004; Kim and Eltahir, 2004;Caylor et al., 2005]. Hack and Goodlett [1960] conductedone of the pioneering process-based field observationsrelating topography, forest vegetation distribution and geo-morphic processes. In their early effort, Langbein andSchumm [1958] examined the relationship between meanannual sediment yields and annual precipitation over de-cadal timescales by grouping and averaging sediment yielddata from U.S. Geological Survey (USGS) gauging stations

and reservoirs. In the Langbein and Schumm [1958] curve,sediment yield increases with precipitation in arid andsemiarid climates, reaches a maximum where precipitationis approximately 300 mm/year, and trails off as precipitationgrows. Interestingly, Langbein and Schumm [1958] alsonote that the turn over point in this curve corresponds toecosystems where a transition from shrub to grasslandsoccurs, effectively protecting soils from runoff and rainsplash erosion.[4] In a more comprehensive study, encompassing much

wetter regions with precipitation totals more than 2500 mm/year, Walling and Kleo [1979] presented multiple peaks inthe relationship between sediment yield and precipitation. Intheir relationship the first peak appears to correspondapproximately with the location of the Langbein andSchumm’s peak, while the other two were attributed tospecific climate characteristics in different rainfall regimes,without any detailed explanations for the underlying phys-ical factors causing them [Walling and Kleo, 1979;Knighton, 1998].[5] The interplay between the effects of climate and

vegetation in shaping erosion rates were also reported formuch longer timescales. Global data show significantincreases in erosion rates around the world, with approxi-mately 4–5 times larger fluxes from the lands to the oceans,during the past few million years [Hay et al., 1988; Molnar,2001; Zhang et al., 2001]. It has been hypothesized thatthese periods of increased sediment transport is a conse-quence of enhanced aridity as a result of global cooling in

1Department of Geosciences, Department of Biological SystemsEngineering, University of Nebraska-Lincoln, Lincoln, Nebraska, USA.

2Department of Civil and Environmental Engineering, MassachusettsInstitute of Technology, Cambridge, Massachusetts, USA.

Copyright 2006 by the American Geophysical Union.0043-1397/06/2005WR004113

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WATER RESOURCES RESEARCH, VOL. 42, W06418, doi:10.1029/2005WR004113, 2006

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the late Cenozoic, leading to a pattern of long-term climatevariability with high-amplitude fluctuations (e.g., glacial-interglacial). Such fluctuations caused frequent and dramaticchanges in regional temperatures and precipitation regimes,with resulting impacts on ecosystem functioning, andfluvial and glacial erosion processes [Zhang et al., 2001].Growing erosion rates under a fluctuating climate wererelated to two primary causes: (1) nonlinearities in land-scape geomorphic response, and landscape reaction time-scales that prevented landscapes from establishingequilibrium states [Zhang et al., 2001]; (2) thresholddependence and inherent nonlinearity in erosion and sedi-ment transport mechanics [Leopold, 1951; Tucker and Bras,2000; Molnar, 2001; Tucker, 2004]. While the latter worksstatistically characterized the direct effects of precipitationfluctuations on erosion rates, however, their indirect effectson geomorphic response via altering vegetation cover is notyet addressed.[6] Another good example for increased erosion rates

under a variable climate is arroyo development in the aridand semiarid southwest United States. In a climate regimehistorically characterized by wet and dry cycles, known asthe El Nino–Southern Oscillation (ENSO) pattern, arroyoformation in the southwest was argued to be driven byvegetation-erosion feedbacks under a fluctuating climateregime [e.g., Huntington, 1914; Bryan, 1940; Cooke andReeves, 1976; Bull, 1997]. In the region, depletion of rootzone soil moisture during a dry period often results in areduction in vegetation cover across the landscape, leavingsoil surface susceptible to erosion. Some field observationssuggest flooding in wet periods, following extendeddroughts, as the primary trigger of gully erosion and cutand fill cycles in the southwestern United States [Schummand Parker, 1973; Waters and Haynes, 2001].[7] In recent studies, with respect to the current climate,

global climate models (GCMs) predict a global temperatureincrease due to enhanced greenhouse gases in the atmo-sphere, leading to an increase in climate variability, withreduced rainfall frequencies and increased magnitudes [e.g.,Easterling et al., 2000]. Such model predictions are alsoverified by recent studies of in situ observations of majorvariables of the hydrological cycle in the United States[Groisman et al., 2004]. Growing insights from field andtheoretical work suggest that predicted changes in rainfallregime as a result of global warming may reduce soilmoisture, affect surface water balance, and deteriorateecosystem functioning [Knapp et al., 2002; Porporato etal., 2004]. These predicted trends in the climate call forthree key questions for soil mantled and vegetated land-scapes: (1) How does sediment transport intensity relateto drought length and severity? (2) How does short- andlong-term rainfall variability affect vegetation dynamicsand sediment yields? (3) What is the role of vegetationon the relationship between sediment yields and annualprecipitation?[8] In this paper we describe a first attempt in linking

runoff erosion with climate-soil-vegetation dynamics. Sec-tion 2 describes the simple one-dimensional model used inthis study, that combines random forcing of rainfall with acoupled representation of a dynamic soil-vegetation system,and runoff erosion mechanics. In section 3, the model isused in three related modeling experiments to address the

research questions posed above. Of these examples, the firstone investigates the sensitivity of sediment transport poten-tial to drought length, referred to as the ‘‘drought experi-ment’’. The second example discusses the consequences ofan increase in rainfall variability, a predicted trend as aresult of global warming, on sediment transport potentials.Finally, the last simulation attempts to capture the effects ofa range of different precipitation regimes, from arid tohumid regions, based on a simple characterization of thegeneral rainfall climatology of the United States.

2. Model Description

2.1. Soil Water Balance at a Point

[9] Depth averaged conservation of water in the root zoneis modeled as [Eagleson, 1982; Rodriguez-Iturbe, 2000]:

nZrds

dt¼ Ia s; p;Vð Þ � ET s;Vð Þ � D sð Þ ð1Þ

where Zr is the effective root depth, n is soil porosity, s isrelative soil moisture content, 0 � s(t) � 1, V is vegetationcover fraction, and p is rainfall rate. Infiltration rate Iarepresents the rate of water flux into the soil column inexcess of interception and surface storage. ET is evapo-transpiration rate that includes evaporation from bare soilsurface and plant transpiration. D is leakage from the rootzone. All flux terms in the water balance equation arestrongly dependent upon both soil moisture level andvegetation cover, making the equation difficult to evaluateanalytically, especially when vegetation cover is dynamic.[10] For a stationary climate and in the absence of any

lateral moisture fluxes (i.e., arid to semi arid regions) thelong-term annual averages of equation (1), gives hIai = hETi+ hDi, and the long-term water balance of the system can bewritten as

Ph i ¼ CIh i þ Rh i þ ETh i þ Dh i: ð2Þ

Over the long term, mean annual precipitation is partitionedinto mean annual canopy interception, hCIi, runoff, hRi,evapotranspiration, hETi, and drainage hDi, with no changein soil moisture storage. Both equations presented aboveassume a sufficiently deep groundwater table, such thatthere is no influx from groundwater to the root zone. Whilethis is often true for many arid and semiarid regions withthick vadose zones (deep saturated zones) [e.g., Walvoordand Phillips, 2004], it might be inappropriate for areas withshallow water table.[11] Eagleson [2002] andRodriguez-Iturbe and Porporato

[2004] give extensive reviews of the recent applications ofequations (1) and (2) in ecohydrology. The followingsections explain the models used in this study for eachcomponent of the water balance equation, starting with thestochastic rainfall forcing.

