Post on 25-Jul-2020
CONTROLS ON DOWNSTREAM CHANGES IN GRAIN SHAPE AND SIZE IN THE MAMEYES
RIVER, PUERTO RICO
Christiana Dietzen
Project Design for Masters of Science in Applied Geosciences Department of Earth and Environmental Studies
University of Pennsylvania - Spring 2012
Primary Reader: Dr. Douglas Jerolmack Secondary Reader: Dr. Robert Giegengack
ABSTRACT
CONTROLS ON DOWNSTREAM CHANGES IN GRAIN SHAPE AND SIZE IN THE MAMEYS RIVER, PUERTO RICO
Christiana Dietzen
Dr. Douglas Jerolmack
Changes in grain shape along a river can indicate if in-stream abrasion is a dominant process in determining grain size relative to sorting. To examine this question, I used image processing to extract three bulk shape parameters from images of grains sampled randomly from 36 locations along the Mameyes River and its tributaries, located in the Luquillo Critical Zone Observatory in northeastern Puerto Rico. By averaging these data for each location, I was able to determine that grain shape changes significantly with distance downstream along the Mameyes. These data can serve as a measure for the abrasion that occurs as grains are transported, and indicate its relative importance on the downstream fining of grains. I expected to find that as grains travel downstream, not only would grain size become finer, but grain shape would change as well. My analysis did, in fact, show subtle changes in grain shape in the lower portion of the river that were consistent with my hypothesis. However, the most significant trend was the drastic change in grain size that occurred at the transition between the bedrock-controlled upstream channel reaches and alluviated lower channel, which coincided with large changes in boundary shear stress and stream gradient. I posit that continual sediment input from tributaries in the bedrock-controlled upper channel reaches obscured downstream trends in grain shape and size, while both sorting and abrasion became significant in lower alluvial reaches where sediment inputs were limited.
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Acknowledgements:
I would like to extend innumerable thanks to Dr. Douglas
Jerolmack and Kimberly Litwin for their constant guidance throughout the course
of my research and writing, in addition to their assistance and good company in
the field. This project would not have been possible without their continued
support.
Many thanks also to Dr. Robert Giegengack for offering to serve as my
secondary reader, and many more thanks for his invaluable advice throughout my
time at Penn.
I would also like to thank the students and faculty of the Earth and
Environmental Studies department, who have taught me so much and been so
supportive during the course of my research and throughout my time in the
department.
This project was supported by the Luquillo Critical Zone Observatory
(NSF agreement EAR-0722476).
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Table of Contents:___________________________________________________
List of Figures v
List of Plots and Tables v
Introduction 1
Study Area 9
Methods 18
Results 23
Discussion 26
Conclusion 30
Plots and Tables 32
Works Cited 38
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List of Figures:
Figure 1: Map of Study Area 9
Figure 2: GPS locations of sampling sites 16
Figure 3: Example image of a sample grain 17
Figure 4: Image Processing Steps 18
Figure 5: Binary Image and Best Fitting Ellipse 20
Figure 6: Geologic map of study area. 27
Figures 7 & 8: Large grains deposited in the transitional area before 28 the alluvial plain
List of Plots and Tables:
Plot 1: Stream Profile 32
Plot 2: Stream Gradient against Distance 32
Plot 3: Base Flow and Active Flow Boundary Shear Stress against 33 Distance
Plot 4: Shield’s Stress for the d50 Grain Size against Distance 33
Plot 5: Grain Size against Distance 34
Plot 6: Dispersion of Grain Sizes 34
Plot 7: Roundness against Distance 35
Plot 8: Circularity against Distance 35
Plot 9: Convexity against Distance 36
Plot 10: Convexity at Several Locations against Grain Size 36
Table 1: Grain Data from each Location 37
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Introduction:
Previous research has demonstrated conclusively that downstream fining
of bedload material occurs in gravel-bed rivers [Ferguson et al., 1996; Kuenen,
1956; Kodama, 1994]. Unless significant amounts of coarse sediment enter the
river along its course, grain size tends to decrease approximately exponentially
with distance downstream [Ferguson et al., 1996]. Experimental field research,
flume studies, and numerical models have established that fining is caused by a
combination of the sorting of grains by size-selective transport and the abrasion of
these particles, both as they move over the riverbed and in place through impact
from other grains [Robinson & Slingerland, 1998; Hoey & Ferguson, 1997;
Pizzuto, 1995].
Sorting is a process by which a river preferentially entrains and transports
certain grains, usually according to grain size [Shields, 1936; Smithson et al.,
2002]. Shields [1936] developed a parameter, now called “Shields stress”, that
characterizes the potential mobility of a grain. The Shields stress is based on the
ratio of force acting to entrain the grain- boundary shear stress- to the weight of
the particle. In order for a particle to be entrained, the fluid flow must be above
the critical Shields stress [Shields, 1936; Wiberg & Smith, 1987]. On a uniform
bed, this means that grains with smaller diameters are more easily entrained, as
they have smaller mass. However, this can be complicated in the case of mixed
gravel beds. In mixed beds larger grains protrude more from the bed and therefore
more shear stress from the flow is working to entrain them, while smaller grains
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tend to hide in small pockets where the flow cannot exert as much shear stress
upon them [Wiberg & Smith, 1987]. This effect can lead to the phenomenon of
equal mobility, in which the all grain sizes on a bed require the same critical shear
stress for the initiation of motion [Wiberg & Smith, 1987]. Even under these
conditions, however, small grains travel greater distances than large ones once
entrained [Hill et al., 2010]. This process is known as selective transport, and can
create the effect of downstream fining [Krumbein, 1941].
