On the dynamics of soil moisture, vegetation, and erosion: Implications of climate variability and change



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

1. Introduction

[2] In water limited ecosystems spatial and temporal vegetation dynamics are predominantly controlled by soil water availability, driven by climate and modulated by landscape morphology. Vegetation in turn regulates basin water balance, soil moisture dynamics [Eagleson, 2002; Rodriguez-Iturbe and Porporato, 2004], as well as the form and tempo of erosion and landscape evolution [Collins et al., 2004; Istanbulluoglu and Bras, 2005].

[3] Basin topography and soils are recognized among the most critical controls of the hydrological response and the resulting spatial organization of terrestrial vegetation patterns [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] conducted one of the pioneering process-based field observations relating topography, forest vegetation distribution and geomorphic processes. In their early effort, Langbein and Schumm [1958] examined the relationship between mean annual sediment yields and annual precipitation over decadal timescales by grouping and averaging sediment yield data from U.S. Geological Survey (USGS) gauging stations and reservoirs. In the Langbein and Schumm [1958] curve, sediment yield increases with precipitation in arid and semiarid climates, reaches a maximum where precipitation is approximately 300 mm/year, and trails off as precipitation grows. Interestingly, Langbein and Schumm [1958] also note that the turn over point in this curve corresponds to ecosystems where a transition from shrub to grasslands occurs, effectively protecting soils from runoff and rain splash 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 in the relationship between sediment yield and precipitation. In their relationship the first peak appears to correspond approximately with the location of the Langbein and Schumm's peak, while the other two were attributed to specific climate characteristics in different rainfall regimes, without any detailed explanations for the underlying physical 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 for much longer timescales. Global data show significant increases in erosion rates around the world, with approximately 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 that these periods of increased sediment transport is a consequence of enhanced aridity as a result of global cooling in the late Cenozoic, leading to a pattern of long-term climate variability with high-amplitude fluctuations (e.g., glacial-interglacial). Such fluctuations caused frequent and dramatic changes in regional temperatures and precipitation regimes, with resulting impacts on ecosystem functioning, and fluvial and glacial erosion processes [Zhang et al., 2001]. Growing erosion rates under a fluctuating climate were related to two primary causes: (1) nonlinearities in landscape geomorphic response, and landscape reaction timescales that prevented landscapes from establishing equilibrium states [Zhang et al., 2001]; (2) threshold dependence and inherent nonlinearity in erosion and sediment transport mechanics [Leopold, 1951; Tucker and Bras, 2000; Molnar, 2001; Tucker, 2004]. While the latter works statistically characterized the direct effects of precipitation fluctuations on erosion rates, however, their indirect effects on geomorphic response via altering vegetation cover is not yet addressed.

[6] Another good example for increased erosion rates under a variable climate is arroyo development in the arid and semiarid southwest United States. In a climate regime historically characterized by wet and dry cycles, known as the El Niño–Southern Oscillation (ENSO) pattern, arroyo formation in the southwest was argued to be driven by vegetation-erosion feedbacks under a fluctuating climate regime [e.g., Huntington, 1914; Bryan, 1940; Cooke and Reeves, 1976; Bull, 1997]. In the region, depletion of root zone soil moisture during a dry period often results in a reduction in vegetation cover across the landscape, leaving soil surface susceptible to erosion. Some field observations suggest flooding in wet periods, following extended droughts, as the primary trigger of gully erosion and cut and fill cycles in the southwestern United States [Schumm and Parker, 1973; Waters and Haynes, 2001].

[7] In recent studies, with respect to the current climate, global climate models (GCMs) predict a global temperature increase due to enhanced greenhouse gases in the atmosphere, leading to an increase in climate variability, with reduced rainfall frequencies and increased magnitudes [e.g., Easterling et al., 2000]. Such model predictions are also verified by recent studies of in situ observations of major variables of the hydrological cycle in the United States [Groisman et al., 2004]. Growing insights from field and theoretical work suggest that predicted changes in rainfall regime as a result of global warming may reduce soil moisture, affect surface water balance, and deteriorate ecosystem functioning [Knapp et al., 2002; Porporato et al., 2004]. These predicted trends in the climate call for three key questions for soil mantled and vegetated landscapes: (1) How does sediment transport intensity relate to drought length and severity? (2) How does short- and long-term rainfall variability affect vegetation dynamics and sediment yields? (3) What is the role of vegetation on the relationship between sediment yields and annual precipitation?

[8] In this paper we describe a first attempt in linking runoff erosion with climate-soil-vegetation dynamics. Section 2 describes the simple one-dimensional model used in this study, that combines random forcing of rainfall with a coupled representation of a dynamic soil-vegetation system, and runoff erosion mechanics. In section 3, the model is used in three related modeling experiments to address the research questions posed above. Of these examples, the first one investigates the sensitivity of sediment transport potential to drought length, referred to as the “drought experiment”. The second example discusses the consequences of an increase in rainfall variability, a predicted trend as a result of global warming, on sediment transport potentials. Finally, the last simulation attempts to capture the effects of a range of different precipitation regimes, from arid to humid regions, based on a simple characterization of the general 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 zone is modeled as [Eagleson, 1982; Rodriguez-Iturbe, 2000]:

equation image

where Zr is the effective root depth, n is soil porosity, s is relative soil moisture content, 0 ≤ s(t) ≤ 1, V is vegetation cover fraction, and p is rainfall rate. Infiltration rate Ia represents the rate of water flux into the soil column in excess of interception and surface storage. ET is evapotranspiration rate that includes evaporation from bare soil surface and plant transpiration. D is leakage from the root zone. All flux terms in the water balance equation are strongly dependent upon both soil moisture level and vegetation cover, making the equation difficult to evaluate analytically, 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) the long-term annual averages of equation (1), gives 〈Ia〉 = 〈ET〉 + 〈D〉, and the long-term water balance of the system can be written as

equation image

Over the long term, mean annual precipitation is partitioned into mean annual canopy interception, 〈CI〉, runoff, 〈R〉, evapotranspiration, 〈ET〉, and drainage 〈D〉, with no change in soil moisture storage. Both equations presented above assume a sufficiently deep groundwater table, such that there is no influx from groundwater to the root zone. While this is often true for many arid and semiarid regions with thick vadose zones (deep saturated zones) [e.g., Walvoord and Phillips, 2004], it might be inappropriate for areas with shallow water table.

