Geomorphology and Ecohydrology of Water-Limited
Ecosystems: A Modeling Approach
by
Daniel B. G. Collins
B.E. (Hons.), University of Canterbury (1999)
S.M., Massachusetts Institute of Technology (2002)
Submitted to the Department of Civil and Environmental
Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in the field of Civil and Environmental
Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2006
(2006 Massachusetts Institute of Technology. All rights reserved.
...................................
Author ............ ..
Department of Civil and Environmental Engineering
June 29, 2006
_
........................
Rafael L. Bras
Edward A. /Abdun-Nur Professor of Civil and Environmental
Certified by ....
......
Engineering
1'0
is Sioerniisor
... , ..
Accepted by ..................................... .-..
Andrew Whit
MASSACHUSETTS INSTITUTE
Chairman, Department Committee on Graduate Students
OF TECHNOLOGY
DEC 0 5 2006
LIBRARIES
ARCHNES
Geomorphology and Ecohydrology of Water-Limited Ecosystems:
A Modeling Approach
by
Daniel B. G. Collins
Submitted to the Department of Civil and Environmental Engineering
on June 29, 2006, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in the field of Civil and Environmental Engineering
Abstract
The role of vegetation in shaping landforms and how these landforms respond to
disturbances are the subjects of this work. A numerical model is developed to help
develop a mechanistic understanding of the hydrological, ecological and geomorphic interactions in water-limited ecosystems. The growth of vegetation suppresses
increases in runoff, thus reducing erosion efficiency and increasing topographic
slopes as rainfall increases in dry climates. Moving along a climatic gradient to
wetter climates leads to the point where the effect of vegetation is overwhelmed
by increasing runoff, thus erosion efficiency increases and slopes decrease. This
transition in vegetation controls translates into a minimum in drainage density for
a semi-arid climate. Erosion efficiency is also affected by down-slope increases in
vegetation, fostered by subsurface flow, an effect that reduces channel concavity.
Plant characteristics also play a role in erosion by changing the variability of the
vegetative effects. Comparing regions with the same fractional vegetation cover,
those with faster growing or deeper rooted plants have greater erosion efficiencies.
The landforms' responses to disturbances depend largely on the recovery time,
which in turn depends on the climate and successional characteristics of the vegetation. The erosional response to sustained changes in mean annual rainfall depends
on the magnitude and direction of the change as well as on the mean rainfall prior
to the change. This means that landscapes most sensitive to erosion differ depending on whether rainfall increases or decreases. Hence, a landscape's sensitivity to
erosion is a function of present state as well as change in climate.
A second model explores the ecohydrological determinants of plant rooting
strategies. Emphasis was placed on soil moisture, and on the factors that govern
moisture availability. Results are consistent with observations, and show how rooting depth may respond to environmental factors that determine infiltration depth.
Roots are deeper in coarser soils, and in wetter and cooler climates. For a given
total rainfall, roots are deeper also where storms are shorter and more frequent.
Thesis Supervisor: Rafael L. Bras
Title: Edward A. Abdun-Nur Professor of Civil and Environmental Engineering
ACKNOWLEDGMENTS
Thanks to my advisor, Rafael Bras, for the opportunity and challenge of the
Ph.D., and to my committee, Charlie Harvey, Paul Moorcroft and Kelin Whipple,
all of whom offered rigorous and rapid guidance across an evolving Ph.D. landscape. Thanks to group members, Gautam Bisht, Frederic Chagnon, Jean Fitzmaurice, Homero Flores, Lejo Flores, Valeriy Ivanov, Ryan Knox, and Jingfeng Wang,
for ever-present aid and feedback at the grassroots level. Thanks to Brent Newman for hosting a visit to the Los Alamos National Laboratory. The visit provided
me with invaluable discussion and observations that grounded my understanding
of the dynamics of water-limited ecosystems. Thanks to Craig Allen also for invaluable discussion and the opportunity to visit an on-going field study. Thanks to
innumerable other colleagues and friends. Thanks also to family.
Thanks for financial support from the Army Research Office (DAAD19-01-1-0513
and DAAD19-99-1-0161), Consiglio Nazionale delle Ricerche, NASA Earth System
Science Fellowship (NGT5-30339), and MIT's Martin Family Society of Fellows for
Sustainability.
TABLE OF CONTENTS
1 Introduction
17
18
1.1 Sediment Transport ............................
1.2
1.3
1.4
1.5
19
21
21
23
..........
Sediment Yield ....................
Topographic Signatures of Vegetation . .................
Erosion and Landform Evolution Modeling . ..............
Research Agenda .............................
2 Modeling Development and Calibration
2.1
25
Comparison Site: Semi-Arid Steppe, CPER . ..............
25
2.2 CHILD: Model Overview .........................
26
2.3 Sediment Transport ........
27
2.4 Dynamic Vegetation
2.5
...................
...........................
30
Soil M oisture ...............................
32
2.6 Subsurface Flow .............................
2.7 Runoff, Runon and Infiltration....
37
...............
....
..
38
2.8 Rainfall . . . . . . . .. .. .. . . . . . . . . . . . . . . . . . . . . . 40
2.9 Model Calibration
2.9.1
............................
42
Calibration: Infiltration Capacity . ...............
42
2.9.2 Calibration: Rainfall .......................
43
2.9.3
43
Calibration: Dynamic Vegetation . ...............
2.9.4 Calibration: Sediment Transport
2.10 Summary ...............................
. ...............
3 Vegetation and Soil Moisture Control of Landforms
3.1 Model and Simulations ..........................
3.2 Example of an Evolving and Evolved Landscape .........
49
52
55
56
. . . 57
3.3 Lateral Moisture Redistribution . . . .
60
3.4 Mean Annual Precipitation . . . . . . .
3.5 Vegetation Characteristics . . . . . . .
65
3.5.1
70
Recovery Time-Scale, T, .
73
3.5.2 Rooting Depth, Z . . . . . . .
75
3.5.3 Life Form: Grasses vs. Shrubs .
78
3.6 Discussion ................
81
3.7 Conclusions ...............
84
4 Erosional Responses to Disturbances
85
4.1 Model and Simulations . . . . . . . . .
86
4.2 Reductions in Vegetation Cover . . . .
87
4.2.1
Percentage Reductions . . . . .
87
4.2.2
Absolute Reductions . . . . . .
89
4.3 Climate Change . . . . . . . . . . . . .
92
4.4 Discussion ................
92
4.5 Conclusions ...............
95
5 Plant Rooting Strategies in Water-Limited Ecosystems
5.1 Model Description ...........
.......
5.2 Simulations ...............
5.3
Identifying the Optimal Profile
5.4 Soil Texture ...............
5.5 Climate ...............
97
98
101
·
·
·
·
·
·
·
·
·
·
·
·
·
·
. . . .
103
103
.......
'..
5.6 Plant Physiology ............
5.7 Discussion ................
5.8 Conclusions . . . . . . . . . . . . . . .
6 Conclusions
6.1 Summary of Results . . . . . . . . . .
6.1.1 Vegetation and Landforms . . .
6.1.2 Disturbance and Erosion. . . .
6.1.3 Rooting Strategies . . . . . . .
6.2 Directions for Future Research . . . . .
105
.
·
.
·
·
..
o
·
.
·
·
·
o. .
109
109
111
113
113
113
114
115
115
LIST OF FIGURES
1-1
(A) Three alternative relations between annual sediment yield and
effective or mean annual precipitation. (B) The Dendy and Bolton
[1976] curve with the data points on which it is based, converted
from runoff by Hooke [2000]. (From Hooke [2000].) .........
20
2-1 Data compiled from Prosser and Slade [1994] and Prosser et al.
[1995], excluding the experiments with aquatic plants. To a first approximation, critical shear stress for erosion increases linearly with
prone plant cover. 7, = 184 Pa and T, = 23 Pa.............
2-2
. 30
Solution to Equation 2.15 for three combinations of p, C, and Vo. ..
32
2-3 Soil moisture loss rate as a function of soil moisture, for V = 30%,
PET = 1254 mm, V), = -4 MPa, C* = -0.1 MPa, and sandy loam.
Total losses are the sum of contributions from evaporation, transpiration and drainage. ...........................
35
2-4 Decay of soil moisture from saturated conditions. Blue grama; V =
30%; sandy loam; PET = 1254 mm. ..................
36
2-5 Decomposition of subsurface flow vector, q,,, into vertical and downslope components, qss,z and qss,x respectively, within anisotropic soil,
following Cabral et al. [1992] .......................
38
2-6 Contribution of slope to the partitioning of total drainage (q,a) to
downslope subsurface flow (qs,X).
. ..................
.
39
2-7 Example hyetograph with corresponding Poisson pulse storm and
scaled Poisson pulse storm with a of 7.4. . ................
42
2-8 Dependence of the runoff coefficient, Q/MAP, on the Poisson model
scaling parameter, a, shows graphically how the appropriate value of
a, that yields Q/MAP of 10%, may be determined. a = 7.4. ......
44
2-9 The annual mean (thick line) of ten realizations (gray lines) of dynamic vegetation cover evolving at a point. Zr = 0.30 m, kg = 0.2,
and
km
varies from 1.25 to 2.75. ...................
. 45
2-10 Description as above. Zr = 0.30 m, kg = 0.3, and k varies from
km
1.25 to 2.75. .
.............
..........
.......
.
45
2-11 Description as above. Z, = 0.30 m, kg = 0.5, and L varies from
km
1.25 to 2.75 .
..............................
46
2-12 Description as above. Zr = 0.30 m, kg = 0.8, and
1.25 to 2.75 .
..............................
..................
varies from
46
2-13 Description as above. Z, = 0.30 m, kg = 1.0, and
1.25 to 2.75 .
km
km
varies from
............
47
2-14 Ensemble means for kg from 0.2 to 1.0, covering k from 1.25 (the
bottom-most lines) to 2.75 (the top-most lines) . . . . . . . . . . . . 47
2-15 Dependence of mean equilibrium vegetation cover at a point on g
km
k
for kg from 0.2 to 1.0. The dashed lines indicate the value of k for
km
kg that yields a cover of of 30%......................
48
2-16 Relationship between km and kg for an equilibrium vegetation cover
at a point of 30% .................
............
48
2-17 Least squares fits of Equation 2.13 to time-series of vegetation cover
for combinations of kg and km estimated to produce equilibrium vegetation covers of 30%. ..........................
49
2-18 The relationship between the recovery time, T,, and growth rate,
kg, for point simulations that yield equilibrium vegetation covers of
30%. For T, of 50 years, kg = 0.54 ....................
50
2-19 Taking the value of kg determined graphically from figure (2-18), km
is determined graphically from figure(2-15). . ..............
50
2-20 Topographies, shaded by vegetation cover, along with their slopearea relationships. Lower kr produces a steeper and land incised
landscape. The landscape that appears most reasonable is that produced by k, of 0.00004 yr3/2m-1/ 2 kg- 3/2 . . . . . . . . . . . . . . . . 51
3-1 Snapshots of an evolving landscape from the initial condition of a
perturbed plateau of 60 m. Contours are at 5-m intervals, the axes
are in meters, and the surface is colored by vegetation density. The
initial landscape is random - elevation perturbation about a mean,
soil moisture, and vegetation cover. (Continued on subsequentpage.)
58
3-2 See Figure 3-1 for description. . ..................
59
10
...
3-3 Equilibrium landscape, shaded by vegetation cover. The heavily outlined polygons trace the major channels. Vegetation cover is more
dense downslope ..............................
61
3-4 Slope-area relationship for the vegetated landscape with MAP of 321
mm. Denser vegetation is present at higher drainage areas. The
hillslope-fluvial transition occurs within the drainage area of 80009000 m2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3-5 Time-averaged vegetation cover for cells of different drainage area
(a) and local slope (b). Circles represent the major channels, and
dots; the remainder. ............................
62
3-6 Slope-area diagrams for MAP of 321 mm with cell sizes of either 60
m (the standard size) and 30 m.......................
63
3-7 (a) Initial vegetation cover for the lateral moisture redistribution
simulations. (b) Vegetation cover after 100 years with hydrological processes unchanged. (c) Vegetation cover after 100 years with
subsurface flow switched off. (d) Vegetation cover after 100 years
with run-on switched off. Increases of cover downslope is dependent on subsurface flow. Run-on only marginally amplifies existing
differences in cover. ...........................
64
3-8 Comparisons of the longitudinal characteristics of landscapes evolved
with and without moisture redistribution: (a) and (b) slope; (c) and
(d) runoff; (e) vegetation; and (f)
roughness coefficient. ........
66
3-9 Temporal averages over 1000 years of equilibrium simulations across
the MAP gradient. (a) Catchment elevation. (b) Mean catchment
vegetation cover. (c) Mean catchment roughness coefficient, kt. (d)
Mean outlet discharge per storm, including storms that do not produce runoff. (e) Mean catchment effective bed and critical shear
stresses .....................
.............
68
3-10 Relationship between drainage density and mean (or effective) annual precipitation as derived by Moglen et al. (1998). The present
results suggest the inverse trend. . ..................
. 70
3-11 Slope-area relationships for MAP of 241, 281, 321, and 963 mm.
The drainage area where the transition from diffusion-dominance to
fluvial-dominance occurs is the greatest for 321mm, and therefore
drainage density is the lowest. Concavity is the lowest for 281 mm,
increasing with more and less rainfall. . . . . . . . . . . . . . . . . . 71
3-12 Longitudinal variations of vegetation cover and roughness coefficient
across the climatic gradient ........................
72
3-13 Longitudinal variation of mean storm runoff across the climatic gradient. ....................................
73
3-14 Mean catchment elevations (a) and discharge (b) for vegetated and
unvegetated landscapes across a climatic gradient. Reported discharge is the mean for all storms, including instances when no flow
occurs .............
......
..............
.....
74
3-15 Mean elevation (a) and vegetation cover (b) for landscapes evolved
under vegetation with response time-scales of 25, 50, 75 and 100
years. Dark bars represent simulations with lateral moisture redistribution, light bars without. The upper and lower bounds indicate the
maximum and minimum spatial mean elevation during 10,000 years
(sampled every 500 years). .......................
76
3-16 Temporal averages over 1000 years of equilibrium simulations across
T,. (a) Catchment elevation. (b) Mean catchment vegetation cover.
(c) Mean catchment roughness coefficient, kt. (d) Mean outlet discharge per storm, including storms that do not produce runoff. (e)
Mean catchment effective bed and critical shear stresses. ......
. 77
3-17 Mean elevation (a) and vegetation cover (b) for landscapes evolved
under vegetation with rooting depths of 15, 30 and 60 cm. Lateral
moisture redistribution is disabled. The upper and lower bounds
indicate the maximum and minimum spatial mean elevation during
10,000 years (sampled every 500 years). . ................
78
3-18 Temporal averages over 1000 years of equilibrium simulations across
Z,. (a) Catchment elevation. (b) Mean catchment vegetation cover.
(c) Mean catchment roughness coefficient, kt. (d) Mean outlet discharge per storm, including storms that do not produce runoff. (e)
Mean catchment effective bed and critical shear stresses. . . . . . . . 79
3-19 Variance of catchment vegetation cover (a), outlet discharge (b), and
catchment effective bed shear stress (c), as determined from 1000
years of data. ........................
........
:
..
80
3-20 Mean catchment elevation and vegetation cover for grass and shrubs
across the climatic gradient ........................
82
4-1 Vegetation and erosional responses to absolute reductions in vegetation cover of 10%, 20%, and 50%. The latter is equivalent to the
complete removal of vegetation. MAP = 321 mm. .........
. . 88
4-2 Erosion and vegetation responses to different percent reductions in
vegetation cover across a climatic gradient. (a) Ratios of cumulative erosion over 50 years between disturbed and undisturbed landscapes. (b) Cumulative difference in vegetation cover over 50 years
between disturbed and undisturbed landscapes. . ............
90
4-3 Erosion responses to a 10% percent reduction in vegetation cover
across a climatic gradient for T, of 50 and 100 years. ..........
91
4-4 Erosional response to different magnitude absolute reductions in vegetation cover. Reductions that would result in negative values are
adjusted to 0.00001% cover. .......................
92
4-5 Erosional response to abrupt and sustained shifts in MAP. Values
along the abscissa refer to MAP prior to the change. ...........
93
4-6 Three alternative relations between annual sediment yield and effective of mean annual precipitation. (From Hooke [2000]) .......
96
5-1 Schematic representation of the one-dimensional model's hydrological fluxes. Stochastic rainfall is intercepted by the canopy, part of
which is intercepted by the canopy. Throughfall is partitioned between runoff and infiltration, and soil moisture is redistributed with
Richards equation. Gravity drainage occurs across the bottom of the
soil column. Evaporation from the soil surface and plant-water uptake are functions of soil moisture, evaporative demand and root
distribution ..............
.....
....
....
......
99
5-2 Seasonal changes in effective MAP, for MAP = 500 mm, At, = 0.3,
f, = 0.5, and T, = 0.35.
........................
5-3 Two vertical root profiles following the LDR model [Schenk and Jackson, 2002b] sampled from the D50 -D95 state space explored by the
simulations (inset).................
.............
100
102
5-4 Transpiration, evaporation, plant stress, and drainage across the D5 0 D95 state space for silty soil. Circles identify the optimum; dashed
line denotes the optimal region ......................
104
5-5 Rooting depths, fluxes and plant stress for optimal profiles across
MAP-PET state space ............................
107
5-6 (a) Optimal D 95 for silty soil across the combined MAP-PET gradients. Deeper optimal rooting profiles arise for the greater MAP and
lowest PET. (b) Conceptual model of the relationship between absolute maximum rooting depths and climatic variables, from Schenk
and Jackson [2002a]. The region enclosed in the dashed line approximates the MAP-PET state space explored by the current study. . 108
LIST OF TABLES
2.1
Climatic, edaphic, and plant model parameters. ............
. 43
2.2 Model parameter values ..........................
53
3.1 Dynamic vegetation model parameters calibrated for different T,. ..
73
3.2 Dynamic vegetation model parameters calibrated for different Z,..
3.3 Model parameters for the two sets of shrub simulations. ........
. 76
80
5.1 Optimal root profiles and corresponding mean annual fluxes and
. . 105
plant stress for four soil textures. .....................
5.2 Optimal root profiles and corresponding mean annual fluxes and
plant stress for different seasonalities, for silty soil and MAP of 500
mm. Values in parentheses are At,,.. . . . . . . . . . . . . . . . . . . 108
5.3 Optimal root profiles and corresponding mean annual fluxes and
plant stress for different storm and interstorm durations, for silty
soil and MAP of 500 mm. Values in parentheses are Tb . . . . . . . . 109
5.4 Optimal root profiles and corresponding mean annual fluxes and
plant stress for different wilting points and stomatal closure pressures, for silty soil and MAP of 500 mm. Values in parentheses are
110
V*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CHAPTER 1
INTRODUCTION
"The effect of vegetation is of high interest to the geologist, when he
is considering the formation of the valleys which have been principally
due to the action of rivers."
Charles Lyell, 1834.
Vegetation plays key roles in the evolution of the Earth's surface, diverse roles
that cover the spectrum of sediment development and transport [Viles, 1990]. Plant
exudates and products of decomposition provide a chemical means of weathering
rock, their roots a physical means. Roots and organic matter bind the soil together,
increasing the force required to detach sediment from the ground. This erosive
force is altered, often diminished but also augmented, by the physical structure of
the plant. Plants interfere with the hydrological fluxes - runoff and infiltration which drive fluvial sediment transport and aid mass wasting. In contrast, roots that
anchor soil to bedrock act to restrain mass wasting. Above ground, plants and their
litter alter hydraulics, changing rates and locations of sedimentation and scouring
by aerial [Bullard, 1997] and sub-aerial processes.
Vegetation's role in geomorphic change is most visible following disturbances
and land use change, by natural of human means. Perhaps the best-known example
in North America is the combined drought and agricultural mismanagement that
led to the Dust Bowl [O'Hara, 1997]. Deforestation, logging, and wildfires are frequently causes of accelerated erosion [Glade, 2003; Guthrie, 2002]. Changes of a
purely ecological nature also bring about geomorphic change, for example by ecological succession following disturbance [Cammeraat et al., 2005; Cerda and Doerr,
2005] or the encroachment of shrubs [Parizek et al., 2002; Wilcox et al., 1996].
One notable instance is the wholescale collapse of terrestrial ecosystems ca. 252
Ma, which drove a massive efflux of sediment and nutrients to the oceans, leading
to eutrophication and the end-Permian mass extinction [Sephton et al., 2005].
The coupling of vegetation and erosion is important in very different landscapes.
Two such landscapes are steep terrain with shallow regolith in humid regions, and
marshes. Where regolith is shallow, plants may anchor the soil to the underlying
bedrock, raising the threshold of slope instability [Schmidt et al., 2001]. Where
surface waters are slow moving, as in marshes, the transport of sediment is largely
dictated by the presence or absence of plants [Temmerman et al., 2005]. The morphology of both landscapes depends on the control of sediment transport by vegetation, and both have been considered by numerical studies [eg Fagherazzi and Sun,
2004; Istanbulluoglu and Bras, 2005] Semi-arid regions are a third type of landscape to exhibit the importance of vegetation. Here, plants control the erosivity of
the rainfall and the erodibility of the soil. The spatial and temporal variability of
the plant cover, driven by variability in rainfall and soil moisture, makes the effects
of plants even more pronounced. The role of vegetation in semi-arid environments
has not been considered by numerical models. This environment, and water-limited
ecosystems in general, are the subject of the current research, and the subsequent
discussion.
1.1
Sediment Transport
Sediment transport in soil-mantled, low relief, semi-arid landscapes is largely
driven by runoff from episodic rainfall, and is mediated by plant cover. Hillsides are
both primary sources and temporary sinks of sediment. Channels export the sediment from the landscape. Plants alter the erosivity of the precipitation and runoff,
as well as the erodibility of the soil, across hillslopes and channels. To understand
how vegetation affects gemorphological processes it is necessary to consider the
suite of physical processes involved in sediment transport.
Runoff is generated primarily as infiltration excess overland flow during rain
storms, though saturation excess overland flow, subsurface return flow, and snowmelt
may also play a role. Before rainfall becomes runoff it is first reduced by canopy
interception, infiltration, and detention in microtopographic depressions. Each of
these is a function of plant cover. The surface comprises a mosaic of plants and
intervening bare soil. This translates into a mosaic also of runoff generation and
run-on infiltration across the hillslope.
Runoff applies a shear stress to the underlying ground. A common model holds
that when stress exceeds a critical threshold, sediment is detached from the surface
and transported downslope. The applied stress is greater in steeper, less vegetation slopes with greater runoff. A portion of the flow energy is absorbed by the
plants themselves, or dissipated by turbulence generated by the plants' structures.