However, the process of abrasion can also play a significant role in the
development of downstream fining patterns. Abrasion is the wearing down of
grains by the friction that occurs in particle-to-particle and particle-on-bedrock
collisions [Bullard et al., 2004]. Abrasion can take place through a variety of
pathways, though different authors have used different terminology to describe
these processes [Kuenen, 1956; Marshall, 1927; Wentworth, 1931, Krumbein,
1941]. The three processes that are most discussed are the impact of grains on one
another, the effect of them rubbing against each other, and the crushing of finer
grains by coarser ones [Marshall, 1927; Kuenen, 1956]. Kuenen [1956] broke the
distinct processes of abrasion down even further into splitting, crushing, chipping,
cracking, grinding, chemical attack, and sandblasting. Grains traveling as bedload
will undergo abrasion by colliding with grains on the bed, abrading the grains
making up the bed as well. Alternatively, they may roll or slide along the bed,
grinding and crushing other grains in the process [Lewin & Brewer, 2002]. There
is a long history of research on the effects of abrasion, beginning with Daubree’s
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1879 study, which used a tumbling mill to demonstrate the rounding effects of
abrasion on feldspar and granite fragments [Kuenen, 1956]. His work was
followed by a number of other tumbling mill studies, including more recent
research using equipment built to better simulate natural abrasion processes,
leading to a better understanding of the effects of abrasion on grain shape [Durian
et al., 2006; Durian et al. 2007; Kuenen, 1956]. These studies have uncovered two
interesting phenomena: first, changes in grain shape occur most rapidly in early
stages of transport, and second, that grain shape approaches a limiting value that
is related to its original shape, rather than spherical [Kuenen, 1956; Krumbein,
1941]. Abrasion causes the diminution and rounding of grains through repeated
elementary cuts that remove material from the parts of the grain that protrude the
most [Bullard et al., 2004]. This process converts young, angular grains with
polyhedral-like shapes into more spherical shapes with small vertices and small
sides [Durian et al., 2007]. Initially, an angular grain can be abraded quickly as
the sharp, protruding edges are easily chipped off by impact. As easily-removed
material is worn off the grain, abrasion-induced shape change slows [Kuenen,
1956; Krumbein, 1941].
Stream characteristics in the headwaters can speed the initial rounding of a
young, angular grain. In their upper reaches, streams tend to have higher
velocities and larger particle sizes, leading to energetic grain collisions; lower
stream reaches have finer sediment which does not abrade because collisions are
damped by the fluid [Kuenen, 1956, Bullard et al., 2004; Durian et al., 2007;
3
Jerolmack and Brzinski, 2010]. The shape that a grain finally achieves will be
related to its initial shape. Only a cube will develop into a perfect sphere;
irregularly shaped grains, such as those found in nature, will ultimately develop a
more ellipsoidal shape [Krumbein, 1941]. Therefore, shape parameter
measurements for a certain grain will tend to approach a final value
asymptotically, and that value is determined by the original shape and size of the
grain [Krumbein, 1941; Jerolmack et al., 2011].
Though the relative importance of sorting and abrasion on downstream
fining remains a topic of continued debate and research, each process has been
heavily studied individually [Durian et al., 2007; Durian et al., 2006; Attal &
Lavé, 2009; Ferguson, 1996]. It is, however, difficult to tease apart the effects of
these two processes and their relative importance on downstream fining, as they
are tied together by feedback mechanisms. Smaller particles are more easily
entrained, but the amount of time spent in transport determines the rate of
abrasion. Abrasion in turn decreases grain size, allowing for increased ease of
mobility [Jerolmack et al., 2011]. The relative importance of these two processes
likely varies with the characteristics of different rivers and the lithology- the type
of rock- and the resistance to wear of both the bedrock and the sediment being
transported [Hoey & Ferguson, 1997; Jerolmack et al., 2011]. Both lab
experimentation and observation in natural settings have provided ample evidence
of the influences of both abrasion and sorting on downstream fining [Lewin &
Brewer, 2002]. Fining observed over distances too short for abrasion to be
4
effective, such as along channel beds and bars, can be attributed solely to
selective transport. If the sediment being transported is known to be of a highly
resistant lithology, the presence of fining in this situation is also indicative of
sorting [Lewin & Brewer, 2002]. Ferguson et al. [1996] found that larger grains
travel significantly shorter distances than smaller grains by using tracer particles
in the field. This finding is also supported by what we know of the physics of
particle transport in a flow [Lajeunesse et al, 2010]. Flume studies have also
demonstrated this [Gasparini, 1999; Wilcock, 1993], and numerical models have
indicated that when abrasion cannot act on grains with highly resistant lithologies,
selective sorting is the primary cause of downstream fining [Hoey and Ferguson,
1997; Robinson and Slingerland, 1998]. Abrasion, which is more variable
according to lithology and initial grain shape, is somewhat more difficult to study,
and laboratory experiments on fining often neglect it [Lewin & Brewer, 2002].
Lithology, however, along with downstream grain rounding and evidence of
breakage, provides a means for identifying the occurrence of abrasion in nature
[Lewin & Brewer, 2002]. The occurrence of sorting by lithology is an indicator
that one lithology being transported in a stream is more easily and quickly
abraded than another. The resulting difference in sizes makes it possible for
selective transport to separate these different lithologies [Kodama, 1994;
Ferguson, 1996]. Laboratory experimentation has replicated the abrasion of
pebbles in a stream and has proven that it can be responsible for changes in grain
size and shape [Krumbein, 1941; Kuenen, 1956]. Durian et al. [2006]
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demonstrated the rounding of grains by eroding square, clay pebbles in a rotating
basin. Numerical models later reproduced these results by randomly removing
material from corners [Krapivsky and Redner , 2007].
