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Multiscalar model for the determination of spatially explicit riparian vegetation roughness


Abstract and Figures

Improved understanding of the connection between riparian vegetation and channel change requires evaluating how fine-scale interactions among stems, water, and sediment affect larger scale flow and sediment transport fields. We propose a spatially explicit model that resolves patch-scale (submeter) patterns of hydraulic roughness over the reach scale caused by stands of shrubby riparian vegetation. We worked in tamarisk-dominated stands on the Yampa and Green Rivers in Dinosaur National Monument, northwestern Colorado, USA, where questions remain regarding the role of vegetation in inducing or exacerbating documented channel changes. Hydraulic roughness patterns were derived from patch-scale measurements made with detailed terrestrial laser scan (TLS) data that were extrapolated to reach scales based on correlation with light detection and ranging (LiDAR) (ALS) data. Two-dimensional, patch-scale, hydraulic models were used to parameterize the stage dependence of hydraulic roughness of typical patch types (i.e., sparse, moderate, and dense patches). We illustrate the value of using this approach to characterize vegetation roughness by applying our results to a two-dimensional hydraulic model of flow for one of our study sites. Results from this work predict that the roughness of vegetated floodplains increases with flow depth and is dependent on patch-scale stem organization. Geomorphically relevant patterns (i.e., areas of low or high shear stress that are likely to scour or fill during high flows) become apparent with the detail introduced by spatially explicit, depth-dependent roughness. To our knowledge, the multiscalar analysis presented here is the first to mechanistically account for shrubby riparian vegetation stand structure, and associated hydraulic roughness of vegetation patches, at the reach scale.
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Multiscalar model for the determination of spatially explicit
riparian vegetation roughness
Rebecca Manners,
John Schmidt,
and Joseph M. Wheaton
Received 16 August 2011; revised 4 November 2012; accepted 5 November 2012; published 27 January 2013.
[1] Improved understanding of the connection between riparian vegetation and channel
change requires evaluating how ne-scale interactions among stems, water, and sediment
affect larger scale ow and sediment transport elds. We propose a spatially explicit model
that resolves patch-scale (submeter) patterns of hydraulic roughness over the reach scale
caused by stands of shrubby riparian vegetation. We worked in tamarisk-dominated stands
on the Yampa and Green Rivers in Dinosaur National Monument, northwestern Colorado,
USA, where questions remain regarding the role of vegetation in inducing or exacerbating
documented channel changes. Hydraulic roughness patterns were derived from patch-scale
measurements made with detailed terrestrial laser scan (TLS) data that were extrapolated to
reach scales based on correlation with light detection and ranging (LiDAR) (ALS) data.
Two-dimensional, patch-scale, hydraulic models were used to parameterize the stage
dependence of hydraulic roughness of typical patch types (i.e., sparse, moderate, and dense
patches). We illustrate the value of using this approach to characterize vegetation
roughness by applying our results to a two-dimensional hydraulic model of ow for one of
our study sites. Results from this work predict that the roughness of vegetated oodplains
increases with ow depth and is dependent on patch-scale stem organization.
Geomorphically relevant patterns (i.e., areas of low or high shear stress that are likely to
scour or ll during high ows) become apparent with the detail introduced by spatially
explicit, depth-dependent roughness. To our knowledge, the multiscalar analysis presented
here is the rst to mechanistically account for shrubby riparian vegetation stand structure,
and associated hydraulic roughness of vegetation patches, at the reach scale.
Citation: Manners, R., J. Schmidt, and J. M. Wheaton (2013), Multiscalar model for the determination of spatially
explicit riparian vegetation roughness, J. Geophys. Res. Earth Surf., 118, 65–83, doi:10.1029/2011JF002188.
1. Introduction
[2] Riparian vegetation encroachment onto active alluvial
surfaces can signicantly modify channel form, resulting in
narrowing and simplication of planform [Tal and Paola,
2007; Corenblit et al., 2009]. An improved understanding of
the processes that link vegetation and geomorphic form is
especially important in light of major shifts in riparian com-
munities caused by water development [Rood and Mahoney,
1990; Auble et al., 1994; Merritt and Wohl, 2006], climate
change [Meyer et al., 1999; Gibson et al., 2005], and the inva-
sion of non-native species [Friedman et al., 2005].
3] At a fundamental level, vegetation-induced channel
change results from the interaction of stems, stream ow,
and transported sediment [Schnauder and Moggridge, 2009].
Stems perturb the ow eld, modifying the distribution of
velocity and shear stress, and, as a result, patterns of sediment
entrainment and transport [Nepf et al., 1997; Bennett et al.,
2002; Zong and Nepf, 2010]. Over time, these patterns may
cause net erosion and deposition, which are the mechanisms
that alter the channel cross section and/or planform.
4] Although the processes that cause channel narrowing
occur at small spatial scales, the geomorphic implications of
these processes are typically observed and investigated at lar-
ger spatial scales, such as that of a reach (1020 channel
widths). There has been limited progress in applying the
insights gained from stem-scale studies to the reach-scale
changes that are of geomorphic signicance [Forzieri et al.,
2012]. One approach to applying small-scale insights to larger
scale processes involves development of techniques and
classication schemes that empirically link coarsely measured
vegetation attributes, such as vegetation height [Cobby et al.,
2001; Mason et al., 2003], crown characteristics [Antonarakis
et al., 2008; Forzieri et al., 2011], species [Stoesser et al.,
2003], or vegetation type (i.e., shrub versus grass, exible
versus rigid) [Darby,1999;Brookes et al., 2000], to the
hydraulic resistance of vegetation. Application of these techni-
ques and classication schemes requires assumptions about
Intermountain Center for River Rehabilitation and Restoration,
Department of Watershed Sciences, Utah State University, Logan, Utah, USA.
Now at Grand Canyon Monitoring and Research Center, US Geological
Survey, Flagstaff, Arizona, USA.
Corresponding author: R. Manners, Intermountain Center for River
Rehabilitation and Restoration, Department of Watershed Sciences, Utah
State University, 5210 Old Main Hill, NR 210, Logan, UT 84322, USA.
©2012. American Geophysical Union. All Rights Reserved.
JOURNAL OF GEOPHYSICAL RESEARCH: EARTH SURFACE, VOL. 118, 6583, doi:10.1029/2011JF002188, 2013
stand structure, either applied as typical attributes [e.g., Grifn
et al., 2005], or through inferred relationships linked to a single
variable (i.e., vegetation height) [e.g., Mason et al., 2003].
However, riparian vegetation communities often have species
assemblages and stand ages that result in variable stand struc-
ture. In these cases, techniques based on coarsely measured
variables oversimplify the hydraulic effects of vegetation.
Additionally, many riparian corridors are dominated by shrubby
species [Friedman et al., 2005] whose stand structure is com-
plex and cannot be characterized based on canopy structure.
5] The ability to control environmental conditions in a
laboratory setting has resulted in improved methods to
quantify the stem-scale impact of vegetation on the ow eld.
Such approaches are capable of accounting for specic attri-
butes of vegetation structure, including stem density, stem
spacing, exibility, and relative submergence [Petryk and
Bosmajian,1975;Bennett et al., 2002; Jarvela,2004;Liu et
al., 2008]. These physically meaningful results are limited in
spatial extent, suffer from issues of how to apply the results
to larger scales, and are generally restricted to idealizations
of vegetation, rather than actual plants. Little progress has
yet been made on how to apply the ever-improving insights
gained from small-scale studies in laboratories to the eld
6] In this study, we linked detailed measurements of
stand structure derived from terrestrial laser scanning
(TLS; also called ground-based LiDAR) to reach-scale
riparian vegetation patterns derived from airborne LiDAR
(also referred to as airborne laser scanning [ALS]).
Acknowledging that ne-scale interactions among stems,
water, and sediment may be critical in the accurate identi-
cation of the role of riparian vegetation, we developed a
method that merges small-scale, high-resolution TLS data
and broader extent ALS data. We related TLS data collected
at the patch scale (10
m) to the reach scale (10
using a scaling methodology. This methodology does
not necessitate a brute force approach whereby high-
resolution TLS data are collected for an entire reach. Our
method is inspired by the fact that TLS is not practical to
deploy over large areas or in thick vegetation. We describe
a met hodology to extrapolate detailed TLS data to the reach
scale. We quantify the patch-scale stand structure of shrubby
riparian vegetation using TLS data; relate physically based,
depth-dependent roughness to stand structure; upscale these
relationships from patch scale to reach scale using ALS data;
and describe the response of reach-scale ow hydraulics to
the patch-scale distribution and structure of riparian vegeta-
tion. We conclude by discussing the implications of riparian
vegetation invasion on channel hydraulics by using our
method to model the bed shear stress distribution in the
absence and presence of riparian vegetation. Although we
present only limited eld verication of our model, the
methodology described here represents a novel effort to
account for variable stand structure and its effects on reach-
scale hydraulics.
2. Tamarisk in the Colorado River Basin
[7] We focused on the invasive non-native riparian shrub
tamarisk (Tamarix spp.). During the past century, tamarisk
has densely colonized alluvial valleys of most of the Colorado
River system. A general trend in these valleys has been toward
denser vegetation encroaching along the margins of the active
channel and greater dominance by tamarisk and native willow
species (Salix spp.). A decline of bare, dynamic sand bars has
generally led to the simplication of channel planform [Turner
and Karpiscak, 1980; Webb et al., 2007].
