Volume 46, Issue 15 p. 8852-8861
Research Letter
Free Access

Ecohydrology Controls the Geomorphic Response to Climate Change

Omer Yetemen

Corresponding Author

Omer Yetemen

Discipline of Civil, Surveying and Environmental Engineering, The University of Newcastle, Callaghan, New South Wales, Australia

Correspondence to: O. Yetemen,

[email protected]

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Patricia M. Saco

Patricia M. Saco

Discipline of Civil, Surveying and Environmental Engineering, The University of Newcastle, Callaghan, New South Wales, Australia

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Erkan Istanbulluoglu

Erkan Istanbulluoglu

Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USA

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First published: 30 July 2019
Citations: 15

Abstract

Erosion rate data worldwide show complex and contrasting dependencies to climate. Laboratory and numerical model experiments on abiotic landscapes suggest a positive response: Wetter (drier) shift in climate leads to an increase (decrease) in erosion rates with longer relaxation times under a drier climate. We performed eco-geomorphic landscape evolution model simulations driven by abrupt climate shift in a semiarid climate. With dynamic vegetation, the erosional response to climate shift was opposite to bare soil, variability of erosion rate lessened, and landscape relaxation time scales became insensitive to climate change direction. The spatial geomorphic response to a wetter climate was depositional in vegetated, incisional in barren landscapes, and got reversed with drier climate. A relationship between net erosion rate and mean landscape slope emerged, exhibiting a hysteresis loop. Our study offers insights to the interpretation of observed acceleration of erosion rates and increase mountain relief during Quaternary climate change.

Key Points

  • Vegetation exerts a major control on equilibrium slopes, erosion rates, and response times to climate shifts
  • Vegetated and unvegetated landscapes could show contrasting response patterns to climate change
  • The interpretations of erosional records of past climates need to account for the effect of coevolving vegetation

Plain Language Summary

In semiarid ecosystems, the plant growth is limited by available soil moisture. Therefore, wet years cause denser vegetation than dry years. When there is no vegetation on the ground, soil is prone to erosion; therefore, wet climate causes more erosion than dry climate. However, when the surface is protected by vegetation against erosion, two counteracting factors compete for erosion: more erosive power due to enhanced precipitation and more erosion protection by vegetation due to more vegetation. These counteracting forces shape the landscape in real world. Here we show with a numerical model how a climate shift from dry-to-wet may result in less erosion in vegetated landscapes. The reverse case may happen in wet-to-dry climate shift. However, over the long-time frame of landscape response, uplift-erosion equilibrium is attained in both cases.

1 Introduction

Erosion rates and geomorphic response of landscapes have been related to climate and its variability in observations (Daniels & Knox, 2005; Knox, 1972; Molnar, 2004; Zhang et al., 2001), laboratory experiments (Bonnet & Crave, 2003; Rohais et al., 2012; Singh et al., 2015; Tejedor et al., 2017), and landscape evolution models (LEMs; e.g., Rinaldo et al., 1995; Tucker & Slingerland, 1997; Godard et al., 2013; Braun et al., 2015). The significance of climate control on landscape geomorphic response varies over different space and time scales, depending on other confounding factors (topography, lithology, tectonic, and biotic) as well as the properties of climate oscillations (Molnar, 2004; Perron, 2017).

Generally, three types of erosional response to climate have been reported from observations. (1) Weak response to climate change: Global-scale observational studies have shown that precipitation and temperature appeared to explain a small proportion (10–20%) of the variance of both contemporary suspended sediment yields in rivers (Milliman & Syvitski, 1992; Syvitski & Milliman, 2007) and long-term (103 to 106 years) erosion rates (Portenga & Bierman, 2011; Riebe et al., 2001). At these large scales (space or time or both), landscape relief, basin slope, and elevation became critical predictors of erosion. (2) Strong positive response: observed in regional studies that have shown an increase in long-term erosion rates with precipitation and runoff, sometimes mediated by relief under high uplift rates (e.g., Bookhagen & Strecker, 2012; Garcin et al., 2017; Henck et al., 2011). (3) Strong but complex response: Watershed studies of sediment yield over decadal time scales (Jeffery et al., 2014; Langbein & Schumm, 1958; Wilson, 1973) and evidence from recent millennial-scale hillslope erosion rate estimates (Schaller et al., 2018; Torres Acosta et al., 2015) have shown a hump-shaped response of erosion to an increase in precipitation, sometimes with multiple peaks (Walling & Webb, 1983). In this humped response, a positive dependence was largely limited to arid and semiarid climates; but a further increase in precipitation led to a downturn in sediment yield and to lower erosion rates. The interplay between increasing runoff erosivity and declining efficiency of runoff on erosion under denser vegetation cover has been offered as a mechanism to explain this complex behavior (e.g., Collins & Bras, 2008; Istanbulluoglu & Bras, 2006; Wilson, 1973).

