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5
Revisiting the Morphological Approach: Opportunities and Challenges
with Repeat High-Resolution Topography
Damià Vericat, Joseph M. Wheaton, and James Brasington
5.1 Introduction
The morphology of gravel bed rivers reflects the relative roles of four fundamental geomorphic pro-
cesses: the erosion, transport, deposition, and storage of sediment. Fluvial geomorphologists have long
focused on understanding the controls on bed-material transport, as it is this coarse fraction of the
total sediment load that provides the fundamental building blocks of channel morphology. Attempts
to link quantitatively the observed morphology of channels to formative transport processes have been
approached from two directions. The forward method (after Church 2006) involves using established
physical principles to deduce constitutive equations to estimate sediment transport and predict pat-
terns of sedimentation that build channel morphology. By contrast, the inverse approach, involves
using observations of channel morphology and, specifically, the change in form through time, to infer
rates of sediment transport. While the forward approach offers an attractive grounding in physically
based relationships, the inverse approach rests on measurements of channel morphology that, at least
superficially, are readily quantifiable. Moreover, the spatially explicit nature of the inverse approach
offers the opportunity to gain insights into longitudinal variations in form and transport that cannot be
established readily from the at-a-point or section predictions associated with the forward approach.
As outlined in the next section, the inverse method is based on the sediment continuity equation and
dates back to Exner’s (1925) formulation for the motion of a travelling wave. This original approach
(and similar later formulations, e.g. Wittmann 1927; Hubbell 1964) related bed-material discharge
explicitly to the celerity of bedforms, notably dunes. Most applications of the inverse or, as also known,
‘morphological’method (after Ashmore and Church, 1998), however, involve accounting for more
general changes in net sediment storage derived from repeat measurements of channel topography.
Customarily, these measurements have been based on cross-section surveys (Brewer and Passmore
2002) and, not surprisingly given the complexity of channel topography, have been shown to exhibit
significant dependency to survey technique (precision and reproducibility) and the spatial and tem-
poral frequency of sections (e.g. Lane, Chandler, and Richards 1994; Fuller et al. 2002). The advent of
survey methods capable of generating dense topographic data that, in turn, enable the construction of
continuous digital elevation models (DEMs) have therefore been greeted with great excitement by the
fluvial research community, and has stimulated a large and growing body of research emphasizing the
potential opportunities afforded by what is increasingly recognized as a fundamental data revolution
(Lane, Westaway, and Hicks 2003).
121
Gravel-Bed Rivers: Processes and Disasters, First Edition. Edited by Daizo Tsutsumi and Jonathan B. Laronne.
© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.
Early research in this theme was largely restricted to deriving storage budgets from DEMs of small
reaches, intensively surveyed using electronic tacheometry and differential global positioning systems
(GPS; e.g., Lane, Richards, and Chandler 1995; Brasington, Rumsby, and Mcvey 2000; Eaton and
Lapointe 2001). Rapid progress in geomatics has, however, facilitated dramatic enhancements in
the density and extent of data acquisition, illustrated most obviously by the advent of channel models
derived from light detection and ranging (LiDAR; Westaway, Lane, and Hicks 2003). This technolog-
ical development has seen typical datasets describing channel morphology to grow from a few tens of
cross-sections, perhaps comprising a few hundred survey observations, to airborne LiDAR surveys
incorporating millions of points, and now mobile terrestrial laser scan data sets with even a greater
density of observations; an increase of seven orders of magnitude (Brasington, Vericat, and Rychkov
2012). Rescher (1996) argued that the advancement of modern science is intimately intertwined with
such technological escalation. He contends that advances in technology are essential to provide new
observations and perspectives to deepen and generalize our view of reality. He illustrates this with
reference to Eddington’s parable of the experimental fisherman, who trawls the ocean with a single
net of fixed mesh to study and measure the diversity of life in the oceans. However, in common with
all empiricists, technology limits his insights and all fish smaller than his mesh slip through, leading to
a distorted and partial view of aquatic life.
Given the subtle amplitude of channel morphology and deformation, the refinement of our observa-
tions has had tangible implications for the quality of models of channel change (Brasington, Langham,
and Rumsby 2003; Brasington, Vericat, and Rychkov 2012). Moreover, the technological overheads
associated with high-frequency monitoring of topography are also diminishing with time, most nota-
bly through advances in low-cost methods such as structure-from-motion (SfM) stereopsis (e.g. Fon-
stad et al. 2013; Javernick, Brasington, and Caruso 2014). This raises the prospect of widely available
high-quality topographic data over the coming decade, and the tangible possibility to acquire datasets
at temporal frequencies tuned to the driving processes of the natural environment.
This chapter seeks to provide a timely review of the application and scope of the morphological
method following the advent of this high-resolution topography (HRT) revolution. Specifically, we
seek to summarize the tools that are now available to apply the morphological method for utilizing
information from repeat HRT surveys. However, we also argue that while this data revolution enables
ever more precise measurement of topography, problems with the inverse method persist, so that per-
haps the more significant opportunities of this empirical bounty lie in the richness of the spatial pat-
terning of channel change we can now quantify. These spatial models offer fundamental insights into
the process mechanisms (erosion, deposition, and change in storage) that underpin channel morpho-
dynamics in different fluvial contexts and forcing regimes, and provide vital data needed to parame-
terize and test numerical models suitable for generalizing empirical results. We contend that there is a
pressing need to refocus the energy of our community away from tantalizing methodological ‘tinker-
ing’and instead employ the broader space–time perspective these data now offer to address basic
questions about how gravel-bed rivers function.
5.2 The Morphological Approach: a Primer
The morphological approach has been reviewed thoroughly elsewhere and we refer readers to
Ashmore and Church (1998) and Brewer and Passmore (2002), as well as Church (2006) for more
thorough treatments. Ashmore and Church (1998) presented their review of the morphological
approach to estimating bed-material transport at the 4th Gravel Bed Rivers Workshop in Colorado.
Gravel-Bed Rivers: Processes and Disasters122
It is therefore fitting that four workshops later, we revisit their ‘new paradigm’in the light of recent
advances, both technological and theoretical. Somewhat presciently, Ashmore and Church (1998)
recognized, albeit cautiously, the potential promise of ‘distributed, terrain-sensitive surfaces’(i.e.
DEMs) in reference to the initial efforts by Lane et al. (1994). Here, we briefly review the basics of
the morphological approach before emphasizing the dividends that HRT might offer.
The morphological approach is typically described as an inverse-solution to estimating sediment
transport, in contrast to direct measurements and hydraulically-based predictions of sediment trans-
port. The starting point for this approach is sediment continuity (i.e. conservation of mass), in which
changes in topography through time (∂z∂t) can be formally linked to bed-material transport per unit
channel width (q
b
):
∂qb∂x+∂qb∂y+1−p∂z∂t+∂Cb∂t=0 5 1
where pis sediment deposit porosity and C
b
is the concentration per unit bed area of sediment in
motion. As Church (2006) highlights, the solution to Equation 5.1 typically involves approximating
this two-dimensional formulation to a simplified one-dimensional case, by neglecting the lateral over-
bank sediment transport, and assuming that temporal variations in sediment concentration are aver-
aged over the typically long sampling intervals used in repeat topography. Under these assumptions,
Equation 5.1 is reduced to:
∂Qb∂x+1−p∂z∂t=0 5 2
in which Q
b
refers to the bed-material transport as a cross-sectionally averaged quantity. Equation 5.2
represents a one-dimensional form of the Exner equation fundamental to morphodynamic models
(see Paola and Voller (2005) for a helpful review). Recasting this in finite difference form yields the
more familiar statements of continuity in a sediment budgeting context:
ΔQbΔx+1−pΔzΔt=0 5 3
i e 1−pΔV=Qbin −Qbout Δt5 4
in which Qbin and Qbout represent bed-material flux (in mineral volumes) into and out of a river reach
with no significant tributary inputs, and ΔVis the net change of the volume of sediment stored in the
reach. If we only consider conservation of mass in volumetric terms,
ΔV=Vin −Vout 5 5
where V
in
and V
out
are the volumetric equivalents of Qbin and Qbout over the same period Δt. It is worth
noting that Equation 5.5 is also an expression for a simple sediment budget for a reach (see review by
Brewer and Passmore 2002). It follows that any term can be solved for, if the other two are known. In
practice, all three quantities are typically highly uncertain (Grams et al. 2013) and closure (i.e. mea-
suring all three terms) is very rarely attempted, much less successfully achieved (e.g. Erwin et al. 2012).
However, the morphological method is primarily concerned with estimating sediment flux. Therefore,
the integration form of Equation 5.3 or 5.4 over space (i.e. the control volume of our reach) and time
(i.e. time between surveys) is required to solve Q
b
.
Early attempts to apply these relationships sought to quantify the rates of transport associated with
mobile bedforms in sand-bedded rivers (e.g. Exner 1925; Simmons, Richardson, and Nordin 1965).
While the generic form used is arguably applicable, mobile bedforms (i.e. dunes) in gravel-bed rivers
are relatively rare, such that application of the morphological method is of limited interest in this con-
text. By contrast, we focus here on the two primary ways the inverse method is used to estimate sed-
iment flux in gravel-bed rivers.