A better understanding of how abrasion affects pebble shape and size
could improve the ability of sedimentologists to interpret preserved sedimentary
deposits and gather information regarding the flow regime, mode of
transportation, and the environment that deposited these beds [Durian et al., 2006;
Pelletier, 1958]. Fluvial abrasion resulting from the transport of grains along a bed
is a primary source of bedrock erosion [Johnson & Whipple, 2007; Johnson et al.,
2009; Sklar & Dietrich, 2004]. Therefore, the modification of these grains has a
direct impact on the capability of montane streams to erode bedrock and drive
landscape evolution [Attal & Lavé, 2009; Johnson & Whipple, 2007; Sklar &
Dietrich, 2004]. Grain size and sediment supply are two of the dominant controls
on the rate of bedrock incision [Sklar & Dietrich, 2004]. The amount of sediment
being input into a stream has opposing effects on the rate at which the river
incises into the bedrock: an influx of sediment initially increases the rate of
incision by supplying abrasive material. However, at a certain point, there is so
much sediment in the stream that the bedrock is no longer exposed and cannot be
eroded efficiently. Therefore, maximum rates of incision occur when a moderate
amount of sediment is delivered to the river relative to the amount it is capable of
transporting. Grain size is also one factor that determines the amount of shear
stress needed to initiate movement. Therefore, grain size determines how often
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grains can cause abrasion based on the typical range of flow velocities in a river.
Additionally, grain size will factor into what fraction of sizes are being
transported, as opposed to covering the bed and preventing incision. Only large
grains are able to remain immobile and armor the bedrock, while fine sediment
may be transported in suspension and will not impact the riverbed. Intermediate
sized grains are therefore the most efficient tools for bedrock incision, as they are
both mobile and come in contact with the bed [Sklar & Dietrich, 2004; Sklar &
Dietrich, 2001].
There are few studies that have systematically examined changes in grain
shape and grain size in a natural stream, and most field studies do not provide an
adequate analysis of relevant transport parameters – such as downstream changes
in fluid shear stress – that would allow a definitive test of sorting and abrasion
mechanisms. In order to address this gap, I undertook a study to quantify all of
these relevant parameters in the Mameyes River, a bedrock and alluvial channel
that is known to exhibit significant changes in grain size and shape over a few
tens of kilometers. By quantifying particle shape and making use of available data
on grain size, topography, and flow, I was able to assess how transport and
geology control grain size and shape patterns in a natural stream.
Pike et al. [2010] demonstrated conclusively that downstream fining is
occurring in the Mameyes through an in-depth study of grain sizes in the river
consisting of 42 pebble counts along the stream. However, it is impossible to
conclude whether downstream fining is due to hydraulic sorting or abrasion
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simply from observations of grain size along the stream [Krumbein, 1941]. My
research intends to complement their data with an investigation of the evidence of
abrasion and its contribution to the downstream fining in the Mameyes River.
Significant changes in grain shape indicate that abrasion may be playing a role in
the process of down stream fining by wearing grains down to smaller sizes as they
move down the channel, while minimal changes in shape along the river indicate
that downstream fining is likely due to sorting [Durian et al., 2006; Durian et al.,
2007; Lewin & Brewer, 2002]. Though shape can minimally affect the threshold
for the entrainment of a particle, grain size is the primary determinant of the shear
stress required for particle transport to occur [Boggs, 2001; Jerolmack et al.,
2011]. As sorting by shape is unlikely, abrasion should be the only significant
factor affecting the downstream changes in shape observed in my study.
Measuring changes in shape downstream should therefore allow for quantification
of abrasion with minimal influence from sorting – as long as any inherited
relation between size and shape of parent material is quantified [Jerolmack et al.,
2011]. Previous studies have attempted to quantify abrasion by inferring them
from fining rates, but these results are likely to be incorrect, as they neglect the
effects of sorting [Gasparini et al., 1999].
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Study Area:
Figure 1: Map of Study Area [LCZO]
The Mameyes River has its headwaters in the Luquillo Mountains and its
mouth on the northeastern shore of Puerto Rico. These steep mountains are the
result of uplift of volcaniclastic rocks resulting from oceanic island-arc
subduction. This tectonic activity also caused complex faulting and dips of
greater than 30º [Pike et al., 2010]. These marine-deposited volcaniclastics
consist of a variety of lithologies, including sandstones, shales, conglomerates,
and breccias, as well as tuffs and solidified lava [Seiders, 1971a; Briggs &
Anguilar-Cortés, 1980]. Some of the volcanoclastics were affected by contact
metamorphism as a result of the intrusion of a granodiorite batholith, which
created a 1-2 kilometer thick zone of hornfels surrounding it [Seiders, 1971b].
9
These hornfels are significantly more resistant to weathering than the surrounding
layers and form the tallest peaks of the Luquillo Mountains. The landscape also
includes a number of plutonic intrusions and dikes, as well as quaternary alluvium
on the coastal plain fringing the mountains [Seiders 1971a, Briggs and Anguilar-
Cortés 1980].