[11] Eagleson [2002] and Rodriguez-Iturbe and Porporato [2004] give extensive reviews of the recent applications of equations (1) and (2) in ecohydrology. The following sections explain the models used in this study for each component of the water balance equation, starting with the stochastic rainfall forcing.

2.2. Stochastic Rainfall Model

[12] Three essential characteristics of precipitation are storm intensity, p (mm/h), storm duration Tr (h), and time between storms, Tb(h). Storm intensity and duration determine water availability for infiltration and runoff during a single event, while the time between storms defines the duration of deep percolation and evapotranspiration. Storm intensity, duration and time between storms are described by exponential distributions [Rodriguez-Iturbe and Eagleson, 1987], given in generic form below,

equation image

where x is exponentially distributed variable. In our application x represents storm rate p, duration Tr, and time between storms Tb. Storm depth is the product of rainfall intensity and duration, P = pTr. The exponential distribution has shown to represent rainfall statistics well, and the model parameters 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 on vegetation canopy for subsequent evaporation. Interception is related to many vegetative and climate factors, including leaf area index (LAI), storm intensity and duration, as well as the surface tension forces on the canopy resulting from canopy configuration and liquid viscosity [Ramírez and Senarath, 2000]. Among these factors LAI and p have the most pronounced effects. Interception scales positively with LAI and negatively with p as the larger the raindrop size, the higher the amount of water displaced from canopy due to raindrop impact [Wells and Blake, 1972; Ramírez and Senarath, 2000].

[14] In our simplistic model we use a lumped variable CI to represent both canopy interception and surface retention defined as the sum of total water storage capacity of vegetation canopy Sc and evaporation rate Ep during the storm [Bras, 1990]

equation image

Water storage capacity is related to LAI and p in the following way [Ramírez and Senarath, 2000],

equation image

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

equation image

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

equation image

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

2.4. Infiltration and Runoff Generation

[16] Some recent ecohydrology models assume no limitations in infiltration rate and rainfall is stored in the root zone until soil saturation occurs. The rainfall depth in excess of soil storage is then converted to surface runoff [e.g., Laio et al., 2001a]. This assumption has certain limitations especially in arid and semiarid regions where infiltration rates are highly variable due to vegetation patchiness, and runoff is produced via infiltration excess mechanism. In the absence of vegetation, surface sealing by rain splash erosion occurs as detached soil particles by raindrop impact clog pores on the soil surface. Subsequently, upon soil drying, a hard crust forms on the soil surface significantly reducing infiltration rates [Brady and Weil, 1996]. However, on vegetated slopes biological activity and root penetration significantly improve soil aggregation and macroporosity, enhancing infiltration rates and soil hydraulic conductivity. Field observations consistently report higher infiltration rates under vegetation canopy than intercanopy [e.g., Cerdà, 1998; Dunkerley, 2002a, 2002b; Bhark and Small, 2003; Ludwig et al., 2005], leading to runoff generation in bare soils and runon input to vegetated patches.

[17] Storm average infiltration capacity of a soil parcel is approximated as a weighted average of infiltration capacity of bare and vegetated soils

equation image

where Ic is average infiltration capacity, IS and IV are infiltration capacity of bare and vegetated soils respectively, and V is uniformly distributed vegetation cover fraction. This assumption, although simple, is consistent with some field observations [e.g., Cerdà, 1998].

[18] Infiltration is modeled when precipitation depth is larger than potential canopy interception. In the model, the actual infiltration rate depends on the root zone soil moisture. When root zone is unsaturated, infiltration is the smaller of infiltration capacity or precipitation rate. When root zone is saturated, infiltration is assumed to be limited to the rate of water loss to deep drainage from the root zone. This model is expressed by

equation image

where Ia is actual infiltration rate, and D is in-storm water leakage when the root zone is saturated. Leakage during storms for unsaturated soils is neglected in the model. This introduces some limitations for applications especially for humid regions, receiving low-intensity long-duration rainfalls. In such cases, the potential effect of neglecting leakage during storms would be a reduction in the time required for soil saturation during rainfall.

[19] The dependence of actual infiltration on soil moisture state naturally yields two different runoff generation mechanisms: infiltration and saturation excess. In both cases, runoff is generated when rainfall rate (or rain + runon rate if applicable) exceeds the actual infiltration capacity described in equation (9). Runoff rate R is expressed as

equation image

On the basis of the initial soil moisture and actual steady state infiltration rate, the time required for soil saturation under constant rainfall is determined by the ratio of the volume of empty pores that can accommodate water to the actual infiltration rate by

equation image

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

2.5. Leakage Losses

[20] Assuming constant soil texture, porosity and hydraulic conductivity, and ignoring the influence of soil suction forces beneath the root zone, one-dimensional gravity drainage from the root zone is related to unsaturated hydraulic conductivity according to Campbell [1974]:

equation image

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

equation image

where Ψs is soil matric potential, and Π and b are empirical parameters determined from experimental data. Typical values for Π and b are widely published in the literature for different soil texture classes [e.g., Clapp and Hornberger, 1978; Laio et al., 2001a]. Equation (13) can be used to obtain soil moisture values (by solving for s), from the corresponding values of soil matric potential defined for plant activities and soil evaporation.

2.6. Evapotranspiration

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

equation image

where Ep and ETp are potential bare soil evaporation and potential evapotranspiration from vegetation cover; βs and βV are evaporation and evapotranspiration efficiency functions for bare soil and vegetation under limited root zone soil moisture conditions. Following Rodriguez-Iturbe et al. [1999] and Laio et al. [2001a], evaporation efficiency terms used in this paper are

equation image
equation image

where sh is soil hygroscopic capacity, and sw and s* are soil moisture levels corresponding to plant water potentials at wilting point, and incipient stomata closure [Porporato et al., 2001]. In equation (16), evaporation for bare soil begins diminishing when soil moisture is below field capacity and continues to drop until soil moisture reduces to the hygroscopic water content. For grass cover, evapotranspiration continues at potential rate until soil moisture falls below s*. Then for s < s* evapotranspiration decays linearly in response to soil moisture in deficit of s* until the wilting point is reached [Laio et al., 2001a].

2.7. Vegetation Growth

[22] Soil moisture affects the production of organic carbon by photosynthesis, respiration, biomass production as well as mineralization and uptake of nutrients from the soil. Field observations show a direct linkage between soil moisture and vegetation productivity [e.g., Fay et al., 2003; Scanlon et al., 2005]. Following Fernandez-Illescas and Rodriguez-Iturbe [2004], we develop a simplistic approach for grass cover dynamics by linking a traditional population growth model with evapotranspiration efficiency.