2.2. Stochastic Rainfall Model

[12] Three essential characteristics of precipitation arestorm intensity, p (mm/h), storm duration Tr (h), and timebetween storms, Tb(h). Storm intensity and duration deter-mine water availability for infiltration and runoff during asingle event, while the time between storms defines theduration of deep percolation and evapotranspiration. Storm

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intensity, duration and time between storms are described byexponential distributions [Rodriguez-Iturbe and Eagleson,1987], given in generic form below,

fX xð Þ ¼ 1

xexp � x

x

� �ð3Þ

where x is exponentially distributed variable. In ourapplication x represents storm rate p, duration Tr, and timebetween storms Tb. Storm depth is the product of rainfallintensity and duration, P = pTr. The exponential distributionhas shown to represent rainfall statistics well, and the modelparameters can be easily obtained from rain gauge data[Eagleson, 1978a; D’Odorico and Porporato, 2004].

2.3. Rain Interception

[13] Interception is the amount of water retained onvegetation canopy for subsequent evaporation. Interceptionis related to many vegetative and climate factors, includingleaf area index (LAI), storm intensity and duration, as wellas the surface tension forces on the canopy resulting fromcanopy configuration and liquid viscosity [Ramırez andSenarath, 2000]. Among these factors LAI and p have themost pronounced effects. Interception scales positively withLAI and negatively with p as the larger the raindrop size, thehigher the amount of water displaced from canopy due toraindrop impact [Wells and Blake, 1972; Ramırez andSenarath, 2000].[14] In our simplistic model we use a lumped variable CI

to represent both canopy interception and surface retentiondefined as the sum of total water storage capacity ofvegetation canopy Sc and evaporation rate Ep during thestorm [Bras, 1990]

CI ¼ Sc þ EpTr ð4Þ

Water storage capacity is related to LAI and p in thefollowing way [Ramırez and Senarath, 2000],

Sc ¼ SLALAI exp �cdpð Þ ð5Þ

where SLA is maximum depth of water storage per unit LAI,and cd is a coefficient that controls the rate of decay ofinterception capacity with rainfall rate. For simplicity, andto be consistent with the dynamic vegetation modeldescribed in the following section, we use fractionalvegetation cover, V instead of LAI in equation (5). Forgrass vegetation, fractional cover is related to LAI by anexponential relationship [Lee, 1992]

V ¼ 1� exp �0:75LAIð Þ ð6Þ

Solving equation (6) for LAI, substituting LAI into (5), and(5) into (4) gives the final form used to model interception

CI ¼ �SLAln 1� Vð Þ

0:75 exp cdpð Þ þ EpTr: ð7Þ

[15] Typical values used for SLA range between 0.1 mmand 0.3 mm, and are usually obtained through calibration ofgeneral circulation and biosphere models [e.g., Sellers et al.,1989].

2.4. Infiltration and Runoff Generation

[16] Some recent ecohydrology models assume no limi-tations in infiltration rate and rainfall is stored in the root

zone until soil saturation occurs. The rainfall depth in excessof soil storage is then converted to surface runoff [e.g., Laioet al., 2001a]. This assumption has certain limitationsespecially in arid and semiarid regions where infiltrationrates are highly variable due to vegetation patchiness, andrunoff is produced via infiltration excess mechanism. In theabsence of vegetation, surface sealing by rain splash erosionoccurs as detached soil particles by raindrop impact clogpores on the soil surface. Subsequently, upon soil drying, ahard crust forms on the soil surface significantly reducinginfiltration rates [Brady and Weil, 1996]. However, onvegetated slopes biological activity and root penetrationsignificantly improve soil aggregation and macroporosity,enhancing infiltration rates and soil hydraulic conductivity.Field observations consistently report higher infiltrationrates under vegetation canopy than intercanopy [e.g., Cerda,1998; Dunkerley, 2002a, 2002b; Bhark and Small, 2003;Ludwig et al., 2005], leading to runoff generation in baresoils and runon input to vegetated patches.[17] Storm average infiltration capacity of a soil parcel is

approximated as a weighted average of infiltration capacityof bare and vegetated soils

Ic ¼ IS 1� Vð Þ þ IVV ð8Þ

where Ic is average infiltration capacity, IS and IV areinfiltration capacity of bare and vegetated soils respectively,and V is uniformly distributed vegetation cover fraction.This assumption, although simple, is consistent with somefield observations [e.g., Cerda, 1998].[18] Infiltration is modeled when precipitation depth is

larger than potential canopy interception. In the model, theactual infiltration rate depends on the root zone soil mois-ture. When root zone is unsaturated, infiltration is thesmaller of infiltration capacity or precipitation rate. Whenroot zone is saturated, infiltration is assumed to be limited tothe rate of water loss to deep drainage from the root zone.This model is expressed by

Ia ¼

Min p; Ic½ ; 0 � s < 1; P > CI

D s ¼ 1; P > CI

0 P � CI

8>>>><>>>>:

ð9Þ

where Ia is actual infiltration rate, and D is in-storm waterleakage when the root zone is saturated. Leakage duringstorms for unsaturated soils is neglected in the model. Thisintroduces some limitations for applications especially forhumid regions, receiving low-intensity long-duration rain-falls. In such cases, the potential effect of neglecting leakageduring storms would be a reduction in the time required forsoil saturation during rainfall.[19] The dependence of actual infiltration on soil mois-

ture state naturally yields two different runoff generationmechanisms: infiltration and saturation excess. In bothcases, runoff is generated when rainfall rate (or rain + runonrate if applicable) exceeds the actual infiltration capacitydescribed in equation (9). Runoff rate R is expressed as

R ¼p� Iað Þ p > Ia

0 p � Ia

8<: ð10Þ

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On the basis of the initial soil moisture and actual steadystate infiltration rate, the time required for soil saturationunder constant rainfall is determined by the ratio of thevolume of empty pores that can accommodate water to theactual infiltration rate by

Tsat ¼1� sIð ÞnZr=Ia; 0 � s < 1

0 s ¼ 1;

8<: ð11Þ

where sI is the initial soil moisture. Root zone soil saturationoccurs when rain duration, for a fixed storm intensity, islarger than time required for saturation Tr > Tsat. With soilsaturation, the actual infiltration rate reduces to the rate ofleakage, Ia = D (equation (9)).

2.5. Leakage Losses

[20] Assuming constant soil texture, porosity and hydrau-lic conductivity, and ignoring the influence of soil suctionforces beneath the root zone, one-dimensional gravitydrainage from the root zone is related to unsaturatedhydraulic conductivity according to Campbell [1974]:

D sð Þ ¼Ko; Tr > Tsat

Kos2bþ3ð Þ; sfc < s � 1

8<: ð12Þ

where Ko is saturated hydraulic conductivity (L/T). In themodel, bare soil infiltration is assumed to be equal tosaturated hydraulic conductivity, IS = Ko. Parameter b is theexponent used in soil water retention equation that relatessoil matric potential to relative soil moisture content[Campbell, 1974]

ys ¼ �s�b ð13Þ

where Ys is soil matric potential, and � and b are empiricalparameters determined from experimental data. Typicalvalues for � and b are widely published in the literature fordifferent soil texture classes [e.g., Clapp and Hornberger,1978; Laio et al., 2001a]. Equation (13) can be used toobtain soil moisture values (by solving for s), from thecorresponding values of soil matric potential defined forplant activities and soil evaporation.

2.6. Evapotranspiration

[21] Actual evapotranspiration is defined as the sum ofbare soil evaporation and evapotranspiration from vegeta-tion [e.g., Eagleson, 1978b; Cordova and Bras, 1981;Shuttleworth, 1993; Williams and Albertson, 2004, 2005]

ETa sð Þ ¼ Epbs sð Þ 1� Vð Þ þ ETpbVsV ð14Þ

where Ep and ETp are potential bare soil evaporation andpotential evapotranspiration from vegetation cover; bs andbV are evaporation and evapotranspiration efficiency func-tions for bare soil and vegetation under limited root zonesoil moisture conditions. Following Rodriguez-Iturbe et al.[1999] and Laio et al. [2001a], evaporation efficiency termsused in this paper are

bV sð Þ ¼

0; sh < s � sw

s� sw

s*� sw; sw < s � s*

1 s* < s

8>>>><>>>>:

ð15Þ

bs sð Þ ¼s� sh

sfc � sh; sh < s � sfc

1; sfc < s

8<: ð16Þ

where sh is soil hygroscopic capacity, and sw and s* are soilmoisture levels corresponding to plant water potentials atwilting point, and incipient stomata closure [Porporato etal., 2001]. In equation (16), evaporation for bare soil beginsdiminishing when soil moisture is below field capacity andcontinues to drop until soil moisture reduces to thehygroscopic water content. For grass cover, evapotranspira-tion continues at potential rate until soil moisture fallsbelow s*. Then for s < s* evapotranspiration decays linearlyin response to soil moisture in deficit of s* until the wiltingpoint is reached [Laio et al., 2001a].