Revisiting the Morphological Approach 123
The first approach involves sediment budgeting principles, to infer the value of either V
in
or
V
out
of a reach (i.e. a reference sediment flux), and measuring ΔVfrom repeat topography, to
then back-calculate the other unknown term (i.e. V
in
or V
out
). The second does not require sed-
iment budgeting, and instead relies directly on the quantification of erosion from topographic
change, combined with information about the virtual velocity of bed material (i.e. its path length),
to estimate the bed-material flux. Figure 5.1 illustrates application of morphological data with
repeat HRT and the definition of terms.
5.2.1 Transport Rates from Sediment Budgeting
The specification of transport rates from explicit channel sediment budgeting requires knowledge of
one boundary flux, which is used to provide the upper or lower boundary condition to a longitudinal
numerical solution to Equation 5.3. Typically, this has been approached using one of the following two
strategies.
1) Define the study region to incorporate an unambiguous zero-flux boundary, e.g. a distal
gravel–sand transition (e.g. Griffiths 1979; McLean and Church, 1999) or an upstream lake
or reservoir (Merz, Pasternack, and Wheaton 2006) where sediment transport is known to
approach to zero.
2) Discretize the study reach into a streamwise series of subreaches and specify the boundary flux into
or out of one section under one of the following assumptions, from which a numerical solution can
be obtained for all other reaches:
a) assume a zero-flux boundary into a net-erosional subreach (from a net-depositional reach),
such that overall transport rates represent lower-bound estimates (i.e. the minimum possible
flux, e.g. Eaton and Lapointe 2001);
b) use actual continuous measurements of flux across one boundary (e.g. Grams et al. 2013);
c) use an estimate of the time-integrated net flux computed either from an empirical (e.g. Erwin
et al. 2012) or theoretical (e.g. Anderson and Pitlick 2014) sediment transport rating curve/
model across any given boundary.
It is worth mentioning that for strategy 2the length of the subreaches needs to be larger than the
expected step-length in order to prevent the sediment being exported from one reach passing through
the following reach. Figure 5.2 and Table 5.1 illustrate application of strategy 2a in a braided gravel
river. Beyond the specification of boundary conditions, clear definition of the control volume and
fluxes is critical. As Ashmore and Church (1998) note, a significant potential danger arises in assuming
that the volumetric budget comprises solely the bedload flux. They note that observed volumes of
erosion (V
e
) or deposition (V
d
), calculated topographically, are likely to incorporate significant
volumes of fine sand and/or fine gravel that pass through the conservation volume not as bedload
(i.e. in saltation or even in suspension in strong currents). Failure to account for this labile fraction
is likely to bias bed-material flux estimates.
5.2.2 Transport Rates from Path Lengths
An alternative to explicit sediment budgeting is to use estimates of the velocity of bed-material load in
conjunction with measurements of the volume of eroded bed material. In the context of repeat top-
ographic surveys, we can define the particle path length along a streamline (i.e. L) as the mean distance
travelled by sediment particles over a time T. This definition gives rise to the concept of a virtual
Gravel-Bed Rivers: Processes and Disasters124
Morphological sediment budget:
(–) Erosion (red)
(+) Deposition (blue)
(Qbin –Q
bout) Δt = (1–p)ΔVDoD
Vin –V
out = ΔVDoD
Qb = vbdsws (1–p)ρs
Qb = vbΣVe (1–p)ρs
LC
Morphological approaches to estimating transport:
Sediment continuity:
Step length based:
Using
Vertically
Averaged
Erosion
Using
DoD
Erosion
Volume Streamwise length
over control volume
Sediment
density
Porosity
Virtual
velocity Path length
Time between
surveys
Active
width
Erosion
depth
DoD (El. change in m)
> –2.5
–2.5 to – 1.0
Volumetric flux
difference
Change in
storage
DoD measured
–1.0 to – 0.9
–0.9 to – 0.8
–0.8 to – 0.7
–0.7 to – 0.6
–0.6 to – 0.5
–0.5 to – 0.4
–0.4 to – 0.3
–0.3 to – 0.2
–0.2 to – 0.1
–0.1 to 0.0
0.0 to 0.1
0.1 to 0.2
0.2 to 0.3
0.3 to 0.4
0.4 to 0.5
0.5 to 0.6
0.6 to 0.7
0.7 to 0.8
0.8 to 0.9
0.9 to 1
1.0 to 2.5
– Old DEM
= DoD
New DEM
Elevation change (m)
Change in storage
volume (m3)
30
25
20
15
10
5
0
–1.5 –1.0 –0.5 0.0 0.5 1.0
ΣVe = erosion
volume
VW = Vout – ΣVe = Vin – ΣVd
ΔVDoD = ΣVD – ΣVE
Vin = ΣVd + VW
ΣVe + VW = Vout
ΣVd = deposition
volume
Erosion Deposition
Flow direction
Digital elevation model (DEM)
DEM of difference
(DoD)
DoD elevation change distribution
Washload
=L
T
vb
Figure 5.1 Definition diagram for terms related to the morphological approaches to estimate bed-material transport in
fluvial systems.
Revisiting the Morphological Approach 125
Minimum flux:
Minimum Vin
back-calculated
to fit zero flux
(ΔVs) from net
depositional sub-
reach B
Minimum
0100 200 300 400 500 Metres
40,000 30,000 20,000 10,000 0
March 28, 2010 to May 1, 2010
Duration above Qcrit: 8.6 days
Peak Qs: 226 & 403 cumecs
Porosity: 0.26
Qcrit: 30 cumecs
Volume (m3)
0
A
B
C
D
E
Subreach
Subreach
*START
HERE
F
G
HΣVE
ΔVA = –33 m3
ΔVB = 873 m3
ΔVC = –1710 m3
ΔVD = –7966 m3
ΔVE = –7317 m3
ΔVF = –9338 m3
ΔVG = –7294 m3
ΔVH = –3984 m3
ΔVI = –337 m3
ΣVD
I
A
B
C
D
E
F
G
H
I
10,000 20,000
Vin = ? = 840 m3
Vout = 37,227 m3Vout (m3)
QboutA = 75 m3/day
QboutB = 0 m3/day
QboutC = 147m3/day
Let Voutb = Vinc = 0 m3
QboutD = 834 m3/day
QboutE = 1465m3/day
QboutF = 2270 m3/day
QboutG = 2895 m3/day
QboutH = 3285 m3/day
QboutI = 3209 m3/day
Vout = Vin – ΔVDoD
Figure 5.2 Example illustration of application of morphological approach using sediment budgeting principles and
assuming a no-flux boundary to back-calculate out a minimum V
in
at the top of reach to support observed net changes
(ΔV). Example from Rees River, New Zealand for two events exceeding critical discharge. See Table 5.1 for data.
Gravel-Bed Rivers: Processes and Disasters126
velocity: vb=L T. Thus, revisiting the integration of Equation 5.4, Church (2006) showed that
bed-material flux Q
b
can be approximated as:
Qb=vbdsws1−pρs5 6
where d
s
is the scour depth, w
s
is the active width of the channel bed, and ρ
s
is the sediment density.
Equation 5.6 is ideally suited to one-dimensional applications in which depths of erosion can be esti-
mated from scour chains (e.g. Laronne et al. 1994) or burial depths from tracer studies (e.g. Hassan
and Ergenzinger 2003). Scour chains have been used to obtain discrete observations of erosion or dep-
osition at a point (see the pioneering study by Emmett and Leopold (1965) and subsequent studies by
Hollingshead (1971) Ergenzinger, Schmidt, and Busskamp (1989), Hassan (1990), Laronne et al.
(1994), Haschenburger (1996) Wilcock et al. (1996), Vericat, Batalla, and Garcia (2008), Vázquez-Tar-
río and Menéndez-Duarte (2014), and Chapuis et al. (2015)). This approach is normally limited to
small spatial scales (e.g. bar-scale studies) and does not typically provide information on the spatial
distribution of topographic changes.
For applications using repeat HRT, we can specify d
s
in Equation 5.6 from a spatially averaged ero-
sion volume (e.g. ∑VeAe; where A
e
is the area experiencing erosion or area of interest). Alternatively
the erosion volume ∑Vecould be used directly if Equation 5.6 is modified so that:
Qb=vb∑Ve1−pρsLc5 7
in which we introduce a characteristic length scale L
c
to normalize the virtual velocity v
b
and keep Q
b
dimensionally consistent (i.e. a volumetric rate). L
c
needs to be longer than the step lengths L, and thus
implies that the reach or control volume from which ∑Veis determined must be large enough to allow
typical step lengths to occur.
Table 5.1 Example calculations using sediment budgeting principles and following the morphological approach to
estimate a minimum Qbout by assuming a no-flux boundary at the transition from reach B to C. That value is used to back
out a minimum V
in
of 840 m
3
(i.e. ΔVB+ΔVA) at the top of the reach. See Figure 5.2 for illustration.