8] Tamarisk's spread through the basin was concurrent
with other environmental shifts, including the closure of
large dams and 20th century climate change [Graf, 1978;
Allred and Schmidt, 1999; Birken and Cooper, 2006]. As a
response to the changes in these environmental drivers,
channel narrowing has been ubiquitous [e.g., Hereford,
1984; Grams and Schmidt, 2002]. There is extensive docu-
mentation of channel narrowing by inset oodplain forma-
tion in many parts of the Colorado River basin [e.g., Graf,
1978; Hereford,1984;Grams and Schmidt, 2002]. These
studies implicate either of two causes of narrowing. One
potential cause is the invasion of riparian vegetation that results
in increased bank stabilization and roughness that induces sedi-
ment deposition [Graf,1978;Birken and Cooper,2006;Dean
and Schmidt, 2011]. The other potential cause is decreased
ood ows due to water development. Decreased ows may
result in sediment mass balance surplus, leading to the devel-
opment of inset oodplains, regardless of whether or not inva-
sive riparian vegetation is present [Everitt,1993;Allred and
Schmidt, 1999]. Improved understanding of the mechanisms
by which riparian vegetation affects the local hydraulics
through tamarisk stands and, in turn, larger scale ow patterns
is essential for understanding the relative role of these two
causes of narrowing [Schnauder and Moggridge,2009].
3. Study Area
[9] Our study involved two sites in Dinosaur National
Monument (Figure 1), located in the middle Rocky Mountains
in eastern Utah and western Colorado: Laddie Park in Yampa
Canyon on the Yampa River, and Seacliff in Whirlpool
Canyon on the middle Green River downstream from the
Yampa. The channels at both of these sites have progressively
narrowed during the 20th century [Grams and Schmidt, 2002].
The oldest surviving tamarisk individual recovered to date in
this area germinated in 1938 [Cooper et al., 2003]. We ana-
lyzed extensive geomorphic, hydrologic, and vegetative data
obtained from ongoing data collection efforts at the two sites
[Manners et al., 2011]. Additionally, ALS data were obtained
from a ight over the study sites in October 2008, and three-
band multispectral imagery was obtained from a ight in
June 2010.
10] The two study sites are both 0.6 km long (Figure 2).
Laddie Park is in the downstream part of Yampa Canyon
where the Yampa River has established a series of incised
meanders. The average channel slope is 0.0009, and the
average channel width is 106 m [Larson, 2004]. In contrast,
the Green River in Whirlpool Canyon has a steeper slope
(0.002) and narrower channel width (64 m) [Grams and
Schmidt, 2002]. Whirlpool Canyon is affected by debris
fans. In such a canyon, fan-eddy complexes occur wherever
debris fans partly constrict the channel, thereby creating
backwaters upstream from the debris fan and lateral separa-
tion eddies and expansion gravel bars downstream [Schmidt
and Rubin, 1995]. The ow regime of the Yampa River is
relatively unregulated, but the ow regime of the middle
Green River reects the combined inuences of the Yampa
River and the ow regulation by Flaming Gorge Dam on the
upper Green River [Grams and Schmidt, 2002].
11] Laddie Park is in a relatively wide part of Yampa
Canyon where there are discontinuous oodplains, an island
that splits the channel, and mid-channel bars. Laddie Park is
upstream from a pronounced bedrock bend in the river
whose radius of curvature is small. At ood stage, ow is
backwatered upstream from this bend. The island and parts
of the oodplain in Laddie Park have been progressively
colonized during the past 70 years with tamarisk, sandbar
willow (Salix exigua), and,to a lesser extent, box elder (Acer
negundo). Today, the woody riparian vegetation community
of the Laddie Park reach is 86% tamarisk, 11% sandbar
willow, and 3% box elder.
12] The Seacliff site consists of a series of small debris
fans and eddy bars on river left. We focus on the eddy bars
that have been progressively colonized by tamari sk during
the past 60 years. Today, the woody riparian vegetation
community of these bars in the Seacliff reach is composed
of 62% tamarisk and 38% box elder.
4. Characterization of Patch-Scale Stand
Structure and Depth-Dependent Roughness
[13] Extrapolation of the results of small-scale processes
to large areas can be accomplished in a spatially explicit
manner by appropriate parameterization. For example,
Hodge et al . [2007] used a discrete element model of the
entrainment and transport of individual grains at the patch
scale to develop basic transport relations, which were
upscaled and used to parameterize a much broader reach-
scale, reduced complexity, morpho dynamic model. In the
case of scaling roughness caused by vegetation, parameteri-
zation must account for the differences in growth and
Figure 1. Study areas in Dinosaur National Monument, Colorado.
Figure 2. Twelve vegetation patches captured with the terrestrial laser scanner. These patches are
located at two study sites, (A) Laddie Park on the Yampa River and (B) Seacliff on the Green River.
Dashed lines delineate tamariskdominated oodplain areas wh ere the multiscalar model was applied.
distribution of riparian vegetation that cause complex and
highly variable interactions among in dividual plants. There-
fore, spatially explicit characterization of vegetation's role in
perturbing the ow eld should account for the patterns of
riparian vegetation growth and density and how these char-
acteristics change with height above the ground surface.
14] Our multiscalar analysis began at the patch scale. We
dened a patch to be a cluster of similarly sized, spaced,
and aged individual plants with similar stand structure
(i.e., height, dominant stem size, stem spacing). High-density
TLS point clouds (i.e., >200 pts/m
) were used to characterize
the patch-scale stand structure, which we dened as the
height-dependent stem density and vertical projected area.
We used the detailed TLS data to parameterize the patch-
scale roughness.
4.1. Methodology: Deriving Stand Structure From
Terrestrial Laser Scan Data
4.1.1. TLS Data Collection
15] We positioned a Leica Scan Station 2 upstream from 12
patches to acquire a high-resolution (0.005 m point spacing)
point cloud (Figure 3 and Table 1). Data were acquired in July
2010 during base ows when the patches were not inundated.
The ground topography of each patch was relatively at. Tree
ages, as determined by the germination year of a sample of
tamarisk stems within or close to a patch, ranged between 10
and 60 years. The substrate in these patches was either sand
or gravel. Individual plants in some patches had been buried
after germination by as much as 3.5 m of sand and mud, as
observed in oodplain trenches [Manners et al., 2011].
The bed-parallel area of each patch varied between 10
; patches with denser vegetation were of smaller size.
16] In the eld, the scanner was positioned to collect data
from the perspective of the predominant direction of over-
bank ows. One scan per patch was collected. We assumed
that the ow direction on the oodplain is approximately the
same at all ows. Thus our single-scan perspective was a
reasonable characterization of how vegetation interacts with
the ow. We also assumed that the maximum streamwise
patch length of 39 m prevented signicant occlusion, or
shadowing, of stems because TLS measurements are line
of sight [Warmink, 2007]. We occupied several control
points throughout the two eld sites in order to register the
scans to each other and convert scan data to universal trans-
verse mercator (UTM) coordinates. Each scanner setup lasted
Figure 3. Schematic of the procedure used to quantify vertical projected area proles from a three
dimensional point cloud. We established a cylindrical polar grid, composed of threedimensional cells
or voxels, for each patch centered on the scanner location. Each cell's vertical height (z) was 0.20 m.
The depth along the radial distance from the scanner (α) was 0.10 m. The third dimension was dened
by the angular distance (ϕ) that was set to 2°. Thus, the length of this dimension varied based on the
distance of the cell to the scanner along the plane dened by αϕ. For illustrative purposes, we only show
a single 0.20m horizontal slice, composed of grid cells all located at the same height above the ground
surface. Vertical projected area (A
) was rst calculated within each cell and then summed over the
patch at each 0.20m interval. Patch total A
values were normalized by the bed parallel area of the
patch, resulting in normalized vertical projected area values (A
). We use two types of curves from
this analysis: a vertical projected area curve that is representative of the vertical distribution of stems
through the prole, and the cumulative vertical projected area curve that represents the sum of all stems
through the prole and is closer to what the ow eld encounters.
between 1 and 4 hours and acquired a total of 10
per patch.
4.1.2. Scan Data Analyses
17] We calculated the stand structure of different horizon-
tal slices of the patch above the ground surface usi ng the
method of Straatsma et al. [2008]. A series of models and
Python scripts were created in ESRI's ArcGIS ModelBuilder
to convert raw point cloud data into metrics, such as vegeta-
tion density and vertical projected area. While the majority
of vegetation studies using TLS data have quantied vegeta-
tion density by identifying individual stems [e.g., Thies
et al., 2004], Straatsma et al. [2008] adopted MacArthur
and Horn's [1969] gap fraction method and quantied vege-
tation density as the ratio of laser pulses emitted to those not
intercepted. Such a methodology treats TLS returns as a
proxy for density, which is appropriate for tamarisk and
other shrubby riparian species with complicated branching
patterns (Figure 4).