My field site’s tropical location also significantly affects landscape
processes. Rainfall is frequent, occurring almost daily, and intense tropical storms
are common [Schellekens et al. 1999; van der Molen 2002]. The combination of
high mean annual rainfall and the steep slopes of the Luquillo Mountains creates a
powerful, high-energy flow regime, capable of intense erosion that dissects the
landscape, creating deep valleys [Pike et al., 2010]. Tropical climates also lead to
relatively high rates of physical and chemical weathering, increasing the amount
of material that is being fed into the stream and the rate at which that material can
be abraded as it is transported down the channel [White et al. 1998]. The process
of downstream fining can be disturbed if there are large influxes of coarse
sediment along the stream profile, such as those introduced by the frequent
landslides in the Luquillo Mountains [Ferguson, 1996; Pike et al., 2011]. The
addition of this coarse sediment can create discontinuities in grain size and shape
patterns [Pizzuto, 1995; Brummer and Montgomery, 2003].
The headwaters of the Mameyes river begin on the highest ridges of the
Luquillo Mountains in the Luquillo Experimental Forest, a 113 km2 preserve
managed by the United States Forest Service [Pike et al., 2010]. The steep valley
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walls in the headwaters of the river have prevented the channels of the Mameyes
and its tributaries from significantly changing their locations [Monroe, 1980]. The
Mameyes watershed, which has an area of 44 km2, drains from the protected
primary forest at its headwaters, mature secondary forest at mid-elevations, and a
variety of agricultural areas, urban developments, fields, and pastures that are
being reforested along the coastal plain [Pike et al., 2010]. Land use and cover
along the lower elevations have changed frequently as the coastal plain underwent
various stages of development following the colonization of Puerto Rico by the
Spanish in the 1700s [Pike et al., 2010].
The bedrock lithology also affects the morphology of the river channel
significantly. The bedrock underlying the Mameyes is composed primarily of
volcaniclastics, excluding a small area of the granodiorite batholith outcrops in
the uppermost portions of the headwaters [Pike et al., 2010]. The higher portions
of the stream are characterized by cascade and step-pool morphologies, while the
lower portions are composed of plane bed and pool-riffle sequences. Both
cascades and step-pools tend to occur in the presence of steep gradients and
narrowly confined streambeds [Montgomery & Buffington, 1997]. Cascade
channels feature continuous tumbling over individual large clasts, while in step-
pool channels large clasts block flow in such a way as to create pools followed by
significant drops over the large clasts to the next, lower level of the channel.
Plane-bed morphology occurs in relatively straight channels with moderate to
high gradients, and is characterized by extended stretches of relatively featureless
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beds and a lack of rhythmic bedforms. Pool-riffle channels occur in areas with
lower gradients and are defined by the presence of an undulating riverbed, which
leads to the development of a sequence of pools, riffles, and bars. In the upper
portions, where bedrock is often exposed, the stream may follow faults, and
knickpoints- sharp changes in channel elevation or gradient- may occur at
lithologic boundaries [Pike et al., 2010; Whipple & Tucker, 2002].
The Mameyes has been classified as “flood dominated,” as the
combination of steep slopes and frequent (often heavy) precipitation creates rapid
runoff, causing frequent, though short-lived, flooding [Pike et al., 2010]. The
largest of these floods, which are associated with hurricanes and other tropical
storms, rework boulder channels [Scatena & Larsen, 1991]. The river is also
significantly affected by the occurrence of landslides, which are common due to
steep hill slopes. These landslides deliver tremendous amounts of coarse
sediment, including large boulders. In fact, the landslides are responsible for
delivering 80-90% of the total sediment that enters the channel. As much of this
material enters in large pulses, landslides can be responsible for local changes in
channel morphology [Pike et al., 2010].
My field site is part of the Luquillo Critical Zone Observatory, which was
selected as a particularly interesting setting to study sediment abrasion because it
contains two watersheds, the Mameyes and the Icacos, which have similar
climate, relief and drainage area but different underlying lithologies. The
volcaniclastic bedrock of the Mameyes weathers into a large range of grain sizes,
12
making this gravel bed river suitable for the study of grain shape [Pike et al.,
2010]. The availability of Pike et al.’s complementary data set, which provides
detailed grain size and channel geometry data for the Mameyes, has made it
possible to focus additional field research on studying grain shape.
Methods:
To examine changes in shape along the river, I focused on three shape
parameters: roundness, convexity, and circularity. Roundness indicates how
closely a grain approaches a spherical, rather than elliptical, shape. Convexity is a
measure of the sharpness of corners and angularity of edges on a grain. It
indicates the smoothness of the grain perimeter. Circularity is a somewhat less
sensitive parameter since it incorporates both area and perimeter and can be
affected by changes in both smoothness and shape [Cox & Budhu, 2008].
Roundness and circularity can be easily calculated if the area, perimeter, and
longest axis of the grain can be measured. To calculate convexity, it is not only
necessary to calculate the perimeter of the grain, but also the convex perimeter of
the grain [Cox & Budhu, 2008]. These parameters can be used to collect
information about grains, such as the resistance of the grain to abrasion, the type
of transport process it underwent, and the distance of transport [Boggs, 2001].
Castano et al. [2002] used similar shape parameters as an easy way to gather
geologic information from images taken by the Mars rover. A number of
researchers have investigated methods of quantifying grain shape, but advances in
technology have replaced many of the classical methods of measuring grain shape
13
with computer automated ones [Wadell, 1932; Cox & Budhu, 2008]. This has led
to the development of new shape parameters, such as circularity and convexity,
which are more easily measured. Additionally, some existing parameters, such as
roundness, have been given new mathematical definitions [Cox & Budhu, 2008].
Though Wadell [1932] originally defined roundness as the arithmetic mean of the
roundness of the individual corners in a plane, most image-processing software
uses a mathematic formula based on the area and length of the major axis,
variables that can be easily measured by the software [Cox & Budhu, 2008].