In the simplest case of an abiotic landscape and over geomorphically significant time scales, common findings of both laboratory table-top (e.g., Bonnet & Crave, 2003; Singh et al., 2015) and LEM experiments (e.g., Armitage et al., 2013; Godard et al., 2013; Rinaldo et al., 1995; Tucker & Slingerland, 1997) have shown that landforms adjust toward a dynamic equilibrium following changes in climate conditions (i.e., precipitation). A dry-to-wet climate transition first boosts runoff erosivity and sediment export (positive response) and is followed by a period of relaxation as landscape morphology declines, and erosion rates return to uplift-erosion equilibrium. The opposite behavior occurs during a wet-to-dry transition but with a much more gradual response. Whereas these numerical and laboratory studies support the observation-based positive response behavior in absence of vegetation change, more importantly, they stress the importance of topographic legacy of past climates, the direction of climate change, the landscape transient response, and its relaxation time on erosion rates (e.g., Armitage et al., 2013).

Observational studies often relate erosion rates to contemporary climate and vegetation data across sites. This may lead to misinterpretations when space for time substitution is applied to infer climate change impacts (Perron, 2017; Portenga & Bierman, 2011). Most LEM studies examining climate variability have often disregarded changes in land surface properties (e.g., soil, vegetation) that also coevolve with climate. By including the potentially counteracting effects of climate-driven changes in vegetation cover and runoff in a LEM, Collins and Bras (2010) found that equilibrium landscape elevations, rather than sediment yields, result in a humped response to precipitation.

A conceptual framework that integrates space and time scales to guide interpretation of field observations and numerical model experiment design for studying climate change in geomorphology is clearly needed. In order to generate this framework, we address the following questions: (1) Do landscapes evolve to a climatic steady state with distinct characteristics of landform and erosion rates? (2) How do landscapes respond to the direction of climate change? (3) When does climate dominantly control erosion rates over other compounding factors? We use an ecohydrologic LEM in a semiarid climate range, where complex response of erosion in relation to climate change is expected (e.g., Baartman et al., 2018; Collins & Bras, 2010; Pelletier et al., 2016; Saco & Moreno-De Las Heras, 2013). We investigate the sensitivity of coupled eco-geomorphic landscape evolution to abrupt climate change to lay the basis to later study the more realistic (but complex) case of cyclic climate variability.

2 Approach and Methods

We used the CHILD LEM (Tucker et al., 2001) in two scenarios: (a) barren surface, for comparison to earlier laboratory and computer model studies, and (b) dynamic vegetation, in which rainfall and solar radiation drives vegetation growth and senescence (Yetemen, Istanbulluoglu, & Duvall, 2015; Yetemen, Istanbulluoglu, Flores-Cervantes, et al., 2015). Our model has been previously parameterized and tested using soil moisture, runoff, and satellite-derived leaf area index data in central New Mexico and Arizona (Yetemen, Istanbulluoglu, Flores-Cervantes, et al., 2015); thus, in this study we used a precipitation range broadly consistent with paleoclimatological evidence from the Southwestern United States (e.g., Hall & Penner, 2013). Below, a brief overview of the model is presented; a full description can be found in Yetemen, Istanbulluoglu, Flores-Cervantes, et al. (2015).