18] We created a grid of three-dimensional cells, or voxels,
based on a cylindrical polar coordinate system in ArcGIS
(Figure 3). The vertical height of each cell (z) was 0.20 m;
thus, the grid was composed of a series of 0.20-m-thick
adjoining layers that spanned the vertical distance from the
ground surface to the top of the tamarisk stand. The depth
of each voxel along the radial distance from the scanner
(α) was 0.10 m. Therefore, the number of voxels in the radius
from the scanner depended on the depth to which the laser
pulses penetrated the patch, as explained below. The third
dimension of each voxel, the angular distance (φ), was held
constant at 2°. Thus, the length of this dimension varied based
on the distance of the cell to the scannerparallel plane dened
by αϕ. After manually removing ground points in Leica's
Cyclone Software, we then used this polar cylindrical grid to
quantify vegetation density (D
) from the point cloud. For
each grid cell, vegetation density, D
. was approximated as:
where T
is the total number of emitted laser pulses that
would have passed through the distal boundary of the cell
if no obstructions were present, B
is the number of pulses
intercepted between the scanner and the cell, and G
is the
number of points intercepted within the cell. As vegetation
density is dened as the vertical projected area per unit
volume, the vertical projected area of the stems in the cell,
), was then calculated as:
¼ D
0:2 (2)
where A
is the basal area of the individual voxel parallel the
plane dened by αϕ. Vertical projected area (A
), dened
as the area of the vegetation projected normal to the ow,
was summed over the patch to get a single value of A
for each 0.20-m horizontal slice. We divided A
by the
bed-parallel basal area of a given patch (A) to get a normal-
ized vertical projected area (A
) to account for the
variability in patch size. Both vertical projected area and
cumulative vertical projected area curves were obtained by
this method and used to evaluate the structure of tamarisk
stands (Figure 3).
4.2. Methodology: Quantication of Stage-Dependent
19] We created two-dimensional hydraulic models of ow
in each patch to link stand structure to the patch's hydraulic
roughness (Figure 5). Scan data were converted into two-
dimensional stem maps that described the vertical projected
area and spatial organization of each patch. These maps used
the cumulative A
value for each voxel to dene the size
and position of vertical cylinders. Due to the vertical averaging
implicit in a two-dimensional representation of vegetation, we
created a unique stem map for each 0.20-m-thick increment
to depict the vertically changing s patial conguration of the
cumulative A
. In reality, not all stems line up with the
voxels. A clustering of high A
voxels is likely a product
of a stem whose diameter exceeds the angular distance of
the voxel (Figure 3). We accounted for this by merging
adjacent cylinders that intersect. This new merged cylinder
was then moved along the αϕ plane so that its center
Table 1. Attributes of the 12 Tamarisk Patches Whose Stand
Structure Was Characterized by Terrestrial Laser Scans
Size (m
) Age (years) Substrate
1 LP1 28.9 20 s 160 moderate
2 LP2 18.7 5560 s 190 dense
3 LP3 10.3 5055 s 85 dense
4 LP4 21.2 60 s 125 moderate
5 LP5 29.2 45 s 300 moderate
6 LP6 136.5 20 g 0 sparse
7 LP7 11.9 <10 s 50 moderate
8 LP8 37 20 g 0 sparse
9 LP9 9.8 20 g 0 sparse
10 SC1 12.8 15 s 110 dense
11 SC2 6.5 50 s 140 dense
12 SC3 9.8 15 s 35 dense
LP denotes patches located at the Laddie Park study site on the Yampa
River, and SC denotes patches located at the Seacliff site on the Green River
Age was determined by identication of the germination year of a sample
of tamarisk located either within or close to each patch.
s=sand and g=gravel
Depositional history refers to the amount of ne sediment that has been
deposited around those individuals recovered for aging. We measured the
amount of deposition as the total accumulation of sediment above the germi-
nation point.
Figure 4. Example of a patch of Tamarix spp. (tamarisk) at
Laddie Park. Flow is from left to right in photo.
matched the center of those voxels used to dene it
(Figure 5). We acknowledge that vertical, cylindrically
shaped stems are an oversimpli cation of the complex
three-dimensional branching pattern.
20] We used River2D to develop the stem map mesh and
run the various ow scenarios. We chose River2D as it uses
a triangular unstructured networks (TIN)-based unstructured
mesh, which is suitable for varying the resolution to
adequately capture the two-dimensional stem maps. River2D
uses a nite element method to solve the basic equations of
vertically averaged two-dimensional ow [Stefer and
Blackburn, 2002]. Mass and momentum are conserved in the
two horizontal dimensions, solving for bed and bank shear
stresses with the Manning equation and a Bousinessq-type
eddy viscosity, respectively. Because the fundamental goal
of the two-dimensional patch model was to resolve the ow
eld through individual stems, we assigned high node spac-
ing at the edges of the stems (0.00030.0004 m), represented
as no-ow boundaries. Elsewhere, node densities were
relaxed. Stefer and Blackburn [2002] suggest that a mini-
mum of four nodes along an obstruction in each of the four
horizontal directions (i.e., positive and negative streamwise
direction and positive and negative cross-stream direction)
are necessary to reliably resolve a feature in the ow eld.
Thus, in the coarsest sense, our meshes accounted for stems
with 0.001-m diameters, while the majority of the stems in
our stem maps had diameters greater than 0.005 m. This is
important as it means the computational mesh can be con-
structed to allow us to adequately represent the impact of the
obstructions on the ow eld and back out the effective drag
from the solution.
21] The model domain extended beyond the dened
patch to ensure unobstructed ow conditions in the upstream
and lateral directions (Figure 5). Node spacing through the
patch, outside of the stems, was set to 1 m. A unique numer-
ical mesh was created for each stem map. We created
meshes with the intent of making depth-averaged predictions
from the bed, for 0.20-m ow depth increments, to evaluate
changes in roughness and hydraulics. To ensure that ow
depth within the patch was less than the upper boundary of
the 0.20-m increment, we assigned th e ow depth at the
downstream boundary as 0.05 m less than the upper bound-
ary of the cumulative A
prole. For example, for a stem
map created for the cumulative A
prole whose upper
limit was 0.80 m above the bed, the assigned downstream
ow depth was 0.75 m.
22] Each mesh was assigned a bed roughness height (k
consistent with the dominant bed material type for a given
patch; gravel (k
=0.4 m) or sand (k
=0.1 m). Bed roughness
heights were assumed constant for all ow depths within a
given patch [Whiting and Dietrich, 1990]. In order to simplify
our approach and focus on vegetative roughness, we did not
account for bed form roughness, although we recognize that
parts of the bed surface in the patches could support ripples
at some ows. We converted bed roughness height into rough-
ness coefcients (Manning's n), in order to solve for total patch
roughness (see below), and thus, bed roughness became
depth-dependent based on the following equation:
n ¼
where g is the acceleration from gravity and y is ow depth.
23] Flow rates for individual model runs were chosen so
as to maintain constant water surface slope (~0.001) through
the patches. All ows lled the extent of the model domain,
and thus, the model did not need to account for the wetting
and drying of elements. Results were iteratively solved for
depth and velocity at each node by River2D until the model
reached a steady state.
24] Total patch roughness, n
, was partitioned into
roughness caused by the bed, n
, and roughness caused
by vegetation, n
, based on
¼ n
þ n
where bed roughness was derived from the bed roughness
height (k
)specied for each patch type. For vegetation rough-
ness, we adopted an approach rst proposed by Petryk and
Bosmajian [1975] and subsequently used by many researchers
[e.g., Fathi-Maghadam and Kouwen,1997;Jarvela,2004;
Musleh and Cruise, 2006] that relates a roughness coefcient
to the energy extracted by vegetative elements
where C
is the vegetative drag coefcient, A
is the cumu-
lative vertical projected area of the vegetation, and A is the
bed-parallel, basal area of the patch. While C
values may
be derived from the literature [e.g., Nepf, 1999], our goal
was to link the specic stand structure of tamarisk patches
to their effects on channel hydraulics. Consequently, we
back-calculated C
for each two-dimensional patch model
from the drag force equation
Figure 5. Example of a single twodimensional patch
model run for patch LP2. Tamarisk stems depicted here
are a series of vertical cylinders (red circles) representative
of the cumulative vertical projected area and spatial organi-
zation of a patch at a given height. The River2D depth
(contours) and velocity (vectors) solutions are shown. See
text for further explanation of the modeling proced ures.
where F
is the bulk-streamwise drag force on the stems,
ρ is the density of water, and U
is the upstream reference
velocity taken as the average velocity across the upstream
boundary of the control volume.
25] To quantify F
, we calculated the momentum
extracted through the control volume surrounding each
patch (Figure 5) [Shields and Gippel, 1995; Manners et al.,
2007]. The lateral boundaries of the control volume were
delineated based on the extent of the patch-inuenced ow
eld dened as the transition from ow vectors with a
cross-stream component to those with no cross-stream
component. We consistently dened the boundaries in this
manner and did not evaluate the sensitivity of the drag calcu-
lation as a result of the location of the control volume bound-
ary. The net external force on a system (F
) is equal to
the change of momentum through the control volume
- F
¼ F
[26] Assuming steady ow and dening the two external
forces within each patch model that change the momentum
through the system as the shear stress exerted by the bed
) and the forces exerted by the stems (F
), we relate
these external forces to the forces across the upstream and
downstream control volume boundary
þ F
¼ F
þ F
þ F
where F
is a pressure force that is equal to the hydro-
static pressure, p, of the water normal to ow,
¼ pdA
and F
is the momentum ux across the control volume
boundary (either upstream or downstream),
¼ ρU
: (10)
[27] In equations (9) and (10), U is the depth-averaged
velocity at a point across the boundary, and A
is the area
vector that has the magnitude of the area and is directed
normal to the control volume boundary in question. The
force exerted by the bed is de ned as
¼ τ
dA (11)
where τ
is the near bed shear stress obtained as model output,
and A is the area parallel to the bed within the control volume.