[23] In the absence of soil water limitations for plant growth (ss*, i.e., high precipitation in the growing season) and under static resource levels (e.g., nutrients and solar radiation), dynamics of site occupancy for single species vegetation can be related to the difference between the rate of colonization in empty sites and the rate of site vacancy due to plant mortality [Levins, 1969; Tilman, 1994],

equation image

where dV/dt is rate of change in fractional vegetation cover, and kc and km are rates of plant colonization and mortality respectively. In the equation, the rate of site occupancy is obtained by the product of the rate of propagule production by the vegetated sites, kcV, and the unoccupied space fraction (1 − V). The mortality term, kmV, gives the vegetation density-dependent rate at which sites become vacant. In this equation, mortality rate reflects the effects of limitations of resources (except water), diseases and other disturbances on plant death. Vegetation cover attains equilibrium when dV/dt = 0, also known as ecosystem carrying capacity. Maximum vegetation cover at carrying capacity is Vmax = 1 − (km/kC). This function was also modified and used by Tilman [1994] for modeling multiple species competition.

[24] Water stress begins affecting plant physiology with the incipient stomata closure, a plant response to water scarcity to reduce water losses through transpiration. Complete stomata closure occurs with soil moisture at wilting. Porporato et al. [2001] nonlinearly related plant water stress to soil moisture deficit when s < s*. Plant growth (biomass production, reproduction, and fertility) is maintained by photosynthesis, driven by transpiration [Crawley, 1997; Kerkhoff et al., 2004]. Thus it is logical to assume that the higher the evapotranspiration efficiency (equation (16a)), the lower the plant water stress. On the basis of evapotranspiration efficiency the static water stress of Porporato et al. [2001] can be obtained as

equation image

where δ is water stress, and ps is the exponent that describes the nonlinearity in the effects of moisture deficit on plant activities. In the growing season, not only the intensity but also the duration of water stress would influence plant growth. To incorporate a time dimension to static plant water stress (equation (18)), Porporato et al. [2001] developed a mean dynamic water stress for a given growing season as a function of the mean value of static water stress as well as the frequency and duration of times when soil moisture is below s*. Fernandez-Illescas and Rodriguez-Iturbe [2004] incorporated the dynamic water stress concept of Porporato et al. [2001] in the population growth model given in equation (17) to study the effects of interannual precipitation variability on the ecosystem. However, neither of these studies link the changes in vegetation cover to evapotranspiration and water stress calculations.

[25] In water limited ecosystems vegetation cover responds to both dry and wet periods. Vegetation cover also alters soil infiltration and evapotranspiration rates. Therefore, in order to directly link grass dynamics with climate, we accumulate vegetation water stress between storms, instead of using a mean stress for the entire growing season. Cumulative plant water stress is defined by integrating the static water stress equation as a function of time:

equation image

where t is the duration in which plants are under stress. This time is limited to the portion of the interstorm period when soil moisture is below s* defined as, tTbts*, where ts* is time required, within the interstorm period, for soil moisture to drop to s*, if s > s*. Rainfall events that increase soil moisture above s* reset the cumulative water stress (ξ = 0).

[26] During droughts vegetation water stress grows until permanent damages appear on plant tissues, leading to plant death [e.g., Pockman and Sperry, 2000]. Following Porporato et al. [2001] we use a threshold cumulative water stress for plant death. A normalized cumulative water stress is defined by dividing the cumulative stress by the threshold stress, ξT, as

equation image

The threshold term was defined as the proportion of time, k, that plants can experience water stress during the growing season, Tseason, without suffering permanent damages, ξT = kTseason [Porporato et al., 2001].

[27] We can now incorporate the normalized cumulative water stress with the population growth model given in equation (17). To do so, we consider two modifications in the original model. The first assumption is that vegetation colonization rate, kC, decreases linearly with the cumulative stress, kC(1 − Φ(t)). Second, following the same logic, we assume that water stress increases the mortality rate, reaching a maximum value when Φ = 1. The modified version of the Levins [1969] equation becomes:

equation image

where kmS is mortality rate under plant wilting. While models with much greater complexities are available in the literature [Scanlon and Albertson, 2003; Williams and Albertson, 2005], by directly linking vegetation cover to soil moisture, the approach used here provides a simple model with limited number of input requirements. In implementing the model, soil moisture losses are calculated adopting the analytical solutions provided by Laio et al. [2001a] and Rodriguez-Iturbe and Porporato [2004]. Cumulative water stress is calculated in discrete sums of 4 hour time steps. For each time step, the analytical solution of equation (21) is used to update vegetation cover fraction.

2.8. Sediment Transport

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

equation image

where qs is unit sediment transport capacity (L3/T/L), kf is transport efficiency coefficient, τ is flow shear stress and τc is critical shear stress for sediment entrainment, both in Pa, and the parameter η is consistently 1.5 in bed load, and as high 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 shear stress (shear stress acting on soil surface) to flow resistance due to crop biomass, Istanbulluoglu and Bras [2005] proposed the following equation for overland flow effective shear stress:

equation image
equation image
equation image
equation image

where τf is the effective shear stress written as a fraction of total shear stress, τb; Fτ is shear stress partitioning ratio related to Manning's roughness coefficient for bare soil, ns, and vegetation, nV; q is unit water discharge (L2/T); S is slope; ρw, and g are specific weight of water and gravity of acceleration respectively; and kτ, m and n are parameters that may vary with flow geometry. For overland flow and flow 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 vegetation cover, V relative to a mature vegetation cover, VR, that has a known roughness coefficient of nvR. Mature vegetation cover here is defined as grass cover fraction under no water limitation and assumed as 0.95. Relating surface roughness caused by vegetation to the fraction of ground cover itself establishes a dynamic link between sediment transport potential and the climate, soil and vegetation system. This model was calibrated using flow and erosion data from flume experiments of Prosser et al. [1995] leading to ω = 0.5 [Istanbulluoglu and Bras, 2005].

[31] For the purposes of our sensitivity analysis we simplify the sediment transport relationship and write it as proportional to runoff and vegetation related variables. Instead of predicting absolute sediment transport rates, this simplification would predict relative changes in transport rate controlled by runoff and grass cover. In this one dimensional model discharge for unit area is equal to the runoff rate, q = R. A proxy for sediment transport rate as a function of runoff and vegetation cover can be written by substituting equations (23) and (24a), (24b), and (24c) into (22):

equation image

An important limitation of this proportionality is that it ignores an erosional threshold term (i.e., critical shear stress), which often depends on the hillslope sediment size. Including such a threshold would require the definition of a basin area in the model. This would make model results relative to an arbitrarily selected watershed size. As it stands, equation (25) can be viewed as an index for potential sediment transport with no reference to any surface sediment size.