If the shear stress drop, so too does the capacity to transport sediment. This is
realized either by the diminished detachment of sediment from the surface, or by
the deposition of sediment already being transported. The critical threshold for
sediment detachment depends on vegetation. Experimental studies on hill surfaces
and channels have provided a measure of this property as it varies with plant cover.
Ree [1949] considered the threshold of erosion of artificial, vegetation channels.
Prosser and Slade [1994] and Prosser et al. [1995] conducted experiments on unincised and vegetated hollows. In all cases, they made distinctions among soil and
vegetation types (mainly grasses), and among qualities of vegetation cover.
The patchwork of plants and bare ground in semi-arid environments translates
to patchiness in shear stress and critical stress. Accordingly, the ability of runoff to
erode, transport, and deposit sediment also varies spatially [Ludwig et al., 2005;
Puigdefibregas, 2005]. Sediment eroded at one point on a hillslope during a storm
may become deposited before reaching a channel, depending on the proximity to
the channel, and on the transport capacity and duration of the runoff. The influx of
sediment from the hillslopes to the channels is thus not a direct measure of erosion
during a single storm, but of integrated erosion and deposition across the hillslope
over many storms [Trimble, 1975].
Channels are spasmodic conveyors of sediment from uplands to the basin outlet.
As they evacuate sediment from the catchment they also transmit any signal of
baselevel change from the outlet to the uplands.
1.2 Sediment Yield
Catchment sediment yield is an integration of cumulative erosion and deposition over space and time. Because sediment travels through a catchment in an
episodic manner, sediment yield at a point in time reflects erosion that took place
across the catchment at different times [Trimble, 1975]. It is not an accurate measure of contemporary catchment erosion rates, but rather of long-term denudation.
Differences in sediment yield among basins have been attributed to a combination
of relief, lithology, basin size, disturbance, precipitation, and vegetation [Hooke,
2000]. Perhaps the most celebrated of studies connecting vegetation with sediment
yield is that of Langbein and Schumm [1958].
Langbein and Schumm collected data on sediment yield from 94 gauging stations and 163 reservoir sedimentation surveys with the U.S., as well as annual
catchment runoff. Based on Langbein [1949], runoff was transformed into effective precipitation - the precipitation required, on average, to produce the observed
runoff for a climate with a mean temperature of 10oC. Sediment data were grouped
climatically (six groups for the gauging stations eight for the reservoirs), adjusted
for catchment size, and averaged. The result was a curve tracing sediment yield
from zero at zero effective precipitation, to a peak at around 300 mm/year, and
then drop as precipitation increased further (Figure 1-1). The cause for the peak,
they argued, was that at low precipitation, erosion is inhibited by vegetation cover.
An intermediate precipitation range provides significant runoff while not accommodating widespread vegetation growth, resulting in maximum sediment yield.
This was the first time such data were collated, though the idea was not new.
A
B
4W
-Lonqcin
"E 330
onr4 Schumm 1958)
RReservoir dot
a Sedment station dato
a
1
*
S
S
300
--
- Oouglas (1967)
ODy an*
d Solton (1976)
1250
E
1450
Ci
soI00
-l
e50
AJ"
0 f00 400
too200
100
Effective precipitation, mm/yr
20s
Figure 1-1: (A) Three alternative relations between annual sediment yield and effective or mean annual precipitation. (B) The Dendy and Bolton [1976] curve with
the data points on which it is based, converted from runoff by Hooke [2000]. (From
Hooke [2000].)
The hypothesis is all but formulated in Gilbert's seminal 1887 report [Gilbert, 18771.
Three quotations illustrate the connection.
"Transportation [of eroded material] is favored by increasing water supply."
"Vegetation is intimately related to water supply."
"The general effect of vegetation is to retard erosion."
Further data in the sediment yield-precipitation relationship were assembled by
researchers after Langbein and Schumm [Dendy and Bolton, 1976; Douglas, 1967;
Fournier, 1960; Schmidt, 1985; Wilson, 1973]. Some of the relationship differed
significantly from one another (Figure 1-la). Their differences are due, at least in
part, to differences in environment factors being controlled, and to the accuracy of
the sediment yield data and averaging. Hooke [2000] considered the most reliable
data set to be that of Dendy and Bolton [1976], because their data set was relatively
large and variation in relief, lithology, and catchment area were minimal (Figure 1Ib). Their peak in sediment yield occurs at 500 mm/year of precipitation.
The results of Langbein and Schumm and others are not without their critics.
When plotted as raw data, not grouped by climatic ranges, the trend is not at all
clear [Walling and Webb, 1983]. Furthermore, the data may have been derived
from catchment in transient states, having experienced different histories of disturbance [Trimble, 1975; Walling, 1999]. Lastly, cosmogenic data suggest that there
20
is no long-term relationship between precipitation and erosion at all [Riebe et al.,
2001]. The theoretical argument underpinning this last statement is that a landscape in erosional equilibrium with uplift must erode at a rate independent from
climate. The results of Langbein and Schumm thus remain the subject of controversy.
1.3
Topographic Signatures of Vegetation
It is clear from the preceding sections that vegetation is one factor controlling
the rate of geomorphic change, but how does this translate to landforms, if at all?
Studies linking topographic indices to vegetation characteristics abound [eg Pickup
and Chewings, 1996]. The work of Hack and Goodlett [1960] is an example of a
joint gemorphological and ecological assessment of a landscape. Hack and Goodlett
surveyed a drainage basin in north-west Virginia. Twenty-five of the 45 tree species
surveyed were closely correlated with topographic position, due, they argue, to the
soil moisture! conditions during the growing season, conditions governed primarily
by slope, curvature, and aspect. In New Mexico, Caylor et al. [2005] also found that
the hydrological character of a basin acted as a template for species distributions.
However, based in such correlations across landscape, it is difficult to identify which
is the cause and which is the effect.
On short time-scales, disturbances illustrate the connection between vegetation
and landforms well. Gullies and mass wasting scars are often reminders of vegetation disturbance or removal from steep landscapes. However, a review by Dietrich
and Perron (2006) found no evidence of a landform unique to vegetation-mantled
landscapes. Though their search was not exhaustive, they suggested the effect of
vegetation, or life in general, on landform evolution was to change the scale and
abundance of particular landforms rather than introduce novel ones. This is corroborated by the handful of landform evolution models that have investigated the
influence of vegetation.
1.4
Erosion and Landform Evolution Modeling
Modeling is a common approach for understanding erosion and geomorphic
change. Vegetation has been incorporated into such models with differing degrees of complexity. Treatment of vegetation in soil erosion models for agricultural
purposes has been standard for many decades. The Universal Soil Loss Equation
(USLE) uses an empirical approach to account for vegetation, while the Water Erosion Prediction Project (WEPP) is more mechanistic. In geomorphic models, vegetation has been incorporated to varying degrees beginning with Thornes [1985]. The
more straightforward approaches considered vegetation to be static, and modeled
erosion subject to a fixed plant cover [eg Boer and Puigdefabregas, 2005; Siepel
et al., 2002]. Erosional response to single disturbances has been studied, such
as drought [Giakoumakis S.G., 1997] and fire [Istanbulluoglu et al., 2004]. Fully
dynamic vegetation-erosion coupling has also been modeled, addressing diverse
biogemorphic phenomena such as dune fields [Hugenholtz and Wolfe, 2005], grazing [Thornes, 2005], fire and steep terrain [Gabet and Dunne, 2003], and riparian
channels [Hooke et al., 2005].
Moglen et al. [1998] used the theoretical underpinnings of the slope-area relationship of a fluvial landscape to compute drainage density as a function of precipitation. Drainage density is related to the drainage area that marks the transition between diffusion-dominated slopes and fluvial erosion-dominated channels.
Moglen et al. derived an expression for drainage density in terms of denudation
rate, or catchment sediment yield, They then used the empirical expression of sediment yield derived by Langbein and Schumm [1958] (Figure 1-1) to derive the
dependence of drainage density on mean annual precipitation. Drainage density
was found to peak at an intermediate value of precipitation, consistent with observations reported by Gregory [1976].
While plants have featured heaviy in models of erosion, only in more recent
years have landform evolution models taken them into account. Kirkby [1995] and
Roering et al. [2004] both simulate the evolution of a linear hillslope. Kirkby [1995]
accounts for vegetation, which does not evolve over time, by adjusting a threshold
that governs runoff generation - vegetation inhibits runoff generation. With more
vegetation, runoff is suppressed leading to a greater hillslope length and a shift of
the channel head further from the summit. Roering et al. [2004] evolve hillslopes
under diffusional sediment flux, at a rate governed by an active soil depth. The
active depth may be interpretted as a rooting depth. A hillslope with a deeper
active rooting depth denudes faster, producing a hill of lower relief.
Vegetation was incorporated into 3-dimensional models of landform evolution
beginning with Howard [1999]. In his model, the topographic surface is deformed
subject to baselevel change and diffusive and fluvial sediment transport. Fluvial erosion follows the excess shear stress model, in which the critical shear stres's is tied
to the vegetation cover, though vegetation is not explicitly modeled. Simulations included stepwise perturbations of the critical shear stress, representing disturbance
and recovery of the vegetation cover. Differences among the thresholds for erosion,
accelerated erosion, and recovery produced topographically distinct landforms with
different degrees of gully development. Evans and Willgoose [2000] parametized
vegetation within the model SIBERIA via different values for the three parameters
governing fluvial sediment transport. These parameters were a sediment transport
rate coefficient, an exponent describing the dependence of sediment flux on discharge, and an exponent describing the dependence of discharge on drainage area.
In each of their 1000-yr simulations, these parameters were fixed and the vegetation cover static. Differences among simulated landscapes centered on the degree
of gully development.
The notion of fully dynamic vegetation was introduced by Collins et al. [20041.
In their model, equilibrium landscapes were evolved subject to diffusive and fluvial
drivers. As in Howard [1999] model, vegetation controlled the critical shear stress
for erosion. Vegetation dynamics incorporated density-dependent colonization and
erosion-driven mortality. Both form of the landscape and the tempo of its development depended on the vegetation characteristics. The more the vegetation inhbited
erosion, the greater the relief, the longer the hillslopes, and the more extreme are
the elevation fluctuations once a quasi-equilibrium state is attained. Steeper and
more temporally variable topography also resulted from vegetation that dies more
slowly. The work by Collins et al. [2004] was extended by Istanbulluoglu and Bras
[2005] who accounted for vegetation in three additional ways: its effect on shear
stress, its effect on diffusive flux, and its effect retarding landsliding. The incorporation of vegetation shifted the simulated landscape from fluvially dominated erosion
to landslide-dominated.
Numerical models, such as those cited above, are important to both geomorphology and ecology, and have been flagged as an important element in the course
of biogeomorphological research [Naylor et al., 2002]. The models, even if not
predictive, can offer valuable insight into complex systems by providing a common
framework for the integration of a set of hypotheses about how natural systems
function. They may be used to seek inconsistencies in established theories, to propose new hypotheses, or to help guide observational work by highlighting important
considerations from a theoretical perspective.
1.5
Research Agenda
The overarching theme of this work is to explore linkages among vegetation,
landscapes, and landform change in water-limited ecosystems, using numerical
modeling as a tool. Research questions center around vegetation's dependence on
soil moisture, and the resulting erosional dynamics. Particular questions address
characteristics of plants and plant communities that are ultimately important to geomorphic processes. These include rooting depth and how communities respond to
disturbances.
A modeling approach is used to for three reasons: to better understand the
implications of existing hypotheses regarding geomorphic, ecological, and hydrological processes; to propose new hypotheses regarding their integrated dynamics;
and to identify areas of research that would be particularly useful in furthering the
study of biogeomorphology. In calling for more research on the effects of vegetation
on landform change, Dietrich and Perron [2006] emphasized studies of sediment
transport. In light of conditions in semi-arid environments, this must be extended
also to drivers of sediment transport, in particular water balance and vegetation
cover. Here, a modeling framework is used to identify the relative importance of
different processes involved.
The model is developed in Chapter Two. The model extends the capabilities of
a pre-existing model, CHILD, by adding geomorphic, ecological, and hydrological
processes relevant to semi-arid environments. These processes are formulated into
compatible mathematical expressions, and incorporated into a numerical modeling
framework. Choice of parameter values is guided by studies by other researchers in
grasslands within North America and Australia.
In Chapter Three, quasi-equilibrium landscapes are simulated and compared
with one another to assess the influence of specific processes and environmental
factors on landform evolution. In a reflection of Langbein and Schumm [1958], one
set of simulation considers the effect of mean annual precipitation on topography
and erosion. Further simulations investigate the effect of variability in vegetation
cover, considering both successional characteristics and rooting depths. Impact of
lateral moisture redistribution and plant life form are also analyzed.
In Chapter Four, transient responses of quasi-equilibrium landscapes to ecological disturbances and climate changes are explored. Simulations shed light on how
environmental changes manifest themselves on catchment-scale erosion, and offer
further insight into how dependent landscapes across climate gradients are to vegetation cover.
In Chapter Five, the ecohydrological implications of root distributions are explored. Rooting depth plays an important role in soil moisture dynamics. However,
little is known about such and important feature of plants, and measuring root profiles is difficult. This chapter seeks a theoretical understanding of plant rooting
patterns, and the interacting roles played by soil texture, climate, and physiological
factors.
CHAPTER 2
MODELING
DEVELOPMENT AND
CALIBRATION
The model used to investigate the implications of vegetation-erosion coupling at
the landscape scale and in water-limited ecosystems is the CHILD model. Processes
particular to such ecosystems are incorporated, and parameters governing these
processes are obtained from representative environments. Following are the details
of the model and data sources.
2.1
Comparison Site: Semi-Arid Steppe, CPER
The objective of model development is to establish a tool to generate general
hypotheses about interactions between vegetation and landforms in water-limited
environments, not to formulate predictions about the evolution of a particular site.
However, for the model to be as realistic as possible it helps to base the model
construction and calibration on a particular site. The site chosen is the Long Term
Ecological Research (LTER) site at the Central Plains Experimental Range (CPER),
a semi-arid shortgrass steppe in northern Colorado (40o49' N, 107'46' W) covering
an area of 2680 ha and consisting of abandoned agricultural fields.
Mean annual precipitation is 321 mm with an approximate range of 100-500
mm [Dodd and Lauenroth, 1997], and mean monthly temperature ranges from 5'C in January to 22 0 C in July [Coffin and Lauenroth, 1988]. The majority of the
annual rainfall falls during convective thunderstorms from May to August. Potential
evapotranspiration has been estimated at 1254 mm [Sala et al., 1992]. The topography consists of flat uplands and lowlands connected by gentle slopes [Coffin and
Lauenroth, 1988], and the streams are ephemeral [Sala et al., 1982]. Soil texture
is variable, ranging from fine to coarse [Dodd and Lauenroth, 1997]. Vegetation is
typical of the shortgrass steppe. Basal plant cover ranges from 25-40%, of which
85-90% consists of blue grama (Bouteloua gracilis H.B.K. Lag ex Griffiths). The
remainder of the species include other grasses, succulents, half-shrubs, and forbs.
Blue grama is a long-lived, C4 perennial grass native to North America, most
commonly occurring from Alberta east to Manitoba and south across the Rocky
Mountains, Great Plains, and Midwest states to Mexico [Anderson, 2003]. Blue
grama accounts for most of the net primary productivity in the shortgrass prairie
of the central and southern Great Plains. It grows on a wide array of topographic
positions, and in a range of well-drained soil types, from fine to coarse textured.
Plant height at maturity ranges from 15-30 cm. Roots generally extend up 30-46
cm from the edge of the plant, and 0.9-1.8 m deep. Maximum rooting depth is
approximately 2 m. Lee and Lauenroth [1994] observed the majority of roots in the
upper 30 cm.
Blue grama is readily established from seed, but depends more on vegetative
reproduction via tillers. Seed production is slow, and depends on soil moisture
and temperature. Dispersal by wind reaches only a few meters; farther distances
are reached with insects, birds, and mammals as dispersal agents. Seedling establishment, survival, and growth are greatest when isolated from neighboring adult
plants, which effectively exploit water in the root zone of the seedlings. Successful
establishment requires a modest amount of soil moisture during the extension and
development of adventitious roots. A modeling study by Lauenroth et al. [1994]
illustrated the roles climatic variability and soil texture play in providing a suitable
moisture environment. For sandy loam, the soil texture considered in the present
study, they hypothesized a return time for recruitment events from 30-55 years at
the CPER site. Established plants are grazing-, cold-, and drought-tolerant, though
prolonged drought leads to a reduction in the root number and extent. They employ an opportunistic water-use strategy, rapidly using water when available, and
becoming dormant during less favorable conditions.
In terms of successional status, blue grama is a late seral to climax species. Recovery following disturbance is slow and depends on the nature and extent of the
disturbance. One factor for its slow recovery is the low rate of seed production.
Another is the possible prevalence of a bi-stable system where disturbed landscapes
follow a successional progression that does not end in blue grama dominance [Laycock, 1991]. Numerical simulations by Coffin and Lauenroth [1989] suggested that
recovery times may vary from 30-300 years, depending on the mechanism of recovery and on disturbance size. Samuel and Hart [1994] similarly suggest a century
timescale based on field monitoring. Much of the variability in recovery time may
also depend on the vagaries of interspecific competition [Coffin and Lauenroth,
1996].
2.2
CHILD: Model Overview
CHILD is a geomorphic model developed to investigate the evolution of landforms at the catchment scale [Tucker et al., 2001a]. By integrating a variety of
geomorphic and associated processes into a common computational environment,
the model acts both as a repository of hypotheses about how nature works, and
as a sand box for generating new hypotheses. The processes are incorporated as
modules, whose inclusion depends on the nature of the hypotheses being proposed.
The computational environment consists of a triangular irregular network (TIN)
with associated hexagonal Voronoi cells [Tucker et al., 2001b], which represents a
topographic surface deformed by an interplay of erosion, sedimentation, and base
level change.
Investigating the interplay of soil moisture, vegetation, and erosion in waterlimited landscapes requires a particular suite of hydrological, ecological, and geomorphic processes. Stochastic rainfall is partitioned between infiltration and runoff.
Soil moisture evolves in response to inputs from rainfall, run-on and subsurface
flow, and to demands from soil evaporation, plant transpiration, and drainage. Vegetation cover grows and contracts as soil moisture conditions permit. Sediment
transport proceeds by diffusional and fluvial processes, where the latter is inhibited
by vegetation cover. Lastly, the domain is continually uplifted, which is equivalent to the outlet being lowered. The details of each process are explained in the
following sections.
Moisture and vegetation dynamics are assumed to act uniformly across each
Voronoi cell, as is diffusion. Fluvial processes, on the other hand, operate within an
empirically defined channel embedded within the cell; any resultant hydrological or
elevation changes are distributed over the entire cell. The majority of the hexagonal
cells that comprise the landscape have an area of 3600 m2 , equivalent to a 60 m
by 60 m square cell. Simulating at this spatial scale is a compromise between the
need to represent a landscape by elements smaller than the size of a hillside, but
not so small as to make the simulations excessively long and thus reduce the scope
of the study. The greatest simplification that results from this resolution is that
no distinction is made between soil moisture and vegetation along a hillslope and
within a channel within a given Voronoi cell. Compared with basins larger than that
considered here (1 km 2 ) and where flow is perennial, the physical and ecological
processes operating within the channels will diverge less from their neighboring
hillslopes, thus reducing the impact of the spatial simplification.
A single metric will be used to quantify vegetation, the percent areal vegetation cover, V. This will be used to scale transpiration losses, hydraulic roughness,
and sediment detachment. It is also the variable on which empirical vegetation
dynamics are based. Using just one metric in this way is a simplification, though
it is largely :imposed by the scarcity of data relating different plant attributes to
one another, and to the hydrological, hydraulic, and geomorphic processes to be
modeled.
2.3
Sediment Transport
Evolution of a topographic surface at a point follows continuity of sediment mass
at
az(x,t)
1
W(1 -pS)
= U - kdVz - min[Dc, W(1
Vq].
(2.1)
Elevation, z(x, t), changes in response to an interplay of geomorphic processes that
vary in space and time. The first term in Equation 2.1, U (L/T), embodies the
steady, uniform increase in elevation relative to the outlet. This is akin to uplift
or base level lowering. The second term in Equation 2.1 accounts for diffusion
of regolith on shallow to moderate slopes [Culling, 1960; McKean et al., 1993].
The third term in Equation 2.1 reflects fluvial sediment flux. This is the minimum
of two terms, the first of which represents detachment-limitation and the second
transport-limitation [Tucker et al., 2001a]:
DC = kr(b - T~a)a
(2.2)
q, = kfW(Tb - Tct)P
(2.3)
where kr and kf are erodibility parameters, rb is the bed shear stress, -da
and rd are
critical shear stresses corresponding to detachment and entrainment respectively,
a and p are coefficients associated with the transport processes (pvaries from 1.5
(bed load) to 2.5 (total load) [eg Yang, 1996]; a = 1.5 when modeling unit stream
power), and W is the channel width. The parameter k, is not well constrained.
Identification of a suitable value for the simulations is discussed later in the chapter.
kf is calculated from the mean grain size of the soil texture modeled (50 pm; sandy
loam), using the following equation:
kf =
g(ps/pw - 1)d3
50
(pwg(pslpw -- 1)d
1)d50)o
g(
(2.4)
where , is 20, g is the gravitational constant, p, and p, are the sediment and water
densities respectively, d50 is the mean grain size, and p is 2.5.
Incorporating both detachment and transport limitations is justified as follows.
Erosion of soil beneath vegetation is generally considered detachment-limited, because the soil organic matter and roots bind soil particles together, and the roughness of the aboveground biomass reduce flow rate. Transport-limited sediment flux
is more applicable for bare ground. In a patchy plant community, some areas would
be sources of sediment and other sinks [Ludwig et al., 2005; Moir et al., 2000;
Nearing et al., 2005b] requiring both modes of transport.
Because part of the shear stress applied to the bed is absorbed by form roughness, including the vegetation itself, rb is replaced by an effective shear stress, Tf,
that acts on the soil particles alone [Istanbulluoglu and Bras, 2005]:
Tf =
kt q0.6 S0.7
28
(2.5)
and
pwgn1.5
kt =
(2.6)
where kt is the roughness coefficient, p, is the density of water, g the gravitational
constant, n, Manning's roughness of bare soil, nvr Manning's roughness of the reference vegetation cover, V the vegetation cover, V, the reference vegetation cover,
w is an empirical parameter, q is discharge per unit width, and S is slope. This
was derived from Manning's equation, in which the roughness coefficient was split
into contributions from soil and vegetation. The contribution from vegetation is
estimated based on a power law dependence on vegetation cover [Istanbulluoglu
et al., 2004]:
n =v n
V]
(2.7)
Based on data from Prosser et al. [1995], and approximating Vr as 95%, Istanbulluoglu and Bras [2005] found w to equal 0.5. They also use obtained values for n,
and nuV of 0.025 and 0.6, respectively.