Rearranging equation (8) to solve for the bulk, streamwise
force on the stems, and substituting equations (9)(11),
¼ F
þ F
þ F
¼ p þ ρU
−∫p þρU
[28] We also accounted for stem exibility of tamarisk
patches as the patches becom e submerged. As ows in-
crease, the force of the water on the stems pushes the stems
downstream, and the effective stem height (i.e., the height
interacting with the ow in the vertical) decreases. We took
a simplied approach to quantifying the deected height of
stems. With a known U and C
, we adopted a version of
the beam elasticity equation applied to the midpoint of the
stems to quantify the deection of a single representative
stem [Kubrak et al., 2008; Velasco et al., 2008], or displace-
ment of the stem axis in the water ow direction δ(x),
δ x
where d is the average stem diameter, E is the stiffness
modulus of which a constant value experimentally determined
for tamarisk of 13.1×10
was used [Freeman et al.,
2000], and I is the cross-area inertial modulus calculated from
the average stem diameter. In equation (13), the numerator
represents the force, or hydrodynamic thrust, on the midpoint
of the modeled stem, and the denominator is a mechanical
property of the stem.
29] To account for submergence and deection, we
decreased A
/ A in equation (5) based on the ratio of
the ow depth that interacts with the vegetation to the por-
tion of ow depth that does not. For example, based on the
elasticity of a typical tamarisk stem, a ow depth of 2.4 m
interacting with a 2.2-m-tall patch of tamarisk deects the
midpoint of the average stem in the streamwise direction
(δ(x)) by 0.09 m, thereby reducing the effective height
(i.e., the total amount of the ow column interacting with
the stem) to 2.07 m. Thus, 0.33 m (or 8%) of the water pro-
le is not di rectly obstructed by the vegetation. A
/A was
reduced by 8%, and equation (5) was then solved for the
new vegetation roughness value.
30] We acknowledge that this approach has limitations.
Bending of stems in the ow and the submergence of
vegetation is fundamentally a three-dimensional problem
[Stephan and Gutknecht, 2002]. By using a depth-averaged
velocity, we likely underestimate velocities, and, as a result,
thedegreeofstemdeection. Additionally, we do not update
values in equation (6), which were calculated for stiff
stems. This simplication, along with our representation of
complex tamarisk patches as single stems by using the
patch-average stem diameter in equation (13), introduces
4.3. Results: Vegetation Proles and Hydraulic
31] The 12 cumulative, normalized, vertical projected
area (A
) proles of the tamarisk-dominated patches
were classied into three groups (Figure 6). An analysis of
variance among the three groups indicates that their A
values are statistically different (P<0.001). Relatively
young (<20 years old) patches whose stand height was short
(<3 m) made up one group (Table 1). Hereafter, we refer to
this group of patches as the sparse group. These patches
occur on low-elevation gravel bars that are inundated by
common oods. This hydraulically stressful environment
presumably causes the short stature and sparse plant density.
Cumulative A
values for this group range from a mini-
mum of 0.01 to 0.18 m
. Patches of the other two groups
grow in ne sediment. Maximum height of these patches
was similar and ranged between 3.0 and 5.9 m and in age from
<10 to 60 years old (Figure 6). One of this group's cumulative
values ranged between 0.03 and 0.61 m
refer to these patches as the moderate group. The other
group's cumulative A
values ranged between 0.07 and
1.10 m
, and we refer to these patches as the dense
group. We used this prole classication scheme to extrapo-
late the characteristics of tamarisk to the reach scale.
32] Drag coefcients calculated for hydraulic model
runs for each patch and for different stages ranged from
0.1 to 1.9. We used an analysis of variance to evaluate
differences in C
among the three vertical projected area
prole groups (sparse, moderate, dense). For ow depths
of 1 m and less, C
was not statistically different among
the three groups (mean=1.0, sd=0.3). However, C
different among groups for ow depths greater than 1 m
(P<0.001). Drag coefcients were greatest for the dense
patches (mean=1.5, sd=0.2) and smallest for moderate
patches (mean=1.1, sd=0.1); sparse patches had intermediate
values (mean=1.3, sd=0.1). We explore the potential cause of
the observed trend in C
values for the different density
patches in section 6.1.
33] Patch roughness caused by ow through vegetation
generally increases with increasing ow depth to the point
where the vegetation is completely submerged; thereafter,
roughness decreases (Figure 7). Roughness increases with
depth because cumulative vertical projected area also
increases with depth. However, the relationship between
projected area and roughness is not linear. This is especially
apparent for ow depths less than 1.2 m. As expected, we
nd that A
for the moderate group is greater than for
the sparse group. However, the vegetation and total patch
roughness for the sparse group are slightly greater than those
for the moderate group (Figure 7). We attribute some of the
greater patch roughness values of the sparse group at low
ows to the gravel substrate. For ow depths less than 0.6 m
in the sparse group patches, the bed contributes greater rough-
ness than do the stems (Figure 7). However, this difference
may also be attributed to a slightly higher C
value in the
sparse group than in the moderate group.
34] Where ow depth exceeds 1.2 m, roughness values
for moderate density patches increase at a greater rate than
do the values for sparse patches. A maximum n value of
0.178 occurs at ow depths between 2.8 and 3.0 m in
moderate patches. Sparse patches become fully submerged
when the local ow depth exceeds 2.2 m. From 2.2 to
3.0 m, the vegetation roughness of sparse patches decreases
from 0.106 to 0.099. Stage-dependent vegetation roughness
values are greatest for dense patches and range from 0.045 at
a ow depth of 0.20 m to 0.293 at a ow depth of 3.0 m.
Figure 6. Cumulative normalized vertical projected area
) curves for the 12 patches, classied into three
vegetation density groups: sparse, moderate, and dense.
Figure 7. Average roughness proles for the three vegetation density groups. (A) Total patch roughness
) for the dense group (squares), moderate group (circles), and sparse group (diamonds).
(B) Proles of n
(black) and n
(gray) for the three groups. The moderate and dense groups have the
same n
values. Total patch roughness, vegetation roughness, and bed roughness are shown separately to
illustrate the signicant contribution of vegetation to total roughness. A
/A data (same value as A
used to quantify n
(from equations (5) and (14)) are averages of all patches within that group. Error bars
were calculated from standard deviation of backcalculated C
values from twodimensional patch models.
In general, vegetation roughness and total patch roughness increase with increasing depth. The exception is
the sparse group. When the sparse group is overtopped at a ow depth of 2.4 m, roughness begins to decrease.
The x shown in Figure 7A is a data point taken from the experimental work of Freeman et al. [2000] and
shows good agreement with our results.
5. Upscaling From the Patch Scale
5.1. Methodology
35] Patch-scale data are insufcienttodescribereach-scale
riparian vegetation patterns, because patch data alone do not
inform how those data can be extrapolated to the reach scale.
We took advantage of the overlap in coverage of TLS and
ALS data in the study areas to extrapolate patch-scale eld
measurements to the reach scale by creating a relation between
stand structure and the corresponding hydraulic roughness.
Thus, we leveraged the precision of the detailed TLS data
against the spatially extensive, yet coarser, ALS data set. First,
we created a model that related ALS to TLS data using the
12 patches and then extended this model to the entire study
area. While the scales over which we attempted to match these
data were variable, two aspects of our methodology allowed
us to create a scale-independent relationship. We took a prob-
abilistic approach to the likelihood of ALS data intercepting a
branch or stem for discrete vertical slices, because ALS
data are signicantly sparser than TLS data, on the order of
ALS points per tamarisk patch versus 10
TLS points
per patch. Stand structure values (i.e., vertical projected area)
were summed and normalized by bed-parallel area of the
patch. Hereafter, the term patch is used to describe the scale
over which TLS data were collected and analyzed. Model
development was based on observations made from the TLS
patches (section 5.1.2).The term window is used to describe
the scale over which the model was applied at the reach scale
(section 5.1.3).
5.1.1. ALS Probability Maps
36] Using a series of morphological lters, developed in
part using the methodology of Zhang et al. [2003], the
ALS data were classied as either bare ground or vegetation.
Averaging 1.5 pts/m
, we used the bare ground points to cre-
ate a 0.5-m resolution, bare-earth digital elevation model
(DEM) of the study areas. A 0.5-m DEM ensured sufcient
topographic detail of the smallest patch (SC2, 6.5 m
). The
height above the bare ground of each vegetation point was
determined as the difference between the elevation of each
vegetation point and that of the ground surface. We took
0.20-m-thick horizontal slices of the ALS vegetation point
cloud, corresponding to the 0.20-m horizontal slices used
in the analysis of TLS data (section 4.1.2).
37] Probability maps (0.5-m resolution) of the incidences
of ALS points for each of the 0.20-m horizontal slices were
created using indicator kriging [Todd et al., 2003]. To
construct probability maps, we used all LiDAR returns
(i.e., ground and vegetation points) within the tamarisk-
dominated oodplains and transformed them into indicator
variables. For a given horizontal slice, those returns that
were within the 0.20-m limits (e.g., between 2.0 and 2.2 m
above the ground surface) were assigned a value of 1, while
all other values for vegetation returns outside of the horizon-
tal slice range and ground points were assigned a value of 0.
As a result, each probability map provides a measure of the
probability of a LiDAR pulse (ALS) being returned from
vegetation at the associated height.