3. Model Analysis

[32] We used three model experiments in order to demonstrate the potential implications of dynamic climate-soil-vegetation coupling on runoff driven sediment transport potentials. Table 1 gives the parameter values used in the experiments, which are mostly taken from other related modeling studies [e.g., Laio et al., 2001a, 2001b; Caylor et al., 2005]. Soil infiltration capacities under bare soil and vegetated conditions are approximate mean values of the ranges reported in, or inferred from various publications in the literature [e.g., Abrahams et al., 1995; Cerdà, 1998; Dunkerley, 2002a, 2002b; Wainwright et al., 2000; Bhark and Small, 2003; Fiedler et al., 2002].

Table 1. Parameters Describing the Soil Characteristics Used in the Model
Soil Texturebnsfcs*swshIS, mm/hIV, mm/h
Loamy sand4.380.420.450.240.10.0830100

3.1. System Response to Storm Timing: A Drought Experiment

[33] Erosion and sediment transport is argued to be more efficient in arid to semiarid climates [Leopold, 1951; Molnar, 2001]. Field observations show correlations between drought severity and erosion activity following droughts [Balling and Wells, 1995]. Therefore it is important to explore the sensitivity of sediment transport potential to drought severity.

[34] One way to address this is to construct a relationship between sediment transport potential, driven by a fixed storm rate and duration, and drought length for a range of initial vegetation cover conditions. In the model experiment reported in this section we use a single high-intensity, and short-duration storm event (70 mm/h for 1 hour duration). The storm rate and duration is selected to represent typical small-scale convective storms in semiarid regions. For initial conditions we used grass covers ranging from 0.05 to 0.95, and saturated root zone soil moisture. With storms arriving at selected days (e.g., 1, 2, 3, 4, …200 days) after initial saturation, this experiment design captures a range of different soil moisture conditions from saturation to hygroscopic water content, shg as soil dries during droughts and vegetation responds dynamically to soil moisture. In the model vegetation cover is updated daily using the accumulated 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 runoff volume (Figure 1c), and normalized sediment transport index (Figure 1d), as a function of days after soil saturation beginning with day one. Note that because the sensitivity of the coupled system to drought length is investigated, each storm is considered to be independent and does not modify soil moisture. Therefore the values plotted in Figure 1b represent antecedent soil moisture conditions prior to each storm arrival. Runoff and sediment transport are normalized with their respective minimum values, both generated under 0.95 grass cover fraction, with the storm pulse arriving when soil moisture is at field capacity. In Figure 1a, in the first 50 days after soil saturation grass responds to the initial abundance of soil moisture in the root zone depending on its initial 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 increasing (for initial V ≅ 0.4 − 0.6) its fraction on the ground. Continuing drought eventually eliminates grass vegetation on the surface.

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 texture is used (Table 1) with vegetation parameters selected for grass in Table 2.

[36] The rate of soil drying is faster under a dense cover because of larger evapotranspiration rates (Figure 1b). If soil infiltration capacity were constant, rapid soil drying would provide larger root zone storage for the simulated fixed depth of rainfall, reducing runoff as drought length increases. In contrast, however, runoff rate amplifies with drought length in the model (Figure 1c). This is solely because of a reduction in infiltration capacity as a result of vegetation loss as drought continues. Because of the nonlinear dependence of sediment transport positively to runoff and negatively to grass cover, sediment transport potential increases several orders of magnitude during drought (Figure 1d).

3.2. Effects of Storm Variability in Different Precipitation Regimes

[37] Climate change predictions suggest variations in the frequency and size of individual rainfall events, but often with no significant changes in seasonal or annual totals [e.g., Easterling et al., 2000]. A recent manipulative field experiment in northeastern Kansas investigated the influence of climate variability on a native grassland ecosystem for four years [Knapp et al., 2002; Fay et al., 2003], by artificially increasing both the time between observed storms and rainfall amounts per each storm while maintaining the total annual precipitation unchanged. A 50% increase in the time between storms led up to a 20% reduction in measured net carbon assimilation resulting from reduced photosynthesis. Porporato et al. [2004] reproduced these field observations using the analytical model of Daly et al. [2004a, 2004b], derived as a function of a probabilistic representation of climate, soil moisture, and fixed vegetation characteristics. Using the model, Porporato et al. [2004] projected persistent reductions in net carbon assimilation rate with increased storm frequency for mean seasonal precipitation between 400 and 600mm.

[38] With this background, the next logical step is to investigate the potential impacts of climate change on runoff sediment and nutrient transport processes in natural and managed ecosystems. Here we address the former, using the outlined model, by fixing the mean seasonal precipitation in the growing season, 〈P〉, and varying the mean time between storms, equation imageb. Since our objective is to focus on the sole control of grassland dynamics on sediment transport, we purposely fixed the mean rainfall rate constant and varied storm duration in order to conserve mass as mean time between storms is varied. Experiments are performed for different climate regimes characterized by a simple humidity index (i.e., inverse of Budyko's dryness index [Budyko, 1974]) that normalizes 〈P〉 with potential growing season evapotranspiration PET (sum of daily ETp):

equation image

This index gives the fraction of potential evapotranspiration satisfied by total precipitation within a growing season, and the higher the index the wetter the seasonal climate. The mean seasonal or annual precipitation is simply the product of the number of storms Ns, mean storm rate equation image and mean time between storms equation imageb:

equation image

where Nh is the number of hours within a specified time (e.g., growing season), and equation imager is mean storm duration. In the experiments with a fixed humidity index 〈P′〉, we set equation image equal to the bare soil infiltration rate for loam, equation image = IS, and adjusted equation imager to maintain a constant 〈P〉. Using a fixed equation image allows the investigation of indirect effects of the dynamic behavior of the ecohydrologic state variables (V, Ic and s) on sediment transport capacity, rather than the rainfall rate. In order to represent a range of precipitation regimes we used humidity indices 〈P′〉 ranging between 0.3 (the driest) and 1 (the wettest). This range seems to be reasonable to represent grasslands as with larger precipitation forests tend to dominate, and with smaller 〈P′〉 grasslands are usually replaced by desert shrubs. With the selected parameters in Table 2 the model does not predict grass cover for humidity indices less than or equal to 0.1. For each selected 〈P′〉, equation imageb is varied between 2 and 40 days. Loam soil texture is used to represent average soil texture conditions (Table 1) with grass vegetation parameters given in Table 2. For each equation imageb, given 〈P′〉, the model is run for 1600 years with no seasonality.