2.7. Vegetation Growth

[22] Soil moisture affects the production of organic carbonby photosynthesis, respiration, biomass production as wellas mineralization and uptake of nutrients from the soil. Fieldobservations show a direct linkage between soil moistureand vegetation productivity [e.g., Fay et al., 2003; Scanlonet al., 2005]. Following Fernandez-Illescas and Rodriguez-Iturbe [2004], we develop a simplistic approach for grasscover dynamics by linking a traditional population growthmodel with evapotranspiration efficiency.[23] In the absence of soil water limitations for plant

growth (s � s*, i.e., high precipitation in the growingseason) and under static resource levels (e.g., nutrientsand solar radiation), dynamics of site occupancy for singlespecies vegetation can be related to the difference betweenthe rate of colonization in empty sites and the rate of sitevacancy due to plant mortality [Levins, 1969; Tilman,1994],

dV

dt¼ kcV 1� Vð Þ � kmV ; ð17Þ

where dV/dt is rate of change in fractional vegetation cover,and kc and km are rates of plant colonization and mortalityrespectively. In the equation, the rate of site occupancy isobtained by the product of the rate of propagule productionby the vegetated sites, kcV, and the unoccupied spacefraction (1 � V). The mortality term, kmV, gives thevegetation density-dependent rate at which sites becomevacant. In this equation, mortality rate reflects the effects oflimitations of resources (except water), diseases and otherdisturbances on plant death. Vegetation cover attainsequilibrium when dV/dt = 0, also known as ecosystemcarrying capacity. Maximum vegetation cover at carryingcapacity is Vmax = 1 � (km/kC). This function was alsomodified and used by Tilman [1994] for modeling multiplespecies competition.[24] Water stress begins affecting plant physiology with

the incipient stomata closure, a plant response to waterscarcity to reduce water losses through transpiration. Com-plete stomata closure occurs with soil moisture at wilting.Porporato et al. [2001] nonlinearly related plant waterstress to soil moisture deficit when s < s*. Plant growth(biomass production, reproduction, and fertility) is main-tained by photosynthesis, driven by transpiration [Crawley,

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1997; Kerkhoff et al., 2004]. Thus it is logical to assumethat the higher the evapotranspiration efficiency (equation(16a)), the lower the plant water stress. On the basis ofevapotranspiration efficiency the static water stress ofPorporato et al. [2001] can be obtained as

d tð Þ ¼ 1� bV sð Þ½ ps¼

1; s < sw

s*� s tð Þs*� sw

� �ps

; sw � s � s*

0; s* < s

8>>>><>>>>:

ð18Þ

where d is water stress, and ps is the exponent that describesthe nonlinearity in the effects of moisture deficit on plantactivities. In the growing season, not only the intensity butalso the duration of water stress would influence plantgrowth. To incorporate a time dimension to static plantwater stress (equation (18)), Porporato et al. [2001]developed a mean dynamic water stress for a given growingseason as a function of the mean value of static water stressas well as the frequency and duration of times when soilmoisture is below s*. Fernandez-Illescas and Rodriguez-Iturbe [2004] incorporated the dynamic water stress conceptof Porporato et al. [2001] in the population growth modelgiven in equation (17) to study the effects of interannualprecipitation variability on the ecosystem. However, neitherof these studies link the changes in vegetation cover toevapotranspiration and water stress calculations.[25] In water limited ecosystems vegetation cover

responds to both dry and wet periods. Vegetation coveralso alters soil infiltration and evapotranspiration rates.Therefore, in order to directly link grass dynamics withclimate, we accumulate vegetation water stress betweenstorms, instead of using a mean stress for the entire growingseason. Cumulative plant water stress is defined by inte-grating the static water stress equation as a function of time:

x tð Þ ¼

Z t

0

d tð Þdt ¼Z t

0

s*� s tð Þs*� sw

� �ps

dt; s < s*

0; s > s*

8>>><>>>:

ð19Þ

where t is the duration in which plants are under stress. Thistime is limited to the portion of the interstorm period whensoil moisture is below s* defined as, t � Tb � ts*, where ts*is time required, within the interstorm period, for soilmoisture to drop to s*, if s > s*. Rainfall events thatincrease soil moisture above s* reset the cumulative waterstress (x = 0).[26] During droughts vegetation water stress grows until

permanent damages appear on plant tissues, leading to plantdeath [e.g., Pockman and Sperry, 2000]. FollowingPorporato et al. [2001] we use a threshold cumulativewater stress for plant death. A normalized cumulative waterstress is defined by dividing the cumulative stress by thethreshold stress, xT, as

F tð Þ ¼x tð ÞxT

; x tð Þ < xT

1; x tð Þ � xT

8><>: ð20Þ

The threshold term was defined as the proportion of time, k,that plants can experience water stress during the growingseason, Tseason, without suffering permanent damages, xT =kTseason [Porporato et al., 2001].[27] We can now incorporate the normalized cumulative

water stress with the population growth model given inequation (17). To do so, we consider two modifications inthe original model. The first assumption is that vegetationcolonization rate, kC, decreases linearly with the cumulativestress, kC(1 � F(t)). Second, following the same logic, weassume that water stress increases the mortality rate, reach-ing a maximum value when F = 1. The modified version ofthe Levins [1969] equation becomes:

dV

dt¼ kc 1� F tð Þð ÞV 1� Vð Þ � km þ kmSF tð Þð ÞV ð21Þ

where kmS is mortality rate under plant wilting. Whilemodels with much greater complexities are available in theliterature [Scanlon and Albertson, 2003; Williams andAlbertson, 2005], by directly linking vegetation cover to soilmoisture, the approach used here provides a simple modelwith limited number of input requirements. In implementingthe model, soil moisture losses are calculated adopting theanalytical solutions provided by Laio et al. [2001a] andRodriguez-Iturbe and Porporato [2004]. Cumulative waterstress is calculated in discrete sums of 4 hour time steps. Foreach time step, the analytical solution of equation (21) isused to update vegetation cover fraction.

2.8. Sediment Transport

[28] Sediment transport capacity is traditionally related toflow shear stress in excess of a critical threshold. Manysediment transport equations, including those for bed andtotal load can be expressed in a simplified form given below[e.g., Yang, 1996]:

qs ¼ kf t� tcð Þh ð22Þ

where qs is unit sediment transport capacity (L3/T/L), kf istransport efficiency coefficient, t is flow shear stress and tcis critical shear stress for sediment entrainment, both in Pa,and the parameter h is consistently 1.5 in bed load, and ashigh as 3 in total load equations [Garde and Raju, 1985].[29] Following the shear stress partitioning idea of Foster

[1982] in agricultural crop lands, relating effective shearstress (shear stress acting on soil surface) to flow resistancedue to crop biomass, Istanbulluoglu and Bras [2005]proposed the following equation for overland flow effectiveshear stress:

tf ¼ tbFt ¼ ktqmSnFt; ð23Þ

Ft ¼ns

ns þ nV

� �3=2

ð24aÞ

kt ¼ rwg ns þ nVð Þ6=10 ð24bÞ

nv ¼ nRvV

VR

� �w

ð24cÞ


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where tf is the effective shear stress written as a fraction oftotal shear stress, tb; Ft is shear stress partitioning ratiorelated to Manning’s roughness coefficient for bare soil, ns,and vegetation, nV; q is unit water discharge (L2/T); S isslope; rw, and g are specific weight of water and gravity ofacceleration respectively; and kt, m and n are parametersthat may vary with flow geometry. For overland flow andflow in wide channels, suggested values are: m = 6/10, n =7/10 [Willgoose et al., 1991].[30] In the model described above, Manning’s roughness

for vegetation is represented as a power function of vege-tation cover, V relative to a mature vegetation cover, VR, thathas a known roughness coefficient of nv