2.1 The Landform Evolution Model

The continuity of sediment gives the rate of change in elevation, Z, as a function of uplift, U (LT−1), and the divergence of volumetric sediment flux per unit width by hillslope diffusion, ∇·qsd (LT−1), and by fluvial transport, ∇·qsf (LT−1):
(1)
Fluvial transport in equation 1 is based on excess effective shear stress, τf (Pa), τf = (τeff − τc), which is the difference between effective shear stress, τeff, and critical shear stress for incipient motion, τc. In this study, τeff is calculated based on the concept of shear stress partitioning between soil and vegetation cover for a parabolic flow cross section derived from the Manning's formula for flow velocity (Yetemen, Istanbulluoglu, Flores-Cervantes, et al., 2015):
(2)
where C is a shape constant; Q is runoff discharge; S is local slope; ns and nv are Manning's roughness coefficients for bare soil and surface vegetation cover, respectively (Istanbulluoglu & Bras, 2005). In bare soil, (nv = 0), and the shear stress acts directly on soil grains. In each iteration of the model, nv is calculated from total vegetation cover fraction, Vt, composed of live and dead proportions:
(3)
where VR is reference vegetation cover fraction, VR = 0.95, representing full grass cover conditions, and nVR is the Manning's roughness coefficient for reference vegetation cover, nVR = 0.5 (Istanbulluoglu & Bras, 2005). In this study, coarse sand properties are used for surface soil with ns = 0.05 and τc = 5 Pa.

2.2 The Ecohydrology Model

Ecohydrologic soil moisture and vegetation dynamics for grass vegetation is modeled using a single-layer bucket model that represents uniform soil moisture within the root zone and distributed spatially using laterally connected elements in the direction of flow (Supporting Information S1 for more detail). Each model cell is covered by grass (live and dead) and bare soil fractions, updated following every storm event. Storm frequency and magnitude are simulated following a rectangular Poisson pulse rainfall model, parameterized from seasonal storm statistics. Each bucket receives local rainfall as well as run-on and lateral soil moisture contribution (if there is any) from upslope cells and loses water through surface runoff, lateral leakage, and evapotranspiration (ET). ET is driven by slope and aspect-dependent potential ET (PET) but is limited to root-zone soil moisture storage and scales with live leaf area index calculated by the vegetation dynamics routine. Net Primary Productivity of grass biomass (g/m2) is calculated as a function of interstorm ET and Water Use Efficiency and allocated to aboveground and belowground biomass compartments. Biomass decays following a first-order reaction kinetics, regulated by water stress (Yetemen, Istanbulluoglu, Flores-Cervantes, et al., 2015), and gets disrupted during erosive fluvial events at a rate proportional to excess shear stress (e.g., Tucker et al., 2006; Yetemen, Istanbulluoglu, Flores-Cervantes, et al., 2015). Biomass is converted to cover fraction used by the erosion model.

2.3 Simulations

Landscape response to climate change is investigated by abruptly varying mean annual precipitation (MAP) between 200 and 600 mm, consistent with MAP ranges reported in paleoclimate studies for the Southwestern United States (e.g., Hall & Penner, 2013; Menking et al., 2004). The model operates on a daily storm (rainfall) time scale, characterized stochastically by seasonally varying rainfall depth, duration, and interstorm period statistics (Tucker & Bras, 2000) estimated from MAP (Istanbulluoglu & Bras, 2006). Seasonality in PET is captured by a sinusoidal function of day of year around the mean daily PET value (e.g., Small, 2005). Mean daily PET was inversely related to MAP based on regression analysis constructed using data from grassland sites (Istanbulluoglu et al., 2012). Model parameters used are those reported in Yetemen, Istanbulluoglu, Flores-Cervantes, et al. (2015).

The CHILD model is run on a 900 m by 900 m triangulated irregular network domain constructed using 20-m regularly spaced nodes with an initial east-facing, 7%-inclined slope. Fluxes of surface runoff and sediment are permitted only through the bottom of the slope. We present results for four simulations designed using two sets of climate transitions (wet-to-dry and dry-to-wet) on two land-cover types (bare soil and dynamic vegetation).