Vegetation also affects the detachment threshold, Td. Flume experiments on
vegetated slopes by Prosser and Slade [1994] and Prosser et al. [1995] suggest -cd
may be simply modeled as a linear function of fractional cover of flattened vegetation (Figure :2-1) [Collins et al., 2004]:
Tcd -= cs + Vc,,,
(2.8)
where Ts and m,, are the contributions to the total critical shear stress from the
soil and vegetation respectively. These field experiments made measurements of
flattened plant cover. Here, the more common metric of non-prone areal cover
will be used to describe plant density. Because of a lack of measurements relating
prone cover to non-prone cover, the two are considered equivalent throughout this
study. If there were a systematic difference between the two quantities it seems
reasonable to conjecture that flattened cover would be greater than non-flattened
cover for a given plant, and so the resultant predicted erosion would be greater to
some degree.
Before the shear stress may be calculated, discharge per unit width, q, must first
be determined from volumetric discharge, Q (q = Q/W, where W is width of the
flow or channel). This conversion is based on the hydraulic geometric relationships
of Leopold and Maddock [1953]. Tucker and Bras [2000] obtain an expression for
channel width, W, as
W =
QWb-WsQws
(2.9)
where k,, Wb, and ws are coefficients with values of 3 yr/m 2, 0.5, and 0.26, respec-
I~,
in 200
U,
c 150
CZ
U
100
C,
*j
o
50
0
20
40
60
80
100
Prone Cover (%)
Figure 2-1: Data compiled from Prosser and Slade [1994] and Prosser et al. [1995],
excluding the experiments with aquatic plants. To a first approximation, critical
shear stress for erosion increases linearly with prone plant cover. r, = 184 Pa and
,,8 = 23 Pa.
tively. Qb is the characteristic discharge, approximated by Tucker and Bras as the
product of drainage area, A, and mean annual rainfall, Pa. However, with infiltration losses and a runoff coefficient of 0.1, Qb is instead approximated here as
the product of A, Pa, and the runoff coefficient. The runoff coefficient of 0.1 is
inferred from Lauenroth and S. Darbyims [1976] who reported roughly 90% of the
annual precipitation became evapotranspiration. Almost the entirety of the remainder would have become runoff.
2.4
Dynamic Vegetation
Soil moisture imposes the dominant control on vegetation dynamics in waterlimited ecosystems. To reproduce this relationship we need a dynamic vegetation
model that reflects the role soil moisture plays in plant growth and mortality. The
most readily quantifiable linkages between soil moisture and plant physiology are
transpiration and plant water stress. The ecohydrological model that addresses
these factors will be detailed in section 2.5. In contrast to Collins et al. [2004],
vegetation changes do not depend on erosion itself.
A popular model of population growth, whose previous use has included erosional studies [eg Thornes, 1985], is the logistic equation:
dN
dt = rN(1 at
N),
(2.10)
where r is the growth rate, and N is the measure of the individual or community
size, in our case vegetation cover, V. To couple this to soil moisture, two modifications are made. The first is make the growth rate a linear function of transpiration.
The second is to add a mortality term linearly dependent on plant stress. This
30
is based upon a model of annual grass production in an African savanna [Scanlon et al., 2005b], with only slight modification to account for self-limiting growth
[Levins, 1969]. The simplicity of the mortality component is in part an outcome of
the paucity of well-tested models of water stress-induced plant death. We do not
consider any other sources of mortality because (i) we assume water stress is the
dominant cause of mortality in water-limited ecosystems, (ii) the scarcity of data
with which to calibrate the model degrade the meaning of any model and parameter values we may obtain, and (iii) interpretation of results is simplified with a
simpler model. The dynamic vegetation model to be used is thus
dV
dt = kgTV(1 - V) - km(V,
(2.11)
where kg is the intrinsic growth rate of the species, T is the transpiration per unit
plant cover per unit time, km is the intrinsic mortality rate following plant stress,
and ( is plant stress. T and ( will be covered in the following section.
Despite addition of the mortality term, Equation 2.11 remains a logistic model.
The equilibrium plant cover, or carrying capcity, is
C = 1- km
kT'
(2.12)
where ( and T are the mean plant stress and transpiration, respectively. By substituting the effective growth rate
kk T - km(
kgT
-Cg
kgT
(2.13)
we obtain
dV = pV(1 - V ).
dt
C
(2.14)
and
V(t)
=
VoC
V + (C
V+(C- VO)e-Pt
(2.15)
where V, is the initial cover. The dependence of C and p on T and ( illustrate the
role soil moisture, and ultimately climate and soil, has on plant cover and dynamics.
The time-scale of response, T,, depends on p, C, and on the threshold designating
attainment of equilibrium, f (eg. 95%):
Tv = In I
(00+
+1 ,
(2.16)
-
50
-.- --
•p =0.15; C=50%
> 40
0
or
a)
-.
- ---.
= 0.1 C = 30%
20
>
--
p = 0.2; C = 30%
*......
30
--
10
n
0
I
I
I
I
I
10
20
30
40
50
60
Years
Figure 2-2: Solution to Equation 2.15 for three combinations of p, C, and Vo.
To obtain an appreciation of the first order effects of vegetation-moisture coupling on landform evolution only a single species of plant is considered, the dominant perennial blue grama. Growth is treated as year-round. Blue grama's ability to
respond physiologically to even brief and minor rainfall events [Sala and Lauenroth,
1982] justify the model's assumption that growth will proceed dependent only on
water availability and not be delayed. Because this model accommodates the complete loss of vegetation cover, from which it is unable to recover, the minimum
cover is set to 0.01%. It is likely that there are processes by which plants establish
themselves that are not sufficiently represented by the above model. Our limited
understanding of dynamics of plant populations in water-limited ecosystems, particularly water stress-induced mortality, poses a significant constraint on estimation
of the parameters kg and km. Calibration of these parameters will be addressed later
in the chapter.
2.5
Soil Moisture
Transpiration and plant stress used to drive vegetation dynamics are determined
using an ecohydrological model developed from an earlier model by RodriguezIturbe and Porporato [2005], and tailored to fit the needs of the current study.
Following is an overview of the earlier model, and the methodology behind the
developments.
Rodriguez-Iturbe and Porporato presented a stochastic model of soil moisture
evolution. In their model water balance at a point is represented as
nZ,
ds
= I(s,t) - ET(s) - L(s),
dt
(2.17)
where n is soil porosity, Z, is the active rooting depth (m), s is the soil saturation
within the root zone, I(s, t) is the infiltration (m), ET(s) is evapotranspiration (m),
32
and L(s) is leakage of water below the root zone (m). Each of the three hydrological
fluxes is dependent on soil moisture conditions, while infiltration is also a function
of the stochastic rainfall input. Evapotranspiration is modeled as
0
E,
ET(s) =
s8< Sh
S -
Sh
8 h < S <sw
(2.18)
s - sh-
Ew + (Emax - Ew) -
sw < s < s*
s* -
Sw
Emax
S* < s
where sh is the hygroscopic point, below which the soil is so dry as to eliminate any
further moisture loss; s, is the wilting point, below which plants are unable to transpire; s, defines the transition between stressed and unstressed transpiration; E, is
the rate of evaporation at sw; and Emax is the maximum rate of evapotranspiration.
Instantaneous plant water stress, (, is modeled by
S < SW
)q SW
S*- SW
(-S=
0
((s)
< S < S*
(2.19)
s* < s
where q is a dimensionless parameter that reflects the non-linearity of the physiological response to water limitation. Leakage occurs when soil saturation is above
field capacity, sfc, and is modeled as
L(s)
Ks
e3(1-sc) -
- s
1 (e1(s fc) - 1)
(2.20)
where Ks is the saturated hydraulic conductivity (m/s), and 3 is a drainage coefficient.
For the current applications vegetation cover must be dynamic, growing and dying in response to transpiration and plant stress. As such, the above ecohydrological
model must be adapted to disaggregate evaporation and transpiration, and to vary
each according to the amount of bare ground or vegetation cover, on an areal basis.
Water balance at a point thus becomes
nZr•
ds
= I(s, t) - E(s) - T(s) - L(s),
(2.21)
where E(s) and T(s) are soil evaporation and plant transpiration, respectively.
Leakage is modeled as above.
Soil evaporation depends on the amount of energy partitioned to the soil, and
on the degree of soil saturation. Evaporation from a bare and fully saturated soil is
expected to proceed at the potential rate. As soon as soil is unsaturated, evaporation
rate drops below potential, and continues to decrease as soil moisture decreases.
Where the soil is partly vegetated, the energy driving evapotranspiration, on an
areal basis, is partitioned between vegetation cover and bare soil. The areal average
rate of soil evaporation is reduced, accounting for the reduced areal coverage of
bare ground. As vegetation completely covers an area, soil evaporation losses are
negligible. The effects of plant cover and soil moisture on evaporation may be
approximated as
0
S < sh
(1- V)PET - Shh
E(s)
(2.22)
where V is the fractional vegetation cover (1 - V is thus the bare ground fraction),
and PET is potential evapotranspiration. To accommodate analytical tractability,
evaporative flux above field capacity is modeled as being independent of soil moisture. Because this coincides with the larger flux of drainage, and would be rare in
water-limited environments, the errors introduced by this simplification would be
small. The final evaporation model becomes:
0
E(s)E(s)
=
< Sh
(1 V)PETsS1
1 --
Sh
-
(1- V)PETSc Sh
1 - Sh
Sh<8<Sfc
s
<sf
(2.23)
> Sfc
Transpiration is modeled in a similar fashion as evaporation. Instead of varying
linearly between sh and sfc, transpiration varies linearly between s, and s*, as
embodied in the original ecohydrological model. Leaf water potential of blue grama
was shown to follow the pattern of atmospheric demand closely [Sala et al., 1982].
Following the argument regarding the areal partitioning of energy between bare
ground and plants, the average transpiration over an area is modeled as:
(0
T(s)=
VPET
VPET
' S<s,
s
s*- sw
< s < s*
(2.24)
s > s*
Evaporation, transpiration, and leakage losses from the soil are superimposed
(Figure 2-3), resulting in a soil moisture loss function that resembles the original
but possesses the extra degree of freedom of variable plant cover. The combined,
normalized soil moisture loss function becomes
34
E
€-
0
0.2
0.4
0.6
0.8
Soil moisture, s
Figure 2-3: Soil moisture loss rate as a function of soil moisture, for V = 30%, PET
= 1254 mm:, 0. = -4 MPa, V* = -0.1 MPa, and sandy loam. Total losses are the
sum of contributions from evaporation, transpiration and drainage.
s < Sh
Sh 77h
+ ;ý
ds
7
-
Sh)
Sh < S < Sw
77 + Sw - 'S* (S- s,)
17*
+ 7*
- ?7fc(S- *)
S* - Sfc
dt
Sw < S < s*
(2.25)
s* < s < Sfc
?rfc + m(e 3(s- sfc) - 1)
* <
where
(2.26)
77 h = 0
1
rw =nZ [(1 - V)PET.
nZr
TI*
=
77f =
1
nZr
- Sh
1 - Sh
[V -PET + (1 - V)PET
S*-S
1-
(2.27)
h]
1 [VPET + (1 - V)PET s f c - Sh
1- Sh
nZ,
Ks
nZr(eO(1-sf
c)
-
1)
(2.28)
Sh
(2.29)
(2.30)
Analytical expressions for the soil moisture decay from an initial condition, so,
are as follows:
Drainage + evapotranspiration
0.6
-......
0.4
... .. . ..
.1.
Evapotranspiration .........
Evaporatio.n
S
.. . . . . . . . .. . . . . . . . .
0.2
0
0.5
1
1.5
2
2.5
3
3.5
Months
Figure 2-4: Decay of soil moisture from saturated conditions. Blue grama; V =
30%; sandy loam; PET = 1254 mm.
s < sh
Sh)
Sh + (SO -
S(t)
77w - 77h
8
e
o0- sh
sossow_q*
_
-t'
wlh
Sh < s < s,
*
S, < s < S*
77w -77h
77W
s* < s < sfe
1In[(7* sg
- m+ me.(So-8f))ePt(*-m) - mef(8o-0fc) /
Sfc < s
(2.31)
The decay of soil moisture is illustrated in Figure 2-4. The times taken to reach the
lower soil moisture bounds of the different soil moisture domains, starting from ani
initial condition of So, are:
th
tsw
ts*
In(7 )
=
so - S r*
-
r(
s•
77fe -
t8,,
(rlw )
So - Sh
Sh < S
sw
SW <S
< S*
s* < s < Sfc
7r*
1
m 77*)
NM,
(s
-
+
77* - m + mep(so-sfC)
77*
Sfc < s
(2.32)
In addition to evolving the soil moisture, we must also identify the proportion
of the soil moisture loss that is due to transpiration. This is trivial for soil moistures
outside the range sw < s < s*, because transpiration proceeds at a constant rate
(either zero or non-zero). Within this soil moisture range we must account for the
changing proportions of both transpiration and evaporation as soil moisture decays.
The approximate rate of soil moisture loss due to transpiration is
(so - s(t)) -s
AST - VPET 2
s" -
(2.33)
-
Sw
and the approximate rate of soil moisture loss due to evaporation is
ASE -- (1 - V)PET2(O - s(t))
1 -
sh
h
(2.34)
The fraction of moisture loss due to transpiration is thus
T
T
E +T
As
T
AST(2.35)
ASE+ AST(
Finally, to be compatible with the dynamic vegetation model, transpiration is
normalized by both vegetation cover and the time over which soil moisture loss is
calculated.
Major assumptions made in this model include the absence of seasonality of
PET and plant growth. Temporal variability in evaporative demand and in physiological behavior would certainly change the water balance and vegetation dynamics, in turn having some effect on erosion. Ascertaining how much effect is a
worthwhile pursuit, but is considered outside the scope of the present study.
2.6
Subsurface Flow
Subsurface lateral flow is a rare occurrence in dryer climates [Ridolfi et al.,
2003], though important where it does occur [Newman et al., 1998]. Combined
with run-on, subsurface lateral flow can provide a means for moisture to accumulate
downslope, fostering more abundant vegetation growth in zones of convergence. To
provide this additional degree of freedom, a simple model is employed, borrowed
from Cabral et al. [1992]. Where soil hydraulic conductivity is anisotropic, percolating moisture will have a tendency to move downslope. Cabral et al. decomposed
the corresponding flow vector, q,,, into horizontal and vertical components (Figure
2-5). Here, q,, is equated to drainage of soil moisture above field capacity (L(s)
from Equation 2.20). The subsurface flow paths are assumed to mimic the surface flowpaths. The proportion of drainage that is partitioned in the downstream
direction is:
qss,x = qss(cospsinr3)(ar - 1)
(2.36)
Figure 2-5: Decomposition of subsurface flow vector, q,ss, into vertical and downslope components, qss,z and qs,x respectively, within anisotropic soil, following
Cabral et al. [1992].
where 3 is the slope in degrees, and ar is the anisotropy ratio. If q,8,, leads to
saturated soil downslope, the excess is redirected as drainage locally. The maximum
fraction partitioned downstream occurs on slopes of 450, reducing for any change in
slope above or below this value (Figure 2-6). Soil depth is assumed to be sufficiently
deep so that no bedrock can force percolating water laterally.
2.7
Runoff, Runon and Infiltration
In arid and semi-arid landscapes, runoff is generally produced by the infiltration
excess mechanism. Bare soils are often sealed by the high impact from thunderstorm raindrops, causing much of the high intensity rainfall to be shed as overland
flow. This is juxtaposed with the prevalence of run-on, where the runoff thus generated flows onto a surface with high infiltration capacity, and infiltrates. The dual
processes of runoff and run-on are important in modulating the runoff and sediment
yield from a catchment.
The processes of runoff, runon, and infiltration are modeled in tandem. Water
flux available for infiltration is the sum of the local precipitation and the runoff
from immediately upstream areas. For portions of the landscape with no upslope
contributing area, rainfall is the only input. Water that does not infiltrate becomes
local runoff, which is used to determine the effective shear stress, rf, and which
contributes to the inflow immediately downslope. Runoff from a cell is determined
as follows:
Qout = (p - I)A + Qin
(2.37)
0.5
0.4
, 0.3
r 0.2
0.1
n
0
0.2
0.4
0.6
0.8
1
Slope (m/m)
Figure 2-6: Contribution of slope to the partitioning of total drainage (q,s)
downslope subsurface flow (qss,x).
to
where I is the infiltration, and Qi, is the inflow into the cell. Runoff across the
landscape is approximated as quasi-steady state, that is whatever runoff produced
upslope of a point is aggregated at one time, regardless of how far upslope the different contributions of flow originated. The duration of the flow equals the duration
of the storm.
Infiltration is constrained by three factors: (1) the combined rainfall and upslope
runoff rate; (2) the infiltration capacity; and (3) the existing soil moisture. This is
modeled mathematically as follows:
I = min{p + Q.n/A, Ic, n Zr (1 - s)/tr},
(2.38)
where Ic is the infiltration capacity, s is soil moisture, Zr is the depth of the root
zone, and t, is the storm duration. The first term represents the supply of water.
The second term embodies the infiltration excess model of runoff production. The
third term in effect limits infiltration to a rate that would just reach saturation by
the end of the storm, and thus embodies saturation excess runoff production.
Infiltration capacity, I,, is modeled after Dunne et al. [1991]:
Ic = Ic,b(1 - V) + Ic,vV
(2.39)
where Ic,b and Ic,, are the infiltration capacities corresponding to bare ground and to
fully vegetated ground, respectively. Identifying suitable values for Ic,b and Ic,, is not
trivial, in part because of constraints imposed by the dynamic vegetation model. If
vegetation becomes too sparse, infiltration would be too low, and vegetation could
not recover. The selection of suitable parameter values is explained later in the
chapter.
2.8
Rainfall
In the simulations, precipitation falls solely as rain, following a modified version
of the Poisson rectangular pulse model of Eagleson [1978]. The pulses represent
rainstorms with steady rainfall intensity, p (L/T), storm duration, tr (T), and spacing, tb (T), each sampled from independent exponential distributions:
Storm intensity f (p)= 1 -PI
P
Storm duration f(t,) =
T,
Interstorm period f(tb) =
e-tr/Tr
ebTb
Tb
(2.40)
(2.41)
(2.42)
where the three parameters P, Tr, and Tb are the mean storm intensity, storm duration, and interstorm period, respectively. The mean number of storms per year
is
Ns =
1
Tr + Tb
(2.43)
and the mean annual rainfall is
Pa = NsT,P.
(2.44)
The Poisson model is used in ecohydrologic and geomorphic analysis [eg Laio
et al., 2001b; Tucker, 2004], and geomorphic simulations [eg Tucker and Bras,
2000] because of its analytical tractability, its ability to mimic a wide range of climatic conditions, and the availability of monthly parameter values compiled for 75
sites across the continental United States [Hawk, 1992]. While the capacity exists
to model seasonality, we consider only a steady climate. We also consider rainfall to be spatially uniform. Interception losses are also neglected, which is largely
equivalent to a slightly wetter climate.
Despite its advantages, the Poisson model also has a significant disadvantage.
In reality, rainfall intensity varies throughout a storm. Intensity may exceed the
infiltration capacity for portions of the storm, but not for the entire storm. During
those times when the rainfall rate is high enough, runoff will be produced. However, by fitting a natural storm to a rectangular pulse, as is the method to obtain
Poisson model parameters, this natural within-storm variability is lost. The result40
ing mean storm intensity is less likely to exceed the infiltration capacity, and thus
produces less runoff, or possibly no runoff at all [Wainwright and Parsons, 2002],
of particular importance in arid and semi-arid climates.
The implications of this artificial outcome for landscape evolution modeling are
twofold. Greater infiltration leads to a wetter soil environment than would be expected, favoring greater plant growth. This in turn increases the critical shear stress
for sediment detachment and reduces the stress partitioned to the soil. In parallel,
reduced runoff leads to lower shear stress available to mobilize and transport sediment. Erosion would be significantly diminished as a result.
There are various approaches available to overcome this hurdle: (1) use an
"effective" infiltration capacity, calibrated to produce the observed runoff ratio over
the long-term; (2) scale the Poisson parameters to produce, in concert with realistic
values of infiltration capacity, the observed runoff ratio over the long-term; (3) vary
infiltration capacity spatially, so that some areas will have a capacity lower than the
rainfall rate and thus produce runoff [eg Brath and Montanari, 2000]; or (4) use
an alternative rainfall model that reproduces within-storm variability, such as the
Neyman-Scott or Bartlett-Lewis models [Rodriguez-Iturbe et al., 1987].
The most mechanistically faithful option is a combination of (3) and (4), but
this comes at a price of greater computational burden and data requirement. The
first option is the least faithful, by disregarding a parameter for which we have
field data - infiltration capacity. The second option, which is employed herein, conserves the field observations of infiltration capacity while adjusting what is already
a simplification - the rectangular Poisson storm model. By scaling the Poisson parameters appropriately, more emphasis is placed on those storms, and the attributes
of those storms, that are responsible for partitioning of rainfall between infiltration
and runoff. The scaling factor, a, is used to increase the mean storm intensity and
reduce the mean storm duration(Figure 2-7):
P' = aP
(2.45)
T' = Tr/a
(2.46)
The mean interstorm duration is also scaled to preserve the mean number of storms,
Tb = Tb + (Tr - Tr)
Calibration of a is presented in the following section.
(2.47)
Scaled Poisson pulse
>,
(0
7'
C
C
·· ,,
C15
4-
Storm hyetograph
C
CC
ed
[r"
Poisson pulse
r-i
i I
i
i
i
i•':
.. /,
I
I
LI
Time
Figure 2-7: Example hyetograph with corresponding Poisson pulse storm and scaled
Poisson pulse storm with a of 7.4.
2.9
Model Calibration
Where needed, model parameters are calibrated based on observations (Table
2.1) available from the CPER site. Final parameter values are recorded in Table 2.2.
What follows are details of how these parameters are calibrated.
