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.

ii

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

iv

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

1

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

2

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]

5

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

6

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

7

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].

8

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

10

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

11

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

14

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

18

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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