A dry regime (MAP = 200 mm/year; PET = 1,850 mm/year) and a wet regime (MAP = 600 mm/year, PET = 1,529 mm/year) are simulated, representing the plausible lower and upper limits of semiarid climate, consistent with paleoclimatological range of the Southwestern United States prevailed in the Late Pleistocene (e.g., Menking et al., 2004). Simulated landscapes are evolved to dynamic equilibrium between erosion (E) and uplift (EU), driven by U = 0.1 mm/year for both wet and dry climate regimes. Climate change is imposed on equilibrium landscapes by abruptly shifting climate to the opposite regime (Figures 1a and 1b).

Details are in the caption following the image
Modeled geomorphic response of barren and vegetated landscapes to abrupt climate change. Mean annual precipitation (MAP; continuous lines) and generated annual precipitation (AP; dots) for (a) dry-to-wet and (b) wet-to-dry shifts. Spatially averaged elevations and 1-Kyr running average erosion rates for landscapes modeled with bare soil (c, d) and dynamic vegetation (g, h). Spatially averaged annual grass cover fraction (dots) and 1-Kyr running average (solid line) grass cover fraction for dynamic vegetation runs (e, g). Dashed lines (c, d, g, and h) represent the rate of uplift, U = 0.1 mm/year. Solid black lines (c, d, g, and h) represent the 10-Kyr running mean of erosion rates.

3 Results

3.1 Erosional Response to Changes in Climate for Bare-Soil and Semiarid Vegetated Landscapes

The responses to the climate shifts of mean landscape elevation and annual erosion rate are investigated for bare soil (Figures 1c and 1d) and dynamic vegetation conditions (Figures 1g and 1h). In the barren landscape, an abrupt change to a wetter climate induces a sudden increase in the spatial mean erosion rate, E, over 2 orders of magnitude greater than U (for 1-Kyr average rates). This initial response is followed by an exponential-like decay to equilibrium, as the landscape loses mass and slopes decline (Figure 1c). This response is driven by the increase in mean annual runoff. Within this response time scale, the landscape adjusts to a wetter erosional equilibrium (EU) with lower relief and higher annual runoff.

In the opposite case of wet-to-dry climate change on the barren landscape, reduced runoff decreases E to over an order of magnitude of the equilibrium rate (EU). The landscape begins to build up due to this uplift surplus; slopes begin to steepen; shear stress across the landscape enhances; so that E gradually ramps up to compensate U.

Figures 1c and 1d show a disparity in the landscape relaxation times (i.e., time to regain equilibrium) for the different directions of climate change. The dry-to-wet shift leads to declining elevations and a much faster relaxation time (~50 Kyr) than that of the wet-to-dry shift responsible for mountain buildup over (>500 Kyr). This result is consistent with previously reported simulations (e.g., Armitage et al., 2018; Densmore et al., 2007). A major reason for this disparity is that the initial landscape, for the dry-to-wet climate shift in the barren case, corresponds to a dry equilibrium landscape with steeper slopes than those of the wet equilibrium landscape. The runoff enhancement due to the dry-to-wet switch combined with steep slopes leads to a rapid rise in E and thus a shorter relaxation time. In the opposite case of wet-to-dry shift, E plummets due to reduced runoff acting on gentler slopes, and the recovery time is dominated by uplift that increases elevations and steepens slopes until erosion rates counteract uplift, and equilibrium is attained.

When vegetation dynamics is driven by climate, the direction of model response to climate change reverses, and erosion rates become a lot less variable about the uplift rate as compared to barren landscape (Figures 1g and 1h). An abrupt change to a wetter climate leads to a decrease in erosion rates and a corresponding growth in elevations, as E < U (Figures 1g and 1h), attributed to increased grassland productivity in a wetter climate; spatial mean vegetation cover grows from 20% (MAP = 200 mm) to 50% (MAP = 600 mm; Figure 1e). Although more runoff is generated on the landscape in the wetter climate, higher grass cover leads to a proportionally greater loss in effective shear stress (equation 2). On the contrary, as MAP changes from 600 to 200 mm/year, the reduction in vegetation cover leads to a proportionally greater increase in effective shear stress than the loss caused by lower runoff (equation 2; Figures 1f and 1h). Regulated erosion by vegetation leads to landscape relaxation times insensitive to the direction of climate change.