5.1.2. Creation of a Model to Link ALS to TLS
38] We assumed th at all the tamarisk-dominated stands in
the two study reaches belonged to one of the three vertical
projected area prole groups: sparse, moderate, or dense.
For each of the three prole groups, we developed relations
between height above the bed (H) and cumulative A
(Figure 8). Each of these relations was dened as a
band with upper and lower bounds based on the cumulative
curves of the 12 patches. Assignment of a patch into
one of these three bands, and therefore as one of the three
types of vertical projected area proles (sparse, moderate, or
dense), required knowledge of at least one height-dependent
cumulative A
value. With the expressed goal of upscal-
ing patch-scale observations using spatially robust ALS
datasets, the height-dependent cumulative A
must ultimately be derived from the vertical structure of the
ALS data.
39] ALS probability maps only provided us with an esti-
mate of the likelihood that a branch or stem exists at a point
Figure 8. Space dened by height above the bed and normalized vertical projected area for the three
projected area prole groups (sparse, moderate, and dense) and the predicted positions of the maximum
and median A
of those TLS patches used to create the TLSALS model (Table 2). Bands were dened
by the range in values measured from the 11 TLS patches. (LP2 was not included; see text for explanation.)
This space was used to classify values extracted from the ALS data in the movingwindow analysis. Horizon-
tal error bars correlate to the 20% error in the predictive model, and vertical error bars correlate to the 6% error
between stand height measured from ALS and TLS. Solid error bars are associated with predicted median
values. Dashed error bars are associated with predicted maximum values. The SC and LP numbers refer to
specic patches at Seacliff and Laddie Park, respectively.
on the oodplain. These maps did not provide us with a
direct measure of the vertical projected area of tamarisk
stands. To relate ALS probability maps to vertical projected
area proles derived from TLS scan data, we extracted the
probability value from the ALS probability maps for every
0.20-m horizontal slice and applied those data to the centroid
of each grid cell (section 4.1.2). Summed over the area of the
whole patch, we quantied a vertical distribution of block-
age (m
), dened as a measure of vegetation density
from the top-down perspective, for each patch,
where P(ALS)
is the probability extracted from the ALS
probability map at the centroid of each polar grid cell, A
is the bed-parallel area of the cell, and A is the bed-parallel
area of the TLS patch. From the vertical distribution of
blockage, we constructed cumulative distribution curves of
blockage from the ground to the maximum height of the
vegetation in the patch. Both the cumulative Bk
and cumulative A
curves were converted into cumula-
tive frequency curves (Figure 9). We quantied A
quantiles from these cumulative frequency curves.
40] For each patch, we calculated two H-A
the maximum and the median points (Table 2). The
maximum value was the largest cumulative A
). This value necessarily occurs at the top of
the vegetation canopy. The median value (A
) was
identied as the 50th percentile of the cumulative A
distribution (Figure 9). The height at which the A
occurred was dependent on the prole shape and was not
immediately apparent from the ALS data.
41] To quantify these two points from ALS data, we
determined the maximum height from the ALS data
) and calculated the maximum cumulative block-
age (Bk
) (Figure 9). The relationship that we estab-
lished between Bk
and A
was based on 11
of the 12 patches. We excluded patch LP2, where we deter-
mined that the canopy density was too thick to characterize
the rest of the prole (Bk
=1.8). We assumed that patches
whose Bk
values exceeded 1.5 m
belonged to
the dense group. Based on the remaining 11 patches for
<0.50 m
, a positive power law relationship
exists between Bk
and A
b=1.92, R
=0.76) while for 0.5<Bk
<1.5 m
a negative relationship exists (a=2.24, b=1.07, R
The presence of a threshold at 0.5 m
indicates that
the canopy begins to lter out points greater than this value
and that the lower portion of the plant is hidden from the
ALS data acquisition process. Similar relationships were
established between the maximum blockage (Bk
and the median A
value (A
) for values of
<0.50 m
(a=13.5, b=1.92, R
=0.76) and
>1.5 m
(a=2.98, b=1.07, R
=0.77) . These
relationships allowed us to calculate both A
from Bk
, a value derived from ALS data
alone. Error between the quantied A
and the predicted A
) using these rela-
tionships was approximately 20%. Additional relationships
were established for A
and A
as a means
of evaluating the shape of the A
prole, as explained
42] To determine the height of A
, we identied
a pattern in the relationship between the cumulative distribu-
tion of blockage and the cumulative distribution of A
for a given patch. These relationships reect differences in
the perspective from which the ALS and TLS data sets
were collected; ALS data are collected from directly above
(i.e., airborne) each area of vegetation, and TLS data are
collected from a low-oblique perspective (i.e., a tripod).
For patches whose maximum tree heights were greater than
or equal to 5 m, Bk
occurred 2.3 m (sd=0.02) higher
in the prole than A
. For patches whose maximum
heights were between 4 and 5 m, the difference was 1.4 m
(sd=0.2). For patches whose maximum height was less than
4 m, the difference was 0.2 m (sd=0.2) (Table 2).
43] Accounting for the 20% uncertainty in quantied
and predicted A
values (horizontal error bars), and a
6% difference in the maximum height of the vegetation
(Table 2) within a patch between TLS and ALS (vertical
error bars), we predicted the correct A
prole group
(i.e., sparse, moderate, or dense) for 9 of the 11 patches
using the H
- A
values and 6 of the 11 patches
using the H
- A
values (Figure 8). On average,
Figure 9. Cumulative curves used to relate TLS data to ALS data. Example is shown for patch LP4. (A)
Cumulative maximum blockage (Bk
) occurs at the maximum height from the ALS data (H
). (B) Cumulative frequency curve for A
(solid black line) and Bk
(dashed gray line).
The median values of A
and Bk
were used to dene the median heights for the H
from the cumulative frequency curves, respectively. A relationship between the heights at which
the median values occurred at a single patch for the A
and Bk
was identied that was subsequently
used in the application of the TLSALS model to the reach scale.
the A
was overpredicted by 0.22 m
, while the
was underpredicted by 0.28 m
44] The discrepancy between data collected from a top-
down perspective and that collected parallel to the ow is
greatest for dense canopies. A
values for SC2 and
SC3 were signicantly underpredicted by the model. We
attribute this divergence in model success to an extremely
dense canopy, where the ratio between Bk
is relative ly large. For SC2 and SC3, this ratio
was greater than 7, while for the remaining nine patches,
the ratio was on average 2. In patches such as SC2 and
SC3, the density of the top of the canopy essentially
shadows the lower portion of the prole, thereby altering
the cumulative blockage curve. We determined that an
adjustment of 50% from the predicted value was appropriate
to correct for the canopy blockage.
5.1.3. Application of the Model
45] With these relationships established, we extended the
patch-scale observations to the entire study area. To do this,
we used a 2-m, 3-m, and 4-m circular moving window.
Within each moving window, we summed the blockage
values derived from the ALS probability maps. The window
was used as a proxy for the patch. We used various window
sizes to determine the best scale over which to apply
the ALS-TLS model. Both the maximum and median
- A
values were calculated in order to provide
the best gage for the patch type to which each discrete
window belonged. The 50% correction was applied to those
proles that had a predicted ratio of Bk
greater than 7.
46] A 2-m grid overlaying the study area extracted the
summed probabilities at the center of each grid cell. We
applied the same methodology as described in section
5.1.2 to extract maximum height, maximum blockage, and
the height and value of the quartile values of blockage over
the window. We classied the two reaches by the type of
vertical projected area prole and therefore the type of
depth-dependent roughness prole, based on these values
and the empirical models that link Bk
to A
and A
.We estimated the various metrics for
modern alluvial deposits that were dominated by tamarisk
and did not apply the model to areas of vegetation domi-
nated by other species, such as box elder.
47] Thus, we applied our TLS relations to the two study
reaches, based on the ALS data, the result of which was a
map of vegetation density (i.e., classied into the three pro-
le groups: sparse, moderate, or dense) present within each
map cell (Figure 10). We evaluated the model, and the size
of the moving window, by comparing the model predictions
of conditions in the 12 patches to those estimated from the
ALS data (Figure 10 and Table 3). Because individual
patches are larger than the scale of the grid (4 m
), the
roughness map consisted of multiple grid cells within each
patch. We acknowledge that the discrepancy in scale, both
between patch and window sizes as well as between patches
and the grid over which we validated the model, inevitably
resulted in differences in model prediction. For example, if
a 50-m
patch is evaluated using a 2-m ci rcular window
(12.5 m
), the stand structure of sections of this patch, while
characterized as one group in the development of the model,
may belong to two or more groups. Variability in density
existed within a given patch. While averaging during model
development masked density differences, this patch-scale
variability was highlighted during model application, espe-
cially when using different wind ow sizes.
5.2. Upscaling Results and Interpretation
48] The moderate and dense patche s were best captured
with a moving window of 3 m (Table 3). The model cor-
rectly classi ed 84% and 70% of the cells within the three
moderate and ve dense patches, respectively. In contrast,
the sparse patches performed the best when the moving
window was 4 m; the success rate in this case was 42%.
However, the difference in performance for the sparse
patches did not vary greatly for the different window sizes
(36% and 35% for a 2-m and 3-m moving window, respec-
tively). The sparse patches had the lowest success in applica-
tion of the ALS-TLS model. Based on the above ndings,
we considered that the 3-m window was best applied to
these study reaches.