Subreach
ΣV
e
m
3
ΣV
d
m
3
ΔV
m
3
V
in
m
3
V
out
m
3
Q
b-out
m
3
/day
Cumulative ΔV
m
3
A 8496 ± 2278 8463 ± 2040 −33 ± 3058 840 873 75 −33
B 13 146 ± 3363 14 019 ± 3323 873 ± 4728 873 0 0 840
C 10 800 ± 3358 9090 ± 2272 −1710 ± 4054 0 1709 147 −869
D 17 021 ± 4408 9055 ± 2639 −7966 ± 5137 1709 9675 834 −8835
E 16 371 ± 4382 9055 ± 2556 −7317 ± 5074 9675 16 992 1465 −16 152
F 15 129 ± 3914 5791 ± 1934 −9338 ± 4366 16 992 26 330 2270 −25 490
G 11 400 ± 2502 4151 ± 1371 −7249 ± 2828 26 330 33 579 2895 −32 739
H 7477 ± 2254 3493 ± 1303 −3984 ± 2603 33 579 37 563 3238 −36 723
I 8546 ± 2327 8883 ± 2609 337 ± 3496 37 563 37 227 3209 −36 387
Total 108 387 ± 28.786 72 001 ± 19 992 −36 387 ± 35 343 840 37 227 3209 −36 387
ΣV
e
, total erosion volume in a given reach; ΣV
d
, total sedimentation volume in a given reach; ΔV, net change of the volume of
sediment stored in the reach; V
in
, volume of bed material into a reach; V
out
, volume of bed material out of a reach, Q
b-out
, bed-
material flux out of a reach.
Revisiting the Morphological Approach 127
Regardless of whether Equation 5.6 or 5.7 is used, the estimate of the path length Litself is critical. At
least two methods exist for estimating L: (i) tracer studies (e.g. Figure 5.3); and (ii) linking transportpath-
ways and modes of morphological adjustment to the characteristic length scale of fluvial units (e.g.
Figure 5.1). Exhaustive reviews of tracing techniques are presented in Sear et al. (2000) and Hassan
and Ergenzinger (2003). Pyrce and Ashmore (2003) synthesized and reanalysed results from published
tracing experiments in gravel-bed rivers to identify the variety of possible path-length distributions for
differing channel morphology, channel dimensions, bed particle size, and flow magnitude. They also
looked for occurrences of path length coinciding with the length scale of the morphology. Their results
showed that path-length distributions may be variable (from positively skewed to multimodal; e.g.
Church and Hassan 1992). Variability in path-length distributions may be related to multiple factors
(e.g. event magnitude, system size) so it is very difficult to establish general models. However, gravel-
bed rivers often have regularly spaced erosion (potentially corresponding with concavities such as pools)
and deposition (potentially corresponding to bars) units and, consequently, it is reasonable to expect that
particle path lengths should be related to this morphological scale (Pyrce and Ashmore, 2003).
One way to overcome the limitationsof tracers in providing a representativeestimate of the travelling
distance ina given period is byinvestigating the distribution of sediment sources (erosional features) and
sinks (depositional features). This approach was first applied by Neill (1971) for meandering rivers; he
considered the travel distance as equal to one half of the meander wavelength under the assumption that
material is typically transported from outer-bank meander bends to point bars. This assumption is clearly
morphology specific. Carson and Griffiths (1989), Ferguson and Ashworth (1992), and Goff and Ashmore
(1994) presented an alternative approach for dynamic braided rivers that involved matching successive
loci of erosion and deposition (see figure 7.3 in Ashmore and Church 1998). If topographic surveys are
performed frequently (e.g. event-based), successive erosional and depositional areas of similar volumes
can be distinguished and the distance between the centroids used to provide an estimate of the transport
lengths.
While apparently simple, Ashmore and Church (1998) highlighted the difficulties of matching
erosion–deposition volumes in rivers with spatially complex topographic changes. They suggested
that estimating mean travel distance could, by contrast, be based on erosional/depositional features
such as bar-pool or step-pool spacing. Pyrce and Ashmore (2003) also indicated that travel distances
are often related to channel morphology, especially during highly competent flows. They concluded
that there is a need for deliberate systematic investigation of the relation between path-length distri-
butions and channel morphology to establish the types of channels and particle mobility conditions in
which particle transfer is, or is not, primarily stochastic. Following this, a recent flume study by
Kasprak et al. (2015) demonstrated the importance of channel bars in acting as sedimentation zones
for particles in braided rivers. These results have the potential to improve simplified relationships
between channel morphology and sediment transport distances. Finally, the estimate of the virtual
velocity (v
b
) also requires knowledge of the duration over which the particles moved. As shown by
Milan (2013), the competence duration (T) of a given event is controlled by the grain size of the
bed-material flux. An under- or overestimation of Tcan have a direct impact on estimation of v
b
and, consequently, it will skew the estimation of the bed-material flux (Q
b
).
5.3 Applying a Morphological Approach with HRT
Fundamental to either of the approaches to using a morphological method as described above is the
measurement of topographic change (i. e. Δz/Δt). Channel changes between two periods can be
determined by a variety of repeat surveys, ranging from simple one-dimensional vertical depths based
Gravel-Bed Rivers: Processes and Disasters128
Maximum displacement: 75 m
Maximum displacement: 77 m
Minimum displacement: 18 m
Minimum displacement: 2 m
Maximum displacement: 131 m
Minimum displacement: 32 m
Original position of the tracers
Recovered tracers
Initial location of
RFID tracers
Maximum step-length
20 m
Maximum displacement
(b) (d)
(c)
(a)
Flow direction
Flow direction
0
Figure 5.3 Examples of tracer deployment for estimating path lengths to drive morphological approach. (a) Painted
tracers in dry exposed bars: example of displacement of painted tracers on a gravel bar in the River Rees (New Zealand)
after a small magnitude flood event. (b) A mobile radio frequency identification system (RFID) to track the displacement
of particles in a gravel-bed river: Mobile antenna and RFID tracers grouped by size classes. (c) Four individual tracers in
which the location of the RFID transponders can be seen. (d) Example of particle step lengths after a spring flood in the
River Noguera Pallaresa (Southern Pyrenees, Spain).
on scour chains to complex high-density three-dimensional point clouds (e.g. Lague, Brodu, and
Leroux 2013). Fundamental to the choice of technique is the density of observations (spatial resolu-
tion). Coarser resolution sampling (e.g. lower point density, sparse cross sections, coarse grid sizes)
can negatively bias topographic changes. Beyond these conditions, all studies of topographic change
require measurements within a robust frame of reference (coordinate system) that facilitates accurate
reoccupation of position. This can be achieved using monumented survey marks or, as is increasingly
popular, by establishing control on-the-fly from established continuous GPS networks. Such control
networks may need to be established outside the active survey area, and may then be used to position
temporary control within the active channel on a survey-by-survey basis (Columbia Habitat Monitor-
ing Program 2012). As one-dimensional approaches to this problem have been reviewed thoroughly
elsewhere, here we focus on approaches that utilize raster DEM differencing methods based on HRT;
defined as topographic surveys that exceed metre resolution data (i.e. > 1 point/m
2
, see Passalacqua
et al. (2015) for a broader discussion).
5.3.1 Digital Elevation Models and DEMs of Difference
If DEMs from repeat surveys are prepared appropriately as orthogonal rasters, with consistent projec-
tions and datums (see Passalacqua et al. 2015), models representing the topography at two epochs can
be subtracted to produce a DEM of Difference (DoD; see Williams 2012). As the DoD calculation is a
simple subtraction of elevations on a cell-by-cell basis, it is critical that rasters align and that unnec-
essary resampling artefacts are not introduced. Under this assumption, simple raster algebra can be
used to derive the ΔVterm in Equation 5.4:
ΔVDoD =∑Vd−∑Ve5 8
where ∑Vdis the total volume of deposition in the same reach, and ∑Veis the total volume of erosion in
a reach. Both ∑Vdand ∑Veare calculated directly from the DoD by taking the Δz/Δtand multiplying
by the respective cell area to derive sediment volumes.
While the calculation of Equation 5.8 is essentially the same when applied to cross-section or point
data, the use of high-resolution DEMs provides a near continuous sampling of topography that results
in robust continuum statistics. This approach therefore dramatically reduces the potential for bias that
might arise when sampling channel change volumes with more typical low-density cross-section sur-
veys (i.e. major source of historical survey data). This effect is visualized in Figure 5.4, which compares
these two approaches using field data obtained from the River Feshie (Scotland) in 2006 and 2007
respectively. Here, the three randomly placed cross sections in Figure 5.4a illustrate the possible bias
that may be incorporated into reach-averaged volumetric estimates when the frequency of sections is
significantly lower that the spatial distribution of scour-fill units, shown here by the DoD in
Figure 5.4b and c. The spatial distribution of erosion and deposition reflects different processes
(e.g. bank erosion, avulsion) that are only partially sampled by these sparse sections. The dependency
of the volumetric budget estimated from such low-frequency cross-section-based surveys will be
strongly dependent on the style (length-scale and complexity) of morphological change, which will
vary according to the fluvial context. Lane, Westaway, and Hicks (2003) analysed this effect by simu-
lating the reliability of average bed-level estimates derived for a 3-km braided reach of the Waimakar-
ari River, New Zealand. In their experiment, they determined the average bed-level for the entire reach
based on a 1-m resolution DEM and compared this to estimates based on averaging simulated cross-
sections extracted from the DEM at progressively larger and larger spacing. They found that the dif-
ference between the reference DEM-based bed-level and the section-based estimates diverged rapidly
as section spacing increased beyond the scale of typical morphological units (100–200 m; see
Gravel-Bed Rivers: Processes and Disasters130
355.6
355.2
Elevation (masl) Elevation (masl)
354.8
354.4
Old survey
New survey
354.0
353.6
353.2
356.0
355.6
Elevation (masl)
355.2
354.8
354.4
353.6
(a) (b)
(c)
Topographic
survey
Channel changes
(comparing 2 cross-sections)
Topographic changes
(comparing 2 DEMs; DoD)
Topographic changes
(removing uncertain changes)
Changes on
cell elevation
More High
LowLess
Erosion
Deposition
No
detectable
change
Survey
density
MaslObs/sqm
Topographic
model (DEM)
353.2
352.8
352.4
352.0
351.6
020
Old survey
New survey
40 60 80 100 120
Distance (m)
140 160 180
020406080
100 120
Distance (m)
ΔAsection i = ΣAs section i – ΣAe section i
ΣVs = (As section i × li) + (As section i+1 × li+1) + ...