Table 2. Parameters Used for Grass Vegetation Cover
Root depth Zr, m0.35a
Colonization rate kC, 1/yr4
Mortality rate km, 1/yr0.1
Mortality rate with full stomata closure kmS, 1/yr6
Maximum canopy storage per leaf area SLA, mm0.3
Interception decay coefficient, cd0.2
Potential Evapotranspiration ETp, mm/d3.7a
Soil Evaporation after wilting Ew, mm/d0.1a
Exponent of the stress function ps3a
Water stress threshold ξt, days75a
Water erosion exponent η2b
Manning's roughness for soils ns0.025b
Manning's roughness for grass vegetation, nV0.65b

[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 equation imageb for the selected range of humidity indices. Storm depths increase as a function of mean time between storms, for example for 〈P′〉 = 0.3 the mean depth is ∼2.2 mm for equation imageb = 2 days, and approximately 44.5 mm for equation imageb = 40 days. Figure 3 presents water balance components (equation (2)) normalized by the mean seasonal rainfall for 〈P′〉 = 0.4.

Figure 2.

Mean values of the (a) modeled grass cover and (b) normalized sediment transport index (STI) as a function of the mean time between storms. Mean seasonal precipitation is fixed for each curve but varies among curves as related to the humidity index 〈P′〉. Higher values of 〈P′〉 represent larger growing season precipitation.

Figure 3.

Components of water balance for 〈P′〉 = 0.4, where 〈CI〉, 〈R〉, 〈D〉 and 〈ET〉 are mean annual depths of canopy interception, runoff, drainage and evapotranspiration, divided by mean seasonal precipitation 〈P〉. The difference between any two curves from top to bottom gives the fraction of water loss to a particular process indicated between lines. The global maximum point observed in evapotranspiration minimizes water loss to rain interception, drainage, and runoff and corresponds to the location of maximum grass cover for 〈P′〉 = 0.4 plotted in Figure 2.

[40] First of all, the overall response of the system to growing 〈P′〉 is an increase in grass cover for all values of equation imageb. The system response to changes in equation imageb is, however, more complex and closely related to the humidity index. When the climate is humid, 〈P′〉 = 1, the grass cover reduces with rainfall variability. As climate becomes more arid vegetation cover first increases, reaches a maximum, then decreases as a function of increased mean time between storms (or reduced storm frequency). As was addressed by Laio et al. [2001a] and Porporato et al. [2001] for fixed vegetation conditions, here the optimal partitioning between the timing and amount of rainfall provides the most favorable soil moisture conditions such that, evapotranspiration is maximized, while losses due to runoff and leakage are minimized. This can be seen in the components of water balance for 〈P′〉 = 0.4 in Figure 3. Since the limiting resource is soil moisture in this model, vegetation cover evolves to a state at which benefits of plant transpiration (i.e., increase in grass cover) 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 variable rainfall regime, relative amounts of both runoff and drainage in the water budget grow.

[41] One interesting outcome of the model is that the interplay between climate, soil and vegetation results in differences in the location of maximum vegetation cover under different humidity indices in Figure 2a As climate becomes more arid, the maximization of vegetation cover is attained with a more variable rainfall regime. Because the mean seasonal precipitation depth is kept constant, as climate becomes drier, only less frequent storms with larger relative magnitudes can satisfy soil moisture to a level that efficient plant transpiration begins (i.e., ss*), leading to vegetation colonization.

[42] From the geomorphic point of view, reduction in both runoff generation and shear stress efficiency with the optimum combinations of rainfall characteristics (equation image, equation imager, equation imageb) that maximize vegetation cover, results in the minimization of sediment transport capacity in Figure 2b. In Figure 2b each curve is normalized by its mean value. Thus the plotting does not allow comparison of absolute sediment transport 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 from reduced number of storms arriving with larger magnitudes. For example for 〈P′〉 = 0.3, the maximum sediment transport is about 3.5 times larger than the minimum, while in the case of 〈P′〉 = 1, the maximum sediment transport is up to 1000 times larger than the minimum. Unless dynamic vegetation is modeled, no significant difference would occur in sediment transport rates as the rate of rainfall is fixed in this example.

[44] Figure 4 plots the effects of soil texture in mediating the dynamic response of vegetation cover and sediment yields to changes in equation imageb for 〈P′〉 = 0.5. As a result of its low hydraulic conductivity clay soils produce larger runoff. Thus reduced total amounts of infiltration, and higher water potentials for plants to overcome for unstressed evapotranspiration (i.e., higher s*), cause a significant reduction in grass cover, and a shift in the maximum point for plant cover to a higher equation imageb compared to other soil types (Figure 4a). As a result of limited vegetation cover, variation in the erosion potential with rainfall variability is also limited in clay. This response is similar to what is observed in Figure 2, for loam, with 〈P′〉 = 0.3 (i.e., smaller precipitation). While absolute magnitudes of the water balance components may vary, similarity in the response suggests that changes in soil texture from fine to coarse would have a response similar to an increase in humidity under fixed soil texture. This is also evident in the case of loamy sand in Figure 4a, which, under a drier rainfall regime, 〈P′〉 = 0.5, produces a response to changing equation imageb similar to loam in a wetter climate (〈P′〉 = 1, Figure 2). Steady state vegetation cover show remarkable differences from clay to sandy soil textures, resulting in a complex response in sediment transport.

Figure 4.

Effects of soil texture on (a) mean vegetation cover and (b) normalized mean sediment transport index (STI), modeled for clay, loam, and loamy sand soil textures for 〈P′〉 = 0.5.

[45] The results presented here can be elaborated under the context of the inverse soil texture effect hypothesis, first proposed by Noy-Meir [1973]. This hypothesis suggests that the same plant that is found on coarse soils in a dryer climate, can be found on fine soils in a wetter climate. Using their probabilistic water balance model, Laio et al. [2001b] proposed the inverse soil texture effect as a potential explanation for the existence of the dominant plant species in north central Colorado, where spatial variability in soil texture is high. Fernandez-Illescas et al. [2001] also investigated the role of inverse soil texture effect with interannual rainfall variability on plant species in a southern Texas savanna. In both studies, water stress was used as a surrogate for species suitability to the environment, with no dynamic 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, under essentially 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 current climate determine biomass production and erosion response as the time between storms grows (i.e., higher rainfall variability) with climate change (Figures 2 and 4). For example in both loamy soil for 〈P′〉 = 0.3 (Figure 2b), and clay soil for 〈P′〉 = 0.5 (Figure 4b), vegetation cover grows with equation image < 10 days, and decreases with larger values of equation image, while sediment transport capacity follows an inverse trend with vegetation cover. A similar behavior is also observed for other humidity indices and soil types with variations in the critical storm frequency that controls the phase change in the relationships between mean time between storms and both vegetation cover and the index for sediment transport potential.