By averaging shape parameter values extracted from each sample, I
found representative shape parameter values for each sample location on the
Mameyes. I expected that as grains travel downstream, not only would grain size
become finer [Pike et al., 2010], but grain shape should change as well. As
abrasion wears away small-scale roughness features on individual grains, their
convexity values should increase fairly rapidly as they move downstream.
Abrasion is also likely to increase roundness and circularity, though this process
should occur more slowly because more material must be worn away from a grain
to change its shape on a larger scale. However, the maximum roundness,
circularity, and convexity a grain can achieve is related to the initial shape of the
grain, so these parameter values may plateau when abrasion slows after most of
the rough edges have been removed and the angularity of the grain has decreased
[Kuenen, 1960]. Abrasion should also slow as the topography becomes less steep
and stream velocities and collision energies decrease [Kuenen, 1960; Jerolmack
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and Brzinski, 2010].
My sampling technique was based on Wolman’s [1954] method and
consisted of randomly selecting grains as I paced across the width of the channel.
At each location, I sampled approximately forty grains from across the entire
width of the river. These grains were placed on a board with the largest face up
and then photographed for later image processing. A ruler was placed on the
board and included in the picture to allow for scaling of the images. Most of the
pictures were taken with the camera on a monopod to enhance their clarity and
consistency. I took samples at 32 points along the Mameyes River, beginning in
its headwaters and continuing to a location immediately preceding the gravel-sand
transition in the main channel, where the bed cover abruptly changes from gravel
to sand, making further sampling impossible [Knighton, 1999]. I attempted to
sample grains at regularly spaced locations along the river in order to acquire an
accurate representation of how grain shape changes downstream. However, my
sampling locations were significantly affected by ease of access, so many of my
samples, particularly in the headwaters, were taken close to roads and trails. I took
samples from tributaries to establish the mean shape of the material being
introduced into the river. Additionally, I sampled just downstream of each
tributary to understand how the material entering the stream affected the mean
shape parameters of the river’s bedload, as tributaries have been shown to disrupt
fining patterns [Ferguson et al., 1996; Hoey & Ferguson, 1997; Pizzuto, 1995].
15
Figure 2: GPS locations of sampling sites
My pictures were taken on a red background with the intention of using
color channel separation to isolate the image of the grain. This was effective in
most cases, but for some locations, issues, such as too much glare, made it
necessary to normalize the images instead. First, the red color channel was
extracted from the image, as this grayscale version of the image had the most
contrast between the grain and the background. Robert Bemis’ thresh_tool, a free
Matlab toolbox, which provides an interactive interface that allows for manual
selection of the threshold value for each image, was used to see how different
thresholds affected the images. The tool was usually able to automatically select a
fairly accurate threshold value and did not always need adjusting. This was
16
particularly helpful when light intensity varied widely between images at a
location, so one threshold could not be assigned to all of the images from a
location.
Figure 3: Example image of a sample grain
For some samples, this method proved ineffective. Contrast was not
always strong enough in the red color channel to separate the grain from the
background, especially when extreme glare was present in the image. To improve
contrast in those samples, the original color image was instead normalized, a
process that alters the range of intensity values. This method also minimized
glare, which was especially a problem with images of wet grains. The normalized
images were then converted to binary, and the process was repeated using the
thresholding tool. However, some poor quality images had to be left out of the
analysis, and data from several locations had to be eliminated entirely because
their image quality was not high enough to extract any reliable results. In order to
remove noise from the thresholded image, Matlab’s “bwareaopen” function was
used to eliminate holes in the image of the grain. The binary image was then
inverted and the same function was used to eliminate holes in the background.
17
Finally, several of Matlab’s image processing tools were run on the
images in an attempt to smooth the edges of the grains, which sometimes
appeared rough due to issues with the original images and separation of the grain
from the background. Because the perimeter measurement is vital to shape
parameter calculations, it is important to restore natural smoothness to edges as
much as possible. Increased roughness leads to inaccurately large perimeter
values, which in turn affect both convexity and circularity values. Several
morphological operations were used to smooth the edge of the grain, including
one that removes spur pixels and another that performs morphological closing
(dilation followed by erosion). The effects of these transformations are shown in
Figure 4.
Figure 4: Image Processing Steps
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From these processed images, I was then able to use a built-in Matlab
function to calculate the area, perimeter, and major axis of each grain, measured
in pixels. I used these values to calculate my shape parameters: roundness,
circularity, and convexity.
!
Roundness =
!
(4 " Area) ÷ (# " MajorAxis^2)
!
Circularity =
!
(4" # Area) ÷ (Perimeter^2)
!
Convexity =
!
(ConvexPerimeter) ÷ (Perimeter)
[Cox & Budhu, 2008]
A value of 1 for circularity indicates a perfect circle. As the value approaches 0,
the shape becomes less smooth and more elliptical. Grains become more round as
roundness values approach 1 and smoother as convexity values approach 1.
Last, I tested for correlations between size and shape parameters. Since
Pike et al. [2010] already collected extensive grain size data along the river, it was
unnecessary for us to measure the size of all my samples, except to test for these
correlations. To do this, I selected four locations on the alluvial plain. I used
ImageJ image processing software to scale the image using the ruler included in
the picture. By placing the grain with the largest face up for the picture, the minor
axis in the 2D representation of the grain is, in fact, the median axis of the grain,
which is customarily used to measure grain size [Wolman, 1954]. I extracted the
length of the minor axis of the best fitting ellipse as generated by my Matlab code,
and used this length to represent the median axis. Matlab gives the axis length in
pixels. Those values must then be divided by the number of pixels per centimeter,
determined by scaling against the ruler in the image, in order to find the length of
19
the median axis in centimeters. Grain size could then be plotted against each
image’s shape parameter values to determine the level of correlation. In order to
test for correlation over a larger sample size, data from five sampling sites in
close proximity to one another were combined and similarly analyzed.