ΣVe = (Ae section i × li) + (Ae section i+1 × li+1) + ...
V
III
III
IV
140
Ae section V–VI
As section III–IV
Ae section III–IV
Ae section I–II = area of erosion in section I–II
As section I–II = Area of
sedimentation
As section V–VI
160 180
Old survey
III
III
VI
VVI
IV
New survey
020406080
100 120
Distance (m)
140 160 180 050
100 200 Metres
Figure 5.4 Illustrative comparison of (a) traditional one-dimensional cross-sectional information versus (b) a HRT data set and DEM. (c) DoD-based
information on topographic changes between two different periods (2006–2007) in the River Feshie (Scotland). Note that the location of the cross-
sections in (a) are represented in (c).
discussion in Hicks 2012). The implication is that many standard survey protocols (e.g. the 500–800-m
spacing used by the Canterbury Regional Council on the Waimakariri) are likely to incorporate
significant uncertainty into sediment budget calculations and that ultimately, robust sampling is likely
to require section spacing that is more or less comparable to a continuous DEM.
5.3.1.1 Estimation of DEM Uncertainty
The example described above indicates how uncertainty in the underlying topographic data can
potentially propagate into derived sediment budgets. For cross-section surveys, measurements are
typically well resolved in the vertical dimension, and therefore, in such a case uncertainties are largely
a result of the low spatial sampling frequency. However, while HRT datasets dramatically resolve this
spatial bias they are nonetheless still subject to positional and vertical uncertainties (errors) that result
from a complex combination of instrument errors (both random and systematic), sampling issues,
interpolation, and processing artefacts and blunders (e.g. Bangen et al. 2014a).
Given the low vertical relief that characterises fluvial topography and many channel deformation
processes (e.g. bedload sheets), it is important to develop a framework to separate the topographical
signal of actual channel change from spurious DEM differences that arise from uncertainties in the
before and after surfaces (Brasington, Rumsby, and Mcvey 2000). As DEM uncertainty is likely to
be spatially variable, it follows that this analysis ideally requires a distributed approach to quantifying
DEM uncertainty and accounting for artefacts when estimating volumetric changes (Brasington,
Langham, and Rumsby 2003; Wheaton et al. 2010; Milan et al. 2011). These uncertainties need to
be carefully considered since, as recently demonstrated (Erwin et al. 2012), topographic models
may not be sufficient to determine the sign of the net change in a given reach, even using the most
recent survey techniques and data analysis (e.g. Heritage and Hetherington 2007; Milan et al. 2011;
Grams et al. 2013).
There are three strategies typically employed to estimating DEM uncertainties (elevation errors, i.e.
δz): (i) treat them as spatially uniform; (ii) allow uncertainties to vary in given regions (e.g. according to
survey methods or surface cover classes); or (iii) model uncertainties at the grid-cell scale. Represent-
ing DEM uncertainties as elevation errors is statistically convenient as the change detection problem
can be treated using established error propagation theory (see below). Passalacqua et al. (2015) pro-
vide a more complete review of these methods and in particular the specific situations that warrant
using the simpler versus more complex methods. Here we briefly differentiate these methods.
5.3.1.1.1 Spatially Uniform Methods
Treating DEM uncertainty as spatially uniform is by far the most simple and also most commonly
adopted strategy. Herein, elevation errors are assumed not to be a function of location but approxi-
mated as a constant +/−elevation value across a DEM. Typical methods for estimating representative
DEM error values are to compute simple statistics (e.g. range, standard deviation, root-mean-square
error) using standard cross-validation methods such as hold-out or leave-one-out cross-validation or
reoccupation of check points (Federal Geospatial Data Committee 1998; Brasington, Langham, and
Rumsby 2003). A common, but arguably flawed, practice is to use manufacturer reported estimates
of instrument precision (e.g. point quality metrics in differential GPS surveys) as an approximation of
DEM error. Such estimates are generally far too optimistic and neglect the effects of spatial sampling,
interpolation, and potential blunders. Other approaches include spot elevation checks against inde-
pendent data or measurements of notionally higher accuracy, and/or use of fiduciary check points on
unchanging surfaces (e.g. Kaplinski et al. 2014).
Gravel-Bed Rivers: Processes and Disasters132
5.3.1.1.2 Spatially Variable Methods
A more sophisticated, though still simple, form of error modelling is to use spatially uniform approx-
imations within specific regions. For example, Lane, Westaway, and Hicks (2003) used check-point
data to calculate errors in wet (submerged) versus dry (exposed) areas of the channel. Similarly,
Kaplinski et al. (2014) used a hybrid survey approach to produce a DEM from a mix of multibeam
and singlebeam sonar, total station and LiDAR data, and differentiated spatially uniform error esti-
mates for each survey method, as well as for smooth and rough areas within each method. Differences
in surface texture, vegetation, and survey methods are all good reasons to use different estimates of
elevation error and the critical thing is that clear, mutually exclusive boundaries can be derived for
these different regions (e.g. Williams et al. 2013).
Spatially variable error models can also be derived using independent models of elevation error that
describe how errors vary on a cell-by-cell basis. There are many different approaches to building
spatially variable error models, including full error budgeting, modelling variance of independent
repeat surveys of unchanging surfaces, statistical models of error, bootstrap tests, interpolation error
estimates, and fuzzy inference systems. Not all of these methods are appropriate for all surveys. Full
error budgeting is typically not practical and often results in overly conservative estimates (e.g. CUBE –
combined uncertainty and bathymetry estimator; Calder and Mayer 2001, 2003). Traditional total
station, real-time kinematic (RTK) GPS and even many airborne LiDAR surveys often lack the point
density to hold back a portion of the data to use for building reliable statistical models of error. Where
data density is adequate (e.g. terrestrial laser scanning (TLS) and SfM), statistical methods that look at
elevation variance within a moving window or bins of a defined cell size (Milan et al. 2011) can be
applied.
Wheaton et al. (2010) proposed the use of fuzzy inference systems (FIS) as a pragmatic approach to
model spatially variable errors. Fuzzy inference systems are convenient frameworks for taking the infor-
mation that is known (e.g. point density, slope, etc.) and producing an appropriate output (i.e. a spatial
distributed δzin this case) based on expert-based rule tables (Jang and Gulley 2007; Wheaton et al.
2010). In this approach, both input and output are represented with continuous variables and use fuzzy
membership functions to translate them into categorical data. The key to fuzzy inference systems is that
membership of a given category can overlap and, therefore, multiple rules can apply to any combination
of input, which gives rise to a much richer model output. A simple example is shown in Figure 5.5,
whereby spatially variable (at the grid-size scale), continuous inputs of point density (a proxy for
sampling), slope (a proxy for topographic complexity), and surface roughness (a proxy for subgrid
topographic variability) are combined in a FIS to predict total vertical DEM uncertainty.
5.3.1.2 Error Propagation and DoD Thresholding
Given an error model δzDEMi, the significance of observed vertical changes calculated between two
DEMs can then be readily established. Both Lane and Chandler (2003) and Brasington, Langham, and
Rumsby (2003) suggest using traditional error propagation theory to support the identification of a
minimum level of detection (LOD
min
) to threshold significant vertical changes from noise.
This approach involves first defining the propagated error (i. e. δz
DoD
) associated with vertical dif-
ferencing, which can be taken as the sum of the errors of both DEMs (iand i+ 1) in quadrature (see
Taylor 1997);
δzDoD =δzDEMi2+δzDEMi+125 9
Each elevation difference (i.e. z
i
−z
i+1
) can then, on a cell-by-cell basis, be converted to a tstatistic by
considering the magnitude of change relative to the propagated error;
Revisiting the Morphological Approach 133
t=Zi−Zi+1
δZDEMi2+δZDEMi +125 10
This approach generates a spatial map of t-scores that can be used to threshold the vertical changes
as predicted by the DoD. For example, under a two-tailed test, a t-score of 1.96 or greater (where the
degrees of freedom are taken to be large, i.e. n
x
×n
y
> 30) would indicate changes that are significant
at the 95% confidence limit. In more general terms, this approach enables the definition of a flexible
LoD
min
. Given that ∑Veand ∑Vdestimates are likely to be underestimates of total volumetric changes
FIS input 1
(point density)
2006 2005
Point density (pts/ft
2
)
Roughness (ft)
Elev.unc. (ft)
2006 –2005 DoD (ft)
0–1
0–1
0 – 0.1
0 – 0.1
0.75 – 1
>10
0.75 – 1
>10
<–8
>8
0
300–400
25 – 30
>80
10,000 – 20,000
FIS input 2
(slope)
FIS input 3
(roughness)
FIS surface
(elev.unc.(ft))
Both FIS surfaces
combined to DoD
probability
Percent slope
Figure 5.5 An example of spatially variable inputs (point density, slope and roughness) derived from point clouds and
used as inputs into a fuzzy inference system (FIS) model of elevation uncertainty (elev. unc.) to produce a spatially
variable error models (at the grid-size scale or by cell) for each DEM. (Source: Leary, Wheaton, and DeMeurichy (2012).