R. Mature vegetationcover here is defined as grass cover fraction under no waterlimitation and assumed as 0.95. Relating surface roughnesscaused by vegetation to the fraction of ground cover itselfestablishes a dynamic link between sediment transportpotential and the climate, soil and vegetation system. Thismodel was calibrated using flow and erosion data fromflume experiments of Prosser et al. [1995] leading to w =0.5 [Istanbulluoglu and Bras, 2005].[31] For the purposes of our sensitivity analysis we

simplify the sediment transport relationship and write it asproportional to runoff and vegetation related variables.Instead of predicting absolute sediment transport rates, thissimplification would predict relative changes in transportrate controlled by runoff and grass cover. In this onedimensional model discharge for unit area is equal to therunoff rate, q = R. A proxy for sediment transport rate as afunction of runoff and vegetation cover can be written bysubstituting equations (23) and (24a), (24b), and (24c) into(22):

qs /Rmn3=2s

ns þ nRVVVR

� �w� �9=10

0B@

1CA

h

: ð25Þ

An important limitation of this proportionality is that itignores an erosional threshold term (i.e., critical shearstress), which often depends on the hillslope sediment size.Including such a threshold would require the definition of abasin area in the model. This would make model resultsrelative to an arbitrarily selected watershed size. As itstands, equation (25) can be viewed as an index for potentialsediment transport with no reference to any surfacesediment size.

3. Model Analysis

[32] We used three model experiments in order to dem-onstrate the potential implications of dynamic climate-soil-vegetation coupling on runoff driven sediment transportpotentials. Table 1 gives the parameter values used in the

experiments, which are mostly taken from other relatedmodeling studies [e.g., Laio et al., 2001a, 2001b; Caylor etal., 2005]. Soil infiltration capacities under bare soil andvegetated conditions are approximate mean values of theranges reported in, or inferred from various publications inthe literature [e.g., Abrahams et al., 1995; Cerda, 1998;Dunkerley, 2002a, 2002b; Wainwright et al., 2000; Bharkand Small, 2003; Fiedler et al., 2002].

3.1. System Response to Storm Timing: A DroughtExperiment

[33] Erosion and sediment transport is argued to be moreefficient in arid to semiarid climates [Leopold, 1951;Molnar, 2001]. Field observations show correlationsbetween drought severity and erosion activity followingdroughts [Balling and Wells, 1995]. Therefore it is impor-tant to explore the sensitivity of sediment transport potentialto drought severity.[34] One way to address this is to construct a relationship

between sediment transport potential, driven by a fixedstorm rate and duration, and drought length for a range ofinitial vegetation cover conditions. In the model experimentreported in this section we use a single high-intensity, andshort-duration storm event (70 mm/h for 1 hour duration).The storm rate and duration is selected to represent typicalsmall-scale convective storms in semiarid regions. Forinitial conditions we used grass covers ranging from 0.05to 0.95, and saturated root zone soil moisture. With stormsarriving at selected days (e.g., 1, 2, 3, 4, . . .200 days) afterinitial saturation, this experiment design captures a range ofdifferent soil moisture conditions from saturation to hygro-scopic water content, shg as soil dries during droughts andvegetation responds dynamically to soil moisture. In themodel vegetation cover is updated daily using the accumu-lated water stress calculated in 4 hour time steps.[35] Figure 1 plots the solution space for grass cover

(Figure 1a), soil moisture (Figure 1b), normalized runoffvolume (Figure 1c), and normalized sediment transportindex (Figure 1d), as a function of days after soil saturationbeginning with day one. Note that because the sensitivity ofthe coupled system to drought length is investigated, eachstorm is considered to be independent and does not modifysoil moisture. Therefore the values plotted in Figure 1brepresent antecedent soil moisture conditions prior to eachstorm arrival. Runoff and sediment transport are normalizedwith their respective minimum values, both generated under0.95 grass cover fraction, with the storm pulse arrivingwhen soil moisture is at field capacity. In Figure 1a, in thefirst 50 days after soil saturation grass responds to the initialabundance of soil moisture in the root zone depending on itsinitial cover, either by maintaining its cover, for V < 0.2,where growth is limited by seed availability, and for V > 0.8, where space limitation restrains growth; or slightly

Table 1. Parameters Describing the Soil Characteristics Used in the Model

Soil Texture b n sfc s* sw sh IS, mm/h IV, mm/h

Loamy sand 4.38 0.42 0.45 0.24 0.1 0.08 30 100Loam 5.39 0.45 0.54 0.4 0.23 0.19 10 40Clay 11.4 0.5 0.8 0.64 0.47 0.44 3 15

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increasing (for initial V ffi 0.4 � 0.6) its fraction on theground. Continuing drought eventually eliminates grassvegetation on the surface.[36] The rate of soil drying is faster under a dense cover

because of larger evapotranspiration rates (Figure 1b). If soilinfiltration capacity were constant, rapid soil drying wouldprovide larger root zone storage for the simulated fixeddepth of rainfall, reducing runoff as drought lengthincreases. In contrast, however, runoff rate amplifies withdrought length in the model (Figure 1c). This is solelybecause of a reduction in infiltration capacity as a result ofvegetation loss as drought continues. Because of the non-linear dependence of sediment transport positively torunoff and negatively to grass cover, sediment transportpotential increases several orders of magnitude duringdrought (Figure 1d).

3.2. Effects of Storm Variability in DifferentPrecipitation Regimes

[37] Climate change predictions suggest variations in thefrequency and size of individual rainfall events, but oftenwith no significant changes in seasonal or annual totals[e.g., Easterling et al., 2000]. A recent manipulative fieldexperiment in northeastern Kansas investigated the influ-ence of climate variability on a native grassland ecosystemfor four years [Knapp et al., 2002; Fay et al., 2003], by

artificially increasing both the time between observedstorms and rainfall amounts per each storm while maintain-ing the total annual precipitation unchanged. A 50% in-crease in the time between storms led up to a 20% reductionin measured net carbon assimilation resulting from reducedphotosynthesis. Porporato et al. [2004] reproduced thesefield observations using the analytical model of Daly et al.[2004a, 2004b], derived as a function of a probabilisticrepresentation of climate, soil moisture, and fixed vegeta-tion characteristics. Using the model, Porporato et al.[2004] projected persistent reductions in net carbon assim-ilation rate with increased storm frequency for mean sea-sonal precipitation between 400 and 600mm.[38] With this background, the next logical step is to

investigate the potential impacts of climate change on runoffsediment and nutrient transport processes in natural andmanaged ecosystems. Here we address the former, using theoutlined model, by fixing the mean seasonal precipitation inthe growing season, hPi, and varying the mean time betweenstorms, �Tb. Since our objective is to focus on the solecontrol of grassland dynamics on sediment transport, wepurposely fixed the mean rainfall rate constant and variedstorm duration in order to conserve mass as mean timebetween storms is varied. Experiments are performed fordifferent climate regimes characterized by a simple humid-ity index (i.e., inverse of Budyko’s dryness index [Budyko,

Figure 1. Solution space for (a) grass cover, (b) soil moisture, (c) normalized runoff volume, and (d)normalized erosion index as a function of days after soil saturation. In this example, a loamy soil textureis used (Table 1) with vegetation parameters selected for grass in Table 2.