Figure 5: Binary Image and Best Fitting Ellipse
If there is a correlation between grain size and shape, it could be an
indication that the feedback mechanism connecting sorting to abrasion could be
affecting shape changes downstream. If abrasion causes grains to become not only
more round and smooth but also smaller, then these abraded grains can be more
easily transported. Because rounded grains may travel farther due to their smaller
size, a correlation between size and shape could imply that sorting plays a role in
the trend of grains becoming rounder as the travel downstream. This phenomenon
makes it necessary to investigate not only to what degree shape is changing but
also where these changes occur in comparison to changes in size. If a significant
change in median grain size or the distribution of grain sizes occurs over a
distance too short for abrasion to be effective, it is presumably the result of grain
size sorting. If significant rounding occurs along the same short stretch of the
river, this change is shape is likely due selective transport of grains that are both
20
small and relatively round. If grain shape instead changes consistently along the
stream rather than varying directly and immediately with size, then the rounding
of grains is more likely to be attributable to abrasion.
As my code is designed to run through a file containing all grain images
for a particular location, it is able to store the results of my shape parameter
calculations
in the form of two vectors, each containing the values calculated for each image.
From these vectors, I was able to calculate the mean roundness, circularity, and
convexity at each location. These data were then used to compare how the mean
values shift as grains travel downstream.
From Pike et al’s [2010] data set it is also possible to calculate whether or
not a certain grain size is traveling in suspension or as bedload, which can provide
a better understanding of how frequently a certain grain size is abraded. Mode of
transport is typically determined by the ratio of particle fall velocity, ws, to shear
velocity, u* [Dade & Friend, 1998]. Particle fall velocity, or settling velocity, can
be calculated with this equation:
where g is acceleration due to gravity, D is mean sediment diameter, ν is the
kinematic viscosity of water, R is the submerged specific gravity of a particle in
water, and the constants C1 and C2 are related to the smoothness and shape of the
grain [Ferguson & Church, 2004]. This equation can be simplified using known
21
constants applicable to the setting, allowing ws to be solved for if D is known,
which is here set to the value of D16. In typical situations, g = 9.8 m/s2, the
kinematic viscosity of water at 20 °C can be estimated as 1.0 x 10−6 m2/s, and R
for quartz sediment in water is 1.65. By substituting in an intermediate value of C1
and C2 for natural grains, the equation can be simplified to:
.
Shear velocity can be calculated using Pike et al’s [2010] boundary shear stress
(τb) data in this equation:
where ρ is the fluid density of water, which is approximately 1 g/cm3 [Hsü, 2004].
If the ratio ws/u* results in a value of 1, then particle transport is said to be in the
transitional phase between suspension and bedload [Dade & Friend, 1998]. Pure
bedload results in a value greater than 3, while pure suspended load results in a
value lower than 1/3 [Dade & Friend, 1998].
Image quality is very important when using these techniques to analyze
shape parameters as poor quality images can lead to inaccurate results. My
methods could have been improved by giving more attention to the effects of
water on both the color of the grain and its tendency to create glare on the
background. If a grain is partially wet, the dry portion is often lighter, and has a
tendency to blend in with the background. This could be easily fixed by wetting
22
the whole grain before photographing it. However, dry grains are still preferable
as, depending on the lighting, a wet grain may create a glare that lightens a
portion of the grain and lessens the contrast. More attention should also be paid to
the backdrop itself. Water on the board tends to create glare, making the dry parts
of the board comparatively darker. This can make it impossible to use
thresholding to distinguish the board from the grain, as they now have more
similar and potentially overlapping intensity levels. This issue with contrast can
also be helped by ensuring that the background has the same intensity of lighting
across the board, though this is often not feasible when doing fieldwork due to
variations in natural light. It is possible that using a white background and
normalizing the image rather than using a red background in order to remove
color channels may provide better quality images.
Results:
Pike et al.’s [2010] data set includes a number of parameters describing
stream characteristics at each sampling location. I was able to plot the stream
profile using Pike’s recordings of local elevation (see Plot 1). In the headwaters
elevation decreases rapidly, showing a steep profile that levels out farther down
the stream, approximately 9,500 meters upstream of the mouth of the river.
Outlier patterns indicate the profiles of tributaries. Pike et al. also recorded stream
gradient, which, in Plot 2, indicates that though local slopes are higher above the
9,500 meter point, there is much variation in stream gradient in the headwaters.
After this point variation in slope becomes minimal and values remain relatively
23
low. Boundary shear stress values were calculated for both base flows and active
flows as the product of water density, acceleration due to gravity, hydraulic
radius, and slope. Plot 3 indicates that initially there is a wide range of shear stress
values with a common maximum until the same point, 9,500 meters above the
river’s mouth. At that point, shear stress decreases dramatically and the
distribution of values is very small. The data also indicate a relatively minor
difference between active flow shear stress and base flow shear stress for this
portion of the river, and this pattern continues until the gravel sand transition. As
shown in Plot 4, the dimensionless shear stress, or Shield’s stress, for the d50 grain
increases drastically before dropping off after the same 9,500 meter point. Though
it is the highest in the uppermost elevations of the headwaters, this second peak
occurs at the same point as the shift boundary shear stress.
Pike et al.’s [2010] grain size data also give us the capability to analyze
downstream fining patterns. His data set provides not only median grain size
values (d50)1 at each location, but also values for the sizes of fine grains (d16),
coarse grains (d84), and the maximum grain size sampled (dmax). From these data,
dispersion values- a measure of the wideness of the grain size distribution- can be
calculated as (d84-d16)/d50. Plotting the grain size values of the various size classes
against distance from the mouth (Plot 5) illustrates downstream fining patterns
and provides a general idea of the trends in grain size distribution changes.