Reproduced with the permission of Joe Wheaton.)
Gravel-Bed Rivers: Processes and Disasters134
due to possible compensating changes between surveys (i.e. unobserved cut and fill; Lindsay and Ash-
more, 2002), there is a strong argument for using slightly more relaxed confidence intervals ~80%
(Mapstone 1995; Bradford, Korman, and Higgins 2005).
Once a threshold level of detection has been established, it can be applied to calculate the volumetric
sediment budget in a variety of ways. The most restrictive and least common approach is to subtract
the portion of elevation change below the threshold from the total change (Milan et al. 2011). More
commonly, the LoD
min
threshold is used simply to identify cells where the elevation difference is taken
to be true and the volumetric changes for these cells are preserved and summed to generate the net
budget. Finally, although rarely implemented, it is possible to weight the values of cells below the
threshold and include only part of their values.
5.3.1.3 Geomorphic Change Detection: Workflow and Software
The basic geomorphic change detection workflow described above and illustrated in Figure 5.6 has
become a well-accepted and standardized method for DEM differencing and volumetric budgeting
(Williams 2012; Passalacqua et al. 2015). The main steps in this basic workflow comprise:
1) building orthogonal DEMs;
2) estimating error surfaces independently associated with each DEM;
3) calculating the DEM difference error propagation on a cell-by-cell basis;
4) considering the change detection problem and thresholding to differentiate changes at a given con-
fidence level;
5) determining the zonal statistics and geomorphic interpretation to summarize the ‘significant’
changes into erosion (∑Ve) and deposition (∑Vd) estimates and calculate the net budget between
periods (ΔV
DoD
).
This approach and closely related variants have been variously described in Lane, Westaway, and
Hicks (2003), Brasington, Langham, and Rumsby (2003), Wheaton et al. (2010), Milan et al. (2011),
and James et al. (2012). The workflow can be implemented in a variety of GIS and scripting software
environments and the Geomorphic Change Detection (GCD) software (http:///gcd.joewheaton.org)
provides a project-based software platform to undertake such analyses (Wheaton et al. 2010; Williams
2012). The most common version of the software is available as an ArcGIS 10.X add-in, but command
line, stand-alone, web applications (http://zcloudtools.org and http://opentopograhy.org) also exist.
5.3.2 Extracting DEMs from Hyperscale Point Clouds
Advances in survey technologies have made it progressively easier to acquire three-dimensional point
clouds that capture terrain at extreme resolutions (mm–cm spacing) and over increasingly large spa-
tial extents (Bangen et al. 2014b). These developments have stemmed from a range of evolving tech-
nologies that include terrestrial laser scanning (TLS; e.g. Milan, Heritage, and Hetherington 2007;
Williams et al. 2011, 2013; Brasington, Vericat, and Rychkov 2012); structure-from-motion photo-
grammetry (James and Robson 2012; Westoby et al. 2012; Fonstad et al. 2013; Javernick, Brasington,
and Caruso 2014; Woodget et al. 2014; Smith et al. 2014; Smith and Vericat 2015; Dietrich 2015;
Smith, Carrivick, and Quincey 2015) and multi-beam sonar (Parsons et al. 2005; Grams et al.
2013; Kaplinski et al. 2014). Brasington, Vericat, and Rychkov (2012) used the term hyperscale, in
an analogy to the remote sensing community’s reference to hyperspectral cf. multispectral imaging
(> 4 bands), to highlight that such high-density point clouds facilitate multiple different spatial scales
of analysis. Although their acquisition over larger spatial extents was initially limited, mobile platforms
(e.g. mobile TLS applied to fluvial studies; Wang et al. 2013) and the proliferation of consumer-grade
Revisiting the Morphological Approach 135
unmanned aerial vehicles (Woodget et al. 2015) have allowed data acquisitions over increasingly lar-
ger reaches. Many of these new survey technologies also have the advantage of being ‘non-contact’and
enable the extraction of high-density point clouds (i.e. hundreds to thousands of points per
square metre).
New
DEM
Specify, load or
calculate DEM error
New error
surface
(δzDEM i+1)
Old error
surface
(δzDEM i)
DoD propagated
error surface
(δzDoD)
DoD
(Δz/Δt)
Old
DEM
DEM of difference
(DoD) calculation
Specify, load or
calculate DEM error
Error propagation
Threshold
method?
Specify
Min
LoD
manually
Thresholded
DoD
ECDs
Use propagated
error surface as
Min
LoD (i.e. 1σ)
Compare DoD &
propagated error
(calculate T-score)
Calculate
probability
change is real
Choose confidence
interval (e.g. 95%)
Direct measurements of:
∑V
d
& ∑V
e
Δ
V=∑V
d
– ∑V
e
Figure 5.6 A standardized geomorphic change detection workflow facilitated within the geomorphic change
detection (GCD) software. The outputs of ∑Vdand ∑Veare used to derive ΔV;ΔVcan be used for ‘budget-based’
application of the morphological approach, whereas ∑Vecan be used for path-length-based application. (Modified
from Wheaton et al., 2013.)
Gravel-Bed Rivers: Processes and Disasters136
Passalacqua et al. (2015) review the key steps used to convert point clouds to reliable bare-earth
DEMs, which typically involves unifying and georegistering point clouds acquired from different per-
spectives, vegetation and surface object removal, and manual cloud editing. The automation of this
process is complicated further by the large data volumes involved, so that the adoption of dense point
clouds for change detection has been comparatively slow. However, some practical tools to support
workflows are starting to emerge, such as PySESA (Buscombe, Grams, and Smith 2015), CloudCom-
pare (Girardeau-Montaut 2011) and CANUPO (Brodu and Lague 2012; Lague, Brodu, and Leroux
2013). The Topographic Point Cloud Analysis Toolkit (ToPCAT) offers a computationally efficient
geospatial toolkit to perform intelligent decimation of Tb-sized point cloud datasets that creates
GIS-compatible data models that retain statistical information about the subgrid elevation distribu-
tion (Brasington, Vericat, and Rychkov 2012). Figure 5.7 illustrates the ToPCAT workflow and the
outputs generated. This decimation algorithm is available in a distributable form as a simple standa-
lone toolbox and is also implemented in the GCD software described previously. Performance tests on
the distribution version of the code by Brasington, Vericat, and Rychkov (2012) revealed its suitability
for desktop deployment without the need for high-performance computing. ToPCAT has been suc-
cessfully used in several studies to provide microscale information about surface topography
(Williams et al. 2011, 2013, 2014, 2015; Bangen et al. 2014b; Javernick, Brasington, and Caruso
2014; Vericat, Smith, and Brasington 2014; Storz-Peretz and Laronne 2015; Smith and Vericat 2015).
5.3.3 What More Might Hyperscale Data Reveal?
While simply being able to produce DEMs from hyperscale point clouds is one challenge, the real
question is whether DEMs derived from point clouds up to two orders of magnitude denser than
typical HRT data offer any advantages from a change detection perspective and whether this helps
matters for estimating transport rates morphologically. As an illustrative example, Figure 5.8 com-
pares the patterns and estimates of channel change based on TLS and RTK-GPS-derived DEMs of
the River Feshie acquired in 2006 and 2007 (see Wheaton et al. (2010) and Brasington, Vericat, and
Rychkov (2012) for further information about data acquisition). For the TLS data, thresholds for
DoDs were established using the locally detrended standard deviation of elevation to define a rep-
resentative DEM uncertainty on a cell-by-cell basis (derived using ToPCAT; see Figure 5.7). For the
RTK-GPS surveys, a uniform standard deviation of error was estimated by using a bootstrap test,
using 5% of the GPS points as check data. These errors were used to define a 1σLoD
min
threshold
(i.e. a 68% confidence interval), below which changes were interpreted as indistinguishable
from noise.
The resulting contrast in DoDs are shown in Figure 5.8. The most notable differences are observed
in the degree of low-magnitude elevation changes that the higher precision, hyperscale TLS data are
able to reveal. For example, there is 35% more estimated erosion in the TLS (∑VeGPS =−7141m3vs.
∑VeTLS =−10 992 m3) and 35% more estimated deposition in the TLS (∑VdGPS = 4618 m3= vs.
∑VdTLS = 7144 m3). Although these overall changes in erosion and deposition volumes do not have
an impact on the direction of change for the net signal, differences exist between the two techniques.
These differences reveal fine-scale sheets of deposition on the braid plain and bar top, as well as lower-
magnitude sculpting of the bar surfaces (e.g. minor chute dissection and head cutting that the GPS
survey did not pick up; Figure 5.8b).
The impact of using these values in the morphological approach depends on whether transport rates
are estimated using sediment budgeting principles (i.e. using the net changes ΔV
DoD
) or are path-
length based (i.e. using just the ∑Ve). In the above example, overall flux estimates will be lower with
the lower-precision GPS data for both because the magnitudes of ΔV
DoD
and ∑Vequantities are both
Revisiting the Morphological Approach 137
Selected point cloud Square domains
Δx
Δy
(a)
Stage 2
Stage 3
Fit local tessellation
across cardinal
neighbours and
detrend points relative
to this set of planes.