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1974]) that normalizes hPi with potential growing seasonevapotranspiration PET (sum of daily ETp):

P0h i ¼ Ph iPET

: ð26Þ

This index gives the fraction of potential evapotranspirationsatisfied by total precipitation within a growing season, andthe higher the index the wetter the seasonal climate. Themean seasonal or annual precipitation is simply the productof the number of storms Ns, mean storm rate �p and meantime between storms �Tb:

Ph i ¼ P0h iPET ¼ Ns�p�Tr

Ns ¼Nh

�Tr þ �Tb; ð27Þ

where Nh is the number of hours within a specified time(e.g., growing season), and �Tr is mean storm duration. Inthe experiments with a fixed humidity index hP0i, we set �pequal to the bare soil infiltration rate for loam, �p = IS, andadjusted �Tr to maintain a constant hPi. Using a fixed �pallows the investigation of indirect effects of the dynamicbehavior of the ecohydrologic state variables (V, Ic and s) onsediment transport capacity, rather than the rainfall rate. Inorder to represent a range of precipitation regimes we usedhumidity indices hP0i ranging between 0.3 (the driest) and 1(the wettest). This range seems to be reasonable to representgrasslands as with larger precipitation forests tend todominate, and with smaller hP0i grasslands are usuallyreplaced by desert shrubs. With the selected parameters inTable 2 the model does not predict grass cover for humidityindices less than or equal to 0.1. For each selected hP0i, �Tb isvaried between 2 and 40 days. Loam soil texture is used torepresent average soil texture conditions (Table 1) withgrass vegetation parameters given in Table 2. For each �Tb,given hP0i, the model is run for 1600 years with noseasonality.[39] Figure 2 plots the mean values of the modeled grass

cover (Figure 2a) and normalized sediment transport index(Figure 2b) as a function of �Tb for the selected range ofhumidity indices. Storm depths increase as a function ofmean time between storms, for example for hP0i = 0.3 themean depth is 2.2 mm for �Tb = 2 days, and approximately44.5 mm for �Tb = 40 days. Figure 3 presents water balance

components (equation (2)) normalized by the mean seasonalrainfall for hP0i = 0.4.[40] First of all, the overall response of the system to

growing hP0i is an increase in grass cover for all values of�Tb. The system response to changes in �Tb is, however, morecomplex and closely related to the humidity index. Whenthe climate is humid, hP0i = 1, the grass cover reduces withrainfall variability. As climate becomes more arid vegetationcover first increases, reaches a maximum, then decreases asa function of increased mean time between storms (orreduced storm frequency). As was addressed by Laio etal. [2001a] and Porporato et al. [2001] for fixed vegetationconditions, here the optimal partitioning between the timingand amount of rainfall provides the most favorable soilmoisture conditions such that, evapotranspiration is maxi-mized, while losses due to runoff and leakage are mini-mized. This can be seen in the components of water balancefor hP0i = 0.4 in Figure 3. Since the limiting resource is soilmoisture in this model, vegetation cover evolves to a state atwhich benefits of plant transpiration (i.e., increase in grasscover) is balanced against the mortality costs of water stress[Tilman, 1988; Kerkhoff et al., 2004]. Note that in Figure 3,because of larger storm pulses in an increasingly variablerainfall regime, relative amounts of both runoff and drain-age in the water budget grow.[41] One interesting outcome of the model is that the

interplay between climate, soil and vegetation results in

Table 2. Parameters Used for Grass Vegetation Cover

Parameter Value

Root depth Zr, m 0.35a

Colonization rate kC, 1/yr 4Mortality rate km, 1/yr 0.1Mortality rate with full stomata closure kmS, 1/yr 6Maximum canopy storage per leaf area SLA, mm 0.3Interception decay coefficient, cd 0.2Potential Evapotranspiration ETp, mm/d 3.7a

Soil Evaporation after wilting Ew, mm/d 0.1a

Exponent of the stress function ps 3a

Water stress threshold xt, days 75a

Water erosion exponent h 2b

Manning’s roughness for soils ns 0.025b

Manning’s roughness for grass vegetation, nV 0.65b

aRodriguez-Iturbe and Porporato [2004].bIstanbulluoglu and Bras [2005].

Figure 2. Mean values of the (a) modeled grass cover and(b) normalized sediment transport index (STI) as a functionof the mean time between storms. Mean seasonal precipita-tion is fixed for each curve but varies among curves asrelated to the humidity index hP0i. Higher values of hP0irepresent larger growing season precipitation.

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differences in the location of maximum vegetation coverunder different humidity indices in Figure 2a As climatebecomes more arid, the maximization of vegetation cover isattained with a more variable rainfall regime. Because themean seasonal precipitation depth is kept constant, asclimate becomes drier, only less frequent storms with largerrelative magnitudes can satisfy soil moisture to a level thatefficient plant transpiration begins (i.e., s � s*), leading tovegetation colonization.[42] From the geomorphic point of view, reduction in

both runoff generation and shear stress efficiency with theoptimum combinations of rainfall characteristics (�p, �Tr, �Tb)that maximize vegetation cover, results in the minimizationof sediment transport capacity in Figure 2b. In Figure 2beach curve is normalized by its mean value. Thus theplotting does not allow comparison of absolute sedimenttransport potentials between different humidity indices.[43] Interestingly, erosion potential in a humid climate

seems to be more sensitive to changes in storm frequency,as vegetation cover is affected more dramatically fromreduced number of storms arriving with larger magnitudes.For example for hP0i = 0.3, the maximum sediment transportis about 3.5 times larger than the minimum, while in thecase of hP0i = 1, the maximum sediment transport is up to1000 times larger than the minimum. Unless dynamicvegetation is modeled, no significant difference wouldoccur in sediment transport rates as the rate of rainfall isfixed in this example.[44] Figure 4 plots the effects of soil texture in mediating

the dynamic response of vegetation cover and sedimentyields to changes in �Tb for hP0i = 0.5. As a result of its lowhydraulic conductivity clay soils produce larger runoff.Thus reduced total amounts of infiltration, and higher waterpotentials for plants to overcome for unstressed evapotrans-piration (i.e., higher s*), cause a significant reduction in

grass cover, and a shift in the maximum point for plantcover to a higher �Tb compared to other soil types(Figure 4a). As a result of limited vegetation cover, varia-tion in the erosion potential with rainfall variability is alsolimited in clay. This response is similar to what is observedin Figure 2, for loam, with hP0i = 0.3 (i.e., smaller precip-itation). While absolute magnitudes of the water balancecomponents may vary, similarity in the response suggeststhat changes in soil texture from fine to coarse would have aresponse similar to an increase in humidity under fixed soiltexture. This is also evident in the case of loamy sand inFigure 4a, which, under a drier rainfall regime, hP0i = 0.5,produces a response to changing �Tb similar to loam in awetter climate (hP0i = 1, Figure 2). Steady state vegetationcover show remarkable differences from clay to sandy soiltextures, resulting in a complex response in sedimenttransport.[45] The results presented here can be elaborated under

the context of the inverse soil texture effect hypothesis, firstproposed by Noy-Meir [1973]. This hypothesis suggests thatthe same plant that is found on coarse soils in a dryerclimate, can be found on fine soils in a wetter climate. Usingtheir probabilistic water balance model, Laio et al. [2001b]proposed the inverse soil texture effect as a potentialexplanation for the existence of the dominant plant speciesin north central Colorado, where spatial variability in soiltexture is high. Fernandez-Illescas et al. [2001] also inves-tigated the role of inverse soil texture effect with interannualrainfall variability on plant species in a southern Texassavanna. In both studies, water stress was used as a

Figure 3. Components of water balance for hP0i = 0.4,where hCIi, hRi, hDi and hETi are mean annual depths ofcanopy interception, runoff, drainage and evapotranspira-tion, divided by mean seasonal precipitation hPi. Thedifference between any two curves from top to bottom givesthe fraction of water loss to a particular process indicatedbetween lines. The global maximum point observed inevapotranspiration minimizes water loss to rain interception,drainage, and runoff and corresponds to the location ofmaximum grass cover for hP0i = 0.4 plotted in Figure 2.