2.9.1
Calibration: Infiltration Capacity
Only rough estimates of the two infiltration parameters are available. Furthermore, there is a constraint imposed on the values used by the dynamic vegetation
model. Because plant growth requires sufficient moisture, and infiltration decreases
with decreasing vegetation cover, it is possible that vegetation can never recover if
it becomes too sparse. This does not seem to be a reasonable outcome, though it is
more a consequence of model limitation than reality. Ic,b is thus selected in part to
avoid it.
Values for both bounds can vary widely. Ic,b in water-limited environments is often much lower than I,, because of surface sealing. When the soil is fully saturated,
Ic,v would exceed the saturated hydraulic conductivity of the porous medium, but
as the soil dries, I,,, would drop. In an absence of thorough field data to calibrate
this model, Ic,, is chosen to equal Ksat. Ic,b is chosen to equal lIc,,, a fraction that
Central Plains Experimental Range (CPER)
Location
321 mm
Pa
precipitationa
Mean annual
Annual potential evapotranspirationb PET 1254 mm
Tr 7 hours
Mean storm duratione
Tb 115 hours
Mean interstorm durationc
0.1
Runoff coefficient
sandy loam
Soil texturea
shortgrass steppe
Biome
blue grama
Dominant plant species
V 30%
Plant coverd
Z, 0.30 m
Rooting deptha
,w -4 MPa
Wilting pointa
V* -0.1 MPa
Onset of stressa
T, 30-300 years
Post-disturbance recovery timese
a Laio et al. [2001a].
b Sala et al. [1992].
Hawk [1992]. Mean of the monthly values for Denver, CO.
d Coffin et al. [1996]. Bare ground ranges from 60-80%.
e Coffin and Lauenroth [1989]. Values obtained from model output.
Table 2.1: Climatic, edaphic, and plant model parameters.
preliminary simulations suggests is unlikely to lead to the complete loss of vegetation.
2.9.2
Calibration: Rainfall
The value of the Poisson scaling parameter, a, is identified by simulating water balance at a point, and determining what value produces an acceptable runoff
coefficient over the long-term. The CPER site is used for the calibration (Table
2.1). The model incorporates the ecohydrologic, hydrologic, and rainfall models
presented above. Vegetation cover is kept constant at 30%, which is the observed
vegetation cover at the site (though it may not be the long-term equilibrium cover).
Figure 2-8 shows how the runoff coefficient varies with a. For Zr of 30 cm, a =
7.4 yields the desired runoff coefficient of 0.1. This is used as an approximation
because inclusion of subsurface flow and run-on may alter the runoff coefficient as
a function of catchment area.
2.9.3
Calibration: Dynamic Vegetation
Calibrating the dynamic vegetation model also uses a series of point simulations,
this time using a as determined above, and allowing V to vary. The objective is to
identify the values of kg and km that produce observed values of plant cover, V, and
a
0
2
4
6
cc
8
10
Figure 2-8: Dependence of the runoff coefficient, Q/MAP, on the Poisson model
scaling parameter, a, shows graphically how the appropriate value of a, that yields
QIMAP of 10%, may be determined. a = 7.4.
the time-scale of recovery from disturbance, T,. The calibration procedure begins
by identifying what combinations of kg and km yield equilibrium vegetation covers
consistent with those observed at the field site (30%). For each pair of kg and km
10 realizations are simulated. After equilibrium is attained, a further 200 years are
simulated, which are then used to provide an estimate of the resultant equilibrium
vegetation cover. Figures 2-9 to 2-13 depict the ensembles for kg from 0.2 to 1.0,
with L9 varying from 1.25 to 2.75. This ratio of independent variables is used
because inspection of Equation 2.12 shows that the two vary proportionally for a
given cover at equilibrium.
For ease of comparison, the ensemble means for each set of realizations are
plotted in Figure 2-14. The equilibrium vegetation covers for each ensemble are in
k
km
kg
that yields 30%
km
turn plotted in Figure 2-15 as they vary with •• . The value of -
vegetation cover may thus be determined graphically as depicted. This leads to a
relationship between kg and km (Figure 2-16), which shows what value km must
adopt, given the value of kg, if V is to equal 30%.
With the values of km determined for a given kg from Figure 2-16, a further set
of five ensembles are simulated, each with 10 realizations. The resulting ensemble
means are plotted in Figure 2-17. Equation 2.13 is fit to the data in Figure 2-17,
producing the least squares estimate of p. The response time, T,, is defined as the
time taken for vegetation cover to evolve from the initially disturbed state of 10%
to within 95% of carrying capacity. This is determined analytically with
1
TV = -lnI
fC\1
(-o + l,
44
(2.48)
0.8
I
gm
gm
0.6
kgm
/k = 1.75
k/k =1.5
k /k =1. 25
0.6
0.4
0.4
> 0.4
BsA
0.2
0.2
ftai ý1
A
0
200
A /3
200
400
U.8?
0.8
0.6
0.6
> 0.4
> 0.4
> 0.4
0.2
0.2
0.2
A
0
200
400
0
0
200
400
0
200
400
400
kgm
/k = 2.25
0.6
n
0
200
400
years
Figure 2-9: The annual mean (thick line) of ten realizations (gray lines) of dynamic
k varies from
vegetation cover evolving at a point. Zr = 0.30 m, kg = 0.2, and kg
1.25 to 2.75.
km
0.8
0.8
k /k
gm
0.6
= 1.25
0.6
0.8
kgm
/k =1.5
0.4
> 0.4
> 0.4
0.2
0.2
0
0
200
200
400
400
0
0.8
0.8
0.8
0.6
0.6
0.6
> 0.4
> 0.4
> 0.4
0.2
0
k/k
= 1.75
gm
0.6
0
200
400
200
400
0.2
0
200
400
200
400
years
kg
Figure 2-10: Description as above. Z, = 0.30 m, kg =0.3, and - varies from 1.25
km
to 2.75.
45
0.8
0.6
I
kgm
/k =1.25
> 0.4
A
Np1
0.2
I
IL "~J~`rT&~E~~,~ekAIYIY~
-w'TT~L
200
400
0.8
0.8
0.6
0.6
> 0.4
> 0.4
0.2
0.2
200
400
200
400
200
400
years
Figure 2-11: Description as above. Z, = 0.30 m, kg = 0.5, and kg varies from 1.25
km
to 2.75.
U.6
0.8
0.6
0.6
,,
U.0
k /k
g
=1.5
0.6
> 0.4
> 0.4
> 0.4
0.2
0.2
0.2
n
0
0.8
100
200
300
200
300
0
n
0
100
200
300
0
100
200 • 300
0
100
200
k /k =2
g
0.6
>0.4
0.2
L.
0
. I
100
300
years
Figure 2-12: Description as above. Z, = 0.30 m, kg = 0.8, and
to 2.75.
46
km
varies from 1.25
0.8
k /k =1.25
gm
0.6
> 0.4
A
> 0.4
•1
0.2
'4
0.2
200
0.8
k /k
k /k =1.75
> 0.4
0.2
i
i~ar~luru~s~yn~?~~a~8ar~lr~AlrRWW~
100
100
200
k /k
200
k /k
0.6
0.6
> 0.4
> 0.4
> 0.4
/
0.2
I
f
I
0
100
200
I
100
200
0.8
= 2.25
0.6
0.2
kkl
0
0.8
=2
gm
0.6
A~
0O
•J
100
kgm
/k =1.5
0.6
= 2.5
0.2
I
0
I
100
200
years
I
0
I
100
200
Figure 2-13: Description as above. Zr = 0.30 m, kg = 1.0, and kg
kg varies from 1.25
km
to 2.75.
0.8
0.6
> 0.4
0.2
n
0
200
400
200
400
0
200*
400
,n,
u.0
0.6
> 0.4
0.2
uo
0
100
200
300
100
200
years
Figure 2-14: Ensemble means for kg from 0.2 to 1.0, covering kg
k from 1.25 (the
bottom-most lines) to 2.75 (the top-most lines).
47
I
0.4
0.3
0.2
0.1
0
'
'
'
I · · ·I
I
K K
1
1.5
2
kgm
/k
k =0.8
0.4
0.3 -
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
2.5
2
kgm
/k
n
2.5
-
1
1.5
2
k gm
/k
k =
0.3
0.1
0.1
1.5
1.5
9
-
0.2
1
1
0.4
0.2
0
k =0.5
.
0.4
0
2
kgm
/k
1
1.5
2
k /k
gm
Figure 2-15: Dependence of mean equilibrium vegetation cover at a point on
kg
km
for kg from 0.2 to 1.0. The dashed lines indicate the value of kg for kg that yields a
km
cover of of 30%.
^0
1u
1i
-1
10 - 1
Growth coefficient, k
g
Figure 2-16: Relationship between km and kg for an equilibrium vegetation cover at
a point of 30%.
48
0.5
0.5
k = 0.2
0
0
0.5
0
0
9
200
400
0
0
0.5
k = 0.8
100
0.5
k =0.3
200
300
0
0
200
k =0.5
9
400
0
0
200
400
k =1
100
200
years
Figure 2-17: Least squares fits of Equation 2.13 to time-series of vegetation cover
for combinations of kg and km estimated to produce equilibrium vegetation covers
of 30%.
where f is the bound of 95%. With p corresponding to kg, T, may also be estimated
(Figure 2-18), allowing a graphical means of identifying the single value of kg that
yields both a cover of 30% and a recovery time of 50 years. 50 years is selected as
an intermediate value of estimated recovery times for blue grama. The corresponding value of km is determined from the relationship between the two parameters
established earlier (Figure 2-19). The calibrated values of kg and km are 0.54 and
0.30, respectively.
2.9.4
Calibration: Sediment Transport
The least certain parameter of the sediment transport model is kr, the detachmentlimited erodibility coefficient. A higher value enhances denudation; a lower value
produces steeper slopes. To identify what value to use, exploratory simulations were
run. A value was sought that yielded a realistic landscape - with realistic relief and
drainage density. Inspection of DEMs of the CPER site showed they would not offer
useful comparisons. That the topography consists of flat uplands and lowlands is
suggestive of disequilibrium, as does the time the simulations took to reach equilibrium. Simulations used values of a, kg, and km as determined above, an uplift rate
(U) of 0.5 rmm/year, a diffusion coefficient (kd) of 0.4, and T-r and T- of 20 and
180 Pa, respectively. To illustrate how k, is selected, three landscapes with different
values of kr are depicted in Figure 2-20, along with the slope-area relaionships. A
value of 0.00001 produces a landscape steeper than may be realistic, while a value
of 0.0001 produces one not steep enough. The value of kr chosen was 0.00004
yr 3/2m- 1 /2kg-3 /2, which produces an acceptable range of slopes degree on fluvial
incision.
49
I
101 I
.
.:....
·
I
I
I
1C0-1
Figure 2-18: The relationship between the recovery time, T,, and growth rate, kg,
for point simulations that yield equilibrium vegetation covers of 30%. For T, of 50
years, kg = 0.54.
E
0
100
0
7,
o
10
1
10- 1
Growth coefficient, k
g
Figure 2-19: Taking the value of kg determined graphically from figure (2-18), km
is determined graphically from figure(2-15).
EA-1
kr = 0.00001
100
150
100
10-1
*""
50
0
1000
1000
3
1n-
2
102
0 0
rB
kr = 0.00004
60
E
- 1.4
10
101
.*
E
40
20
0
1000
1000
- 1. 6
0o
10
0
o
10.8
3EE
..*g.
**
IC)6
104
102
0 0
3
I-€
kr = 0.0001
1000
0E,)
10-1
oi
0o
100
set,...
-
10
10-3
102
0 0
Drainage area (m2 )
Figure 2-20: Topographies, shaded by vegetation cover, along with their slopearea relationships. Lower kr produces a steeper and land incised landscape.
The landscape that appears most reasonable is that produced by kr of 0.00004
yr 3/ 2m - 1/ 2kg- 3/2
2.10
Summary
This chapter has presented the development and calibration of the model to be
used in the landscape evolution simulations of the subsequent two chapters. Final
parameter values are recored in Table 2.2. Physical, biophysical and ecological
processes that are pertinent in low-to-medium relief, water-limited grasslands are
encapsulated into a coherent mathematical framework. Calibration of parameters
is guided by a site in Colorado, though in no case is the model suited to predicting
the specific landscape's evolution but rather to provide general insight regarding
landscapes of this nature.
52
Spatial structure
Domain size
Number of active cells
Basic cell size
Geomorphology and sediment transport
Uplift rate
Diffusion coefficient
Detachment-limited erodibility coefficient
Transport-limited erodibility coefficient
Detachment-limited exponent
Transport-limited exponent
Bare soil manning's roughness
Vegetated manning's roughness
Reference vegetation cover
Reference: vegetation exponent
Bare soil critical shear stress
Vegetated critical shear stress
Climate
Annual potential evapotranspiration
Mean annual precipitation
Mean storm duration
Mean interstorm duration
Poisson storm scale factor
Soil
Soil texture
Saturated hydraulic conductivity
Drainage coefficient
Anisotropy ratio
1000 m by 1000 m
256
60 m
U 0.0005 m/yr
0.4 m 2/yr
k, 0.00004 yr 3/ 2m- 1/ 2kg- 3/ 2
kd
kf
a
p
n,
nvR
0.000001 yr4 m- 3/ 2kg- 5/2
1.5
2.5
0.0025
0.6
VR 1
0.5
w
TJ
Ts 20 Pa
Toy
PET
Pa
Tr
Tb
a
180 Pa
1254 mm
321 mm
7 hours
115 hours
7.4
sandy loam
25 mm/hr
0 13
ar 500
Ksat
Bare soil infiltration capacity
Ic,b
5 mm/hr
Vegetated infiltration capacity
Ic,v
25 mm/hr
Hygroscopic point
Field capacity
Sh
sfc
0.18
0.56
Ecology and physiology
Biome
Plant species
Rooting depth
shortgrass steppe
blue grama
Z, 0.30 m
Wilting point
O,
-4 MPa
Onset of stress
Plant stress exponent
Plant cover
Post-disturbance recovery time
Colonization rate coefficient
Mortality rate coefficient
V)*
q
V
T,
kg
km
-0.1 MPa
2
30%
50 years
0.54
0.3
Table 2.2: Model parameter values.
53
CHAPTER 3
VEGETATION AND SOIL
MOISTURE CONTROL
OF LANDFORMS
Vegetation influences sediment flux and landform development in a variety of
ways. To obtain a thorough, mechanistic understanding of these relationships it
behooves geomorphologists to pare down landscape complexity and focus on specific environmental conditions and processes. Here, water-limited grasslands are
the focus. These landscapes exhibit patchy vegetation cover, which is highly sensitive to changes in precipitation, mediated by the soil environment. The amount of
vegetation, combined with the precipitation and topographical form, govern sediment flux. How these interactions translate to catchment erosion and landform
characteristics is very much an open question.
In arid and semi-arid environments, an overarching factor for both biotic and
abiotic aspects of landscape development is climate. Grassland productivity displays
a strong dependence on mean annual rainfall [Sala et al., 1988]. Many studies
have also pointed to relationships between catchment sediment yield and annual
precipitation with non-linearities introduced by concomitant changes in vegetation
[e.g. Dendy and Bolton, 1976; Douglas, 1967; Langbein and Schumm, 1958]: The
most celebrated of these is that of Langbein and Schumm, who suggested sediment
yield peaked at an intermediate annual precipitation value because of the interplay
between increasing runoff and increasing vegetation.
Controls on vegetation extend also to characteristics of the plants themselves.
Hydrological and erosional effects of different species vary because of their life cycles and above- and belowground architecture. Variability in vegetation cover is
tied to a species' successional status and post-disturbance recovery, and this translates to effects on sediment flux. For example, erosional response to wildfires is to
some degree dependent on recovery of vegetation cover [Cerda and Doerr, 2005].
A control on both vegetation dynamics and water balance is rooting depth. Plants
with shallow roots have access to a more variable supply of water than are deeper
rooted plants [Lee and Lauenroth, 1994]. As a corollary, species that have evolved
in highly variable arid environments with no access to groundwater are more often
shallow rooted [Nobel, 2002]. Under the same climatic conditions, deeper rooted
plants exhibit less variable water stress and transpiration dynamics, in contrast to
their shallow rooted neighbors [Rodriguez-Iturbe et al., 2001a]. The geomorphic
impacts of roots are most vividly expressed in terms of slope and channel bank
stability [Schmidt et al., 2001; Simon and Collison, 2002]. Roots have also been
tied to channel morphology and gully erosion [Gyssels and Poesen, 2003; Toledo
and Kauffman, 2001] and soil creep [Roering et al., 2004]. Control of vegetation
and soil moisture dynamics may provide an alternative pathway for roots to impact
erosion and landform development.
Soil moisture, on which plants depend, is itself dependent on plants and on other
factors. Unvegetated surfaces decrease infiltration rates relative to their vegetated
counterparts, allowing moisture in effect to be redistributed by run-on. Subsurface
is also a means by which moisture is redistributed across the landscape. Lite et al.
[2005] and Pickup and Chewings [1996] both report an increase in vegetation
cover downslope, correlated with processes of moisture redistribution.
Numerical modeling provides an useful tool to investigate coupled hydrological,
ecological, and geomorphic processes in water-limited environments. Models provide the luxury of manipulating a system in ways that are impractical or impossible
in nature. In so doing, careful modeling can disaggregate physical process from
one another to identify their individual roles, and thus highlight those processes
deserving of further field study.
3.1
Model and Simulations
The numerical model presented in Chapter Two is used here to explore the evolution of landscapes in water-limited ecosystems. Quasi-equilibrium landscapes are
simulated from an initial condition of a plateau, 1 km by 1km (16 by 16 cells),
with a single outlet. For brevity, the final landscapes are henceforth termed 'equilibrium'. Both initial soil moisture and initial vegetation cover are random, and'
a random perturbation field is applied to the elevations as well. Simulations are
performed to answer three questions regarding landscape evolution:
1. What is the role of lateral moisture redistribution?
Simulations are designed to identify the effect of run-on and subsurface flow
on vegetation cover and topography. Vegetation differences are distinguished
by selectively switching on or off the two hydrological processes and simulating landscape responses for 100 years. Topographical differences are distinguished by comparing two equilibrium landscapes, one evolved subject to
lateral moisture redistribution, and one with the processes of run-on and subsurface flow disabled.
2. How do landscapesvary with mean annualprecipitation?
An array of landscapes are simulated under different mean annual precipita-
tion regimes. The nominal climate is the mean annual precipitation (MAP)
corresponding to the CPER site - 321 mm. Dryer and wetter climates are
simulated while maintaining all other model parameters constant, including
those related to vegetation. Climates differ only in their mean storm intensity, while the mean storm duration and number of storms per year remain
constant. Seven simulations are conducted, with MAP ranging from 241 to
963 mm (from three quarters of 321 mm to three times 321 mm). Landscapes
completely devoid of vegetation are also simulated along the climatic gradient
to provide a sense of the changes a biotic mantle has on the landscape.
3. How do vegetation characteristicsaffect landforms?
Vegetation attributes that are central to the present model are the dynamic
vegetation parameters (k, and kn), rooting depth (Z,), vegetation roughness
(nv,), and the contribution from vegetation to the critical shear stress for erosion (i-,,). Ultimately, because of the calibration procedure employed, the
response time-scale (T,), and carrying capacity (C), are fundamental parameters in place of k, and km. Simulations explore topographic sensitivity to
T,, to Zr, and to differences between grasses and shrubs which encapsulates
change in a combination of above parameters.
Landscapes are simulated until they attain equilibrium. Their topography is in
essence the static reflection of the dynamical interplay between external forcings
and internal processes. They avoid the confounding issues inherent in transient
systems, and better facilitate comparison among different systems.
3.2
Example of an Evolving and Evolved Landscape
Before examining how vegetation and the physical environment interact to produce landscapes of particular forms, it is fitting to first illustrate how a landscape
evolves, and how the physiography of an evolved landscape is quantified. Figures
3-1 and 3-2 consist of a series of snapshots of a landscape evolving from an initial condition of a plateau 60 m in height. Soil moisture, vegetation cover, and
minor perturbations to the topographic surface are assigned randomly. Incision of
the plateau progresses from the outlet, located at the origin, eroding an ever-larger
portion of the landscape over time. Uplift is acting continually, and is most apparent in the steady increase in elevation of portions of the landscape that are yet to
experience the wave of erosion expanding from the outlet. In time, the combination
of hillslope diffusion and fluvial sediment flux produces a landscape configured to
export sediment equally across the surface at a rate equal, on average, to the influx
of sediment from uplift. Both elevation and vegetation fluctuate thereafter, driven
by stochastic climate forcing, but have achieved a quasi-steady state.
Two important features of the evolving and evolved landscape are the greater
abundance of vegetation downslope, particularly in channels, and the degree to
2000 years
Initial landscape
^
^,
, 70%
o
u
- 60%
0
4.
'
6
4
2
50%
40%
1000
100
30%
100
11
00
00
5000 years
10000 years
8
6
4
2
1000
100
0 0
14
100C
0 0
Figure 3-1: Snapshots of an evolving landscape from the initial condition of a perturbed plateau of 60 m. Contours are at 5-m intervals, the axes are in meters, and
the surface is colored by vegetation density. The initial landscape is random - elevation perturbation about a mean, soil moisture, and vegetation cover. (Continued
on subsequentpage.)
20000 years
15000 years
8
6
4
2
1000
100
1(
100C
0 0
0 0
25000 years
37500 years
8
6
1 00
1000
1(
100C
0 0
75000 years
50000 years
8
6
4
2
1000
100
0 0
100C
1(
0 0
Figure 3-2: See Figure 3-1 for description.
which the landscape is incised by these channels. Figures 3-3 and 3-4 illustrate an
equilibrated landscape and its slope-area relationship. Slope-area diagrams are useful diagnostic tools for discerning geomorphic process dominance [Dietrich et al.,
1992]. For the processes considered here, diffused hillslopes are denoted by an increase in slope with drainage area, and fluvial regions by an approximate power-law
decrease (depicted as a line of negative slope in log-log space). The two diffusional
and fluvial data sets meet at a peak, which identifies the transition in process dominance between diffusion and fluvial sediment transport. Erosion for the fluvial
portion of the landscape is often expressed as
E = KAm
"S
(3.1)
where K is the erosion efficiency, A is drainage area, S is local slope, and m and
n are coefficients, though all may be considered variables. At equilibrium, erosion
must equal uplift, on average, so the variables in Equation 3.1 co-evolve so that this
is the case. Channel concavity, which describes how slopes change downstream, is
expressed as
9 = -m/n
(3.2)
In Figure 3-4 the diffusional-fluvial transition occurs between drainage areas
of 8000 and 9000 m2 , corresponding to a hillslope length of approximately 90
m. Within the fluvial portion of the landscape, the data may be further separated
into channels, whose drainage area increases geometrically, and fluvial portions of
hillslopes, whose drainage area increases linearly. The slope-area diagram in Figure
3-4 also shows that the mean cover increases from low drainages areas to high,
from a density of 30% on hilltops and ridges to 72% at the outlet. This is better
illustrated in Figure 3-5, which shows that slope is a better predictor of vegetation
than drainage area. Many of following simulations are devoted to ascertaining
which physical processes are responsible for the variation in vegetation cover and
the location of the diffusion-fluvial transition.