Derive detrended
elevation statistics
Raw
Output 2
Output 1 (a) Centroid
(c) Centroid
- Minimum(z)
- Detrended minimum(z)
- Maximum(z)
- Minimum(z)
- Maximum(z)
- Kurtosis(z)
- Skewness(z)
- Std. deviation(z)
- Detrended maximum(z)
- Detrended kurtosis(z)
- Detrended skewness(z)
- Detrended std. deviation(z)
- n. Obs.
(b) Precise location:
Files written out
Files
written out
Detrended
Sort points in each cell
and calculate
elevation statistics
Photo-rendered point cloud
ToPCAT
topographic Point Cloud
Analysis Toolkit
Stage 1
Sort laser scan
points into
regular grid
Figure 5.7 Example of processing hyperscale point cloud data to drive morphological approach. (a) The ToPCAT
workflow for filtering three-dimensional point clouds and deriving useful derivatives. (Figure reproduced from
Brasington, Vericat, and Rychkov 2012) (b) Applying ToPCAT in the Upper River Cinca (www.morphsed.es): from the
point cloud to a 1 m grid DEM and roughness map. The roughness map is based on the detrended standard deviation
(dSD) of elevation, while the DEM is based on the minimum elevation (z) in each square domain using ToPCAT (see a).
Gravel-Bed Rivers: Processes and Disasters138
(b)
Bar-scale photo-rendered point cloud
Applying ToPCAT: from the point cloud to the models
The river Cinca
Photo-rendered point cloud
Minimum z
Digital elevation model
Digital elevation
model (masl)
Sub-grid detrended
standard deviation
of elevations
560.6 m
01020 40meters
01020 40meters High
Low
536.1 m
Centroid
Figure 5.7 (Continued )
Revisiting the Morphological Approach 139
RTK-GPS
Topographic channel changes from DEMs of difference
RTK-GPS
RTK-GPS TLS
TLS
TLS
Raw DoD Thresholded DoD
Raw DoD
–Ve: –9680 m3
–Vd: 7383 m3
–ΔVDoD: –2297 m3
Thresholded DoD
–Ve: –7141 m3
–Vd: 4618 m3
–ΔVDoD: –2523 m3
Raw DoD
–Ve: –12790 m3
–Vd: 9198 m3
–ΔVDoD: –3601 m3
Thresholded DoD
–Ve: –10992 m3
–Vd: 7144 m3
–ΔVDoD: –3848 m3
Flow
direction
N
Raw DoD Thresholded DoD
–2.0
0.0
0.5
1. 0
1. 5
2.0
–1.0
Observations (×104)
DEMs of difference (m)
0.0 1.0 2.0 –2.0
0.0
0.5
1. 0
1. 5
2.0 Raw DoD
DoD (m)
(a) (b)
–0.01–0.01
0.01–0.2
0.2–0.4
0.4–0.6
0.6–0.8
0.8–1
1.0–1.2
1.2–1.4
1.4–1.6
1.6–1.8
1.8–2
Below threshold
Thresholded DoD
–1.0
Observations (×104)
DEMs of difference (m)
0.0 1.0 2.0
0
0200 m
40 m
020 m
–2– –1.8
–1.8– –1.6
–1.6– –1.4
–1.4– –1.2
–1.2– –1
–1.0– –1.8
–0.8– –0.6
–0.6– –0.4
–0.4– –0.2
–0.2– –0.01
Figure 5.8 Illustration of additional erosion and deposition mechanisms identified with higher precision, hyperscale TLS HRT data versus traditional
RTK-GPS HRT. (a) Comparison of reach-scale DoDs derived from RTK-GPS versus TLS DEMs for same time periods (2006–2007) from the Feshie River
(Scotland). (b) Detailed close-up of changes on a gravel bar.
lower. However, this is partly an artefact of this budget having only a weak degradational trend in the
context of the total volume of change (i.e. ∑Ve+∑Vd). In general, the impacts of the lower precision
data will be an even smaller minimum transport rate.
5.3.4 Case Study: High Frequency Morphodynamics of the Braided Rees River
While technical advances in geomatics have enabled progressive increases in the spatial frequency of
survey data, the calculation of net sediment budgets is also known to be negatively biased by local
compensation of scour and fill that occurs between surveys and is unaccounted for within the topo-
graphic budget (Lindsay and Ashmore 2002). In this section we use a case study of morphodynamics
on the braided Rees River (New Zealand) to illustrate an application of the morphological method with
event-based, hyperscale topographic monitoring. A principal goal of this research was to use the mor-
phological approach to support the development of a bed-material rating curve for a large braided
river in which direct measurements of flux during floods are practically impossible. As such, the case
study provides a dual illustration of the utility of the morphological method and how hyperscale ter-
rain data can support that goal.
The study period comprised an annual flood cycle, during which 10 flood events were captured.
DEMs were derived using a combination of mobile TLS and optical-depth mapping, and DoDs pro-
duced and thresholds set using a spatially variable LoD
min
(for further details see Williams et al. (2014)
and the illustrative example in Figure 5.2 and Table 5.1). Figure 5.9 reveals that a strong net erosional
signal is evident for the periods with the largest events, which together account for over 50% of the
total erosion during the annual period. In addition to volumetric trends, erosional and depositional
patterns can be quantified in terms of area and average depths. Figure 5.9b reveals that the average
local depth of erosion and sedimentation is largely consistent between events, despite the widely vary-
ing totals of erosion and sedimentation (Figure 5.9a). This points towards a similarity of processes
driving the overall pattern of bed mobility, but as indicated by the changing area between events,
the volumes are a function of this pattern being dispersed over wider areas as the wetted width
increases with discharge (a reflection of the local relief of the channels). This mirrors a similar obser-
vation to Ashmore and Sauks’(2006) observations of hydraulic geometry on the Sunwapta River
(Canada) in that increasing discharge is accommodated largely by increases in wetted width, and
so that no significant increases in mean bed shear stress would be expected and that total transport
may scale simply with width (similarly patterns were also observed in an earlier study by Mosley in
1982). Additionally, results from the Rees also show that the average depth of erosion and deposition
is approximately half the bankfull channel depth, implying that local stalling of bed-material sheets is
likely to reduce local conveyance and encourage channel widening or avulsion within 1–2 events.
The distribution of erosion and deposition across the floodplain of the River Rees for the entire study
period is presented in Figure 5.10a. The net annual DoD reveals that 65% of the bed appears to have
undergone either significant erosion or deposition through the flood season. However, when these
changes are integrated sequentially, event-by-event, the actual areas found to have experienced ero-
sion or deposition were 71% and 72% respectively. This mismatch is explained by the fact that a sig-
nificant proportion of the braidplain (~50%) experienced repeated cut and fill cycles (Figure 5.10b),
where in some cases, the total net bed deformation summed to zero. These results reveal the impor-
tance of the frequency of topographic surveys for the estimates of channel changes. Compensating
erosion and deposition might mask processes if the frequency of surveys is not appropriate, as has
been revealed in previous studies and clearly presented here in Figure 5.10b.
Effective scaling of morphological change into estimates of bed-material transport requires infor-
mation on the typical step length of particle transport or a reference sediment flux in a given
Revisiting the Morphological Approach 141
19 September 2009
(a)
(b)
0
50
100
150
200
250
300
350
E0–E1
E1–E5
–34,134 m
2
34,791 m
2
–79,049 m
2
63,277 m
2
–9,557 m
2
18,639 m
2
–15,738 m
2
12,323 m
2
–34,742 m
2
36,733 m
2
–39,741 m
2
31,441 m
2
–91,170 m
2
81,555 m
2
E5–E6
E6–E7
E7–E8 E8–E9
E9–E10
12%
5%
23% 12% 13% 30%
28 December 2009 7 April 2010 16 July 2010
0
0
0.0
0.1
0.2
0.3
0.4
20
20
40
40
50
30
10
60
80
100
120
E01-E00 E05-E01 E06-E05 E07-E06 E08-E07 E09-E08 E10-E09
E01-E00 E05-E01 E06-E05 E07-E06 E08-E07 E09-E08 E10-E09
E01-E00
Average depth (m) Area (m3) Volume (m3) × 103
E05-E01 E06-E05 E07-E06 E08-E07 E09-E08 E10-E09
Deposition
Scour
Event number
Discharge at invincible (m3s–1)
Figure 5.9 Event-scale DoD from the River Rees (New Zealand) during a flood season (2009–2010). (a) A hydrograph
over the study period, with boxes bracketing the epochs of analysis and pie charts showing the relative proportions of
erosion and deposition for each period. The percentages indicate the proportion of event-based geomorphic change
to the total during the study period. (b) Contrast of the event-based volumes, areas, and average thickness of erosion
and deposition.
Gravel-Bed Rivers: Processes and Disasters142
section (e.g. as illustrated for two of the Rees events in Figure 5.2). However, as reviewed in section 5.2,
both requirements are complicated by the difficulties of field data acquisition and have numerous
uncertainties that directly affect estimates derived from the morphological approach. In the following
sections we present a proxy for the step length of particle transport based on the multi-event HRT
database acquired for the River Rees and developed by Redolfi (2014). We then apply this method
to the entire data set to estimate flood-scale bed-material transport and investigate the relationship
between transport flux and measures of flow intensity.