49] Classied maps of the Laddie Park and Seacliff
reaches qualitatively showed good agreement with eld
Table 2. Measured and Predicted Tamarisk Height (H), ALS Blockage (Bk
), and Normalized Vertical Projected Area (A
Values for 12 Vegetation Patches Used in the Development of the ALSTLS Model
Measured Predicted
Maximum Median Maximum Median
(m) (m
) (m) (m
) (m) (m
) (m) (m
) (m) (m
LP1 4.4 1.88 4.4 1.37 1.5 0.94 3.10 1.60 1.70 1.00
LP2 5.9 5.13 5.7 1.79 2.0 2.57 4.25 ‐‐
LP3 4.4 4.20 4.8 0.75 1.5 2.10 2.80 3.05 1.40 2.00
LP4 5.8 2.54 5.8 0.89 1.8 1.27 4.14 2.55 1.84 1.65
LP5 5.0 3.06 5.2 1.15 2.3 1.53 4.35 1.93 2.05 1.23
LP6 2.6 0.67 2.6 0.21 1.2 0.34 1.25 0.35 1.09 0.35
LP7 3.2 1.94 3.4 0.45 1.4 0.97 1.53 1.46 1.37 1.45
LP8 2.8 0.75 2.8 0.26 1.2 0.38 1.48 0.51 1.32 0.51
LP9 2.2 0.74 2.2 0.20 1.1 0.37 1.15 0.32 0.99 0.32
SC1 4.2 5.40 3.0 0.61 1.4 2.70 2.70 3.84 1.30 2.55
SC2 3.8 3.11 3.2 1.11 1.2 1.56 1.75 3.82 1.52 1.91
SC3 4.2 4.17 3.8 0.40 1.9 2.09 1.70 3.48 0.30 1.74
>7 indicates high canopy blockage, predicted value increased by 50%.
observations (Figure 10). Generally, the sparse group was
restricted to low-elevat ion gravel bars. These stands only
occur in the Laddie Park reach. The tamarisk stands in the
Seacliff reach were predominantly established on eddy bars
and are denser. Many individuals in these groups are buried
by more than 1 m of ne sediment. Moderate and dense
stands also occur in the Laddie Park reach on higher topo-
graphic surfaces. Thick deposits in the central parts of the
islands support relatively dense tamarisk stands.
50] The discrepancy in scale, both between TLS patch
and moving window ALS model sizes and between patches
and the grid over which we validated the model, inevitably
contributed to differences in model prediction of stand type
within the 12 TLS patches, especially for the sparse patches.
Spatial variability exists within a TLS patch, and, therefore,
the larger the size of the patch, the greater the expected
variability in predicted A
groups within that patch.
We expect there to be the greatest within-patch variability
in the sparse-group patches. Extraction of A
from the TLS scan data over the same scale of TLS-ALS
model application (i.e., the 3-m window) increased the
match in A
group type for the sparse groups from
35% to 65% (Table 3). Additionally, cells located closest
to the scanner had greater success, highlighting the difculty
in capturing large areas with TLS.
51] Future work might be able to ne-tune these upscal-
ing relationships and/or more robustly validate their applica-
tion at particular sites and/or their transferability to other u-
vial settings. While the methodology could be developed
using a smaller TLS patch size, and potentially a greater
number of patches, one must be cognizant of the impact of
patch size on identication of the within-patch processes
(e.g., routing of ow around individual stems that in uence
the larger, reach-scale ow eld) (discussed further in
section 6.1). Additionally, greater spatial congruity between
patch and moving window size would likely result in
increased predictive success. However, an increase in the size
of the window to more closely match patch size would result
in unreasonable averaging across vegetated/unvegetated areas
and the locations of high variability in vegetation density.
6. Discussion
6.1. Verication and Uncertainty of Patch-Scale Values
52] To verify the vertical projected areas we determined
from our TLS measurements, we compared our values with
direct eld measurement of tamarisk and willow in other stu-
dies. The majority of studies that report vegetation densities
do so at the reach scale as stem densities (e.g., number of
stems/ha) [e.g., Stromberg et al., 1993; Beauchamp and
Stromberg, 2007]. These bulk values mask the ne spatial
resolution that we captured in our study. However, a few
studies report values collected over spatial scales compara-
ble to the patch scale. Grifnetal. [2005] found that tama-
risk stems greater than 0.01 m in diameter on the Rio Puerco
in New Mexico were spaced 0.20 m apart, and, therefore,
have an A
value of 0.25 m
at a height of 1 m.
Detailed stem measurements of young sandbar willow
(<10 years) growing on a gravel bar on the upper Colorado
Figure 10. Application of the TLSALS model (with a 3m moving window) to the (A) Laddie Park and
(B) Seacliff reaches . The pattern of prole group recognition is generally realistic. We evaluated the model
based on the correct prediction of group type for each 2m square cell within the 12 vegetation patches.
Table 3. Percentage of 2m Cells Within the 12 TLS Patches That
Match the TLS Prole Group in the Application of the TLSALS
Model Using a 2m, 3m, and 4m Moving Window
2m Moving
3m Moving
4m Moving
1. Sparse 36% 35%
2. Moderate 46% 84% 58%
3. Dense 52% 70% 60%
Withinpatch spatial variability of A
proles, analyzed at the same
3m moving window scale as the TLSALS model application, increases
model prediction to 65%.
River had A
values that ranged between 0.06 and
0.14 m
at a height of 1 m [Logan, 2000]. Values for
sandbar willow on tributaries of the South Platte River,
Colorado, ranged between 0.08 and 0.93 m
at a height
of 1 m [Grifn and Smith, 2004]. Generally, the range of
values from these studies ts within the range of A
values quantied for the 12 patches of this study
(0.060.37 m
at a height of 1 m).
53] Without independent, non-TLS eld measurements of
stand structure, we cannot assign a degree of uncertainty or
estimate of error to the vegetation densities calculated in this
paper. Nevertheless, prior studies provide information on the
potential accuracy of the approach used in our investigation.
In the development of the methodology employed here,
Straatsma et al. [2008] measured stem densities for 23 plots.
They determined that their modeling efciency was 63%.
Errors were attributed to (1) the assumption of randomly
distributed stems in the development of the met hodology,
(2) the presence of leaves at the single elevation measured,
and (3) the relatively low resolution of their scans.
However, differences exist between our study and that of
Straatsma et al. [2008], which preclude direct extension of
their reported uncertainties to our work. For one, the types
of vegetation analyzed in the two studies differ greatly, from
a sparse stand of straight-stemmed willow (Salix alba)
[Straatsma et al., 2008] to a densely vegetated stand of
tamarisk with randomly oriented stems (this study). As such,
the assumption of randomly distributed stems might intro-
duce less error to our study, especially for the moderate to
dense stands. We acknowledge that measurement of struc-
ture of tamarisk stands during the growing season adds some
error to the measurements due to the presence of leaves.
However, the stem area to leaf area ratio for tamarisk is
relatively high and unlikely to exert a major inuence.
Finally, the resolution at which Straatsma et al. [2008]
scanned was much coarser than ours: 2381104 pulses per
angular degree [Warmink, 2007] versus 10053016 pulses
per angular degree. This increased density of points has a
greater likelihood of capturing all stems. Additionally, we
limited our scanned patches to relatively small footprints,
thereby limiting shadowing of stems. It should be empha-
sized that our goal with this research was not to build a
highly precise model of vegetation density, but rather to nd
a reasonable proxy for vegetation density that can be used to
estimate its effect on oodplain hydraulics.
54] We back-calculated the drag coefcient (C
) from
the drag force equation as a way to relate stand structure
(vertical projected area proles) to roughness. For vertical
cylinders, a C
value between 1.0 and 1.2 is regularly cited
as the most reasonable value for the range of ow conditions
used in experimental work [e.g., Jarvela, 2004]. A large
literature exists that explores ways in which these values
may be predicted or adjusted given the range of variability
of natural conditions. Nepf [1999] found that for an increase
in density of cylindrical stems, the bulk C
from 1.2 to less than 0.4. In a series of ume experiments
using willow, Jarvela [2002] calculated C
values that aver-
aged between 1.6 and 1.4 depending on the spacing and
distribution of the willow. Other studies using real stems
[James et al., 2004] or measuring drag in a noncontrolled,
eld-based setting [Hygelund and Manga, 2003; Manners
et al., 2007] have reported a much larger range and
maximum values, as high as 20. Average C
values in our
study (1.0 for all groups with ow depth<1.0 m and 1.3,
1.1, and 1.5 for the sparse, moderate, and dense groups,
respectively for ow depths1.0 m) fall well within this
range of experimentally determined drag coefcients.
6.2. Hydraulic Roughness of Tamarisk
55] The increase in hydraulic roughness associated with
colonization of bare alluvial deposits by tamarisk has been
suggested as an important cause of channel narrowing of the
Colorado River and its tributaries [Graf,1978;Birkeland,
2002]. However, few studies have quantied the change in
hydraulic roughness.
56] In this study, we estimated the large-scale distribution
of roughness of tamarisk patches. Patch-scale Manning's n
values ranged from 0.057 to 0.319. The higher end of these
values is greater than those generally reported for vegetated
oodplains (upwards of 0.25) that are often calculated from
the hydraulic conditions (water surface slope and depth) for
small reaches or whole oodplain surfaces [Barnes, 1967;
Arcement and Schneider, 1989; Sandercock and Hooke,
2010]. Averaging conditions over these areas inevitably
accounts for spatial variability in roughness values. In contrast,
we calculated roughness values over smaller spatial scales.