3.2 Reversal in Erosion-Slope Trends

Previous work has reported strong correlations between mean basin slope and erosion rates (Portenga & Bierman, 2011). We plot the trajectory of landscape-scale 10-Kyr-average net-erosion rate (Enet = EU) and slope (Enet, S) between the dry (Bd, Vd) and wet (Bw, Vw) equilibrium states for barren (B) and vegetated (V) simulations (Figure 2). The distance between two subsequent Enet-S points in this plot reflects the change over 10 Kyr. For the barren simulation, the Enet-S trajectory of a dry-to-wet climate shift starts at Bd (Figure 2a). The increase in rainfall results in higher runoff/erosion, and the slope progressively decreases (following blue arrows). This initial trend is followed by a decline in erosion until a new wet equilibrium is reached, Bw, with gentle slopes. For the wet-to-dry shift, the trajectory begins at Bw, and landscape slope and erosion rate gradually increase, returning the landscape state to dry equilibrium (Bd) at a slower pace (red arrows). This behavior is consistent with previous modeling (Armitage et al., 2013, 2018) and experimental landscape evolution results (Singh et al., 2015).

Details are in the caption following the image
Spatially averaged net erosion rates (Enet = EU) as a function of spatially averaged slopes for (a) bare soil and (b) dynamic vegetation simulations reported for every 10-Kyr periods. Positive Enet indicates periods with net incision, and negative values indicate periods of net uplift and aggradation. Squares indicate the equilibrium states for wet (Bw and Vw in blue) and dry climates (Bd and Vd in red) for barren and vegetated landscapes. Blue- and red-filled circles illustrate the trajectories for the dry-to-wet regime shift (blue) and wet-to-dry regime shift (red). The arrows indicate the direction of change following abrupt climate change between two steady states. Filled circles a1 to a4, b1 to b4, c1 to c4, and d1 to d4 correspond to the landscapes shown in Figure 3.

The presence of dynamic vegetation leads to a contrasting erosional response (Figure 2b). In the dry-to-wet shift, starting at Vd (following blue arrows), erosion initially slows down (E < U) due to higher vegetation productivity, and mean slope declines because of deposition in channels (c1 in Figures 2b and 3). Landscape then adjusts to continuing uplift by increasing slopes under the protective role of vegetation cover and reestablishes the steeper equilibrium state, Vw. The wet-to-dry transition (red trajectory in Figure 2b starting from Vw) displays a symmetrical behavior with respect to that of the dry-to-wet transition. Enet-S points initially increase from Vw under dry climate because of vegetation loss but are followed by a subsequent downturn toward a new equilibrium, Vd. As the effect of the climate perturbation dampens, the asymptotic increase and decrease in Enet-S points toward the slope equilibrium states connect the two response loops.

Details are in the caption following the image
Spatial distribution of net erosion in the barren and dynamic vegetation landscapes plotted for select Enet-S datum with identical letter-number combinations as in Figure 2. Frames a and c (1 to 4) for dry-to-wet shift with mean annual precipitation increase from 200 to 600 mm/year. Frames b and d (1 to 4) for wet-to-dry shift with mean annual precipitation decrease from 600 to 200 mm/year. Corresponding time after the climate shift of the plots are given in bottom right.

3.3 Spatial Response to Climate Change

The spatial patterns of Enet along the landscape response trajectory to climate are analyzed at selected a–d points shown in Figure 2. High erosion is pervasive across the barren landscape for the dry-to-wet climate shift, particularly in headwater slopes (Figure 3a1). As the system evolves in this declining transition, equilibrium conditions are progressively achieved from valleys toward hillcrests (Figures 3a2–3a4), until the dynamic equilibrium state Bw is reached (Figure 2a).