Significant changes in the grain size distribution occur over a short reach
24
1 The subscript indicates the percentage of total grains in a sample smaller than the size described.
stretching from approximately 9,000 meters to 10,000 meters upstream of the
mouth of the river. Dispersion values shown in Plot 6 do not indicate a strong
downward trend, but instead show a particularly large distribution of grain sizes
present in this transitional 1,000 meters of the river.
Plotting size against convexity, as shown in Plot 10, indicates that there is
a trend such that smaller grains are smoother. Because this may signal the
presence of feedback mechanisms connecting sorting to abrasion, it is necessary
to evaluate how patterns of shape change correlate with those of size change.
Initially, shape parameters decrease downstream as grains move through the
headwaters. There is an inflection in this trend just before the transition to the
alluvial plain at around 10,000 meters above the river’s mouth, at which point
shape parameter values begin to increase with distance downstream. This trend
continues until approximately 6,000 meters before the river’s mouth, at which
point values saturate and remain fairly stable.
In calculating ws/u* for the d16 grain size and plotting these values along
the length of the Mameyes, it is apparent that values are significantly lower in the
upper portions of the stream. During active flow, the majority of these values in
the headwaters are below 1, indicating that for many locations the d16 grain size is
in the transition to suspended load. In some locations in the headwaters, where
values are lower than 1/3, the d16 grain size is in pure suspended load. At distances
lower than 10,000 meters from the mouth of the stream, all values are greater than
1 and often above 3, indicating a trend towards bedload transport. For baseflow
25
the same patterns emerge along the river, though values are significantly higher,
indicating increased bedload transport relative to active flow.
Discussion:
It is interesting to note that all major changes observed in the river,
including grain size, grain shape, channel geometry, and hydraulic geometry,
occur between nine and ten thousand meters upstream of the river’s mouth. It is
here that the flow regime of the river changes. Plotting elevation, slope, shear
stress, and Shield’s stress against distance from the mouth provides evidence that
flow conditions transition rapidly from those that are characteristic of a montane,
bedrock-controlled stream to those characteristic of the alluvial plain. Fig. 6 shows
the alluvial plain to begin further downstream, but a small alluviated region
surrounds the Mameyes beginning at this transitional area until the alluvial plain
as defined by Brigg’s [1964] geologic map. At this point, slope decreases as the
river enters the flat alluvial plain. At higher elevations, irregular bedrock outcrops
controlled the river, causing an erratic distribution of stream gradients. Slopes are
not only lower on the alluvial plain, but also very uniform. As slope is a factor in
the calculation of a stream’s shear stress, this decrease in slope is the source of the
drastic decrease in shear stress that occurs at the same location.
26
Figure 6: Geologic map of study area. Alluvium is
designated by Qa. [Adapted from Briggs, 1964]
The major shift in grain size distribution also occurs at the transition to
the alluvial plain. Because of the shift in flow regime and lower shear stress, the
river can less easily transport very large grain sizes. It is this rapid drop in
boundary shear stress that caused the deposition of coarse material before the
alluvial plain that evidence of is apparent in Pike et al.’s [2010] grain size data and
through observation of the stretch of river in which this occurs. The accumulation
of large boulders observed just before the transition to the alluvial plain caused by
the discontinued transport of larger grains is evidence of the transition in
topography and resulting decrease in boundary shear stress (See Fig. 7). The
deposition of these large grains causes the drastic increase in size distribution as
27
evidenced by dispersion values. Because the deposition of these large grains
increases the d50 grain size, the shear stress required to entrain these grains
increases as well, accounting for the peak in Shields stress at this location. The
plot of grain size against distance (Plot 5) makes it apparent that the trend of
gradual downstream fining which is common in most rivers is not present in the
Mameyes [Ferguson et al., 1996; Gasparini et al., 1999].
Figures 7 & 8: Large grains deposited in the transitional area before the alluvial plain.
The inflection in shape parameter values occurs at the same location as the
major decrease in variance of grain sizes. This indicates that this shift is related to
grain size sorting patterns as large grains begin to fall out of transport. It is likely
that the smaller, and more rounded, of the large grains at this point travel father
28
according to selective transport principles, allowing for sorting by size, and, on
account of their relation, shape. Rates of rounding in this area are also at their
highest, indicating that here rounding patterns are connected to the intense sorting
occurring in the same area. However, after this transitional stretch, changes in
median grain sizes and in the distribution of grain size seem to slow or cease,
while normal downstream rounding and smoothing of grains continues. This is an
indication that while sorting is no longer a dominant process, abrasion is
continuing to wear away at these grains as evidenced by their continually
increasing shape parameter values. However, values for most grains in transport
seem to saturate at approximately 6,000 meters upstream of the mouth of the
river. This saturation of grain shape has been demonstrated in previous
experiments, and indicates that these grains approached their asymptotic shape
limit imposed by the abrasion process [Durian et al., 2006; Durian et al., 2007].