5.3.4.1 Flood-Based Estimates of Particle Step Lengths
As discussed above, Pyrce and Ashmore (2003) highlighted the variability in the relationship between
path-length distributions and channel morphology in gravel-bed rivers; although they note that at
higher flows travel distances may be related to specific morphological units (e.g. bar-pool spacing).
From a flume study, Kasprak et al. (2015) showed results supporting the idea that step-lengths are
highly related to bar spacing and bar heads were consistent sinks for tracer particles. Establishing
path-length data from long-term field monitoring is constrained by logistics and in wider gravel-
bed rivers the recovery rate of tracers is low and decreases with time due to the spatial extent of dis-
persal and depth of burial (Laronne and Duncan 1989, 1992). As an attempt to circumvent these lim-
itations, Redolfi (2014) presented a proxy for measuring flood-based step lengths of particle transport
Sedimentation (blue)
Erosion (red)
2.0 m
(a) (b)
0 125 250 500
Metres
N0 125 250 500
Metres
Erosion & Sedimentation
Erosion
Sedimentation
N
–2.0 m0.0 m
0.0 m
Figure 5.10 (a) Net annual thresholded DoD from the River Rees and (b) classification of regions that experienced just
erosion, just sedimentation, versus a more complicated, event-transgressive mix of erosion and sedimentation during a
flood season (2009–2010).
Revisiting the Morphological Approach 143
by characterizing the size-distribution of discrete areas of erosion using image processing
(Figure 5.11a). Briefly, discrete areas of erosion were first isolated using a segmentation of the
DoD (i.e. classifying cells that represent erosion, deposition, and no significant change). Erosional fea-
tures were quantified by fitting an ellipse to each erosion patch from which the major axes could be
computed. The length of this ellipse was then weighted according to the volume of erosion to yield the
proxy of the step length (i.e. L; see Redolfi (2014) for more details). Analysis of this metric through the
annual series of events registered in the River Rees is presented in Figure 5.11b. The results reveal that
this method scales strongly with flow magnitude, varying from around 50 m for the low-intensity
events registered in the period E05–E06 and E06–E07, through more than 250 m for the high-intensity
events E01–E05 and E09–E10 (Figure 5.11b). This approach differs from directly matching centres of
erosion and deposition as the complex patterns of channel observed precluded simple identification of
sediment dispersal patterns. While a crude proxy, the scale dependence of this relationship with dis-
charge is encouraging and may provide a means to estimate a lower bound estimate of particle step
length, and opens the possibility to relate step lengths to flow magnitude using data intrinsic to a DoD.
0
00–01
95
301
53 76
126
178
259
L
L (m)
01–05 05– 06 06– 07
Event number
Mean major axis length weighted with the volume of erosion
Estimating flood-based path-length in braided rivers
07–08 08–09 09– 10
50
100
150
200
250
300
(b)
(a)
350
Deposition
Scour
Deposition
Scour
Figure 5.11 (a) Example of estimating flood-based path-lengths (L) of particle transport by characterizing the size-
distribution of discrete areas of erosion using image processing (see text for more details). This approach was first
developed by Redolfi (2014). (b) Assessing flood-based particle step lengths by applying the approach presented in
A to the River Rees data set (Figure 5.9).
Gravel-Bed Rivers: Processes and Disasters144
This approach is still being critically reviewed and it would require a comparison with results obtained
from tracers. Painted and radio frequency identification system (RFID) tracer data obtained in the
River Rees are being analysed to compare the distributions of both path-length models.
5.3.4.2 Reach-Scale Bed-Material Flux and Flow Intensity
Event-based total bed-material flux in the River Rees was estimated using the step-length weighting
model introduced in the previous section and the volume of erosion derived from Figure 5.11b
(recall the step length formulation shown in Figure 5.1). To obtain an estimate of the bed-material
transfer, mean flood-based particle step length was multiplied by total erosion-patch volume. This
estimate is turned into a section-flux by dividing by the reach length and the event duration. How-
ever, the competence duration of each event may have a direct influence on the flux estimate. This
approach yields a storm-by-storm bed-material flux that can then be related to measures of flow
intensity. Simple rating relationships for reach-scale transport are shown in Figure 5.12, where mea-
sures of flow intensity have been normalized so that the range 0–1 corresponds to the maximum and
minimum observed intensity during the study period. These results indicate that the fit to peak dis-
charge and flow duration have strongly positive relationships, but with significant scatter, particu-
larly for the high-intensity events. However, by integrating the flow through time into a combined
measure that characterizes the dimensionless total energy expenditure (~ stream power) during
each event, demonstrates a much stronger relationship to the estimated transport flux
(Figure 5.12a). Weighting this index by an exponent reveals that the strength of the relationship
increases as the exponent is raised from unity (Figure 5.11a) through to 2 (Figure 5.12b), a pattern
that is mirrored in flume experiments (e.g. Bertoldi, Ashmore, and Tubino 2009). These results
show that by combining a proxy for measuring flood-based step lengths of particle and high-
resolution topographic changes, bed-material fluxes can be estimated, compared, and correlated
with different measures of flow intensity.
5.4 Discussion
5.4.1 New Technologies, Old Problems
Since the 4th Gravel Bed Rivers Workshop when Ashmore and Church (1998) reviewed the morpho-
logical method we have gone from an era of one-dimensional abstractions of rivers with cross sections,
longitudinal profiles, planform maps, and occasionally all three (e.g. Brewer and Passmore 2002), to
spatially continuous DEMs (2.5-dimensional surfaces; e.g. Lane and Chandler 2003), to three-
dimensional terrains and high-resolution point clouds (e.g. Lague, Brodu, and Leroux 2013). We term
this period starting in the mid- to late 1990s, the high-resolution topography revolution. The geomor-
phology community did not start this revolution, but has benefited from technological advances in
both data acquisition (e.g. SfM, TLS) and post-processing that have been driven principally by other
applications and industries (Bangen et al. 2014b). While continuous topographic surveys have been
tractable for decades, if not centuries (e.g. plane-table survey since at least the 1550s; photogrammetry
with stereoscopes since at least the 1950s), it was not until the 1990s that ground-based surveys with
total-stations became cost-effective and practical so that researchers were able to implement topo-
graphic surveys of gravel-bed rivers (e.g. Lane, Chandler, and Richards 1994; Milne and Sear,
1997). At approximately the same time, GIS and remote sensing software enabled the ready conver-
sion of these data into DEMs, and these datasets proliferated following the declassification of precise
GPS. The first commercial LiDAR followed shortly thereafter. This confluence of technological,
Revisiting the Morphological Approach 145
remote sensing, and surveying advances spawned the HRT revolution that so many geomorphologists
duly followed. What could be a more perfect battle to fight? This was a revolution that required field
work, but also allowed us to quantify landscapes, landforms, and their changes like never before
(Roering et al. 2013; Tarolli 2014).
0
0.0
Volumetric bed-material flux (103 m3)
0.2 0.4 0.6
R2= 0.941
∫ Qcr dt
Qcr > 30 m3/s
0.8 1.0
2
4
6
8
10
12
14
(a)
(b)
0
0.0
Volumetric bed-material flux (103 m3)
0.2 0.4 0.6
∫ Qcr2 dt
0.8 1.0
2
4
6
8
10
12
14
R2= 0.998
Qcr > 30 m3/s
Figure 5.12 Relationships between bed-material fluxes estimated by means of the morphological approach and flow
intensity. The morphological approach was based on the flood-based estimates of bed erosion presented in Figure 5.9
and the step-length values from Figure 5.11b. Measures of flow intensity have been normalized so that the range 0–1
corresponds to the maximum and minimum observed intensity during the study period (i.e. E00 to E10). Flow intensity
is expressed as: (a) integration of the flow above a critical value (Q
cr
>30m
3
/s) through time and (b) integration of the
flow above the Q
cr
through time but raising the exponent to 2. (Modified from Refolfi 2014.)
Gravel-Bed Rivers: Processes and Disasters146
What is perhaps surprising is that while the morphological approach has been established for over
50 years, the application of the approach with HRT data (e.g. Anderson and Pitlick 2014) remains
relatively rare in the literature. Nonetheless, methods to produce high quality DEMs from HRT
and supporting change detection analyses have matured (Passalacqua et al. 2015), therefore applica-
tions of these data to the morphological approach need to be evaluated. One major impediment to
utilizing HRT data for application of the morphological approach is a lack of basic geomatics training
and practical surveying knowledge (Passalacqua et al. 2015). However, this should be possible to
address. Most of the undergraduate and graduate programmes that produce researchers who study
fluvial geomorphology and gravel-bed rivers do not provide adequate (or in many cases any) training
in geomatics and surveying. Many papers already published contain a disproportionate amount of text
explaining what was done to overcome simple surveying blunders and mistakes, such as datum busts,
miss-matched flight lines, inconsistent control networks between surveys, etc. Many of these errors
are avoidable and standard practices and workflows exist to streamline the post-processing and
change detection analyses.
Application of the morphological approach in many fluvial environments is complicated by long-
standing challenges in simply surveying those environments. In some non-wadeable rivers, techniques
for acquiring bathymetry, such as spectral-depth correlation from imagery (e.g. Legleiter, Roberts, and
Lawrence 2009), green LiDAR (e.g. McKean et al. 2009) and multibeam echosounding (e.g. Hazel et al.