3.3. Erosion Potential Across Precipitation Regimes

[47] In this section we investigate the relationship between sediment transport potential and mean annual precipitation in a range of precipitation regimes. A simplistic approach for capturing the essential changes in rainfall forcing parameters (equation image, equation image, equation image) as a function of mean annual precipitation 〈P〉 is developed based on the reported parameters of the Poisson rainfall model for United States [Hawk, 1992]. Seasonality in both precipitation and evapotranspiration are represented by parsimonious models. With the forcing parameters (equation image, equation image, equation image, and ETp) estimated from 〈P〉, we used the climate-soil-vegetation and erosion scheme to obtain a relationship between sediment transport potential and mean annual precipitation.

3.3.1. Rainfall Characteristics as Related to Mean Annual Precipitation

[48] In an attempt to characterize the general climatology of the rainfall with mean annual precipitation we begin with utilizing a simple rainfall variability factor, derived from equation (27) [Tucker and Bras, 2000]:

equation image

where Nh is the length of the rainy season (the whole year for annual analysis), during which the mean total rainfall 〈P〉 is recorded. In the two alternative definitions given above, annual rainfall variability is typically high in regions with sporadic, high-intensity and short-duration storms (e.g., semiarid southwest United States); and low, in places receiving 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:

equation image
equation image

These simple functional forms suggest that once RVar, and either equation imageb or equation imager are known for a given Nh, all three parameters of the rainfall model can be calculated.

[50] Hawk [1992] reports the monthly parameters of the Poisson pulse rainfall model for more than 60 rainfall stations across the United States. In Figure 5, we plot both annual and seasonal data for RVar (calculated with (28) using data from Hawk [1992]) and equation imageb as a function of precipitation. In the case of the seasonal data, we used only the stations showing distinct seasonal patterns in rainfall, mostly located in the western United States. Because season length varies, seasonal precipitation is scaled up to annual timescale for plotting in Figure 5 by

equation image

where 〈Ps〉 is scaled seasonal precipitation, 〈PRs〉 is the depth of mean seasonal precipitation, and fs is length of season represented as a fraction of the year.

Figure 5.

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

[51] In Figure 5 both RVar and equation imageb are inversely proportional to mean annual precipitation, with some significant scatter. Not surprisingly, the plotted trends are intuitive, as one could expect, humid regions would have more frequent storms, resulting in smaller rainfall variability than arid climates. In Figure 5a both Chicago, Illinois, and Atlanta, Georgia, have much smaller storm variability than Tucson, Arizona, for which two end-member seasons with maximum and minimum variability is plotted. The maximum variability 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 storm variability. Fitted curves in Figure 5 relate mean annual precipitation to rainfall variability and mean time between storms according to power functions:

equation image
equation image

where 〈P〉 is in millimeters and equation image in hours. In a recent study, Small [2005] used a total of 536 station records, each with at least 35 years of data, and found the following relationship between the mean time between storms and annual precipitation,

equation image

Note that this equation is modified from equation (9) of Small [2005], which originally used units in days for equation imageb and centimeters for 〈P〉. The Small [2005] equation plots slightly above the relationship developed in this study. One potential reason for this is that, Small [2005] used stations throughout the western United States where rainfall variability is significant. Whereas Hawk [1992] data used in Figure 5a includes 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 annual precipitation, fP, 0 < fP ≤ 1. For the purpose of estimating the seasonal parameter values of the Poisson rainfall model using the power law functions above, mean seasonal precipitation is related to mean annual precipitation according to

equation image

[53] In the model experiments, the power functions presented above are used to estimate typical mean tendency values for RVar and equation image, for a given mean seasonal 〈Ps〉, or mean annual precipitation 〈P〉. Then, with RVar and equation image known, equations (29a) and (29b) are used to calculate equation image and equation image.

[54] Small [2005] found increased storm frequency in wet seasons, resulting in a reduction in the mean time between storms. In this study the mean time between seasonal storms is approximated by [Small, 2005]

equation image

where both 〈Ps〉 and 〈P〉 are in mm/year. In a wet season, 〈Ps〉/〈P〉 > 1, equation (35) predicts a shorter mean time between storms (equation image < equation image), and in a dry season 〈Ps〉/〈P〉 < 1, a longer mean time between storms (equation image > equation image) 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. we applied a constant rate for daily potential evapotranspiration, ETp, for fixed mean seasonal precipitation (or humidity). While this assumption does not allow for fluctuations in potential evapotranspiration, it provides a reasonable estimate for a mean behavior of the atmosphere within a given season. However, with increasing regional precipitation temperature and humidity gradient of the land surface often decreases resulting in a reduction in potential evapotranspiration rates [Hobbins et al., 2004]. Figure 6 plots mean daily ETp averaged over rainy seasons, as a function of mean annual precipitation compiled from different sources. The best fit linear relationship shows a reduction in ETp with precipitation. This relationship is employed to capture the central tendency in ETp in response to a precipitation increase.

Figure 6.

Potential evapotranspiration as a function of mean annual precipitation. Data are compiled from Eagleson and Tellers [1982], Eagleson [2002], and Eagleson and Segarra [1985].

[56] Seasonal fluctuations in daily ETp is represented by a sinusoidal function [Small, 2005]:

equation image

where image is the difference between the maximum and minimum values of daily ETp throughout the year; LET is the lag between the peak ETp, and solar forcing; and equation image is the mean annual rate of daily potential evapotranspiration; and Nd is the number of days in the year. In this model, for LET=0, peak ETp occurs with T = Nd/2. Equation (36) was reported to show good agreement with seasonal variations in ETp calculated using the Hargreave's equation from daily data [Small, 2005].