Figure 4. Effects of soil texture on (a) mean vegetationcover and (b) normalized mean sediment transport index(STI), modeled for clay, loam, and loamy sand soil texturesfor hP0i = 0.5.


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surrogate for species suitability to the environment, with nodynamic changes in species abundance, biomass or cover.[46] In agreement with the inverse soil texture effect

concept, two important outcomes in Figures 2 and 4, underessentially the same mean seasonal precipitation are (1)grass cover diminishes with the fining of soil texture; and(2) soil texture and the storm frequency in the currentclimate determine biomass production and erosion responseas the time between storms grows (i.e., higher rainfallvariability) with climate change (Figures 2 and 4). Forexample in both loamy soil for hP0i = 0.3 (Figure 2b), andclay soil for hP0i = 0.5 (Figure 4b), vegetation cover growswith Tb < 10 days, and decreases with larger values of Tb,while sediment transport capacity follows an inverse trendwith vegetation cover. A similar behavior is also observedfor other humidity indices and soil types with variations inthe critical storm frequency that controls the phase changein the relationships between mean time between storms andboth vegetation cover and the index for sediment transportpotential.

3.3. Erosion Potential Across Precipitation Regimes

[47] In this section we investigate the relationship be-tween sediment transport potential and mean annual pre-cipitation in a range of precipitation regimes. A simplisticapproach for capturing the essential changes in rainfallforcing parameters (p, Tr, Tb) as a function of mean annualprecipitation hPi is developed based on the reported param-eters of the Poisson rainfall model for United States [Hawk,1992]. Seasonality in both precipitation and evapotranspi-ration are represented by parsimonious models. With theforcing parameters (p, Tr, Tb, and ETp) estimated from hPi,we used the climate-soil-vegetation and erosion scheme toobtain a relationship between sediment transport potentialand mean annual precipitation.3.3.1. Rainfall Characteristics as Related to MeanAnnual Precipitation[48] In an attempt to characterize the general climatology

of the rainfall with mean annual precipitation we begin withutilizing a simple rainfall variability factor, derived fromequation (27) [Tucker and Bras, 2000]:

RVar ¼p

Ph iNh

¼ Tr þ Tb

Tr; ð28Þ

where Nh is the length of the rainy season (the whole yearfor annual analysis), during which the mean total rainfallhPi is recorded. In the two alternative definitions givenabove, annual rainfall variability is typically high in regionswith sporadic, high-intensity and short-duration storms(e.g., semiarid southwest United States); and low, in placesreceiving drizzle-like storms throughout the rainy season(e.g., the Oregon Coast Range, United States).[49] Using equation (28), one can relate the parameters of

the Poisson rainfall model to RVar:

p ¼ RVarN�1h Ph i ð29aÞ

Tb

Tr¼ RVar � 1ð Þ ð29bÞ

These simple functional forms suggest that once RVar, andeither �Tb or �Tr are known for a given Nh, all threeparameters of the rainfall model can be calculated.[50] Hawk [1992] reports the monthly parameters of the

Poisson pulse rainfall model for more than 60 rainfallstations across the United States. In Figure 5, we plot bothannual and seasonal data for RVar (calculated with (28) usingdata from Hawk [1992]) and �Tb as a function of precipita-tion. In the case of the seasonal data, we used onlythe stations showing distinct seasonal patterns in rainfall,mostly located in the western United States. Because seasonlength varies, seasonal precipitation is scaled up to annualtimescale for plotting in Figure 5 by

Psh i ¼ PRsh ifs

ð30Þ

where hPsi is scaled seasonal precipitation, hPRsi is thedepth of mean seasonal precipitation, and fs is length ofseason represented as a fraction of the year.[51] In Figure 5 both RVar and �Tb are inversely propor-

tional to mean annual precipitation, with some significantscatter. Not surprisingly, the plotted trends are intuitive, asone could expect, humid regions would have more frequentstorms, resulting in smaller rainfall variability than aridclimates. In Figure 5a both Chicago, Illinois, and Atlanta,Georgia, have much smaller storm variability than Tucson,Arizona, for which two end-member seasons with maxi-mum and minimum variability is plotted. The maximumvariability for Tucson corresponds to spring precipitation(April to June) and the minimum is the monsoon season(July to September). During the monsoon, more than 50%of the annual precipitation falls in the area, reducing stormvariability. Fitted curves in Figure 5 relate mean annualprecipitation to rainfall variability and mean time betweenstorms according to power functions:

RVar ¼ 700 Ph i�0:6 ð31Þ

Tb ¼ 2350 Ph i�0:5; ð32Þ

where hPi is in millimeters and Tb in hours. In a recentstudy, Small [2005] used a total of 536 station records, eachwith at least 35 years of data, and found the followingrelationship between the mean time between storms andannual precipitation,

Tb ¼ 5014 Ph i�0:59: ð33Þ

Note that this equation is modified from equation (9) ofSmall [2005], which originally used units in days for �Tb andcentimeters for hPi. The Small [2005] equation plots slightlyabove the relationship developed in this study. One potentialreason for this is that, Small [2005] used stations throughoutthe western United States where rainfall variability issignificant. Whereas Hawk [1992] data used in Figure 5aincludes precipitation records from much wetter regions.[52] In the model, seasonality is introduced as a fraction

of the year, fs, receiving some portion of the mean annualprecipitation, fP, 0 < fP � 1. For the purpose of estimatingthe seasonal parameter values of the Poisson rainfall model

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using the power law functions above, mean seasonal pre-cipitation is related to mean annual precipitation accordingto

Psh i ¼ PRsh ifs

¼ fP Ph ifs

: ð34Þ

[53] In the model experiments, the power functions pre-sented above are used to estimate typical mean tendencyvalues for RVar and Tb, for a given mean seasonal hPsi, ormean annual precipitation hPi. Then, with RVar and Tbknown, equations (29a) and (29b) are used to calculate pand Tr.[54] Small [2005] found increased storm frequency in wet

seasons, resulting in a reduction in the mean time betweenstorms. In this study the mean time between seasonal stormsis approximated by [Small, 2005]

TSb ¼ Tb

,0:7

Psh iPh i þ 0:3

� �; ð35Þ

where both hPsi and hPi are in mm/year. In a wet season,hPsi/hPi > 1, equation (35) predicts a shorter mean time

between storms (TSb < Tb), and in a dry season hPsi/hPi < 1,

a longer mean time between storms (TSb > Tb) than the mean

annual values.

3.3.2. Potential Evapotranspiration[55] Potential evapotranspiration is the essential boundary

atmospheric forcing for soil drying. In section 3.2. weapplied a constant rate for daily potential evapotranspira-tion, ETp, for fixed mean seasonal precipitation (or humid-ity). While this assumption does not allow for fluctuationsin potential evapotranspiration, it provides a reasonableestimate for a mean behavior of the atmosphere within agiven season. However, with increasing regional precipita-tion temperature and humidity gradient of the land surfaceoften decreases resulting in a reduction in potential evapo-transpiration rates [Hobbins et al., 2004]. Figure 6 plotsmean daily ETp averaged over rainy seasons, as a functionof mean annual precipitation compiled from different sour-ces. The best fit linear relationship shows a reduction in ETp

with precipitation. This relationship is employed to capturethe central tendency in ETp in response to a precipitationincrease.[56] Seasonal fluctuations in daily ETp is represented by a

sinusoidal function [Small, 2005]:

ETp Tð Þ ¼ DETm

2cos 2p

T � LET � Nd=2

Nd

� �� þ ETp ð36Þ

where DETmis the difference between the maximum and

minimum values of daily ETp throughout the year; LET isthe lag between the peak ETp, and solar forcing; and ETp is

Figure 5. Relationship between mean annual precipitation and (a) rainfall variability, RVar, and (b) meantime between storms. For comparison purposes, all seasonal values are scaled to mean annualprecipitation.