Grain shapes upstream of the transition to the alluvial plain exhibit
abnormal rounding patterns. Rather than becoming rounder and smoother as they
travel downstream, the opposite effect is observed: parameter values decrease
with distance. Previous studies on size and shape have not been carried out in
rivers with such a drastic shift from montane to alluvial; it appears that in the
headwaters of the Mameyes, other factors outweigh abrasion in determining mean
shape values. For instance, the Luquillo Mountains are a landslide-dominated
landscape. It is possible that this mass wasting, in addition to the input of new
material from tributaries, is continually adding large quantities of young, angular
29
grains to the Mameyes throughout its upper reaches. As drainage area continually
increases downstream, so too does the potential for the input of new, angular
material. The quantity of additional new material could outweigh the older, more
rounded material, skewing mean shape parameters towards lower values. My
upstream data points were taken in a number of different tributaries, some of
which do not join the main stem until just before the transitional area at the base
of the mountains. As these tributaries are of different lengths and are transporting
material from different sources, it would be unlikely that the process of abrasion
would be at the same stage in different tributaries at the same distance from the
mouth. This is another likely factor in the abnormal shape parameter patterns
upstream. One more potential factor is that because a large portion of the smaller
grains are traveling in the transitional realm between bedload and suspension
during active flows, they do not come into contact with the bed and other grains
as frequently as larger grains and are therefore abraded less. However, though this
may be occurring, it is likely that differences in shape between material input
from tributaries outweigh the effects of selective transport in creating the
abnormal patterns seen upstream.
Conclusion:
To a certain extent, my methods effectively separated the effects of sorting
from those of abrasion. I saw a dramatic drop in grain size at the transition to the
alluvial plain, evidence of grain size sorting caused by shifts in topography and
stream power, and consistent rounding and smoothing along the alluvial plain
30
though grain size remained stable, the latter serving as strong evidence of
abrasion. At the end of my study area both grain size and shape had both
stabilized, indicating equal mobility and that most of the grains had approached
their final shape. Because size remained stable throughout the reach in which I
observed consistent abrasion, I can conclude that in the Mameyes River abrasion
does not play a large role in determining grain size. However, my results were
dominated by the dramatic change found in the transition from the Luquillo
Mountains to the alluvial plain. This dramatic shift in values in the transitional
area was apparent in all of my data, including grain size, grain shape, boundary
shear stress, slope, and topography. To my knowledge, no previous experiments
studying downstream fining or changes in shape have been performed on an area
with such a dramatic change in topography. My results make it apparent that
normal fining and rounding patterns cannot be expected in an environment with
such strong geologic control. The transition to the alluvial plain overpowers any
other detectable patterns, and the input of material from numerous tributaries
obscures any potential trends above that point. Since variable bedrock exposure,
and spatially-distributed sediment input through landslides and tributaries, are
common to many mountain streams, the study of grain size and shape in other
montane systems will face similar difficulties. Regardless of those obstacles, I
have demonstrated the effectiveness of my methods in quantifying the role of
abrasion in determining grain size in rivers not significantly disturbed by
incoming tributaries, such as the lower portion of the Mameyes.
31
Plots and Tables:
Plot 1: Stream Profile
Plot 2: Stream Gradient against Distance
32
Plot 3: Base Flow and Active Flow Boundary Shear Stress against Distance
Plot 4: Shield’s Stress (dimensionless shear stress) for the d50 Grain Size against Distance
33
Plot 5: Grain Size against Distance
Plot 6: Dispersion of Grain Sizes
34
Plot 7: Roundness against Distance
Plot 8: Circularity against Distance
35
Plot 9: Convexity against Distance
Plot 10: Convexity at Several Locations against Grain Size
36
Location ID:
Table 1: Grain Data from each Location Name
Distance from
Mouth (m) Mean
Roundness Mean
Circularity Mean
Convexity Number of
Samples Used M061011-03 15858.07128906 0.7086 0.6938 0.947 33 M061311-05 15794.53320313 0.665 0.7186 0.9607 34 M061311-04 0.5962 0.6626 0.9486 44 M061411-05 14616.41601563 0.7011 0.717 0.9519 15 M061011-04 14753.95800781 0.6871 0.7021 0.9562 27 M061311-03 0.6497 0.6223 23 M061511-01 12999.78710938 0.659 0.7281 0.9746 23 M061511-02 12190.20312500 0.6459 0.695 0.9475 24 M061511-03 12420.01757813 0.6193 0.6625 0.9589 10 M061411-03 11640.46875000 0.6338 0.6787 0.9439 19 M061411-02 0.6661 0.6763 0.9313 16 M061011-05 10301.77246094 0.6492 0.7042 0.9573 32 M061011-01 0.6703 0.6762 0.9384 21 M061311-01 10576.42285156 0.6418 0.7066 0.9533 21 M061311-02 10412.56152344 0.626 0.6944 0.9501 28 M060611-01 9916.64257813 0.6266 0.7168 0.962 9 M061411-04 9537.64355469 0.6011 0.6035 0.9449 18 M060811-07 8865.60156250 0.6812 0.7206 0.9567 27 M060811-05 8697.40527344 0.6798 0.6689 0.9521 16 M060811-04 8579.74218750 0.6728 0.7336 0.9681 30 M060811-03 8518.74316406 0.6421 0.7025 0.9581 34 M060811-02 8422.01171875 0.6857 0.7134 0.9641 33 M060811-01 8350.54687500 0.7351 0.7124 0.9361 21 M060911-06 7141.81884766 0.713 0.6875 0.9419 19 M060911-04 6410.60400391 0.6803 0.6119 0.9441 32 M060911-05 5985.73046875 0.7025 0.7582 0.9732 36 M060511-01 5738.46044922 0.7343 0.7359 0.9659 18 M060511-03 4360.80468750 0.7046 0.742 0.9671 20 M060511-02 4146.41894531 0.6339 0.6405 0.9387 18 M060911-03 3397.86401367 0.7308 0.7109 0.9611 42 M060911-01 2700.89184570 0.7051 0.7182 0.9565 36
37
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