3.3.3. Model Experiments: Sediment Transport as Related to Mean Annual Precipitation

[57] We investigate the relationship between mean annual precipitation 〈P〉 and sediment transport index using the coupled climate-soil-vegetation and erosion model. Each year is divided into a wet and a dry season, each receiving half of the mean annual precipitation, fP = 0.5. The length of the rainy season is fixed to four months (fs ≅ 0.34), approximately the mean of the wet season length for the western United States [Small, 2005]. The wet season is centered in the middle of the year, starting from June and ending in the end of September. In this setup, the peak value for daily potential evapotranspiration corresponds to the beginning of wet season.

[58] In the model experiments, mean annual precipitation 〈P〉 is systematically increased from 100 mm/year up to 1500 mm/year. Much larger values of precipitation are not considered as most of the parameters of the climate generator are selected for the western United States. The steps followed in obtaining the mean seasonal storm characteristics are as follows: (1) select mean annual precipitation 〈P〉; (2) calculate wet and dry season precipitation rate, 〈Ps〉 (in mm/year) from equation (34); (3) using 〈Ps〉, calculate rainfall variability, RVar (equation (31)), and the mean time between storms, equation image using first equation 33 then 35, for each season; (4) use RVar and 〈Ps〉 in equation (29a) to obtain the mean storm rate, equation image, for each season. Similarly, in assigning daily values for potential evapotranspiration, the steps used are (1) calculate the mean annual value of daily ETp using the relationship in (Figure 6); (2) use equation (36) to calculate the mean trend in ETp as a function of day of the 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 dynamic vegetation cover, we also run the model with both no vegetation cover and full vegetation cover for loamy soil texture.

[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, when used with measured infiltration capacities, would favor more infiltration resulting in reduced runoff generation. For typical ranges of infiltration, approximately 30–70 mm/h depending on soil texture and vegetation cover, and rainfall rates (20 and 40 mm/h) in the western United States [Abrahams et al., 1995; Wainwright et al., 2000; Fiedler et al., 2002; Etheredge et al., 2004], the rainfall to infiltration rate ratio, equation image/Ic, is likely to vary between 0.2 and 1. Therefore, to keep the equation image/Ic ratio at some realistic values representative of the hydroclimatology of the western United States, the infiltration capacities reported in Table 1 are reduced 10 times for loamy sand and loam, and five times for clay.

[61] Figure 7 plots the mean annual sediment transport potential index (equation (25)) as a function of mean annual precipitation for loamy sand, loam and clay soil types along with the original Langbein and Schumm [1958] curve. To facilitate comparison between curves, the Langbein and Schumm curve is normalized by its mean, and the other curves for individual soil types are normalized by the mean sediment transport potential index for loam. The model predictions for different soil types can be compared with each other since they are all normalized by the same number. However, only the shape and the range of variation between the model results and the Langbein and Schumm curve can be compared. The Langbein and Schumm equation, plotted in Figure 7, is

equation image

where Qs is sediment yield in (cm/yr), P is effective annual precipitation, a, α, b, and β are empirical model parameters whose values are given in Figure 7. In this equation, the first term represents the erosivity of climate, and increases nonlinearly with precipitation. The second term represent the erodibility of the land surface, and is a decreasing function of precipitation.

Figure 7.

Modeled sediment transport potential index (STI) as a function of mean annual precipitation for 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, α = 2.3, and β = 3.33.

[62] Overall, although no calibration is performed in the model except setting k = 0.25, that gives ξt = 30 days in equation (20), the predicted shape and the relative magnitude of change in sediment yields are consistent with the Langbein and Schumm curve which was derived from observations. Both the model results and the data show a phase-switching in sediment flux, resulting in a peak sediment transport rate in semiarid to subhumid conditions. In the model the turn over point in sediment flux coincides to critical precipitation depths that favor resistant grass growth. Because of the differences in the physical soil properties (Table 1), precipitation required for the establishment of grass varies. Coarser soils are more favorable for vegetation growth in water-limited ecosystems [Rodriguez-Iturbe and Porporato, 2004], therefore sediment flux peaks in a drier climate for loamy sand, followed by loam and clay as climate grows wetter. Similar to the rainfall variability example discussed in the previous section, we attribute these different locations in the peak sediment transport rates to the inverse soil texture effect [Noy-Meir, 1973].

[63] In order to examine the hydrologic drivers of sediment transport potential across a range of climates, and the effects of dynamic vegetation in modulating them, we plot the normalized sediment transport, mean annual runoff, and mean annual evapotranspiration for loam for three cases: no vegetation, dynamic vegetation, and static full vegetation cover in Figure 8. In Figure 8 the sediment transport index increases for both the bare and the fully vegetated model experiments as humidity grows. Sediment transport for bare soil is larger as there is no shear stress loss to vegetation roughness. In the absence of enough precipitation to favor grass growth evapotranspiration, runoff, and sediment transport of dynamic vegetation simulation follows the bare case (Figure 8). With precipitation sufficient to support grass establishment, evapotranspiration increases rapidly (Figure 8c), resulting in slight reductions in runoff (Figure 8b). Therefore, in this example, the reduction in sediment transport after reaching a peak is not only because of a decrease in erodibility but also some slight reductions in runoff totals.

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 cover conditions: no vegetation, dynamic vegetation, and static full vegetation.

[64] We propose to divide the precipitation–sediment transport capacity domain into three regions, based on the dominant control of climate and vegetation on sediment transport (Figure 8). In arid and semiarid climates with sparse or no vegetation, sediment transport is directly controlled by climate, generating erosive runoff (first region in Figure 8a). As vegetation is favored by growing precipitation, sediment transport diminishes abruptly because of a reduction in both runoff and sediment transport efficiency (equation 24a). Therefore the trend in the second region in Figure 8a is controlled by the counteracting influence of climate forcing and vegetation growth on sediment transport. As precipitation becomes abundant for vegetation growth (i.e., precipitation larger than 1000 mm/yr in the example in Figure 8), vegetation growth is no more limited by water, and therefore sediment transport potential once again is primarily controlled by climatic forcing which may result in an increasing trend in sediment yields. We hypothesize that the boundaries between these three regions would change with soil texture. For example, in Figure 7, for loamy sand, vegetation establishes with a smaller mean annual precipitation and begins restraining sediment transport earlier than the other two soil types. The downtrend continues around mean annual precipitation of 600 mm which supports full grass cover (not plotted). As precipitation grows larger than 600 mm, the model predicts a second rise in sediment transport as a result of increasing storm erosivity acting on fixed vegetation cover.

[65] These model results lead to our working hypothesis that the second rise in sediment yields with increasing humidity observed in some data sets [e.g., Walling and Kleo, 1979] may correspond to ecosystems where vegetation growth is not (or less) limited by water availability. Thus both runoff and runoff-driven sediment transport index approach to fully vegetated conditions with increasing precipitation.