During the inclining response of the barren landscape to the wet-to-dry shift (Figures 3b1–3b4), runoff reduction leads to an initial period of accretion (i.e., E < 0) as eroding sediment from hillslopes by soil creep deposits within the drainage network (Figure 3b1). This depositional behavior results in the small initial overall reduction in net erosion and slope observed in Figure 2a (Point b1). During later stages (b2–b4 in Figure 2a), landscape built-up (E < U; Figure 2a) and the resulting steepening of channel slopes initiate a wave of fluvial erosion that propagates upstream to valleys and hillslopes, bringing the landscape to the state of dry-climate equilibrium, Bd (Figure 3b4).

In the dynamic vegetation simulations, vegetation growth induced by the dry-to-wet shift reduces fluvial erosion throughout the landscape, while sediments from soil creep deposit in channels as the landscape state progresses from Vd to c1 (Figure 2b). This initial depositional response to wetter conditions leads to mean slope decline (c1 and c2 in Figure 2b). Erosional recovery occurs across the landscape with continuing uplift, without obvious spatial patterns. Rapid vegetation loss in the wet-to-dry scenario results in extensive channel erosion. This downcutting effect steepens the surrounding hillslopes, leading to an upslope expansion of erosion (d1 and d2 in Figures 3 and 2b), followed by a decline of erosion rates and slopes (d3 and d4 in Figures 3 and 2b).

4 Discussion and Conclusions

The transient response of modeled semiarid landscapes to abrupt changes in climate is investigated to develop insights to aid the interpretation of long-term erosion rate data. In doing so, we address three research questions:

(1) Do landscapes evolve to a climatic steady state with distinct characteristics of landform and erosion rates? (2) How do landscapes respond to the direction of climate change? (3) When does climate dominantly control erosion rates over other compounding factors?

With respect to the first question, although long-term average erosion rates at equilibrium are only controlled by uplift, we found that climate and vegetation exerted a major control on landscape slopes. Simulated equilibrium slopes for barren landscapes were steeper for dry climate conditions than the wet ones, while the opposite was true for vegetated landscapes (see Bw, Bd, Vw, and Vd in Figure 2). Increased productivity resulting in denser vegetation cover for the wet climate requires a steeper terrain to erode the landscape at the same rate than a dryer climate with less protective cover. This is in line with previous work (both observational and modeling) that found that reductions in landscape relief/slopes were associated with conditions leading to higher erosion efficiency (Collins & Bras, 2010; Istanbulluoglu & Bras, 2005; Whipple, 2009; Whipple et al., 1999). Regardless of equilibrium conditions, steeper mean hillslope gradients have been observed under denser vegetation cover across different regions (e.g., Jeffery et al., 2014; Pelletier et al., 2016; Torres Acosta et al., 2015; Yetemen et al., 2010). Our results from modeled landscapes in equilibrium suggest that considering uniform uplift and soil properties in a watershed, observed relationships between erosion rates and climate (e.g., Henck et al., 2011; Schaller et al., 2018; Torres Acosta et al., 2015), could imply a transient geomorphic response.

When addressing the second question, we found evidence that the erosional response to climate change in a given region should be analyzed in relation to the relaxation time of landscapes and to whether ecosystems evolve following climate change. This is not always considered, and long-term erosion rate estimates are often related to modern annual precipitation and vegetation (Perron, 2017). Our results on average erosion rates over 103–104 years in the barren landscape simulation showed an initial positive erosional response to the wet climate transition, with rates more than an order of magnitude greater than uplift (Figures 1a and 2c). The model broadly suggests that arid landscapes could exhibit increased erosion rates to rainfall increase, when there is a lag in vegetation establishment. Short-lived (~4 Kyr) enhanced erosion rates (>25 to 300 times) over sparsely vegetated landscapes have been reported in East Africa during the onset of African Humid Period, before the establishment of forests, reducing erosion rates (Garcin et al., 2017).