Because the processes of sediment transport are scale-dependent one landscape
is simulated with half the cell size - 30 m. Slopes for this finer topography are
steeper than for a cell size of 60 m, drainage density is greater, while concavity
remains the same (Figure 3-6).
3.3
Lateral Moisture Redistribution
To understand what causes vegetation to be structured the way it is, the first pair
of processes analyzed are those that control the redistribution of moisture across
the landscape - run-on and lateral subsurface flow. Three 100-year simulations are
conducted, each driven by identical climatic forcing and initialized by an identical
Vegetation cover (%)
30
40
50
Major channel
60
70
80
5m contour
Figure 3-3: Equilibrium landscape, shaded by vegetation cover. The heavily outlined polygons trace the major channels. Vegetation cover is more dense downslope.
10 1
Hillslope-fluvial
transition
E
E
els
I.
0
18
o
.J0
ea`
I
Vegetation cover
0ooo00000
i
- 2
30%0/
llJ
,w
45% 60%
......-.
,
75%
. ......
104
Drainage area
,
. ......
105
(m2 )
Figure 3-4: Slope-area relationship for the vegetated landscape with MAP of 321
mm. Denser vegetation is present at higher drainage areas. The hillslope-fluvial
transition occurs within the drainage area of 8000-9000 m 2 .
NO)
10
104
105
Drainage area (m2 )
10- 2
10 -1
Slope (m/m)
Figure 3-5: Time-averaged vegetation cover for cells of different drainage area (a)
and local slope (b). Circles represent the major channels, and dots the remainder.
-1
10
Cell size
E
*
E
3
I'
a)
O
_J I..
Sn
2-
....
I
10o3
.
......
I
.
.
10 4
Drinage area
.....
I
10 5
.......
106
(m2 )
Figure 3-6: Slope-area diagrams for MAP of 321 mm with cell sizes of either 60 m
(the standard size) and 30 m.
landscape (Figure 3-7a) that evolved under regular conditions. The simulations
differ from one another by the activity of run-on and subsurface flow. The control
maintains activity of both processes, while the other two have one or the other
disabled. After 100 years, the control vegetation cover resembles the pattern of
the initial landscape, though cover has become denser owing to more favorable
growing conditions in the latter 100 years (Figure 3-7b). Where subsurface flow is
switched off (Figure 3-7c), vegetation cover becomes homogenous, with a density
equal to that on hilltops and ridges of the control landscape. Where run-on is
switched off (Figure 3-7d) the vegetation patterns remain, though cover is slightly
less dense than in the control case. This demonstrates that, subject to the prescribed
model, structuring of vegetation is achieved by redistribution and accumulation of
moisture by subsurface flow and not by run-on. However, run-on does accentuate
any existing differences in vegetation cover.
Run-on plays a subordinate role to subsurface flow at this scale because when
infiltration excess runoff occurs in one place it often occurs elsewhere as well. In
such cases runoff cannot become run-on. Subsurface flow, on the other hand, is
inhibited only by soil saturation in the downslope cell, which in water-limited environments is uncommon [Ridolfi et al., 2003], so any such flow that does occur will
most likely augment soil moisture immediately downslope. Cascading subsurface
flow downslope, when moisture exceeds field capacity, combined with topographical convergence leads to great water supply to downslope regions and greater vegetation growth.
_ __I
___
_I
r····
I uuu
1 Il II
~___
U 70%
800
800
c 60%
600
600
50%
400
400
S40%
200
200
1000II
0
30%
A
n
v
I UV1
500
1000
600
400
200
800
500
1000
500
1000
800
600
600
4OO
400
200
200
t3
0
0
10001~
uuu
I
800
A
·
U
0
A
500
1000
t'%
0
·
Figure 3-7: (a) Initial vegetation cover for the lateral moisture redistribution simulations. (b) Vegetation cover after 100 years vwith hydrological processes unchanged. (c) Vegetation cover after 100 years with subsurface flow switched off.
(d) Vegetation cover after 100 years with run-on switched off. Increases of cover
downslope is dependent on subsurface flow. Run-on only marginally amplifies existing differences in cover.
To investigate the long-term implications of moisture redistribution for the landscape a simulation with redistribution is compared to one with neither run-on nor
subsurface flow. Figure 3-8a juxtaposes the slope-area relationships for each landscape. Slopes within the hillslope region are the same, as is drainage density, but
the fluvial portion of the landscape with redistribution has a lower concavity (the
slope of the fluvial data in log-log space is less steep), and the mean elevation is
greater (21 m compared with 15 m).
Surface hydrology is also altered by subsurface flow, because when cascading
subsurface moisture does lead to saturated conditions, infiltration cannot occur and
runoff must increase. This is a small but tangible effect in the simulated landscapes.
Figure 3-8c shows the relationship between drainage area and mean runoff for all
storms (including those that produce no runoff). When both mechanisms of lateral
redistribution are disabled the relationship is a power law. When present, subsurface flow causes the relationship to deviate at higher drainage areas, producing
greater runoff. Expansion of this data in Figure 3-8d shows that the fluvial portions of the hillslopes deviate the most. This is caused by a greater accumulation of
subsurface lateral flow resulting from above-slope cells being steeper on average.
Reflecting the results from the 100-year simulations, Figure 3-8e shows vegetation cover increases downslope with the inclusion of redistribution but not without.
This translates into a downslope decrease in the roughness coefficient, kt, with redistribution. This longitudinal decrease in kt overwhelms any increase in runoff,
leading to a longitudinal decrease in erosion efficiency and corresponding steeper
slopes. The differences in channel concavity therefore arise from the effect lateral
subsurface flow has on vegetation growth.
3.4
Mean Annual Precipitation
Rainfall is the source of moisture for vegetation growth as well as the source of
water for surface and channel runoff. Vegetation and runoff have opposite effects
in terms of erosion efficiency, and these effects are liable to change across climatic
gradients. To investigate any shifting dominance between vegetation and runoff,
simulations were performed in which the only parameter varying is mean storm
intensity - mean annual precipitation, MAP, ranges from 241-963 mm (3/4 to three
times the base MAP of 321 mm). Landscapes evolved under different climates differ
distinctly in both topography and vegetation. Mean elevation rises from a low, at
low MAP, to a high, at intermediate MAP (Figure 3-9a). Further increases in MAP
lead to the successive drop in mean elevation. This contrasts with monotonically
increasing catchment vegetation cover (Figure 3-9b).
The explanation for the dependence of elevation on annual rainfall is best considered in terms of erosion efficiency. For a given rick uplift rate, equilibrium landscapes with greater erosion efficiency leads to lower slopes, and vice versa. Thus, a
climate that fosters greater erosion efficiency will be lower, and any trend in mean
-1
10
.4
10-1
10-1.5
10-1.6
10
10- 2
10
3
104
105
106
105
10- 1
10-2
10- 2
10
10
-3
-4
103
104
105
105
106
3.5
Qb
3
a)
0
000
*
4
Ooo
*0
2.5 c0
o
0
30
3
10
104
105
Drainage area (m2 )
106
103
104
105
6
10
Drainage area (m2)
Figure 3-8: Comparisons of the longitudinal characteristics of landscapes evolved
with and without moisture redistribution: (a) and (b) slope; (c) and (d) runoff; (e)
vegetation; and (f) roughness coefficient.
elevation along a climatic gradient (all else being equal) may be interpreted as
changes in erosion efficiency. Erosion efficiency represents the cumulative effects
of runoff and vegetation cover. It is greater with more runoff, and less with more
vegetation. The monotonic increase in mean catchment vegetation cover translates
to a similar increase in critical shear stress (Figure 3-9e), which would contribute
to a drop in erosion efficiency all else being equal. Additionally, the increase in
vegetation increases the hydraulic roughness, reducing the effective shear stress
experienced by sediment. For low MAP, this is expressed as a sharp drop in the
roughness coefficient, kt (Figure 3-9c), which represents the contribution of soil
and vegetation roughness to effective bed shear stress (Equation 2.6). As vegetation cover increases further, kt falls far slower. Any drop in kt, however, reduces
erosion efficiency.
In contrast to vegetation, increases in annual rainfall are associated at first with
a decrease in catchment runoff then a marked increase (Figure 3-9d), translating
to first a decrease in erosion efficiency then to an increase. This dip is associated
with the sharp rise in vegetation cover that augments infiltration at the expense
of runoff, consistent with observations of streamflow following vegetation change
[Brown et al., 2005]. As the incremental increase in vegetation subsides, runoff
begins to swell.
The non-linearity of the relationship between MAP and mean evelation may be
traced through the components of the sediment transport laws to identify which
physical processes are at the root of the behavior. The first fact to consider is that
erosion proceeds according to excess shear stress - the difference between effective
bed shear stress (rf) and critical shear stress (Tcb). What is plotted in Figure 39e is the temporal and spatial mean values for shear stress for a 1000-yr period.
As Tucker and Bras [2000] showed, variation in bed shear stress is also important
because a greater variability will lead more often to a non-zero excess shear stress,
and thus more erosion will take place. While the temporal mean Tcb may exceed
Tf, erosion occurs because the one does not always exceed the other. The nonmonotonic trend seen in z is reflected in rf, while Tcb simply climbs monotonically.
It is therefore Tf that is the proximal cause of the non-linearity in elevation. Tcb
merely shifts the non-linearity, so the peak in z occurs in a drier climate than the
trough in -s,
and so z in wetter climates is lower than the driest climates despite rf
being higher.
Effective bed shear stress, Tf, may in turn be decomposed into contributions
from discharge (Q), the coefficient relating to surface roughness (kt), and slope,
which is reflected by elevation (see Equation 2.5). The non-linearity is present in
Q while kt simply decreases monotonically. The trough in Q is spread across a
wider range of MAP (281 - 481 mm) than the trough in Tf (401 - 481 mm). This
shift results from the decrease in kt towards 481 mm. The sharp decrease in z
between 281 and 241 mm results from the pronounced increase in kt by two orders
of magnitude.
The reason for the dip in Q is because in these climates vegetation redirects most
^_
,,
10'U
20
>-
15
i
d
0%
200
400
600
800
400
600
800 1000
r"
10
5
>,
0
200
400
600
800
1000
- 3
10
1
o
1000
~nn
2uU
2
180
160
101
140
10
U)
120
(D 120
200
400
600
800
1000
I-,
L
a)
mC
C
2Y
A%
0
200
n
400
600
800
MAP (mm)
1000
200
MAP (mm)
Figure 3-9: Temporal averages over 1000 years of equilibrium simulations across
the MAP gradient. (a) Catchment elevation. (b) Mean catchment vegetation cover.
(c) Mean catchment roughness coefficient, kt. (d) Mean outlet discharge per storm,
including storms that do not produce runoff. (e) Mean catchment effective bed and
critical shear stresses.
of the rainfall into infiltration. The sharp rise in V helps to suppress Q, even though
MAP increases, but once the expansion of vegetation slows, runoff begins to swell,
7• climbs, and z decreases. The transition from vegetation dominance to runoff
dominance occurs at V of 50%, as does the peak in z. The peak represents the
transition from decreasing erosion efficiency to increasing erosion efficiency. The
decrease comes primarily from reductions in runoff because of the hydrological
influence of vegetation; the increase comes from vegetation's diminishing ability
to restrain runoff. The presence, and perhaps even location, of the peak is not
affected by the sharp decline in roughness coefficient as vegetation first starts to
appear, though this precipitous decline does suggest the model is overly sensitive to
vegetation cover at low values, and other factors such as form roughness and stones
should be considered.
While the concepts are similar, this explanation contrasts with that offered by
[Langbein and Schumm, 1958] to explain their sediment yield data. Langbein and
Schumm proposed that below a critical MAP, increases in rainfall would lead to a
greater increase in runoff to drive erosion than it would an increase in vegetation to
resist the runoff, and so erosion rates would climb. Conversely, above this threshold,
they suggested increases in rainfall would foster such a dense cover of vegetation
that the erosive power of the runoff would be greatly diminished. What analysis of
the present numerical results suggests is that vegetation is not the dominant factor
above the threshold but below it, and that runoff is not the dominant factor below,
but above.
Inspection of the slope-area relationships of these landscapes shows that those
landscapes with lower elevations have greater drainage densities (Figure 3-11) drainage density is inversely proportional to mean elevation. The hillslope-fluvial
transition is non-existant for the lowest MAP (241 mm), which is entirely fluvial. The transition is the greatest for intermediate MAP (401 mm), and therefore
drainage density is the lowest. The transition drops again for higher MAP. This is
exactly the opposite trend from that modeled by Moglen et al. (1998). Moglen
et al. derived an analytical expression for drainage density based on the position
of the hillslope-fluvial transition in slope-area diagrams. Using the relationship for
erosion suggested by Langbein and Schumm [1958], Moglen et al. then related
drainage density to MAP (Figure 3-10). This resulted in a peak in drainage density
at 300 mm, not a trough as is predicted by the present results. Because Moglen et
al. based their model on results of Langbein and Schumm, it is not surprising that
if the present results disagree with one that they also disagree with the other.
As was seen when the effects of moisture redistribution were studied, the slopearea diagrams also show differences in concavity. For MAP of 241 mm, concavity
is high, but as soon as rainfall is sufficient to promote vegetation growth, at 281
mm, concavity drops to its lowest level. Further increases in MAP bring with them
gradual increases in concavity until 963 mm, when it is equal to that for 241 mm.
Because concavity reflects the longitudinal changes in erosion efficiency, consider
the spatial variations of vegetation, roughness coefficient, and runoff (Figure 3-12
and 3-13), and for the purposes of the analysis compare all concavities with that of
241 mm. When there is no vegetation, there can be no longitudinal variations in
roughness coefficient, kt. As soon as vegetation appears in the presence of moisture
redistribution, kt is no longer uniform. The trends seen in kt in Figure 3-12 are
reflected by the differences in concavity of the slope-area relationships in Figure
3-11. Concavity under 963 mm resembles that of 241 mm because kt shows little
sensitivity to differences in vegetation cover when this cover is high. The models of
lateral flow and of partitioning roughness between vegetation and soil are critical
to these differences.
In studying the effects of vegetation on landscapes it is important to make comparisons with completely unvegetated landscapes. The previous simulations are
thus juxtaposed by landscapes evolved under the same climatic gradient but with
ILL-
............
..
E
................
.......
I
f --
I
-r
10
4%
@9oC
I
75~
A
"
0
_
1
20
i
40
__~
_
P
0o
80
100
12
Efective Antn Preepitation f(m)
i
140
W
Figure 3-10: Relationship between drainage density and mean (or effective) annual
precipitation as derived by Moglen et al. (1998). The present results suggest the
inverse trend.
the complete exclusion of vegetation: infiltration capacity remains at the lowest
level, there is no contribution to surface roughness or critical shear stress from
plants, and no transpiration takes place. The outcome is that instead of a peaked
relationship between mean elevation and mean rainfall there is an exponential decrease (Figure 3-14a). Mean elevation for low MAP (241mm) is essentially the same
as with the corresponding vegetated simulation, because the annual rainfall is too
low to sustain any significant cover. As MAP increases, elevations of unvegetated
landscapes consistently decrease, rather than the peaked trend with vegetation.
This highlights the effect vegetation has in modulating the climatic-driven nature
of landscape form. An increase in elevation with MAP is thus a consequence of
vegetation by retarding erosion. This influence is overwhelmed as the incremental
increase in vegetation cover becomes less and less and the roughness coefficient
changes much more slowly, while runoff steadily climbs. To the right of the elevation peak, the trend resembles that of unvegetated landscapes that share these
changes in runoff.
3.5
Vegetation Characteristics
The final set of simulations are concerned with the vegetation itself, and with
attributes that have the potential to modify hydrological and sediment fluxes. These
are the response time-scale, T,, rooting depth, Z,, and plant life form, in which
broad distinctions are made between grasses and shrubs.
10-1
10- 2
E
E
Qa
0
0
0
10
S-4
10 4
106
Drainage area (m2 )
Figure 3-11: Slope-area relationships for MAP of 241, 281, 321, and 963 mm. The
drainage area where the transition from diffusion-dominance to fluvial-dominance
occurs is the greatest for 321mm, and therefore drainage density is the lowest.
Concavity is the lowest for 281 mm, increasing with more and less rainfall.
100
#..ji.•
•
30u
tII
90
290
280
80 - +H-f
70
-
O 241mm
270
* 281 mm
O 321 mm
260
E1
m n[I
INI lnlmmmmll
E
60
50
40
+'
I
QRR mm
-
rrru
-- vv
-
-
-
C
a,
30 - GM8
--
_
S
Si
o-
0.5
a,
e.
o•
0
o
C.,
U,
20
0.4
CMML
U,
C,
10
•
0.3
cc
=
104
Drainage area (m
+mlt~ynrWwHYW-t~
+I
v.
106
106
2)
e•
Drainage area
(m2 )
Figure 3-12: Longitudinal variations of vegetation cover and roughness coefficient
across the climatic gradient.
· I 1· · ·II
-I
100
mm
[]
o 241
241mm
·
· · · ·· ···
I
281 mm
0 321 mm
+ 963 mr
O 10-1
E 10-2
10
S10,
103
104
105
Drainage area (m2 )
106
Figure 3-13: Longitudinal variation of mean storm runoff across the climatic gradient.
Response time-scale (years)
Vegetation growth parameter
Vegetation mortality parameter
Tv
kg
km
25
0.86
0.38
50
0.54
0.30
75
0.32
0.14
100
0.25
0.11
Table 3.1: Dynamic vegetation model parameters calibrated for different T,.
3.5.1
Recovery Time-Scale, T,
The first of these characteristics to be considered is the dynamic response timescale, Tv. The nominal value used thus far has been 50 years. To explore the sensitivity of the landscape to this parameter, the dynamic vegetation model parameters,
kc and k,, were re-calibrated for Tv of 25, 75 and 100 years, while maintaining
30% vegetation cover at a point (Table 3.1; see Chapter 2). Because subsurface
flow augments vegetation cover, which in turn has a significant effect on erosion
that could overwhelm any effect of T,, simulations both with and without lateral
moisture redistribution are conducted so as to isolate the effect of Tv alone.
Figure 3-15 shows the differences in elevation and vegetation cover among the
simulations. The most notable trend is for greater vegetation cover and elevation
with the inclusion of subsurface flow, as expected. While the vegetation cover appears roughly constant across T,, a slight increase in z is apparent. These trends
are inspected in more detail in Figure 3-16 for the simulations without lateral moisture redistribution. The question to ask is whether the trend in elevation across
the rooting depth simulations can be attributed with enough certainty to rooting
^"r
U.zo
-,
E
E
0.2
CD
-
1
UJ
-
0.15
c)
0.15
0
0.05
C
a)
a)
0
u
u)
2.5
2.5 E
CO)
E
v
2•)
(D
c,)
CU
0C,
-
Cl, -~
2 o')
1.5
c.
1.5 L)
1-o
1c
0.5
CU
(D 0.5
€3
0
200
400
600
800
1000
MAP (mm)
Figure 3-14: Mean catchment elevations (a) and discharge (b) for vegetated and
unvegetated landscapes across a climatic gradient. Reported discharge is the mean
for all storms, including instances when no flow occurs.
depth alone. On closer inspection, mean catchment vegetation cover is not precisely constant among simulations (Figure 3-16b). This is not a sampling problem;
when these data were re-sampled at a different time after the landscape achieved
equilibrium, the same trend appeared, rather the differences arise from the imprecise nature of the calibration. This trend is reflected in the roughness coefficient
(Figure 3-16c) and critical shear stress (Figure 3-16e). However the trend is not
fully reflected in mean outlet discharge (Figure 3-16d). Consider T, of 25 and 75
years - the values of V are very close, and yet those for discharge are not. If more
vegetation were the only factor in reducing runoff, the pattern in discharge would
be different. The pattern in effective bed shear stress (Figure 3-16e) reflects those
of discharge and roughness coefficient, and the pattern in mean elevation (Figure
3-16a) in turn reflects those of the bed and critical shear stresses. The increase in
elevation from 25 and 50 years to 75 and 100 years thus appears to follow from
differences in discharge that do not arise from inaccuracies in fitting the vegetation
parameters, kg and kin, though this conclusion is not absolutely certain because of
the non-linearities of the interacting processes.
If discharge is indeed on average less where vegetation responds to environmental conditions more slowly, while the long-term mean cover remains constant, what
could be the physical explanation? The answer must lie in temporal relationship
between plant growth/mortality and runoff generation. Having switched run-on
and subsurface flow off, the phenomenon must be local, and because rainfall is
spatially uniform this runoff anomaly most likely results from differences in infiltration capacity at the time of runoff-generating storms. Plants with short response
times grow faster when there is sufficient water, and die faster when there is not.
Growth of these plants more often follows the larger storms, and therefore during
these storms vegetation cover must be lower. Slower responding plants also grow
more following large storms, but because they grow more slowly and mean cover
is maintained constant, their density during the storm cannot be as low as with the
faster growing plants. This leads to lower infiltration capacities during large storms
for low T,, therefore greater runoff and lower elevations, as the results indicate.
3.5.2
Rooting Depth, Zr
A further plant attribute studied is rooting depth, Z,. Thus far a value of 30
cm has been used, but to assess landscape sensitivity to this parameter, vegetation
model parameters are again re-calibrated for Zr of 15 and 60 cm (Table 3.2). Because the vegetation parameters and the Poisson storm scaling factor, a, depend on
rooting depth, all three must be re-calibrated. Again, subsurface flow is disabled to
help isolate effects of Zr.
As with T,, V appears roughly invariant across Zr, while there is a strong decrease in z with Z, (Figure 3-17). However, closer inspection of the components of
sediment transport relations shows that vegetation cover increases across the three
simulations (Figure 3-18b). This trend is reflected in the roughness coefficient (Fig-
S50
> 40
0
0
c
.o
30
S 20
4-
a)
>
10
0v
25 yrs
50 yrs
75 yrs
25 yrs
100 yrs
50 yrs 75 yrs 100 yrs
Figure 3-15: Mean elevation (a) and vegetation cover (b) for landscapes evolved
under vegetation with response time-scales of 25, 50, 75 and 100 years. Dark
bars represent simulations with lateral moisture redistribution, light bars without.