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the mean annual rate of daily potential evapotranspiration;and Nd is the number of days in the year. In this model, forLET=0, peak ETp occurs with T = Nd/2. Equation (36) wasreported to show good agreement with seasonal variationsin ETp calculated using the Hargreave’s equation from dailydata [Small, 2005].3.3.3. Model Experiments: Sediment Transport asRelated to Mean Annual Precipitation[57] We investigate the relationship between mean annual

precipitation hPi and sediment transport index using thecoupled climate-soil-vegetation and erosion model. Eachyear is divided into a wet and a dry season, each receivinghalf of the mean annual precipitation, fP = 0.5. The length ofthe rainy season is fixed to four months (fs ffi 0.34),approximately the mean of the wet season length for thewestern United States [Small, 2005]. The wet season iscentered in the middle of the year, starting from June andending in the end of September. In this setup, the peak valuefor daily potential evapotranspiration corresponds to thebeginning of wet season.[58] In the model experiments, mean annual precipitation

hPi is systematically increased from 100 mm/year up to1500 mm/year. Much larger values of precipitation are notconsidered as most of the parameters of the climate gener-ator are selected for the western United States. The stepsfollowed in obtaining the mean seasonal storm character-istics are as follows: (1) select mean annual precipitationhPi; (2) calculate wet and dry season precipitation rate, hPsi(in mm/year) from equation (34); (3) using hPsi, calculaterainfall variability, RVar (equation (31)), and the mean time

between storms, TSb using first equation 33 then 35, for each

season; (4) use RVar and hPsi in equation (29a) to obtain themean storm rate, p, for each season. Similarly, in assigningdaily values for potential evapotranspiration, the steps usedare (1) calculate the mean annual value of daily ETp usingthe relationship in (Figure 6); (2) use equation (36) tocalculate the mean trend in ETp as a function of day ofthe year.[59] The climate data generated for 6000 years are used to

force the model for three soil types: loamy sand, loam and

clay (Table 1). In order to isolate the effects of dynamicvegetation cover, we also run the model with both novegetation cover and full vegetation cover for loamy soiltexture.[60] The Poisson rectangular pulses rainfall model often

underpredicts rainfall rates, specifically in areas where high-intensity and short-duration convective storms are common.In the model, such unrealistically low rainfall rates, whenused with measured infiltration capacities, would favormore infiltration resulting in reduced runoff generation.For typical ranges of infiltration, approximately 30–70mm/h depending on soil texture and vegetation cover, andrainfall rates (20 and 40 mm/h) in the western United States[Abrahams et al., 1995; Wainwright et al., 2000; Fiedler etal., 2002; Etheredge et al., 2004], the rainfall to infiltrationrate ratio, p/Ic, is likely to vary between 0.2 and 1.Therefore, to keep the p/Ic ratio at some realistic valuesrepresentative of the hydroclimatology of the westernUnited States, the infiltration capacities reported in Table 1are reduced 10 times for loamy sand and loam, and fivetimes for clay.[61] Figure 7 plots the mean annual sediment transport

potential index (equation (25)) as a function of mean annualprecipitation for loamy sand, loam and clay soil types alongwith the original Langbein and Schumm [1958] curve. Tofacilitate comparison between curves, the Langbein andSchumm curve is normalized by its mean, and the othercurves for individual soil types are normalized by the meansediment transport potential index for loam. The modelpredictions for different soil types can be compared witheach other since they are all normalized by the samenumber. However, only the shape and the range of variationbetween the model results and the Langbein and Schummcurve can be compared. The Langbein and Schumm equa-tion, plotted in Figure 7, is

Qs ¼ aPa 1

1þ bPb ; ð37Þ

where Qs is sediment yield in (cm/yr), P is effective annualprecipitation, a, a, b, and b are empirical model parameterswhose values are given in Figure 7. In this equation, the firstterm represents the erosivity of climate, and increasesnonlinearly with precipitation. The second term representthe erodibility of the land surface, and is a decreasingfunction of precipitation.[62] Overall, although no calibration is performed in the

model except setting k = 0.25, that gives xt = 30 days inequation (20), the predicted shape and the relative magni-tude of change in sediment yields are consistent with theLangbein and Schumm curve which was derived fromobservations. Both the model results and the data show aphase-switching in sediment flux, resulting in a peaksediment transport rate in semiarid to subhumid conditions.In the model the turn over point in sediment flux coincidesto critical precipitation depths that favor resistant grassgrowth. Because of the differences in the physical soilproperties (Table 1), precipitation required for the establish-ment of grass varies. Coarser soils are more favorable forvegetation growth in water-limited ecosystems [Rodriguez-Iturbe and Porporato, 2004], therefore sediment flux peaksin a drier climate for loamy sand, followed by loam and clay

Figure 6. Potential evapotranspiration as a function ofmean annual precipitation. Data are compiled fromEagleson and Tellers [1982], Eagleson [2002], andEagleson and Segarra [1985].

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as climate grows wetter. Similar to the rainfall variabilityexample discussed in the previous section, we attributethese different locations in the peak sediment transport ratesto the inverse soil texture effect [Noy-Meir, 1973].[63] In order to examine the hydrologic drivers of sedi-

ment transport potential across a range of climates, and theeffects of dynamic vegetation in modulating them, we plotthe normalized sediment transport, mean annual runoff, andmean annual evapotranspiration for loam for three cases: novegetation, dynamic vegetation, and static full vegetationcover in Figure 8. In Figure 8 the sediment transport indexincreases for both the bare and the fully vegetated modelexperiments as humidity grows. Sediment transport for baresoil is larger as there is no shear stress loss to vegetationroughness. In the absence of enough precipitation to favorgrass growth evapotranspiration, runoff, and sedimenttransport of dynamic vegetation simulation follows the barecase (Figure 8). With precipitation sufficient to supportgrass establishment, evapotranspiration increases rapidly(Figure 8c), resulting in slight reductions in runoff(Figure 8b). Therefore, in this example, the reduction insediment transport after reaching a peak is not only becauseof a decrease in erodibility but also some slight reductionsin runoff totals.[64] We propose to divide the precipitation–sediment

transport capacity domain into three regions, based on thedominant control of climate and vegetation on sedimenttransport (Figure 8). In arid and semiarid climates withsparse or no vegetation, sediment transport is directlycontrolled by climate, generating erosive runoff (first regionin Figure 8a). As vegetation is favored by growing precip-itation, sediment transport diminishes abruptly because of areduction in both runoff and sediment transport efficiency(equation 24a). Therefore the trend in the second region inFigure 8a is controlled by the counteracting influence ofclimate forcing and vegetation growth on sediment trans-port. As precipitation becomes abundant for vegetationgrowth (i.e., precipitation larger than 1000 mm/yr in the

example in Figure 8), vegetation growth is no more limitedby water, and therefore sediment transport potential onceagain is primarily controlled by climatic forcing which mayresult in an increasing trend in sediment yields. We hypoth-esize that the boundaries between these three regions wouldchange with soil texture. For example, in Figure 7, forloamy sand, vegetation establishes with a smaller meanannual precipitation and begins restraining sediment trans-port earlier than the other two soil types. The downtrendcontinues around mean annual precipitation of 600 mmwhich supports full grass cover (not plotted). As precipita-tion grows larger than 600 mm, the model predicts a secondrise in sediment transport as a result of increasing stormerosivity acting on fixed vegetation cover.[65] These model results lead to our working hypothesis

that the second rise in sediment yields with increasinghumidity observed in some data sets [e.g., Walling andKleo, 1979] may correspond to ecosystems where vegeta-tion growth is not (or less) limited by water availability.Thus both runoff and runoff-driven sediment transportindex approach to fully vegetated conditions with increasingprecipitation.