The erosional response to the direction of climate change for barren landscapes reverses when dynamic vegetation is considered in our model. A dry-to-wet transition pushes erosion rates below the uplift rate as a result of vegetation growth, compensating the erosive effect of increased runoff; thus, the landscape inclines. When vegetation cover is lost during a wet-to-dry transition, erosion rates grow, and the landscape declines (Figures 1b and 2b). These findings imply that, in settings where vegetation is not constrained by soil and nutrient limitations and is able to respond to climate change, erosion rates could be inversely related to precipitation during landscape relaxation. This is consistent with the complex response hypothesis (e.g., Langbein & Schumm, 1958). Recent studies conducted in similar tectonic settings have provided insights into the relationship between climate and millennial-scale erosion rates. In the Chilean Coastal Cordillera, Schaller et al. (2018) report higher erosion rates in arid and semiarid sites than humid and densely vegetated sites. Similarly, lower long-term erosion rates were reported in humid and vegetated sites despite higher hillslope gradients compared to in sparsely vegetated sites in the Kenya Rift, East Africa (Torres Acosta et al., 2015).

There is a consensus that geomorphic signal of Milankovitch-scale periodicity (104–105) in climate is damped in mountain catchments due to channel response time scales of the order of 106 (e.g., Armitage et al., 2013). Our results for barren landscapes suggest that relaxation times to wet-to-dry shifts (>5 × 105 years) are more than an order of magnitude greater than those for dry-to-wet shifts (i.e., asymmetrical erosional response), broadly consistent with the signal dampening hypothesis (Figures 1c and 1d). However, for landscapes where erosion is mediated by dynamic vegetation, a nearly symmetrical erosional response is obtained in similar landscape response time scales (2 × 105 years) to both directions of climate change. With these reduced response time scales to climate change, a testable hypothesis we propose is that vegetation dynamics plays a role in preserving the signature of climate on landscapes. Perhaps observed associations between contemporary vegetation cover and geomorphic attributes (slope, curvature, and concavity index) in real-world catchment could be attributed to this result (e.g., Jeffery et al., 2014; Torres Acosta et al., 2015; Yetemen et al., 2010).

The trajectory of the transient landscape response to climate change plotted in the Enet-S domain shows an initial positive relationship between erosion and slope when dynamic vegetation is considered (Figure 2b), which is consistent with global data sets on catchment long-term erosion rates (e.g., Portenga & Bierman, 2011). We therefore hypothesize that this positive relation can be attributed to both climate variability and dynamic vegetation (or factors that lead to a decrease in erosivity with wetness). Another important finding is that the response follows a hysteretic behavior. Reduced erosion efficiency and increased deposition during the dry-to-wet shift produce the initial trend of the lower Enet-S loop (c1 and c2 in Figure 2b), while the initial trend of the upper loop is controlled by expansion of channel erosion during the wet-to-dry shift (d1 and d2 in Figure 2b). We argue that the initial trend of the two loops in the Enet-S relationship, reflecting transient stage, could be responsible for the widespread observations between erosion and mean basin slope globally.

Findings of this paper are important for headwater catchments where vegetation is active on hillslopes and partly in channels. As catchment area gets larger, frequent flow disturbances on vegetation in channels prevent vegetation establishment. Thus, a wetter climate could lead to an increase in runoff erosivity in high-order channels but decrease in erosivity on hillslopes and low-order valleys due to vegetation growth. It has been argued that Quaternary climate change (i.e., 104–105 period cycles) accelerated erosion rates and, at the same time, caused an increase in mountain relief globally, without any globally synchronized change in plate tectonics (Molnar, 2004; Molnar & England, 1990). Whipple et al. (1999) argued that flexural-isostatic uplift response to climate change likely played a minimal role and that an increase in relief is possible only when climate variability decreases erosivity along headwater channels and increases runoff erosivity farther downstream. Thus, it is plausible that vegetation could have played a fundamental role in the Quaternary landform evolution.

Acknowledgments

The paper is theoretical, and no data are used. CHILD model is accessible at the CSDMS Model repository. We thank the editor (Bayani Cardenas), the associate editor, and two anonymous reviewers for their comments, which contributed to improving the previous version of this paper. P. M. Saco acknowledges support from the Australian Research Council through grants FT140100610 and DP140104178. E. Istanbulluoglu acknowledges support from NSF through grant NSF-EAR 0963858.