Our values are therefore representative of the local resistance
of vegetation and are solely applicable to the patch scale.
57] When we compare our predicted patch-scale Manning's
n values to those determined experimentally for tamarisk
stands, we nd good agreement. The sparse group best repre-
sents the types of plants used in experimental studies. Our
predicted values (0.0760.141) fall within the range of exper-
imentally determined values (0.0550.180) [Freeman et al.,
2000; Fathi-Maghadam et al., 2011]. Specically, we identi-
ed the experimental conditions in Freeman et al.[2000]that
most closely match our two-dimensional models and found
excellent agreement (Figure 7).
58] We found that roughness increases with ow depth,
generally scaling with the vertical projected area of vegetation
patches. This ndingisconsistentwithexperimentalwork
[Fathi-Maghadam and Kouwen,1997;Musleh and Cruise,
2006]. Musleh and Cruise [2006] reported that roughness
through a patch of partly submerged rigid cylindrical rods
increases linearly with ow depth from 0.06 to 0.24. However,
while other studies documented a linear increase in roughness
with depth, we found that roughness increases in proportion to
changes in the vertical projected area. As expected, roughness
decreases as patches become submerged (Figure 7). For sparse
density stands, total patch roughness decreased after a stand
was completely submerged.
59] Often, hydraulic models assume that roughness
decreases as ow depth increases [Arcement and Schneider,
1989]. This assumption is applicable for in-channel conditions
either where no vegetation exists or where vegetation becomes
fully submerged. The declining contribution of bed roughness
to total patch roughness with increasing ow depths supports
the applicability of the above assumption (Figure 7). However,
for oodplain ows through stands of tamarisk and willow,
and likely other types of shrubby riparian vegetation, our
results predict that total patch roughness increases with
increasing ow depth because cumulative vertical projected
area also increases with increasing ow depth.
[60] Group-average normalized vertical projected area
proles (Figure 11) indicate that the prole shapes for moder-
ate and dense patches are similar, although the magnitude of
projected area is greatest for dense patches. Both have maxi-
mum values around 2 m above the ground surface. However,
the proles differ within 0.5 m of the ground surface. Here,
there is a second maximum A
value in densely vege-
tated patches, on average three times greater than that of the
moderate patch. We hypothesize that this difference may be
attributed to patch-scale organization (Figure 12).
61] Densely vegetated patches may promote more well-
dened ow pathways and channels that occur between
clumps of dense vegetation. A feedback between dense
clumps of stems close to the ground surface and strong ow
paths likely exists [Corenblit et al., 2007]. Dense clumps
redirect and channelize ow, scouring out new vegetation
and maintaining ow paths. Higher velocities in these ow
paths have the potential to shear low-lying stems. When
tamarisk stems break, a greater number of stems regrow,
thereby creating greater stem density. Additionally, because
these ow paths are more well dened and have a larger
proportion of the ow, and therefore faster velocities, they
are capable of transporting woody debris, some of which
may become trapped by stems. Field observations of woody
debris in and around dense group patches support this
notion. All of these factors contribute to high stem density
close to the ground (Figure 12).
Figure 11. Groupaveraged normalized vertical projected
area proles.
Figure 12. Cartoon showing the interaction between tamarisk patch density and ow. Stem spacing
inuences the size and strength of ow paths around and through the patch. If stems are clumped together,
the ow will be channelized, shearing lowlying stems and delivering wood. A greater number of stems
will grow back after being sheared, all of which results in higher stem density and therefore greater vertical
projected area in the 0.5 m above the ground surface. The density and spacing of stems also has an inu-
ence on the hydraulics of ow through a patch (i.e ., on the C
). These relationships suggest that feedbacks
exist among ow and tamarisk growth. It is these feedbacks that control the spatial pattern of vegetation
hydraulic roughness.
[62] Similarly, the sparse group prole shows the same
characteristic secondary peak close to the ground. These
patches grow on gravel bars along the edge of, or even
within, high-ow side channels. High velocities often shear
stems here and deliver woody debris. Thus, similar pro-
cesses may be attributed to determining the shape of the pro-
le. However, the magnitude of these processes and location
within the channel prevents the sparse group from growing
to the same density.
63] The fact that the moderate density patches are gener-
ally composed of evenly spaced stems, while dense (and
sparse) patches tend to have clumps of stems between larger
open areas has a direct impact on the hydraulic effectiveness
of these two patch types. An extensive literature exists on
the hydraulic impact of stem spacing [e.g., Nepf, 1999; Stone
and Shen, 2002; Liu et al., 2008]. Generally, closer spacing
among stems reduces the bulk drag coefcient due to the
downstream sheltering effect [Raupach, 1992]. We might
attribute the lower average C
value for moderate patches
(1.1 as compared to 1.5 for dense patches and 1.3 for sparse
patches) to this effect, whereby the arrangement of stems in a
moderate patch (Figure 12) increases the wake interference.
64] We do not know if tamarisk patches get denser or
sparser as they age, but we have observed changes to tamar-
isk patches as a result of the aggradation of ne sediment.
Tamarisks on gravel bars remain short and sparse as the
stands age, presumably because of the harsh hydraulic envir-
onment. However, we have observed that tamarisk stands
that established on gravel bars, but are now buried by as
much as 3 m of ne sediment, have moderate or dense
vertical projected area proles. Fine sediment deposition
on gravel bars may be a result of an increase in the local
hydraulic roughness, an indication of an alteration to the
ow eld, or of a change in the hydrology and/or sediment
load that has resulted in sediment surplus. In the study
reaches, we nd ne-grained caps on gravel bars in areas
whose hydraulic setting (e.g., upstream from tight bedrock
bends) promotes deposition. However, these caps were not
as spatially extensive prior to the establishment of tamarisk
and willow. The caps have been increasing in size with the
expansion of riparian vegetation. This observation suggests
that within certain hydro-geomorphic environments, estab-
lishment of vegetation increases hydraulic resistance and
promotes deposition of ne sediment. Fine-grained alluvial
deposits provide additional surfaces for the colonization of
new plants. Additionally, eld observations from oodplain
trenches indicate that ne sediment deposition increases the
density of tamarisk stands. Greater coverage and density of
tamarisk further increase vegetative hydraulic resistance,
altering ow elds, and promoting deposition of ne sedi-
ment. Thus, feedbacks exist among ow, sediment, and
tamarisk growth. It is these feedbacks that control the spatial
pattern of vegetation hydraulic roughness.
6.3. Upscaling the Hydraulic Roughness of Patch-Scale
65] As an illustration of how a reach-scale evaluation of
the impact of vegetation on the ow eld might be pursued,
we applied the methodology described in this paper to a two-
dimensional hydraulic model evaluated over the entire
Laddie Park site. Our goal was to illustrate the importance
of incorporating a spatially variable representation of
vegetation roughness. We applied the stage-dependent
roughness curves established for the study sites (Figure 7)
to the two-dimensional hydraulic model River2D.
66] A combination of LiDAR-derived topography,
acquired in 2008, and real time kinematic global positioning
system (RTK GPS)-based bathymetric surveys, acquired in
2010, were used to create a DEM that was sampled onto a
triangular nite element mesh with 2-m node spacing around
the tamarisk-dominated oodplains and 10-m node spacing
elsewhere. A constant discharge upstream boundary condition
was established for two ood discharges, 450 and 935 m
and a constant downstream water surface elevation was
specied. Because a rating relation was not available to use
for specifying ow boundary conditions, downstream water
surface elevations were derived from a one-dimensional
Hydraulic Engineering Centers River Analysis System
(HEC-RAS) [U.S. Army Corps of Engineers, 2008] model
run under steady, subcritical ow conditions with a normal
depth boundary condition (water surface slope of 0.001). For
context, base ows are approximately 15 m
/s; a 450 m
ood has a recurrence of approximately 5 years, and a
935 m
/s ood is the ood of record whose recurrence is
greater than 100 years [Elliott and Anders, 2004].
67] Roughness in the model is provided in terms of a
roughness height (k
). While the roughness height of the
bed does not change with ow depth [Whiting and Dietrich,
1990], we determined in section 4 that the roughness, as
measured by Manning's n, of a patch of tamarisk changes
with ow depth. To account for the changing roughness over
the ow depth, we converted group-specic roughness pro-
les into k
values based on equation (3).
68] We ran two scenarios for each of the two discharges:
1. Constant roughness for the entire reach (k
=0.1 m)
2. Assignment of stage-dependent, spatially variable
roughness as determined for vegetated areas using the
ALS-TLS model. We used the relationships established
between Bk
to A
and A
the stand height to determine the vegetation density
(Figures 8 and 9). The classied map is shown in
Figure 10. With a known vegetation density group, we
assigned the corresponding roughness prole (Figure 7).
Unvegetated areas were assigned values of k
=0.4 m
for gravel and k
=0.1 m for pools/bare sandbars. Unve-
getated areas were delineated based on aerial photo-
graphs and ground surveys.
69] Model validation was based on a few eld measure-
ments made at 450 m
/s in spring 2011. We took discharge
measurements with a Teledyne RD Instruments RiverRay
(acoustic Doppler current proler (ADCP) in the side
channel (river left) of the study site at 450 m
/s. These
measurements are in good agreement with model output
(4% difference from the total discharge of scenario 2).