4. Discussion and Conclusions

[66] Global climate has been historically subject to long-and short-term variability. In the last 3-4 Myr the world’sclimate has changed from a relatively stable regime to anoscillating one with 20–400 kyr periods of glacial intergla-cial cycles, resulting in enhanced sedimentation rates world-wide [Zhang et al., 2001]. Short-term (decadal scale)climate variability in the form of dry-wet cycles driven byENSO patterns and Pacific Decadal Oscillation (PDO), along-lived El Nino-like pattern of Pacific climate variability,also have a direct influence on soil moisture, vegetationcomposition, and erosion rates [e.g., Scanlon et al., 2005;Waters and Haynes, 2001]. Superimposed on the existingshort-term fluctuations, GCM simulations further predict

Figure 7. Modeled sediment transport potential index (STI) as a function of mean annual precipitationfor clay, loam, and loamy sand, normalized by the mean STI of loam, and the Langbein and Schumm[1958] curve normalized by its mean. The parameters of the Langbein and Schumm curve are a = 2.58 �10�5, b = 3.14 � 10�5, a = 2.3, and b = 3.33.


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increased in-season rainfall variability, as a result of globalwarming, leading to less frequent storm events with largermagnitudes for many regions in the United States[Easterling et al., 2000]. With these reported dynamics ofglobal climate, understanding the linkages betweenecohydrological and erosional land surface processes, andtheir collective response to climate fluctuations becomescrucial in hydrological sciences. This paper presentsa parsimonious framework for addressing the coupled

vegetation-erosion dynamics and underscores the impor-tance of representing such linkages in assessing climatechange impacts in three examples.[67] The first example explored the influence of drought

length on sediment transport capacity of a single stormfollowing a drought. This example can be interpreted as theonset of a wet-cycle following a prolonged drought (i.e.,ENSO patterns). The model predicts vegetation loss withincreasing drought length as a result of soil drying. Vege-

Figure 8. Normalized values of mean annual (a) sediment transport index (STI), (b) runoff, and (c)evapotranspiration as a function of mean annual precipitation for loam soil type for three land coverconditions: no vegetation, dynamic vegetation, and static full vegetation.

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tation loss reduces soil infiltration capacity and amplifiesoverland flow erosion efficiency. These factors result inlarger, and more efficient floods in carrying sediment aftervegetation-weakening droughts.[68] These model-based findings are corroborated with

observational results. As discussed by Waters and Haynes[2001], the American southwest experienced increasedfluvial activity resulting in widespread synchronous incisionof large arroyo systems approximately after 4000 14C BP.This period coincides with the development of modernclimate regime, with relatively lower temperatures, anddry-wet cycles with more frequent and strong El Ninopatterns. The establishment of modern desert shrub com-munities in dry valley floors of the southwest also coincidesto this period [Van Devender, 1990]. On the basis of thisclimatic evidence, arroyo cutting and filling cycles in thelast few thousand years in the southwest United States wererelated to a combination of several years of increased ElNino activity, generating large floods, following extendeddroughts [Balling and Wells, 1995; Waters and Haynes,2001]. While we did not fully address the effects of short-term climate variability in the form of dry-wet cycles onsediment transport, the predicted increase in both runoff anderosion rates with drought length is in agreement with fieldobservations reported above.[69] The second example investigated the implications of

rainfall variability in the growing season (i.e., longer dryintervals between storms) on sediment flux rates. Our modelresults suggest a higher sensitivity of sediment transportrates to rainfall variability in humid regions than in arid andsemiarid ones. The simple argument here is that reduction insoil moisture with growing rainfall variability would resultin more vegetation loss in a humid climate, where vegeta-tion is lush, than in semiarid regions with sparse plant cover.[70] This finding is consistent with the sensitivity analysis

of Tucker and Bras [2000] who reported a growing sensi-tivity of runoff erosion to rainfall variability when anerosion threshold is used. Their argument was that in humidregions, with high erosion thresholds imposed by vegeta-tion, the number of times a certain threshold is exceededwould increase as rainfall becomes more variable. In thispaper we did not include any erosion thresholds, becausedoing so would require definition of a watershed area.Instead, in the one-dimensional analysis described here,we relate erosion to runoff rate and a shear stress efficiencyfactor, both linked to dynamic vegetation cover. Includingerosion thresholds in our analysis would further increase thepredicted sensitivity of humid regions to climate variability,because of the reasons discussed by Tucker and Bras[2000].[71] The observed form of the relationship between

sediment yields and annual precipitation with a peak rateoccurring in semiarid conditions, was attributed to therelative dominance of erosivity and soil erodibility bothmodulated by climate (equation (37) and Figure 7)[Langbein and Schumm, 1958; Moglen et al., 1998]. Themodeling experiments with increasing mean annual precip-itation reproduce the general shape of this relationship(Figure 7). In addition, the model underscores the impor-tance of soil texture influencing the location of the switch inthe relative dominance between erosivity and erodibility, aswell as the overall shape of the rising and falling limbs of

the sediment yield curves. An interesting outcome of themodel was the second rise in sediment transport capacitywith precipitation in subhumid and humid climates. Thismodel prediction is consistent with some observationalstudies [Wilson, 1973;Walling andKleo, 1979] that presentedmultiple peaks in sediment yield versus precipitation curves,and attributed these arbitrarily to differences in climatecharacteristics and seasonality. We suggest that the secondrise in sediment yields could correspond to climatic condi-tions that support lush vegetation cover, leading to a systemresponse only controlled by increasing climate erosivity onvegetated landscapes as climate becomes wetter.[72] The importance of soil texture in geomorphology has

long being recognized, perhaps with the first quantitativedata of Shields [1936], documenting the differences in fluidshear stress required to mobilize sediments in different sizeclasses. In addition to this known influences of soil textureon erosion thresholds (i.e., critical shear stress, discharge,rainfall) and soil erodibility, this paper underscores theimportance of soil texture in water erosion via affectingecohydrological processes and vegetation dynamics.[73] The influence of vegetation changes on erosion rates

was largely studied in the context of arroyo development inthe southwestern United States. Conceptual process-re-sponse models directly related the enhanced periods ofarroyo development to vegetation-weakening droughts[Cooke and Reeves, 1976; Bull, 1997]. As the next logicalstep, by quantifying the linkages between climate forcing,vegetation dynamics and erosion rates, the simple modelpresented here opens avenues for process-based research ininvestigating the impacts of climate variability and changeon erosion rates and resulting landscape development.[74] Because our objective here was to introduce a new

‘‘dynamic’’ perspective in modeling earth surface processesusing simple conceptualizations, limitations of our findingshere are a handful. First of all the one-dimensional modelused here does not capture landscape scale processes. Basingeomorphic characteristics (i.e., local slope, slope-areascaling, curvature), soil availability on hillslopes, soil pro-duction rates, tectonic processes, and many other externaland internal landscape complexities that are not includedin this paper, would greatly influence basin sedimentfluxes and the tempo of landscape evolution under varyingclimate.[75] Vegetation processes we employed in our model are

extremely simplistic. Other critical factors, such as theeffects of temperature and seasonality on plant growth, arecomponents that should be represented in the framework. Interms of climate forcing parameterization, it is important torealize that both the long-term (glacial-interglacial) andshort-term (PDO and ENSO) climatic fluctuations are yetto be incorporated in the model. Climate fluctuations invarying timescales, and sometimes superimposed on oneanother, are important aspects of the global climate, whoseimplications on regional geomorphology and sediment fluxrates can be addressed by advancing the simplisticapproaches presented in this paper.

[76] Acknowledgments. This research was supported in part byNASA (agreement NNGO5GA17G), the Consiglio Nazionale delleRicerche, Itlay (Italian National Research Council), and the University ofNebraska Office of Research (WBS26-0514-9002-006). We thank KellyCaylor and Enrique Vivoni for their detailed and constructive reviews that


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improved the original manuscript. This paper is published as Journal Series15063 of the University of Nebraska Agricultural Research Division.

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��R. L. Bras, Department of Civil and Environmental Engineering,

Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

E. Istanbulluoglu, Department of Geosciences, University of Nebraska-Lincoln, Lincoln, 200 Bessey Hall, Lincoln, NE 68588, USA. ([email protected])


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On the dynamics of soil moisture, vegetation, and erosion: …€¦ · Implications of climate variability and change Erkan Istanbulluoglu1 and Rafael L. Bras2 Received 17 March 2005;