The upper and lower bounds indicate the maximum and minimum spatial mean
elevation during 10,000 years (sampled every 500 years).
Rooting depth (cm)
Poisson scaling parameter
Vegetation growth parameter
Vegetation mortality parameter
Zr
a
kg
km
15
7.2
0.51
0.25
30
7.4
0.54
0.30
60
7.4
0.61
0.21
Table 3.2: Dynamic vegetation model parameters calibrated for different Zr.
h
h
~nr
10l.3
nr\
r
U.
0O
C
Cu
16
1U
o
15.5
0
30
0'
0
Iv
0
50
100
,-
>
LV·V
100
0
,,
/0
SU)~
10
52 1
00.521
74
U)rc
CO 72
0
100.518
0
CD
70
U)
)
U)
L
, U.126
a)
.c
E 0.124
a-
("
2
0.122
)
U)
68
66
64
--- Bed shear
62
0.12
-- A-
Critical shear
an
0
50
100
0
50
100
Response time-scale, Tv (years)
Figure 3-16: Temporal averages over 1000 years of equilibrium simulations across
T,. (a) Catchment elevation. (b) Mean catchment vegetation cover. (c) Mean
catchment roughness coefficient, kt. (d) Mean outlet discharge per storm, including
storms that do not produce runoff. (e) Mean catchment effective bed and critical
shear stresses.
cn
17
16
C
40
0
= 15
rc 30
D 14
T
I
T
T
15 cm
30 cm
60 cm
I
20
13
>
12
I,-
10
v
15 cm
30 cm
60 cm
Figure 3-17: Mean elevation (a) and vegetation cover (b) for landscapes evolved
under vegetation with rooting depths of 15, 30 and 60 cm. Lateral moisture redistribution is disabled. The upper and lower bounds indicate the maximum and
minimum spatial mean elevation during 10,000 years (sampled every 500 years).
ure 3-18c) and critical shear stress (Figure 3-18e), but not in the discharge (Figure
3-18d). As with the T, simulations, differences in V may have arisen from the imprecise calibration of kg and kin, but also of a. The trend in discharge with Z, better
reflects the values of a than it does vegetation cover - higher values of a encourage more runoff. However, while discharge is the same for Zr of 30 and 60 cm,
the mean elevations differ by 1 m. The lower elevation for 60 cm is the opposite
of what would be expected from the trend in the roughness coefficient and in the
spatial and temporal mean shear stresses. Nor does the elevations reflect a trend
in the variance of effective bed shear stress (Figure 3-19c), even though the variance of vegetation and outlet runoff both increase with Z,. The physical cause for
the greater erosion efficiency with 60 cm is likely the same as for T,. Because the
moisture content of a deeper root zone is lower than for a shallower root zone, the
vegetation must compensate by growing more rapidly, when moisture does arrive,
in order to satisfy the constraint of 30% vegetation cover. Furthermore, because
vegetation grows preferentially after heavy rainfall, cover of more variable vegetation must be lower during that rainfall, and erosion would be greater and elevations
lower.
3.5.3
Life Form: Grasses vs. Shrubs
The last characteristic of vegetation to be considered is life form, and the collection of associated attributes. A shortcoming of the simulations along a climatic
gradient is that vegetation parameters remained constant. In reality, as the climate
becomes drier, grasslands would give way to shrublands, with markedly different relationships with hydrological and geomorphological phenomena [Abrahams et al.,
1995]. Bare ground within shrublands is more interconnected allowing for more
E
o
17
16
C
a)
15
t-
14
0
20
40
60
20
40
60
E~a1
U,
Cr 0
0
n" oa
la,
0.13
CO)
E
0)
2)
-a
0.12
60
0.11
-e-- Bed shear
-A-- Critical shear
C,
5
U.]]
*
0
20
40
60
r.5r
0
I
20
I
40
60
Rooting depth, Zr (cm)
Figure 3-18: Temporal averages over 1000 years of equilibrium simulations across
Z,. (a) Catchment elevation. (b) Mean catchment vegetation cover. (c) Mean
catchment roughness coefficient, kt. (d) Mean outlet discharge per storm, including
storms that do not produce runoff. (e) Mean catchment effective bed and critical
shear stresses.
x 10- 18
x 10
R
9 c-1
L.
o2
E
ca1
3
S8
Z
2
0
50
100
0
50
100
7
0
50
100
Rooting depth Zr, cm
Figure 3-19: Variance of catchment vegetation cover (a), outlet discharge (b), and
catchment effective bed shear stress (c), as determined from 1000 years of data.
Rooting depth (cm)
Vegetation growth parameter
Vegetation mortality parameter
Critical shear stress for V = 100%
Vegetated manning's roughness
Zr
30
kg 0.54
km 0.30
7,,
90
nv, 0.3
60
0.61
0.21
90
0.3
Table 3.3: Model parameters for the two sets of shrub simulations.
concentrated runoff and erosion. While values for model parameters are far less
known for shrublands than for grasses, an attempt is made to capture the more
pronounced differences. In the forthcoming simulations using shrubs both the critical shear stress and vegetation roughness are halved, rooting depth is either 30 or
60 cm, growth and mortality parameters are the same as with grass (dependent on
rooting depth), and infiltration capacities are the same (Table 3.3).
The pronounced geomorphic diffeirence between grass and shrubs is that landscapes evolved under the latter are substantially lower in elevation and slope (Figure 3-20). This is generally due to the lower resistance to erosion imparted by the
vegetation, but for the case of 281 mm, it is because there is no vegetation present
at all. The peak in elevation for grasses and shrubs with rooting depth of 30 cm
is the same, but when shrubs' root extend twice as deep, this peak shift from 321
mm to 401 mm. A consequence of a more depressed landscape under shrubs compared to grass is that when the climate is too dry, all vegetation dies and landscape
becomes completely eroded. This results from variation in subsurface flow, as does
the shift in peak in elevation with deeper roots.
Subsurface lateral flow depends on the magnitude of the slope. The fraction
of percolating water that is directed laterally is maximized at a slope of 450. As
slopes decrease, so too does this fraction. Consider the landscapes with grass and
with shrubs of 30 cm rooting depth and with annual rainfall of 281 mm. Because
the rooting depth is the same, and the same average V and T, are being used,
they share the same kg and km. However, the shrub-covered landscape is more
dissected and flatter, and completely devoid of vegetation. Because subsurface flow
is responsible for the accumulation of moisture downslope, which supports higher
vegetation cover, lower slopes lead to less subsurface flow, less augmentation of
vegetation, and eventually no vegetation at all.
A deeper rooting zone also inhibits subsurface lateral flow, because saturated
conditions are reached less often. It was shown earlier that downstream increases
in runoff resulted from subsurface flow and saturated soil, but with a deeper root
zone, runoff is suppressed. The transition in control of erosion efficiency from
vegetation to runoff is thus shifted to wetter climates, and the peak in elevation
moves accordingly.
While the erosive response of landscapes occupied by shrubs as opposed to grass
is realistic, their barrenness under the dryer climate is not. This highlights a shortcoming in the dynamic vegetation model, and possibly to a lesser extent the soil
moisture water balance model. The field work required to support such model
improvement is sparse, but to understand the geomorphic evolution of such landscapes, further study of their hydrological and ecological nature and a more accurate representation in numerical form are important.
3.6
Discussion
A common thread running through the results is the importance of erosion efficiency in determining the landscape characteristics. In conjunction with the rate
of baselevel change, erosion efficiency sets the slopes in the fluvial portion of the
landscape, and because rates of diffusion are unchanged, it also sets the drainage
density. Erosion efficiency encapsulates multiple effects arising from hydrological
and ecological processes, the most important of which appear to be augmentation
of critical shear stress and form drag, and diminished runoff. The shifting balance
among the different contributions to erosion efficiency are responsible for the nonlinear trend in catchment elevation along a climatic gradient.
The trend in elevation with climate is reminiscent of the curve generated by
Langbein and Schumm [1958], as is the explanation offered to explain the trend.
However, there are two fundamental differences with Langbein and Schumm's work.
The first is that they reported sediment yield, which must be invariant for equilibrated landscapes with equivalent rates of baselevel change. The second relates
to the explanation they offer for their data. Their narrative is more a reference to
changes in erosion efficiency than to changes in erosion, because drainage area and
slope have been disregarded (see Equation 3.1). It is thus important to distinguish
between the data and the explanation. They claimed vegetation is subordinate to
runoff for dry climates, and thus sediment yield increases with mean annual precipitation; for wetter climates the more abundant vegetation resists the increased
00
Mean annual precipitation (mm)
Figure 3-20: Mean catchment elevation and vegetation cover for grass and shrubs
across the climatic gradient.
erosivity of higher runoff, and sediment yield drops. The controlled simulations
presented here provide a different description of changes in erosion efficiency with
climate. Increasing rainfall in drier climates sees a drop in efficiency because of the
large increase in vegetation cover and concomitant reduction in runoff; the former
results to a significant degree from the model of roughness partitioning. Increases
in rainfall above a threshold fail to produce a vegetation response to suppress the
augmentation of runoff, and erosion efficiency increases. The shift in dominance
between vegetation and runoff is responsible for a peak in elevation of landscapes
across climatic gradients, corresponding to a trough in drainage density. This peak
occurs between MAP of around 320 and 480 mm. The peak suggested by Langbein
and Schumm is around 300 mm. The peak in sediment yield reported by Dendy and
Bolton [1976], based on data from the same region as the present study, is around
500 mm. The similarity among these peaks highlights the potential of extending
the current equilibrium simulations to explore transient conditions, which may be
capable of generating climatic differences in sediment yield, even where baselevel
fall is invariant.
The simulated trend in drainage density differs from that suggested by Moglen
et al. (1998). Instead of a peak in drainage density, as Moglen et al. hypothesize,
the current simulations produce a minimum. The likely cause for this disagreement
is that Moglen base their analysis on Langbein and Schumm, which the present
results suggest is incorrect. However, Abrahams [1984] produced data on drainage
density as a function of mean annual precipitation. The most pronounced trend was
for drainage density to decrease from a high for the driest of climates, reaching a
minimum between 400 and 500 mm, and then to increase as the climates becomes
wetter still. The current study suggests the dip in drainage density would occur
for 321 mm, though this depends on the interplay between vegetation growth and
runoff production, which is a function of vegetation characteristics.
The effect of hydrological processes in these landscapes is of paramount importance. Subsurface accumulation of moisture fosters denser vegetation downslope.
Local plant effects on infiltration integrate to substantial changes in hillslope and
catchment runoff. Landforms adjust to both influences accordingly. Landscape evolution simulations by Tucker and Bras [1998] also showed sensitivity to the prevailing mechanism of runoff generation, though vegetation was not considered. One
means by which vegetation controls the hydrological fluxes is via root-water uptake
over its rooting depth, and when this was varied slight geomorphic changes were
detected. This suggests that variations of soil depth, too, would lead to hydrologically mediated differences in geomorphic behavior if the depth were to constrain
rooting or hydrological fluxes.
There were also slight geomorphic differences when the vegetation response
time-scales was varied. However, along with rooting depth, it is impossible to isolate
the exact cause of the geomorphic change, because not all parameters are mutually
independent. The calibration method assumes a mean vegetation cover of 30% for
hilltops and ridges, and assumes a specified recovery time. If vegetation parameters
were not re-calibrated, a different rooting depth would change the vegetation cover
which itself is known to affect erosion. On the other hand, if the vegetation parameters were re-calibrated, as they were here, the vegetation cover would remain
the same but the dynamics of plant growth and mortality would change. These
problems arise because the study is attempting to isolate variables that cannot be
completely isolated, and it is applying a model of vegetation behavior that is not
biologically faithful.
While the present model improves upon previous models coupling vegetation
and erosion within a semi-arid landscape context, there are many opportunities
for further improvement. Given the influence of expanding vegetation with wetter
climates, and of the collapse of the simulated shrub communities, the dynamic
vegetation model is particularly deserving of more attention. So too is the model of
water balance at a point, given the importance of moisture redistribution and runoff
generation. These improvements require both further efforts in model development
and in field studies.
3.7
Conclusions
Numerical modeling offers a unique perspective on the processes involved in
landform evolution. Focusing on the geomorphic dimensions of vegetation in waterlimited ecosystems, which necessarily requires consideration of soil moisture dynamics as well, simulations provide a means of interpreting the origins of equilibrium landforms, and differences among these landforms. As suggested by Dietrich
and Perron [2006], vegetation alters the scale and frequency of simulated landforms, though the effect depends on climate. Vegetated landscapes are steeper than
unvegetated, but the steepest arise where the landscape is only partly occupied by
vegetation, a condition supported by neither too little nor too much rainfall. This
climatic peak in elevation results from the shift in control of erosion efficiency from
vegetation to runoff, and is absent where vegetation is also absent.
Because these ecosystems are water-limited, any factor that substantially alters
the availability of moisture for plant growth will impact the abundance of vegetation and therefore also erosion efficiency. Inclusion of a simple subsurface flow
routine accentuated vegetation growth downslope and in channels, inhibiting erosion and reducing drainage density. It also altered basin concavity. While run-on
accentuated existing differences in vegetation cover, it was unable to generate them.
Response time-scale and rooting depth had small effects on erosion, though the results were confounded by an imprecise method of calibrating model parameters.
An interesting theoretical outcome of linking subsurface flow and the control of
erosion by plants is that if erosion is not diminished enough by the vegetation, the
topography may become too shallow to offer moisture accumulation necessary to
support that very vegetation in a particularly dry climate.
CHAPTER 4
EROSIONAL
RESPONSES TO
DISTURBANCES
In landscapes where vegetation is instrumental in regulating erosion and topography, disturbances become drivers of not only ecosystem form and function but
also of geomorphic form and function. The most vivid and widespread instances
of this are accelerated rates of erosion, gullying and landsliding that have followed
land use changes throughout the Holocene [Trimble and Mendel, 1995; O'Hara,
1997; Prosser and Soufi, 1998; Guthrie, 2002; Glade, 2003]. Fire, either of natural
or anthropogenic origin, can have a pronounced effect on erosion and landsliding
[Coelho et al., 2004; Roering and Gerber, 2005], an effect that generally disappears
as the vegetation recovers [Cerda and Lasanta, 2005; Cerda and Doerr, 2005]. Succession of vegetation can also have the opposite effect on slope stability, by enhancing infiltration and soil saturation, leading to reduced slope stability [Cammeraat
et al., 2005]. Similarly, replacement of grassland by shrublands has been widely
observed to lead to increased rates of erosion [Abrahams et al., 1995; Parizek et al.,
2002]. Notably, the collapse of terrestrial ecosystems in the end-Permian has been
indicted as the cause of the subsequent collapse of marine ecosystems, through the
intermediary of elevated export of nutrients and eutrophication [Sephton et al.,
2005].
At the catchment scale, net erosion is expressed as sediment yield, which has
been shown to vary along climatic gradients [Dendy and Bolton, 1976; Douglas,
1967; Langbein and Schumm, 1958]. The relationships vary among authors but
posses a common trait that sediment yield peaks in semi-arid environments. That
sediment yield should vary with climate is doubted by Riebe et al (2001), because
if the landscape were in equilibrium, erosion rates should be governed exclusively
by tectonic uplift. However, for transient landscapes this would not be the case.
An oft-cited means of producing the observed variability in sediment yield-climate
data, supporting the idea that landscapes are not in equilibrium, is the prevalence
of anthropogenic disturbance by way of land use change [Douglas, 1967; Hooke,
2000; Trimble, 1983; Walling, 1999].
Disturbances have been a common theme in modeling studies of erosion and
geomorphic change. Particular disturbances considered have included logging and
deforestation [Dhakal and Sidle, 2003; Vanacker et al., 2003], wildfires [Gabet and
Dunne, 2003; Istanbulluoglu et al., 2004; Rulli and Rosso, 2005], drought [Giakoumakis S.G., 1997], and climate change [Coulthard et al., 2000; Nearing et al.,
2005a]. Howard [1999] modeled topographic evolution subject to abstract disturbances in vegetation cover to find that the evolution of transient landforms depend
on the nature of coupling between erosion and vegetation and on the nature of the
disturbance.
The present study seeks to model the geomorphic effects of disturbances in
water-limited ecosystems. Landscapes whose vegetation is highly sensitive to the
availability of water are also highly sensitive to changes in vegetation cover. It
is these sensitivities that the modeling seeks to explore, in particular how these
sensitivities depend on the type of disturbance and on the climate in which the
disturbance occurs. To isolate the geomorphic effects of disturbances from other
transient dynamics, simulations are initialized with landscapes that have previously
attained equilibrium. These initial landscapes were products of the simulations in
Chapter 3. Two particular objectives are (i) to test whether the trends in sediment
yield with climate as reported by Langbein and Schumm (1958) and others are consistent with erosional responses to disturbances, and (ii) to test whether too great
a disturbance can lead to accelerated erosion despite recovery of vegetation, a kin
to simulations of Howard (1999).
4.1
Model and Simulations
The simulations presented here seek to understand how equilibrated landscapes
respond to different types and magnitudes of disturbance, and how this response
is conditioned by the climate under which the landscapes evolved. Initial conditions are the equilibrated landscapes developed in Chapter 3 along the climatic
gradient. Simulations are run for 50 years, again using the model developed in
Chapter 2. The two types of disturbances considered are (1) a sudden reduction
in vegetation cover across the landscape, and (2) a sustained change in the mean
annual precipitation. Control simulations are run in parallel, where disturbances
are absent. Where applicable, climatic drivers are identical across the simulations.
The erosional effects of disturbances are assessed by determining the yearly ratio of
post-disturbance erosion to undisturbed erosion.
Because disturbances may themselves be a function of the prevailing climate,
two approaches are employed to reduce vegetation along the climatic gradient.
The first approach is to reduce the vegetation by a factor, f, as follows
V(, Y).new = fx V(x, y)od
(4.1)
The values of f applied are 5%, 10% and 20%. The second is the reduction of vegetation cover by a fixed amount applied uniformly across the landscapes. The cover
change, AV, is simply subtracted from the existing cover, V(x, Y)old, and adjusted if
the new cover, V(x, y),,,ew, is not feasible:
V(x, y),,,ew = max{V(x, Y)old - AV, 0.00011
(4.2)
The values of AV applied are 10%, 20%, 50%, and 100%. (Note that vegetation
cover is already measured as a percentage.)
Changes in the disturbance regime imposed by the rainfall consist of absolute
shifts in the quantity of the mean annual precipitation, embodied in the model by
changes of mean storm intensity alone. Two shifts of increasing precipitation are
considered (+20 mm and +40 mm), and one decrease (-20 mm). The shifts do
not depend on the pre-change climate.
4.2
Reductions in Vegetation Cover
When considering how different disturbances affect landscapes it is first beneficial to illustrate the ecological and erosional responses over time for a single
climate. Figure 4-1 depicts these responses for AV of 10%, 20%, and 50%, as well
as the control with AV of 0%, each under MAP of 321 mm. Figure 4-1a traces the
recovery of vegetation following the disturbances. The greater the disturbance the
longer the vegetation remains below the level of the control case. Once vegetation
has recovered fully all time-series are identical because they are being driven by
identical rainfall forcings and the memory of the soil moisture is on the order of
months. Figure 4-1b demonstrates the logistic recovery of the disturbed vegetation
relative to the undisturbed vegetation. The relative annual erosion (E') for each
disturbance is depicted in Figure 4-1c. The general trend in each case is for E' to
decrease exponentially in concert with vegetation. Even for AV of 50%, which is
too great a disturbance from which to recover within 50 years, the erosion rates
decrease.
To make comparisons of erosional response across a climatic gradient, instead
of determining the relative annual erosion rates, relative total erosion (E50) over
the 50 years is calculated. This analysis is performed for both means of reducing
vegetation, either as a percentage of the initial cover or as an absolute value.
4.2.1
Percentage Reductions
For percentage reductions in vegetation cover, E50 varies with both f and MAP
(Figure 4-2a). For each f, Eo0 is greatest for MAP of 281 mm, and drops with
any increase in rainfall. For MAP of 241 mm, which is too dry to accommodate
o
L>
0
0
4-a
ci
I
>
cooc
0.8
-
-~--c~-
-
---
r-
-
-
I
"
0.4 -
S()
cn
1
,
~ 0.20
u
IIIIIIIII
|iiitiii
iii
i
l
si
I
1
IIIIIIIII
1I
I.1
111·
IU
(i)
10
O
\
~
~~
0
10
-
**s................,,,,,11111
20
30
I·
40
50
Years after disturbance
Figure 4-1: Vegetation and erosional responses to absolute reductions in vegetation
cover of 10%, 20%, and 50%. The latter is equivalent to the complete removal of
vegetation. MAP = 321 mm.
any vegetation even before a disturbance, Eo0 remains unity for all f. For all other
values of MAP, E'0 increases with f. The cause of the non-linear relationship with
MAP is two-fold, relating both to the time taken to recover and to the sensitivity of
the landscape for a given vegetation cover.
The instantaneous difference in erosion between the undisturbed and disturbed
landscapes depends strongly on the difference in vegetation cover, as demonstrated
in Figure 4-1. The total erosion of the 50 years therefore depends strongly on the
cumulative difference in vegetation cover, denoted E(V, - Vd) in Figure 4-2b, where
V, and Vd represent the undisturbed and disturbed vegetation cover, respectively.
This cumulative difference is greater in dryer climates, because it takes vegetation
longer to recover. This is so for three reasons. The first is that growth depends
on the existing vegetation cover, not just the available space to colonize, and dryer
climates inherently have less vegetation cover. The second is that dryer climates
provide less moisture to drive transpiration and inhibit plant stress. The third is
that a lower vegetation cover leads to less infiltration. The extended period of
depressed cover resulting from these three factors gives rise to greater erosion.
In addition to erosion depending on the time vegetation cover is below average,
erosion also depends on the value of this cover. The decay of E50 with MAP above
281 mm is greater than the corresponding decay in cumulative vegetation difference, which suggests that recovery time does not fully explain the trend in Eo0 .
A fuller explanation is obtained by considering the relative importance vegetation
plays in controlling erosion within different climates. As was established in Chapter
3, using the present model, climates that produce landscapes with less vegetation
cover are more dependent on this vegetation cover to determine erosion rates. As
the climate becomes increasingly hospitable, the swelling runoff overwhelms the
resistance imparted by vegetation and so disturbances in vegetation are of less consequence. Thus, the faster decay in E50 than E(V, - Vd) above 281 mm reflects the
decreasing importance vegetation plays in controlling erosion.