70] The extent of oodplain inundation was slightly sensi-
tive to the addition of spatially variable depth-dependent
roughness at 450 m
/s (Figure 13). The average water depth
through the reach differed by less than 0.30 m for both
discharges. However, the various model runs using different
scenarios show that prediction of the distribution of bed shear
stress differs in important ways (Figure 13). Characterization
of the spatial distribution of shear stress is a critical component
in the prediction of the divergence of the sediment transport
eld and in the prediction of the distribution of scour and ll
that causes channel narrowing or widening. The shear stress
predicted by River2D is the total boundary shear stress, τ
and is the sum of the stress exerted on the vegetation, τ
(i.e., form drag) and the stress exerted on the bed and banks,
, (i.e., skin friction) [Bufngton and Montgomery , 1999; Smith,
2004]. We are interested in extracting the latter component, τ
because of its geomorphic importance in sediment transport.
71] The proportion of τ
from τ
and τ
may be assigned
based on the forces exerted on the stems and on the bed,
respectively, in the two-dimensional patch model. In the pro-
cess of quantifying the vegetative and whole patch rough-
ness in section 4.2, we quantied the force exerted on the
bed, F
, and the force exerted on the stems, F
determined F
as a function of ow depth for each
of the three vertical projected area prole groups (i.e., sparse,
moderate, and dense) (Figure 14). As stress is the force per
unit area, the force ratios for each vegetation group also
specify corresponding τ
ratios. We draped the density
classication for vegetation patches, as determined by the
TLS-ALS model (Figure 10), over River2D τ
output and
applied the τ
ratio, unique to each group, to quantify the
near-bed shear stress (Figure 13).
72] The general patterns of vegetative roughness and the
resulting near-bed shear stress values predicted through the
application of the methodology developed in this paper
appear reasonable based on eld observations, aerial photo-
graph analyses, and an intimate knowledge of the site
[Manners et al., 2011]. Incorporation of a spatially variable
representation of vegetation roughness exposes regions of
very low near-bed shear stresses (Figure 13) that correlate
with thick deposits of ne-grained alluvium. Differences in
the pattern of near-bed shear stress between the spatially uni-
form and spatially variable roughness are more pronounced
for the higher discharge (935 m
/s), because the water accesses
the vegetated oodplain. This example of the Laddie Park site
is a proof of concept that we can use the fusion of TLS and
ALS data across multiple scales. Such a multiscalar analysis
provides a platform to more robustly explore the mechanisms
and feedbacks between vegetative encroachment into active
alluvial surfaces and the geomorphic responses.
7. Summary and Conclusions
[73] The methodology described here demonstrates the
feasibility of incorporating small-scale interactions between
water and stems into a larger scale process-based evaluation
of the role of riparian vegetation on the ow eld. To our
knowledge, the multiscalar analysis presented here is the
rst to mechanistically account for shrubby riparian vegeta-
tion stand structure, and associated hydraulic roughness of
Figure 13. Twodimensional model output at the Laddie Park reach for two discharges (Q=450 and
953 m
/s) and two roughness scenarios. (1) Spatially uniform roughness: A constant k
value was assigned
to the reach. When converted to n, these values varied slightly as a result of the depth dependence of this
relationship. (2) Spatially variable roughness: Application of the TLSALS model expressly accounts for
stand structure in the parameterization of roughness. A constant k
value was assigned separately to pools/
sandbars and to gravel bars/rifes. When converted to n, these values varied slightly as a result of the
depth dependence of this relationship. (Top) The resulting maps of roughness (shown here as
Manning's n) for the two scenarios at the two discharges. (Bottom) The nearbed shear stress (τ
vegetation patches, at the reach scale. Vegetation metrics
that have been repeatedly shown to affect the ow eld,
including stem density and spacing [e.g., Nepf,1999;Bennett
et al., 2002; Jarvela,2002],wereimplicitlyincorporatedina
spatially explicit way into the larger scale parameterization
of vegetation. Although we applied this parameterization to
a reach, the ALS data we used could have been applied to
the entire Yampa and Green River corridors within Dinosaur
National Monument. Through incorporation of this ner scale
detail derived from the TLS data, we believe that the method-
ology presented here has the potential to capture the impact of
riparian vegetation on the ow eld in a detailed and spatially
explicit way at a large scale.
74] Our study formulated a methodology that takes
advantage of the increasing availability of spatially exten-
sive data sets, such as ALS, as well as the accessibility of
high-resolution point clouds from TLS. We present one pos-
sible way to relate the stand structure of discrete patches of
vegetation derived from high-resolution measurements to
the much coarser signature of stand structure derived from
airborne data. Thus, the goal of this methodological devel-
opment has been to capture the detailed structure of riparian
vegetation and extrapolate those inuences out over large
areas. Adoption of the specic relationships formulated here
may not necessarily be possible for other vegetation commu-
nities; however, the methodology presented here probably
transcends geographic location and vegetation community
75] Results from this work predict that the roughness of
forested oodplains increases with ow depth. With rising
stage, the hydraulic resistance of the oodplain increases
until the vegetation is fully submerged; thereafter, roughness
declines. This prediction supports experimental observations
and implies that reach-scale dynamics over a ood event are
continually being altered by the interaction of water and
76] Although there are a variety of other approaches that
can be used for modeling the hydraulic impact of vegetation
[e.g., Nepf, 1999; Kean and Smith, 2004], a key contribution
of this study is the description of a multiscalar model. Appli-
cation of our TLS-AL S model to a two-dimensional hydrau-
lic model of Laddie Park highlights the fact that assigning
spatially explicit, stage-dependent hydraulic roughness values
has the potential to reveal geomorphically relevant hydraulic
patterns at the reach scale that would not be apparent with
simpler characterizations of channel or vegetation roughness.
Ultimately, detection of geomorphically relevant patterns at
these scales provides a rst step in the identication and
prediction of vegetation for both inducing and exacerbating
channel change.
77] The role of riparian vegetation in causing channel
change is an enduring and pervasive question in river man-
agement. For example, the Colorado River basin has been
plagued by the invasion of tamari sk. The rapid establishment
and dominance of this species has contributed to profound
channel narrowing and cross-section simplication to the
detriment of in-channel habitat critical to the survival of
some native sh species [Olden et al., 2006]. The two-
dimensional hydraulic oodplain models developed with
spatially variable, stage-dependent roughness describe d here
have th e potential to reveal areas sensitive to further channel
change and ultimately to build predictive morphodynamic
models of channel evolution.
A bed-parallel area, m
bed-parallel area of a cell, m
ow-perpendicular projected area, m
ow-perpendicular projected area of a cell,
maximum, cumulative, ow-perpendicular,
normalized projected area, []
α depth of the cell along the radial distance from
the scanner, m
number of points intercepted between the
scanner and the cell, []
ALS blockage, []
drag coefcient, []
δ(x) stem deection in the streamwise direction, m
d stem diameter, m
vegetation density, m
vegetation density of a cell, m
E stiffness modulus, N/m
F external or internal forces, N
vegetative drag force, N
number of points intercepted within a cell, [ ]
g gravitational acceleration, m/s
H tamarisk height above the bed, m
tamarisk height measured from ALS data, m
tamarisk height measured from TLS data, m
I cross-area inertial modulus, m
effective roughness height, m
n Manning's roughness value, []
Figure 14. Depthdependent ratio of forces on the stems to
those on the bed (F
) for each of the three vertical pro-
jected area prole groups (i.e., sparse, moderate, and dense).
As stress is the force per unit area, we used the F
ratios to partition total boundary shear stress into the stress
exerted on the vegetation, τ
, (i.e., form drag) and the stress
exerted on the bed and banks, τ
curves had R
values of 0.91, 0.99, and 0.99 for the sparse,
moderate, and dense groups, respectively.
Manning's bed roughness value, []
Manning's patch roughness value, []
Manning's vegetation roughness value, [ ]
p hydrostatic pressure, Pa
ρ density of water, kg/m
φ angular distance, degrees
total number of emitted laser pulses that
passed through the distal boundary
total boundary shear stress, N/m
shear stress on bed, N/m
shear stress on vegetation, N/m
U depth-averaged velocity, m/s
depth-averaged reference velocity, m/s
y ow depth, m
z vertical height of the cell, m
78] Acknowledgments. Many individuals helped with eld logistics
and data collection efforts. We have beneted from the continual support
and encouragement of Tamara Naumann and others on the staff of Dinosaur
National Monument. The TLS data acquisition was funded by a U.S. Geo-
logical Survey Grant to develop a Big River Monitoring Protocol for the
National Park Service's Northern Colorado Plateau Network. This research
was funded by a Quinney Fellowship and National Science Foundation
Doctoral Dissertation Improvement Grant to the lead author. Additional
support was provided by Utah State University and the United States Geo-
logical SurveyGrand Canyon Monitoring and Research Center. We owe
thanks to James Brasington and Rebecca Hodge, whose original work on
TLS patch scanning [Hodge et al., 2009], and upscaling patch-scale discrete
element model results to drive reach-scale reduced complexity models
[Hodge et al., 2007], served as a conceptual seed for the upscaling
approaches we pursued here. The manuscript's clarity and organization
was greatly improved thanks to the helpful and constructive reviews of
Steve Darby, John Bufngton, and two anonymous reviewers.
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