2006), are not always feasible. As such, errors associated with extracting the topography of wet chan-
nels can be considerably greater than for dry beds, where more accurate methodologies and workflows
can be applied (Williams et al. 2013).
5.4.2 Channel Morphodynamics: Beyond Quantifying Flux
As we begin to emerge from this HRT revolution, it is important to refocus our efforts around our
basic geomorphic curiosities. Arguably, we have become overly focused on measuring and estimating
the same old values at the continuum scale: net change in storage (ΔV) and sediment transport rate
(Q
b
). While these metrics provide useful insights into the processes shaping gravel-bed rivers, they are
average expressions of morphodynamic processes that we know vary significantly over both space and
time. We contend that the full value of repeat topography lies in using the rich spatial patterning these
data reveal, to better understand river morphodynamics and longitudinal patterns of sediment trans-
port in the context of other specific erosion and deposition mechanisms (i.e. the dominance of lateral
vs. vertical adjustments, or catastrophic changes, e.g. avulsions). Morphodynamics are defined as the
changes to morphology (i.e. topography) as a result of these processes through time and are thus
reflected in snap-shots of topography and sediment in storage, which ultimately give rise to distinctive
assemblages of geomorphic units (Wheaton et al. 2015). There remains much to learn about how lon-
gitudinal variations in sediment trasport rates, revealed by the morphological method, give rise to spe-
cific assemblages of these geomorphic units (river styles) and, in turn, how these units control
transport rates. There are also other mechanisms by which topography can be modified either natu-
rally (e.g. tectonic uplift, isostasy, compaction, deflation) and by humans (e.g. gravel mining or extrac-
tion, fill, compaction, tilling) or ecosystem engineers (e.g. beaver, willows), but these are not
necessarily the direct result of morphodynamics (Merz, Pasternack, and Wheaton 2006). Wheaton
et al. (2013) defined a morphodynamic signature as ‘a distinct mechanism of erosion or deposition
that leads to a consistent morphological response’. Moreover, Wheaton et al. (2013) and Williams
et al. (2015) have demonstrated how repeat topography can be used to classify net changes in topog-
raphy (i.e. net erosion and sedimentation) into specific morphodynamic signatures such as braiding
Revisiting the Morphological Approach 147
mechanisms, bank erosion, bar-edge trimming, channel incision, confluence pool scour, overbank
gravel/cobble sheets, and lateral bar development (e.g. Figure 5.13).
5.4.3 Future Opportunities and Challenges
While HRT is beginning to open doors to facilitate (and extend) the morphological method, enabling
more accurate, better resolved, more spatially extensive estimates of fluvial processes and mechanisms
of change, these efforts have barely started to help us better understand how gravel-bed rivers really
work. Although there is scope for continued improvements in topographic data acquisition, we need
to be very careful what we ask, because we just might get it. What if we could have HRT point clouds
for every river we wanted at subevent frequency? The result could be data overload that might entail
more methodological reflection and redefinition of workflows, instead of a focus on what these data
actually reveal about the links between morphology and transport. Arguably, technological progress
means that this prospect is neither fanciful nor does it lie in the too distant future. So there is surely
some methodological urgency in building algorithms for post-processing HRT data, estimating errors,
performing uncertainty analysis, and providing reliable change detection outputs in a manner that is
3%
3%
3%
36%
13%
13% 1%
1%
4%0%
0%
9%
7%
7%
26%
15% 2%
11%
11%
1%
18%
10%
24%
24%
0%
0%
0% 0%
0%
0% 0%
40%
2%
8%
5%
5%
24%
9%
9%
9%
9%
8%
27%
2004– 2003 DoD
(a) (b) (c) (d)
(e) (f) (g) (h)
2005–2004 DoD 2006–2005 DoD 2007–2006 DoD
Legend
Central bar development
Transverse bar conversion
Lobe disection
Chute cutoff
Overbank gravel or cobble sheets
Confluence pool scour
Bank erosion
Channel incision
Bar edge trimming
Lateral bar development
Questionable or unresolved changes
Total volumetric chan
g
e in stora
g
e
200 Metres150100500
N
Figure 5.13 Example of using budget segregation of DoD to quantify morphodynamic signatures. (Figure reproduced
from Wheaton et al. 2013.)
Gravel-Bed Rivers: Processes and Disasters148
not just possible with analytical brute force, but in a scalable, computationally efficient manner that
transcends scale and the volume of data we are quickly amassing. Efforts to make algorithms more
scalable and accessible from a variety of web-based, super-computer-backed and cloud-computing
solutions (e.g. http://zcloudtools.org) are scratching the surface in terms of building this capacity
and we believe are the future to building the capacity our community needs.
5.5 Conclusions
The inverse approach to estimating bed-material transport, known also as the morphological
approach, was first stated formally nearly a century ago. Nonetheless, application of this method
has been relatively rare and limited by the high labour demand and costs associated with undertaking
slow topographic surveys. The morphological approach was originally implemented with planform
mapping, scour chains, and sparse monumented cross sections. As we transition from the battle to
acquire better topographic data, to a reality in which HRT surveys are commonplace, the morpholog-
ical approach now has more relevance than ever before as a viable and pragmatic tool. Repeat HRT
surveys can be effectively utilized now to support change detection, and the application of the data
using the morphological approach to estimate bed-material fluxes is now possible. When coupled,
in the traditional sense, with a reference sediment flux or particle step lengths, reliable estimates
of net bed-material transport can be made without direct measurement and local sediment budgets
may also be elucidated. Moreover, new workflows, as demonstrated here for the Rees River, can gen-
erate bed-material flux estimates based entirely on DoDs, through simultaneous measurements of
erosion volumes that also support the definition of proxies for particle step lengths. Such methods
clearly require further evaluation, but are ultimately no more conjectural or subject to more severe
uncertainties than direct methods of sediment transport estimation, which moreover cannot be read-
ily applied in large rivers.
The adoption of HRT data analysis must, however, address the all-to-familiar amateur surveying
blunders, post-processing mistakes, and ineffective study designs. Information and methods exist
to avoid these costly mistakes and as a community we need to pay more attention to basic data acqui-
sition protocols in order to generate more effective data to address our key research questions. Such
progress would enable wider application of the modern morphological approach not just to estimate
sediment flux and net changes, but also to better understand the underlying morphodynamic mechan-
isms responsible for shaping gravel-bed rivers. With the modern morphological approach, we are well
positioned to exploit the explosion of repeat HRT survey data to generate and test the next generation
of hypotheses and theories about how gravel-bed rivers work.
Perhaps more important than just being able to measure topography at ever increasing temporal and
spatial resolution just because we can, is the question of what can all that data tell us that we did not
already know about gravel-bed rivers? What are the major theoretical advances we will be able to make
because of such rich empirical topographic time series? Will this lead to new insights about the mor-
phodynamic signatures and mechanisms by which gravel-bed rivers organize themselves in response
to fluvial disturbance? Will we be able to take this newly found theoretical understanding and be able
to build the next generation of predictive morphodynamic models of gravel-bed-river evolution?
Will these be models so computationally complex we can barely model a handful of floods? Or
will the empirical insights into the mechanisms by which gravel-bed rivers adjust reveal some clever
computational short cuts we can take to better model these dynamics and focus on the most essential
processes? At the moment these are questions that we can pose but not yet fully answer.
Revisiting the Morphological Approach 149
Acknowledgements
The authors wish to thank the organizers of the Gravel-Bed Rivers Workshop for inviting this con-
tribution and being so patient with our manuscript submission. The work presented in this chapter
was supported by different research projects and contracts funded by a UK NERC Grant NE/
G005427/1 (ReesScan), the Spanish Ministry of Economy and Competiveness and the European
Regional Development Fund Scheme (MorphSed, www.morphsed.es; CGL2012-36394), research
contracts funded by Endesa Generación S.A. (Spain), the National Science Foundation (Awards
1147942, 1226145 and 1226127), the US Geological Survey Grand Canyon Monitoring and Research
Center (Awards: 08WRAG0053, G12AC20346), Idaho Power Company (IPC 4568), and Eco Logical
Research, Inc (USU Award 100652). The ReesScan project was also supported by the NERC Geo-
physical Equipment Facility (award GEF 892), the New Zealand’s Foundation for Science and Tech-
nology Grant C01X0308 and Spain’s Ministry of Science and Innovation’sJoseCastillejotravelfund.
The first author is funded by a Ramon y Cajal Fellowship (RYC-2010-06264). James Brasington
wrote this chapter with the support of a Leverhulme Trust International Academic Fellowship
(IAF-2014-038). Many thanks to all members of the ReesScan team, different members from the
Fluvial Dynamics Research Group (RIUS) at the University of Lleida and the members of Utah State
University Department of Watershed Sciences, and Ecogeomorphology Topographic Analysis Lab-
oratory for their valuable assistance during the different stages of the research presented here. The
authors wish to thank the discussion authors and Mike Church for helpful conversations at the GBR
conference, which helped us strengthen the manuscript during revisions. We are especially grateful
to Jonathan Laronne and Daizo Tsutsumi for their patience, encouragement, comments and excel-
lent editorial advice throughout the process that helped us complete the chapter. Authors are
indebted to Chris Gibbins for reviewing the first version of this manuscript and Murray Hicks
for a thoughtful and constructive review. We would also like to thank the authors of the discussions
provided at the end of this chapter for their constructive comments.
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