Because the time taken for the vegetation to recover is so important in determining the erosional response, an additional set of simulations were conducted in
which the response time-scale of the vegetation, T,, was varied. For all other simulations in this chapter, T, is 50 years. The erosional response for a 10% reduction in
Figure 4-2 is now compared for T, of 50 and 100 years (Figure 4-3). The location of
the peak is the same, but the relative erosional response is more than twice as great
for the slower colonizing species. It is greater because vegetation is taking longer to
recover, but it is more than a factor of two greater because within the 50 years, so
the slower growing vegetation has not recovered fully while the faster species has.
4.2.2
Absolute Reductions
For absolute reductions in vegetation cover, the dependence of El0 on both AV
and climate is more complex (Figure 4-4). At MAP of 241 mm for all AV, because a
climate with 241 mm of rainfall is too dry to sustain any vegetation even prior to the
1.15
1.1
1.05
1
I
0.8
S0.6
S0.4
0.2
0
200
300
400
500
600
700
800
900
1000
MAP (mm)
Figure 4-2: Erosion and vegetation responses to different percent reductions in
vegetation cover across a climatic gradient. (a) Ratios of cumulative erosion over
50 years between disturbed and undisturbed landscapes. (b) Cumulative difference
in vegetation cover over 50 years between disturbed and undisturbed landscapes.
1.3
o
'0 1.2
1.1
1
200
300
400
500
600
700
800
900
1000
MAP (mm)
Figure 4-3: Erosion responses to a 10% percent reduction in vegetation cover across
a climatic gradient for T, of 50 and 100 years.
disturbance, E50 is again unity. For AV of 10% and 20%, E50 peaks at MAP of 281
mm, dropping off rapidly for higher MAP. For 50%, a pronounced peak extends from
281 to 401 mm before dropping off, and for 100% the peak is the same as with 50%,
but E50 remains high. As seen in Figure 4-1, when AV is equal to or greater than
the initial cover, vegetation will not recover within 50 years, and E50 will be high.
AV that is any higher will have no further effect. The case of 100% thus marks
the extreme end where landscapes for all MAP become completely devegetated.
The trend in E50 with MAP therefore represents not the contribution of vegetation
to erosion rates, but that of slope. This trend is a reflection of the trend of mean
elevation with MAP for the equilibrated landscapes (Figure 3-9a). As AV drops to
50%, E50 for the wettest climates is low because the vegetation cover immediately
following the disturbance is great enough for a substantial recovery to occur within
50 years. Conversely, the dryer climates are indeed completely devegetated, so
vegetation remains low and E50 is high. As AV drops further to 20% there is
sufficient vegetation post-disturbance for substantial recovery to take place, even
for 281 mm. In this case the peak in E50 no longer reflects the influence of slope,
but that of vegetation as demonstrated in the previous section. Differences in E'0
reflect the degree to which vegetation is able to recover within 50 years, combined
with dryer landscapes being more sensitive to the lower vegetation covers. AV of
10% simply produces a E50 which is a fraction of what it is for 20%.
CD
oU
-0
SU)
OL.
F_0 04MAP (mm)
Figure 4-4: Erosional response to different magnitude absolute reductions in vegetation cover. Reductions that would result in negative values are adjusted to
0.00001% cover.
4.3
Climate Change
Relative erosional responses to changes in climate differ most distinctly from
the previous cases in that there are two extrema in relative erosional response, not
one. Figure 4-5 plots the relative erosion rates across MAP for the three climate
change scenarios. When MAP is reduced by 20 mm, erosion rates for MAP of 241
mm drop. So do those for MAP > 401 mm. Under this climate change scenario
erosion rates only increase for MAP of 281 and 321 mm, because it is for these
two landscapes for which a drop in rainfall brings a substantial drop in vegetation
cover, and thus an increase in erosion efficiency. Erosion efficiency in the driest and
wetter climates is more directly dependent on runoff, and thus drops following the
-20 mm change in MAP. Exactly the opposite trend results from an increase in MAP
of 20 mm, and for the same reasons. Erosion rates pick up for the driest and wetter
climate, but drop for intermediate MAP. This effect only becomes more pronounced
when the climate change is doubled to 40 mm. For MAP > 401 mm, relative erosion rates tend towards unity as climate becomes wetter. In these landscapes, the
additional rainfall following climate change becomes an ever smaller fraction of the
pre-change rainfall depth.
4.4
Discussion
For a given climate, erosion of landscapes disturbed by vegetation loss depends
on the magnitude of the vegetation loss and on the importance of vegetation in de-
1·
1.4
I
>
a, 1.3
U)
1.2
r
- ) 1.1
0.
:
0.9
S 0.8
0.7
200
300
400
500
600
700
800
900
1000
MAP (mm)
Figure 4-5: Erosional response to abrupt and sustained shifts in MAP. Values along
the abscissa refer to MAP prior to the change.
termining erosion efficiency. The magnitude is important because, combined with
the time-scale of vegetation recovery, this determines the duration the landscape is
vegetated less than pre-disturbance levels. It is important to recall that the timescale of vegetation recovery, as defined here (see Chapter 2 for derivation), is relative to a given climate so actual recovery times would differ in wetter and drier
climates. Vegetation's role in erosion efficiency determines the significance of the
relative difference in vegetation. However, there is no magnitude of disturbance
separating different modes of geomorphic response. Even with complete removal
of vegetation, erosion rates return to pre-disturbance levels as vegetation recovers.
Across a climatic gradient, two additional factors become important. The higher
the vegetation cover after the disturbance, the sooner the vegetation will recover
because colonization rate is a function of existing cover. Faster recovery is also
favored by a wetter climate. When disturbances are so great that all vegetation is
removed and recovery takes place over a far longer period of time, the dominant
role in determining differences in short-term erosion rates across a climatic gradient
is the topographic slope.
Sudden and sustained changes in climate illustrate further intricacies in the
vegetation-erosion coupling. Erosional response reflects the relative importance
of vegetation and runoff. If the landscape is conditioned to be highly sensitive to
vegetation cover, as are those with low-to-intermediate MAP, then changes in mean
annual rainfall are expressed through concomitant changes in cover. More rainfall
fosters more growth, and in turn less erosion, and vice versa. On the other hand,
if the landscape is conditioned to be more sensitive to runoff, as are those with
no vegetation or more than 50% vegetation cover, then changes in mean annual
rainfall are expressed through the concomitant changes in runoff - more rainfall
fosters greater runoff, and in turn more erosion. An implication for contemporary
climate change is that the regions to exhibit the greatest increase in erosion will
differ depending on the direction of the climate change. Regions most susceptible
to reductions in rainfall are those already with low rainfall, as long as there is some
pre-existing vegetation. Regions most susceptible to an increase in rainfall are those
with pre-change MAP of around 500 mm. Regions with MAP in the vicinity of 350
mm are the least sensitive to any change in mean annual rainfall.
Climate change may be manifested in more ways than solely changes in storm
intensity or mean annual precipitation [Easterling et al., 2000], with additional
impacts on erosion. Changing seasonality and storm arrivals would affect soil moisture dynamics, vegetation productivity, and community composition [Chesson et al.,
2004; Epstein et al., 1999; Fay et al., 2003]. Shifts in the seasonality of precipitation toward a greater proportion falling in winter favors shrubs over grasses [Brown
et al., 1997; Dukes et al., 2005], a transition which is commonly associated with
accelerated erosion [Abrahams et al., 1995]. The majority of U.S. locations that
Nearing et al. [2004] modeled, using climate changes predicted by global circulation models, showed an increase in erosion, deriving from an interplay between
rainfall erosivity and biomass production.
Much of the erosion following removal of vegetation is contingent upon the
recovery time-scale of the vegetation. Blue grama, the species considered in these
simulations, is a late-successional species, whose recovery from disturbances may
vary from decades to centuries [Coffin and Lauenroth, 1989], if it recovers fully at
all [Laycock, 1991]. Less cumulative erosion would be expected if the vegetation
community were to recover sooner. Furthermore, if instead of a single disturbance,
there is a change in the disturbance regime, what will become important is the
relative time-scales of disturbance and recovery [Turner et al., 1993].
The non-linearity of the erosional response along the climatic gradient may be
considered in light of previous studies of catchment sediment yield. Dendy and
Bolton [1976], Douglas [1967] and Langbein and Schumm [1958], among others,
produced data relating sediment yield to climate (Figure 4-6). Each of their trends
peaked at low-to-intermediate rainfall. For Langbein and Schumm this peak occurred in the vicinity of 300 mm, for Douglas and for Dendy and Bolton the peak
was around 500 mm. Above these peaks sediment yield decreased, and for Douglas
they increased again above 1000 mm. The existence of their peaks is, however,
largely dependent on the assumption that sediment yield must be zero where there
is no rainfall. Schmidt [1985] suggests that if there is a peak at all it lies very close
to the point of no runoff. Studies of sediment yield, particularly as a reflection of
catchment erosion, are confounded in particularly dry climates because sediment is
largely transported by aeolian processes, not fluvial. As channels become ephemeral
in a geomorphic sense, measurement of sediment yield becomes less meaningful,
and so there is some ambiguity regarding how sediment yield should vary.
Despite the ambiguity regarding the dryer portion of the sediment yield data,
physical explanations for the data still offer insight and hypotheses regarding ero-
sional processes. A common explanation for the variations in the reported data sets
is that the catchments studied were subject to disturbance by human intervention,
causing sediment yield to differ from natural conditions. These disturbances were
certainly on a different scale from one another and, combined with variations across
the climatic gradient, this would leave landscapes in different stages of disequilibrium. This suggests that it is transient simulations such as those pursued herein
that may offer numerical insight into the effects of disturbance. Simulation results
presented here indicate that there is indeed a peak in sediment yield, and that it
occurs in arid to semi-arid climates. Exactly where the peak occurs depends on the
nature of the disturbance, and how the disturbance is applied to landscapes across
the climatic gradient. That the occurrence of the peak in dryer climates is a consistent product of these simulations suggests that the peaks in observed sediment yield
data may arise from the same mechanisms, however this explanation runs contrary
to that offered by Langbein and Schumm [1958]. For drier climates, instead of
an increase in runoff from rainfall driving greater sediment yield, as Langbein and
Schumm hypothesized, this increase in rainfall fosters vegetation cover that makes
the landscape more sensitive to disturbances. For wetter climates, instead of a reduction in sediment yield arising from increases in vegetation with more rainfall, as
Langbein and Scumm hypothesized, the reduction in yield comes from the reduced
sensitivity of landscapes to disturbances in vegetation as plants' roles in geomorphic
processes wane. Any difference in magnitudes of the sediment yield peaks among
the data sets and simulations may simply be a reflection of different disturbance
magnitudes.
The results and analysis presented here must be considered in light of the model's
limitations. The more important limitations are that landscape relief is low to moderate, the dominant vegetation is grass, the soil depth does not restrict sediment
production of plant dynamics, and erosional processes are fluvial.
4.5
Conclusions
Numerical simulations were performed to elucidate the effect of disturbances
on the erosion of previously equilibrated landscapes. Magnitude of vegetation loss
and magnitude and direction of climate change produced different erosional effects, and these effects were contingent on the climate under which the landscapes
evolved. Increases in erosion relative to undisturbed landscapes decayed following
recolonization. Attributes that contributed to greater sensitivity to disturbance were
a greater relative dependence on vegetation in governing erosion rates, compared
with runoff or slope. This is predicated to a significant degree on the extent of
vegetation permitted by the prevailing climate. Landscapes with less than 50% vegetation cover, but not zero, were the most sensitive to change. When all vegetation
is removed, what governs subsequent erosion prior to substantial recovery of vegetation is the initial slope, which is a consequence of landscape evolution preceding
the disturbance.
'A. ML
aut
1.95al)
I
r
)
3,
IC
4jC 1o
g
'
Effctive precipitation, mm/yr
Figure 4-6: Three alternative relations between annual sediment yield and effective
of mean annual precipitation. (From Hooke [2000])
The patterns erosional response to disturbance are non-linear with a peak in
the low-to-intermediate range of mean annual precipitation. This coincides with
peaks in sediment yield observed by various other researchers, based on sediment
yield data that is often devalued because it is confounded by the effects of land use
change. However, that the peaks occur in such a similar range of climate suggests
that this feature is a robust feature of landscape response to disturbances.
CHAPTER 5
PLANT ROOTING
STRATEGIES IN
WATER-LIMITED
ECOSYSTEMS
Plants rely on soil moisture as their primary source of water. Growth, reproduction, and survival depend on plants' abilities to absorb sufficient water through their
root systems [Lee and Lauenroth, 1994; Lynch, 1995], which is of paramount importance in water-limited ecosystems [Nobel, 2002]. What constitutes an adequate
root system depends on the spatial and temporal variability of the soil moisture resource, which is driven by climatic forcing and regulated by the soil. Depth and distribution of plant roots varies greatly among biomes and life-forms [Jackson et al.,
1996]. Roots tend to be deeper in coarser soils [Kramer, 1983] and in climates that
are cooler, wetter, or whose wet season occurs during winter [Schenk and Jackson,
2002a]. However, the deepest roots are found in arid environments and those with
a long dry season [Canadell et al., 1996]. Where water is limiting, root penetration
has been related to the depth of infiltration and intensity of evaporative demand
[Noy-Meir, 1973; Schenk and Jackson, 2005; Weaver, 1920].
Roots play a critical role in the hydrologic cycle, nutrient cycling, and carbon sequestration. Rooting depth is an important parameter in general.circulation models
[Desborough, 1997; Zeng, 2001], regulating evapotranspiration. Roots are also the
intermediaries between transpiration demand and the supply of groundwater and
stream flow. Soil nutrients and microorganisms are intimately tied to the physical
and biochemical environment provided by roots [Farrar et al., 2003; Holden and
Fierer, 2005; Jobbigy and Jackson, 2001]. Root distributions are susceptible to,
and a key component in ecosystem changes associated with, land use and climate
change [Jobbigy and Jackson, 2004; Schenk and Jackson, 2002b].
Understanding and predicting ecosystem roles in current and changing hydrologic and biogeochemical cycles requires detailed knowledge of rooting distributions, including how they may change in the future. This study offers mechanical
insight into the nature of root distributions in water-limited ecosystems using a
physically based model to explore the interaction of plants and their environment.
Models offer a means to test our assumptions, to conduct controlled experiments at
a detail impossible to achieve in nature, and to generate new hypotheses. The contribution this study makes emphasizes the ecohydrological facets of the soil-plantatmosphere system rather than the physiological, paying attention to the influence
climate and soil have on the development of root systems. Because root distributions may be seen as a reflection of plants survival strategies, optimization concepts
are used to infer how climatic and edaphic factors contribute to the proliferation of
rooting strategies.
5.1
Model Description
A 1-D ecohydrological model of the coupled soil-plant system is developed (Figure 5-1). The model is similar to that used in [Small, 2005]; the major difference
is the degrees of freedom granted the vertical root profile. The model is driven
by stochastic rainfall [Eagleson, 1978] and periodic potential evapotranspiration
(PET). PET cycles annually with a prescribed mean and amplitude. Rainfall is either
aseasonal or biseasonal. If the latter, the instantaneous mean annual precipitation
(MAP) for a season is determined from the fraction of total rainfall that falls in the
wet season (f), and the duration of the wet season (At,); timing further depends
on the start date of the wet season (T,) (Figure 5-2). Rainfall is first intercepted by
the plant foliage, in proportion to the leaf area index (LAI), which is fixed in time.
One mm of canopy water storage is used, along with an LAI of 1 [Breuer et al.,
2003]. Rainfall that exceeds the foliage storage capacity continues as throughfall
to be partitioned at the ground surface between runoff or infiltration. Runoff is lost
from the system. The rate of infiltration is governed by soil properties and degree
of saturation.
Once in the soil column, water is redistributed vertically following Richards
equation:
dO
- =dt
K (; )
Oz L
z
(5.1)
K (V())
(5.1)
where 0 is the soil moisture, t is time, z is the soil depth, 0 is the soil moisture
pressure, and K(0) is the hydraulic conductivity. The solution follows an explicit,
finite difference method over the 3.5 m soil column, divided into 5-cm layers. Water
retention and hydraulic conductivity are specified by the van Genuchten [1980]
model, with parmaters from Leij et al. [1999]:
Se
n- Or=- (1 + [,vg h]nv
g)
K(O) = Ksat•/•(1 - [1- S1l/m""g
mrnv
mg)2
(5.2)
(5.3)
where 9, is the residual soil moisture content,n is porosity, av,, ng and mg, are
parameters in the van Genuchten model, h is the soil water pressure head in cm,
Figure 5-1: Schematic representation of the one-dimensional model's hydrological
fluxes. Stochastic rainfall is intercepted by the canopy, part of which is intercepted
by the canopy. Throughfall is partitioned between runoff and infiltration, and soil
moisture is redistributed with Richards equation. Gravity drainage occurs across
the bottom of the soil column. Evaporation from the soil surface and plant-water
uptake are functions of soil moisture, evaporative demand and root distribution.
99
Seasonal MAP
Actual MAP
800
E 600
E
L
400
"
200
n
0
0.2
0.4
0.6
0.8
1
Time (yrs)
Figure 5-2: Seasonal changes in effective MAP, for MAP = 500 mm, At, = 0.3, f,
= 0.5, and T, = 0.35.
and Ksat is the saturated hydraulic conductivity. No groundwater table is considered
in these simulations, though when present it has quite significant effects on plant
behavior [e.g. Nepstad et al., 1994; Oliveira et al., 2005]. Between storms Richards
equation is coupled to evapotranspiration. The instantaneous PET is partitioned
between canopy and soil [Ritchie, 1972]:
PETsoil = PET e- c LAI
(5.4)
PETcanop = PET - PET
8soi
(5.5)
where a is 0.4. The fraction applied to the foliage first acts to evaporate any intercepted water, the remainder to transpiration. The fraction of PET applied to the
soil acts to drive evaporation from the uppermost soil layer [Kurc and Small, 2004].
Timesteps vary to optimize numerical calculations, but are always a day or less.
Plant transpiration is the sum of water taken up by roots throughout the soil
column. The uptake from each layer is the product of two root efficiency terms,
al (0) and a2(0), the fraction of total root mass present in the layer, g(z), arid the
PET available to drive transpiration [Lai and Katul, 2000; Rodriguez-Iturbe et al.,
2001b].
T(t) = o a (0)a 2 ()g(z)PETtan,
l (0) ma
20)=
n0
0- 0•
1* -
)x dz
fo' (z)dz
8w < 0 < 0*
0*< 0
100
(5.7)
0 < ow
<,
1
(5.6)
(5.8)
where L is the depth of the entire soil column, and a is the depth of a soil layer.
The parameter ac1(0) represents local and non-local uptake efficiency limits,
switching the location of preferential uptake to accommodate either higher efficiency tap roots, in times of dryer upper layers, or higher efficiency shallow roots,
when the upper layers are close to saturation. a2(0) represents root "shut-down"
as a function of soil moisture. 0, is the wilting point, or water content for 100%
cavitation. As the soil dries, the onset of water stress and stomatal closure occurs
at 0*. Plant stress, (, is modeled as (1 - a2) [Porporato et al., 2001]. 0, and 0* are
functions of the corresponding physiologically relevant pressures, 0, and %*,
and
the soil texture.
The vertical root profile is prescribed by the linear dose response (LDR) model
[Schenk and Jackson, 2002b]:
Y(z)=
1
1 + (z/D
50 )c
(5.9)
where Y is the cumulative fraction of total root mass between the soil surface and
depth, z; D50 is the depth above which 50% of the root mass is located (or z such
that Y = 0.5); and c is a shape parameter as related to D50 and D95 (where D95 =
z such that Y = 0.95) as follows:
c=
2.94
ln(D so/D
5
95)
(5.10)
The fraction of the root mass located below the soil column is redistributed within
the existing layers. Root distributions are fixed during the simulations and are used
to weight the water uptake function. Figure 5-3 illustrates two root profiles for a
given pair of D50 and D95 , as sampled from the state space to be explored by the
simulations.
5.2
Simulations
Experiments consist of 200-yr simulations of the ecohydrological model with
prescribed parameter values. The first 100 years are a spin-up period, the second
100 provide the data. The experiments are designed to isolate the effects of individual edaphic, climatic, and physiological factors on optimal root profiles. The
edaphic factor considered is soil texture. The climatic factors considered are mean
annual precipitation, MAP, annual PET, the timing and intensity of the wet season,
and the timing and duration of storms. The physiological factors considered are ',
and 4*. In this work we define the optimal vertical root profile, with corresponding
D50 and D95, as that which maximizes mean annual transpiration subject to prescribed model and imposed environmental and physiological conditions [Makeldi
et al., 2002]. Assuming that root profiles in water-limited ecosystems distribute
101
0
Root density
0.25
0.5
U
0.5
1.5
D50 (m)
Figure 5-3: Two vertical root profiles following the LDR model [Schenk and Jackson, 2002b] sampled from the D50 -D95 state space explored by the simulations (inset).
their root mass in such a way as to maximize productivity, and assuming such an
outcome is reflected well by the maximization of net transpiration, then these experiments are akin to conducting global surveys of root profiles in varying environments and for various species. Alternatively, the optimum could be defined as that
profile that minimizes plant stress, a proxy for maximizing survivorship. There is no
explicit cost in the optimization *approach,just a limitation on the transpirational
demand which is distributed of the rooting profile proportional to local root density. The optimization procedure identifies where best in the soil column the roots
should be distributed. Kleidon [2004] used an equivalent optimization assumption
to infer global hydrologically active rooting depths based on inverse modeling. His
results corresponded well with rooting depths derived from observations. van Wijk
and Bouten [20011 used a genetic algorithm to identify the optimal root profiles
at four sites in the Netherlands, and rooting depths were one of many parameters
explored by the genetic algorithm employed by Schwinning and Ehleringer [2001].
The objective of these simulations is not to reproduce the root profiles of specific sites, but rather to identify the functional dependencies that affect root profiles
in general. In so doing, the model must overlook a number of influential factors:
lateral surface and subsurface flow; phreatophytes and a groundwater table; preferential flowpaths; soil heterogeneity; plant competition; and temperature effects.
102
5.3
Identifying the Optimal Profile
For each fixed set of environmental and physiological parameters, 104 simulations are run covering the specified D5 0 -D 95 state space (Figure 5-3). Hydrological
fluxes and plant stress may be plotted as a function of D5 0 and D95 , producing the
surfaces seen in Figure 5-4. This allows us to identify the maximum transpiration
rate and corresponding root profile parameters, as well as examine the physical
drivers for such a profile.