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's climate has changed from a relatively stable regime to an oscillating one with 20–400 kyr periods of glacial interglacial cycles, resulting in enhanced sedimentation rates worldwide [Zhang et al., 2001]. Short-term (decadal scale) climate variability in the form of dry-wet cycles driven by ENSO patterns and Pacific Decadal Oscillation (PDO), a long-lived El Niño-like pattern of Pacific climate variability, also have a direct influence on soil moisture, vegetation composition, and erosion rates [e.g., Scanlon et al., 2005; Waters and Haynes, 2001]. Superimposed on the existing short-term fluctuations, GCM simulations further predict increased in-season rainfall variability, as a result of global warming, leading to less frequent storm events with larger magnitudes for many regions in the United States [Easterling et al., 2000]. With these reported dynamics of global climate, understanding the linkages between ecohydrological and erosional land surface processes, and their collective response to climate fluctuations becomes crucial in hydrological sciences. This paper presents a parsimonious framework for addressing the coupled vegetation-erosion dynamics and underscores the importance of representing such linkages in assessing climate change impacts in three examples.

[67] The first example explored the influence of drought length on sediment transport capacity of a single storm following a drought. This example can be interpreted as the onset of a wet-cycle following a prolonged drought (i.e., ENSO patterns). The model predicts vegetation loss with increasing drought length as a result of soil drying. Vegetation loss reduces soil infiltration capacity and amplifies overland flow erosion efficiency. These factors result in larger, and more efficient floods in carrying sediment after vegetation-weakening droughts.

[68] These model-based findings are corroborated with observational results. As discussed by Waters and Haynes [2001], the American southwest experienced increased fluvial activity resulting in widespread synchronous incision of large arroyo systems approximately after 4000 14C BP. This period coincides with the development of modern climate regime, with relatively lower temperatures, and dry-wet cycles with more frequent and strong El Nino patterns. The establishment of modern desert shrub communities in dry valley floors of the southwest also coincides to this period [Van Devender, 1990]. On the basis of this climatic evidence, arroyo cutting and filling cycles in the last few thousand years in the southwest United States were related to a combination of several years of increased El Nino activity, generating large floods, following extended droughts [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 on sediment transport, the predicted increase in both runoff and erosion rates with drought length is in agreement with field observations reported above.

[69] The second example investigated the implications of rainfall variability in the growing season (i.e., longer dry intervals between storms) on sediment flux rates. Our model results suggest a higher sensitivity of sediment transport rates to rainfall variability in humid regions than in arid and semiarid ones. The simple argument here is that reduction in soil moisture with growing rainfall variability would result in more vegetation loss in a humid climate, where vegetation 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 sensitivity of runoff erosion to rainfall variability when an erosion threshold is used. Their argument was that in humid regions, with high erosion thresholds imposed by vegetation, the number of times a certain threshold is exceeded would increase as rainfall becomes more variable. In this paper we did not include any erosion thresholds, because doing 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 efficiency factor, both linked to dynamic vegetation cover. Including erosion thresholds in our analysis would further increase the predicted 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 rate occurring in semiarid conditions, was attributed to the relative dominance of erosivity and soil erodibility both modulated by climate (equation (37) and Figure 7) [Langbein and Schumm, 1958; Moglen et al., 1998]. The modeling experiments with increasing mean annual precipitation reproduce the general shape of this relationship (Figure 7). In addition, the model underscores the importance of soil texture influencing the location of the switch in the relative dominance between erosivity and erodibility, as well as the overall shape of the rising and falling limbs of the sediment yield curves. An interesting outcome of the model was the second rise in sediment transport capacity with precipitation in subhumid and humid climates. This model prediction is consistent with some observational studies [Wilson, 1973; Walling and Kleo, 1979] that presented multiple peaks in sediment yield versus precipitation curves, and attributed these arbitrarily to differences in climate characteristics and seasonality. We suggest that the second rise in sediment yields could correspond to climatic conditions that support lush vegetation cover, leading to a system response only controlled by increasing climate erosivity on vegetated landscapes as climate becomes wetter.

[72] The importance of soil texture in geomorphology has long being recognized, perhaps with the first quantitative data of Shields [1936], documenting the differences in fluid shear stress required to mobilize sediments in different size classes. In addition to this known influences of soil texture on erosion thresholds (i.e., critical shear stress, discharge, rainfall) and soil erodibility, this paper underscores the importance of soil texture in water erosion via affecting ecohydrological processes and vegetation dynamics.

[73] The influence of vegetation changes on erosion rates was largely studied in the context of arroyo development in the southwestern United States. Conceptual process-response models directly related the enhanced periods of arroyo development to vegetation-weakening droughts [Cooke and Reeves, 1976; Bull, 1997]. As the next logical step, by quantifying the linkages between climate forcing, vegetation dynamics and erosion rates, the simple model presented here opens avenues for process-based research in investigating the impacts of climate variability and change on erosion rates and resulting landscape development.

[74] Because our objective here was to introduce a new “dynamic” perspective in modeling earth surface processes using simple conceptualizations, limitations of our findings here are a handful. First of all the one-dimensional model used here does not capture landscape scale processes. Basin geomorphic characteristics (i.e., local slope, slope-area scaling, curvature), soil availability on hillslopes, soil production rates, tectonic processes, and many other external and internal landscape complexities that are not included in this paper, would greatly influence basin sediment fluxes and the tempo of landscape evolution under varying climate.

[75] Vegetation processes we employed in our model are extremely simplistic. Other critical factors, such as the effects of temperature and seasonality on plant growth, are components that should be represented in the framework. In terms of climate forcing parameterization, it is important to realize that both the long-term (glacial-interglacial) and short-term (PDO and ENSO) climatic fluctuations are yet to be incorporated in the model. Climate fluctuations in varying timescales, and sometimes superimposed on one another, are important aspects of the global climate, whose implications on regional geomorphology and sediment flux rates can be addressed by advancing the simplistic approaches presented in this paper.


[76] This research was supported in part by NASA (agreement NNGO5GA17G), the Consiglio Nazionale delle Ricerche, Itlay (Italian National Research Council), and the University of Nebraska Office of Research (WBS26-0514-9002-006). We thank Kelly Caylor and Enrique Vivoni for their detailed and constructive reviews that improved the original manuscript. This paper is published as Journal Series 15063 of the University of Nebraska Agricultural Research Division.