For the case of a non-seasonal, average semi-arid environment with silt soil, the
maximum transpiration (Tma) is 134 mm/yr, and corresponds to the root profile
of 0.15 m D5 0 and 0.4 m D9 5 (Figure 5-4). This is precisely coincident with the
point of minimum evaporation (Emin). As transpiration decreases away from the
optimum, evaporation increases in a reciprocal manner, indicating that the optimum is that which minimizes evaporation. The drainage flux is too small to be
a valuable source of water, so the only flux with which transpiration competes is
evaporation. The drainage surface does show, however, that as roots get deeper
less water infiltrates past the plant's zone of influence. As Tma is also coincident
with the minimum stress ('min), there may be no confusion as to the location of
the optimum if we alternatively define it by maximizing survivability rather than
maximizing productivity.
Because simulations are stochastic, there is uncertainty in the estimate of transpiration, and hence also in the location of the optimum. To identify the approximate optimal region we compare the transpiration time-series of each profile in
the D50 -D95 state space to those of the absolute optimum using the KolmogorovSmirnov test (a = 5%). The resulting region represents a set of root profiles within
which plants may not perceive any significant environmental difference, and thus
are equivalently fit. The same procedure is applied to plant stress. In Figure 5-4
these regions cover a large area of the state space and shows greater sensitivity to
D5 0 than to D9 5 . The size and location of this region differs among experiments.
5.4 Soil Texture
Soil texture is a key variable controlling soil moisture dynamics and distributions, and thus optimal root profiles. In the simulated moderate semi-arid climate,
the coarser the soil the deeper the roots (Table 5.1). The high hydraulic conductivity of sand provides infiltrating water the greatest opportunity to penetrate to
depth, so much so that root-water uptake cannot keep up and significant drainage
occurs. To catch as much of this water as possible, optimized root profiles are as
deep as possible. Evaporation is very low, so transpiration is effectively competing only with drainage. As soils become finer - from silt to loam to clay - optimal
rooting depths become shallower, reflecting the restricted infiltrating depths due to
lower hydraulic conductivities. Loam has only slightly deeper roots than clay. Roots
103
Trqn.niratinn m/vr
0.08
0.10
0.12
Evanoration m/vr
0.14
0.14
0.16
0.18
0.2
3
4
2.5
2
1.5
1
0.5
0.2
0.4
0.6
0.8
1
Plant stress
0.40
3
0.48
0.56
0.64
1
2.5
2.5
2
2
1.5
1.5
1
1
0.5
2
0.5
Figure 5-4: Transpiration, evaporation, plant stress, and drainage across the D5oD95 state space for silty soil. Circles identify the optimum; dashed line denotes the
optimal region.
104
Sand
Silt
Loam
Clay
D50 (m)
1
0.15
0.1
0.05
D95 (m)
3
145
41
82
0.04
0.4
134
137
1.5
0.41
0.3
132
140
1.0x10 - 4
0.41
0.2
125
139
1.6x10 - 5
0.62
Transpiration (mm/yr)
Evaporation (mm/yr)
Drainage (mm/yr)
Plant stress
Table 5.1: Optimal root profiles and corresponding mean annual fluxes and plant
stress for four soil textures.
have little chance competing directly with evaporation [Noy-Meir, 1973], so roots
are not the shallowest they can be. It must be noted that the optimum identified for
sand occurs at the boundary of the state space explored; the true optimum is likely
deeper. Furthermore, of the four textures studied, sand is the only one in which
(min is not coincident with Tmax. For all finer textures in this set of experiments,
transpiration, stress and evaporation extrema are all coincident.
Field data show that the probability of deep roots is higher in coarse and fine soil
textures than in medium textures [Schenk and Jackson, 2005]. Schenk and Jackson
explain this by noting that medium textures have ample moisture in shallow layers,
so deep rooting is not necessary. Coarse soils do not have ample moisture at shallow
depths but do have moisture at depth. Fine textures are less likely to have ample
moisture anyway, in which case the plants are likely to exploit what macropores
exist to reach deeper groundwater, if present. The present model, lacking both
macropores and groundwater, does not produce deep roots for fine textures.
5.5
Climate
When MAP and PET are co-varied (100 to 900 mm/yr and 2.5 to 5.5 mm/day
respectively, selected to reflect the data used by [Schenk and Jackson, 2002a]),
without seasonality and again in silty soil, wetter and cooler climates foster deeper
roots (Figure 5-5). This arises because more water is infiltrating into the soil and
draining from the soil column. As drainage increases, it becomes a more intense
competitor for moisture. The optimum profile responds by extending it roots deeper
(0.4 m D 50 and 1.2 m D 95 for P = 900 mm/yr and PET = 2.5 mm/day; 0.1 m D50
and 0.2 m D95 for P = 100 mm/yr and PET = 5.5 mm/day). ýmin is coincident
with Tmax, though in this instance Emin remains very shallow while only slightly
deepening in wetter climates. These results illustrate that when drainage becomes
substantial, transpiration begins to compete for moisture with both evaporation and
drainage, but minimizes neither of the two fluxes. The results also confirm that the
greater probability of deep roots in less arid regions can arise simply from tradeoffs between infiltration and evaporative demand [Noy-Meir, 1973; Schenk and
105
Jackson, 2005]. For loam and clay the optimal depths are shallow and are quite
insensitive to changes in climatic variables. The optimum in sand remains outside
the D50 -D95 state space explored.
The trend of increasing rooting depth for cooler climates (lower PET) disagrees
with a previous conclusion by Schenk and Jackson [2002a]. Based on field data,
Schenk and Jackson [2002a] concluded that maximum rooting depth is relatively
insensitive to PET for dryer climates, but in wetter climates rooting depths increase
with PET (Figure 5-6). The present results show a similar relationship in D95 for
the driest of climates, but the reverse as rainfall increases. The likely reason for
this disagreement is that the present model considers a very restricted range of
environmental conditions, most notably the absence of groundwater. Maximum
rooting depth as Schenk and Jackson consider it is more likely a specific reflection
of phreatophytes. For regions supplied with sufficient groundwater, which are more
likely in wetter climates, higher evaporative demand would decrease the preference
for shallow roots, as they suggest, by drying the surface soil layers but leaving the
deeper moisture reserves intact. Thus deep roots are deeper.
Combining the results for the texture and MAP-PET experiments offers insight
on the inverse texture effect - that the same type of vegetation may occur in coarse
soil under dry climates and in fine soil in wetter climates [Noy-Meir, 1973]. The
optimal root profile is deeper in coarser soils and in wetter climates. If soils coarsen
at the same time as the climate dries, it is conceivable that the optimal rooting
depth may remain the same. Because rooting strategies are species-specific [Gale
and Grigal, 1987; Poot and Lambers, 2003](Yamada et al., 2005), the reciprocal
changes in soil and climate, in some cases, can indeed provide conditions for a
single species.
Differences in seasonality have less pronounced effects on the optimal root profile than texture, MAP, or PET (Table 5.2). Optimal root profiles are deeper in
winter-rainfall than in summer-rainfall environments - 0.2 m D50 and 1.0 m D95
for winter compared with 0.15 m D50 and 0.6 m D95 for summer for the slightly
seasonal case. Water that infiltrates in the winter is subject to lower evapotranspirational demand than in the summer, and is more likely to infiltrate to depth.
As the wet season becomes more intense, with half the annual rainfall falling in
ever fewer months, runoff increases at drainage's expense, and optimal D50 and
D95 become slightly shallower. Asynchrony of evaporation and transpiration fluxes
is crucial to generate heterogeneity in the landscape and hence diversity of plant
functional types [Paruelo et al., 2000]. These results are consistent with observations by Schenk and Jackson [2005] that the probability of deep roots is higher in
seasonal climates, and with those of Schenk and Jackson [2002a] regarding shrubs.
When we isolate the effects of storm duration and timing, drainage becomes appreciable in the silt experiments provided storms are short and frequent (Table 5.3).
As drainage increases, transpiration starts to compete for moisture with both evaporation and drainage, and thus the optimal profile is slightly deeper - D95 increases
from 0.4 m to 0.8 m. No change in the optimal profile is observed for the coarser or
106
D 95 (m)
'"
1.2
cc
4.75
Rooting depth:
4
Deep
Medium
3.25
Shallow
200
400
600
Low
800
MAP (mm)
Precipitation
High
Figure 5-6: (a) Optimal D95 for silty soil across the combined MAP-PET gradients.
Deeper optimal rooting profiles arise for the greater MAP and lowest PET. (b) Conceptual model of the relationship between absolute maximum rooting depths and
climatic variables, from Schenk and Jackson [2002a]. The region enclosed in the
dashed line approximates the MAP-PET state space explored by the current study.
Non-seasonal
D50 (m)
D95 (m)
Transpiration (mm/yr)
Evaporation (mm/yr)
Drainage (mm/yr)
Plant stress
0.15
0.4
134
137
1.5
0.41
Winter
Summer
(0.4) (0.1). (0.4) (0.1)
0.15
0.15 0.15
0.2
0.6
0.5
0.8
1.0
136
108
107
134
103
132
107
127
1.4
2.2
0.9
1.8
0.35 0.46 0.35 0.43
Table 5.2: Optimal root profiles and corresponding mean annual fluxes and plant
stress for different seasonalities, for silty soil and MAP of 500 mm. Values in parentheses are At,.
108
Tr = 5 hrs
(100 hrs) (400 hrs)
T, = 20 hrs
(100 hrs) (400 hrs)
D5 0 (m)
D 95 (m)
0.15
0.5
0.15
0.4
0.15
0.6
0.15
0.4
Transpiration (mm/yr)
Evaporation (mm/yr)
Drainage (mm/yr)
Plant stress
151
168
2.1
0.34
94
89
0.3
0.62
151
161
2.8
0.27
93
85
0.4
0.58
Table 5.3: Optimal root profiles and corresponding mean annual fluxes and plant
stress for different storm and interstorm durations, for silty soil and MAP of 500
mm. Values in parentheses are Tb.
finer soil textures, because either drainage always overwhelms evaporation, or vice
versa. Altered rainfall regimes have been shown to change net primary productivity
[Fay et al., 2003]. Our numerical experiments suggest that altered rainfall regimes
may also affect root profile preference; the parameter space explored indicates this
would more likely occur in silt.
5.6
Plant Physiology
The two physiological parameters studied define the soil moisture bounds within
which the plant is stressed but still able to transpire. The lowest V*used (-10 kPa)
yields a substantial increase in drainage compared with higher values (up to -1.8
MPa) (Table 5.4). As with the MAP-PET experiments, this drives the optimal profile
deeper. The D95 of the absolute optimum changes little, though the optimal region
changes substantially. The sooner 4* is surpassed the less moisture is taken up by
the plant, and the more remains to infiltrate. VC, has little effect on location of
the optimal profile (varied from -2 to -8 MPa). i* is more influential because soil
pressures are more often more negative compared to 0* than they are to 0,. Our
results correspond to more drought-tolerant species having shallower roots, not
because they can tolerate a more stressful environment in the surface layers, but
because that is where water is more abundant. This is consistent with observations
that cavitation resistance is negatively correlated with rooting depth [Sperry and
Hacke, 2002], a strategy suiting both intensive and extensive soil moisture use
[Rodriguez-Iturbe et al., 2001a].
5.7
Discussion
As the results from the 4*-4, experiments demonstrate, plants themselves alter
the soil environment with feedbacks that affect rooting preference. In these experi109
D50 (m)
D95 (m)
Transpiration (mm/yr)
Evaporation (mm/yr)
Drainage (mm/yr)
Plant stress
,W= -2 MPa
(-0.01 MPa) (-1.8 MPa)
0.3
0.1
0.6
0.6
56
173
198
104
5.7
0.07
0.74
0.23
ow = -8 MPa
(-0.01 MPa) (-1.8 MPa)
0.3
0.1
0.6
0.6
64
177
195
101
5.2
0.08
0.71
0.17
Table 5.4: Optimal root profiles and corresponding mean annual fluxes and plant
stress for different wilting points and stomatal closure pressures, for silty soil and
MAP of 500 mm. Values in parentheses are 0*.
ments we considered only solitary plants, but the inclusion of competition for water
among plants will have a pronounced effect on realized rooting preferences. For example, the genetic algorithms used by van Wijk and Bouten [2001] produced very
different profiles depending on whether or not competition was included. Furthermore, as PET affects optimal rooting depths, so too would LAI. Rooting preferences
would thus also vary with phenophase and developmental stage.
Given that no attempt was made to mimic the global distribution of conditions
observed in nature, it is noteworthy that by far the majority of experiments produce
D50 in the vicinity of 20 cm or shallower, which is the global mean Jackson et al.
[1996]. The drive to send roots deeper when appreciable drainage exists reflects
the greater likelihood of finding deep roots in water-limited systems. However, we
presume the majority of truly deeply rooted plants are phreatophytes [Nobel, 2002]
and thus not considered within this model. The drive to diminish drainage is also
consistent with observations from the U.S. southwest [Scanlon et al., 2005a] and
pre-European Australia [Eberbach, 2003] where vegetation has been responsible
for largely eliminating groundwater recharge.
Changing the root profile often has a significant effect on hjrdrologic fluxes and
plant stress [Rodriguez-Iturbe et al., 2001a]. This further highlights the need to
properly account for root profiles when modeling land-atmosphere interactions,
groundwater recharge, and habitat suitability. Land use changes often lead to altered groundwater recharge and streamflow. If the changes are associated with a
shift in the preferred root profile by plants, a component of the hydrologic response
would arise from the vertical shifts in the belowground biomass.
If differences in rooting preference exist among climates, we can expect climate
changes to foster changes in belowground biomass. This may entail the modification of the existing species' roots to the new depths, or replacement by fitter species.
A substantial increase in winter precipitation in the last quarter of last century in the
U.S. southwest caused a three-fold increase in woody shrub density [Brown et al.,
1997]. Cast in the light of the simulations herein, greater winter precipitation favors deeper rooted plants, such as shrubs, over more shallow rooted herbaceous life
110
forms. Resulting changes in community structure and composition would further
affect ecosystem processes and services [Chapin et al., 1997]. Potential impacts include changes in water, carbon and other nutrient fluxes, as well as the distribution
of soil fauna [Holden and Fierer, 2005; Jackson et al., 2000; Jobbigy and Jackson,
2001; Johnston et al., 2004].
Our results reproduce many of the trends related to root profiles depths in waterlimited ecosystems, supporting that infiltration and evaporative demand are indeed
the mechanisms behind these profiles. However, roots are not static. Plant growth
entails changes both above and below ground, and plasticity is vitally important in
resource acquisition [Grime et al., 1986], though to varying degrees [Wraith and
Wright, 1998]. What is optimal in the long-term may thus be sub-optimal on shorter
timescales. The root profiles we employ are best interpreted as generalist strategies
or static approximations to a dynamic system, providing mechanistic insight on
the root profile snapshots that comprise belowground surveys with which we are
making our comparisons.
5.8
Conclusions
The numerical ecohydrological modeling exercise employed in this chapter provides a window into the ecological relationships that give rise to the diversity of
rooting strategies observed in nature. Root depth and distribution are vital components of a plant's strategy for growth and survival in water-limited ecosystems,
and play significant roles in hydrologic and biogeochemical cycling. Knowledge
of root profiles is invaluable in measuring and predicting ecosystem dynamics, yet
data on root profiles are difficult to obtain. Using an optimization approach, model
simulations thus offered a means to explore the mechanistic relationships among
climate, soil, and plant systems in water-limited ecosystems, and may begin to offer a alternative means of inferring rooting depths without the need for intensive
root surveys. It should be noted that non-invasive techniques using isotopes have
recently been developed [Ogle et al., 2004].
Results of the optimization approach were consistent with profiles observed in
nature. Optimal rooting was progressively deeper moving from clay to loam, silt
and then sand, and in wetter and cooler environments. Climates with the majority
of the rainfall in winter produced deeper roots than if the rain fell in summer. Short
and frequent storms also favored deeper rooting. Plants that exhibit water stress at
slight soil moisture deficiencies consistently showed deeper optimal root profiles. Of
the four soil textures examined, silt generated the greatest sensitivity to differences
in climatic and physiological parameters.
In the absence of groundwater, the depth of rooting is driven by the depth to
which water infiltrates, as influenced by soil properties and the timing and magnitude of water input and evaporative demand. Accounting for groundwater would
add further richness to optimization results, as would the inclusion of competition
111
for water among like species and between life forms.
112
CHAPTER 6
CONCLUSIONS
Climate plays a profound role in the evolution of landscapes, affecting both their
biological and physical make-ups. The biological and physical constituents in turn
affect one another, complicating the identification of mechanistic causes of observable patterns among landforms and landform change. Numerical modeling offers a
means to disentangle the complex mechanistic linkages among biological and physical processes in a controlled fashion. In the current study, this effort is directed
towards landscapes under arid and semi-arid climates, where water is the major
limiting factor in vegetation growth. The study brings us closer to understanding
the characteristics of vegetated landscapes, though work remains to be done in both
modeling and in the field.
6.1
Summary of Results
6.1.1 Vegetation and Landforms
The objective of Chapter Three was to investigate the topographic expression
of vegetation under steady-state conditions. Simulations considered the impacts of
lateral moisture redistribution from subsurface flow and run-on, of mean annual
precipitation, and of vegetation characteristics. The geomorphic outcomes of the
simulations are best interpreted in the context of erosion efficiency, which is a measure of how readily a landscape erodes for a given relief. High erosion efficiency is
associated with low slopes, and low efficiency with high slopes. Vegetation alters
erosion efficiency in two general ways. The first is by increasing infiltration and
thus suppressing runoff; the second by increasing the threshold of runoff required
to detach and transport sediment.
Subsurface flow augmented vegetation cover by creating more favorable conditions for growth downstream. This led to an increase in vegetation cover downslope
113
and a corresponding longitudinal decrease in erosional efficiency. Not only did this
elevate the overall topography, but it changed the concavity of the fluvial portions of
the landscape. In contrast to subsurface flow, run-on played only a subordinate role
in structuring vegetation cover. Because subsurface flow was greater for steeper
slopes, if the landscape's erosion efficiency surpasses a particular threshold for a
given climate, no vegetation can be sustained, and efficiency becomes even greater
and the topography even lower.
Rainfall fosters an increase in both vegetation cover and runoff, which have opposing effects on erosion efficiency. As landscapes are evolved across a climatic
gradient, the dominant factor governing erosion efficiency shifts from vegetation
in dryer climates to runoff in wetter climates. Below a threshold of mean annual
precipitation, an increase in rainfall fosters such an increase in vegetation growth
that an extra runoff is suppressed, but as vegetation cover rises above 50% in wetter climates, the vegetation can no longer offset increases in runoff. This shift in
erosion efficiency translates to landscapes being the steepest, and having the lowest
drainage density, under climates of intermediate mean annual rainfall.
The vegetation characteristics considered were the time-scale of response, the
rooting depth, and the life form, all of which altered the geomorphology. When
controlling for mean vegetation cover, faster growing vegetation and deeper rooted
plants led to an increase in erosion efficiency and thus to lower slopes. Shrubs
also produced a flatter landscape compared with grass, because shrubs were associated with a greater portion of bare ground which is more easily eroded. However,
these results depend on the dynamic vegetation model and values assigned various
vegetation-related parameters, all of which would benefit from more field studies.
6.1.2
Disturbance and Erosion
Chapter Four was concerned with erosional responses of steady-state landscapes
to disturbances in vegetation cover or changes' in the prevailing climate. In all
cases simulations were conducted across a climatic gradient, because results from
Chapter Three concluded that erosion efficiency would vary among arid, semi-arid
and sub-humid environments.
Simulations demonstrated that erosion response of vegetated landscapes depends on the climate, type of disturbance, magnitude of disturbance, and direction
of the environmental change. There was consistently a high response to disturbances for landscapes under climates of intermediate annual rainfall depths. This
is consistent with observations of sediment yield data that have been accruing for
the last half century, that reflect landscapes bearing the signature of human intervention. The magnitude of the response depended most on the time taken for
vegetation to recover from a disturbance, and to a lesser extent on the density of
the vegetation - the longer the recovery and the sparser the vegetation the greater
the erosional response.
114
6.1.3
Rooting Strategies
The motivation for Chapter Five was the observation that rooting depth plays a
pivotal role in ecohydrology, vegetation dynamics, and ultimately sediment transport. Rooting depths vary among climates, so assuming a constant value across a
climatic gradient as was done in Chapter Two and Chapter Three may not be a sufficiently accurate representation of ecological phenomena. To help understand how
rooting depths vary among different climates, soil conditions, or for plants of different physiological attributes, Chapter Five sought to identify the optimum rooting
strategies for plants growing in water-limited ecosystems.
Results were consistent with field observations of rooting depths. Roots were
deeper in coarser soils and wetter climates, and, for environments where groundwater is not a reliable source of moisture, deeper also in cooler climates. This
reflects the tendency for water to infiltrate to particular depths. Roots were deeper
when storms were long and infrequent, a trend that cannot yet be tested with any
observational data. Roots were also deeper for plants that are less drought-tolerant.
6.2
Directions for Future Research
While tthis study has offered novel insights into the mechanistic causes for patterns among landforms, landform change, and rooting profiles, more work remains
to be done. Highlighted here are the more promising and needed directions, for
both modeling and field work.
Development of the CHILD model:
1. Refine the rainfall model employed by CHILD so that no artificial calibration
step is needed to produce realistic hydrological responses to storms.
2. Refine the hydrological models employed by CHILD, since it is the interplay
between suppressed runoff and augmented runoff that causes the peak in
elevation for climates of intermediate total annual rainfall. The two most
importance of these models are infiltration and subsurface lateral flow.
3. Refine the spatial configuration of CHILD so that channels are treated separately from hillslopes.
Field work to support model development and hypothesis testing:
1. Gather more data on the control of sediment transport under different vegetation types.
2. Gather more data on vegetation dynamics and plant physiology so that the
dynamic vegetation model may be improved and verified.
115
Further landscape simulations:
1. Once there is sufficient data on the ecohydrological and geomorphic aspects of
different species and life-forms, multi-species simulations would offer insights
into the geomorphic effects of plant diversity and competition.
Rooting strategies: model and data
1. Identify those environments where groundwater plays no appreciable role in
the dynamics of vegetation, and re-analyze the dependence of rooting depth
on potential evapotranspiration.
2. Expand the 1-D ecohydrology model to account for groundwater.
3. For field studies of altered rainfall timing, investigate whether rooting profiles
are adapting to the altered environment.
4. Expand the ecohydrology model to account for temporal variations in plant
biomass.
116
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