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This is to certify that the
thesis entitled

USING DIGITAL ELEVATION DATA TO PREDICT
SLOPES OF COASTAL SAND DUNES IN
BERRIEN COUNTY, MICHIGAN

presented by

Juliegh R. Bookout

has been accepted towards futﬁllment
of the requirements for the

MA. degree in Geography

 

 

MW

Major Professor’s Signature
I 2/1 I / 2.0%

 

Date

MSU is an Afﬁrmative Action/Equal Opportunity Institution

 

LIBQARY
Michigan State
University

 

 

 

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PLACE IN RETURN BOX to remove this checkout from your record.
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DATE DUE

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2/05 p:/C|RC/DaleDue,indd-p.1

 

USING DIGITAL ELEVATION DATA TO PREDICT SLOPES OF COASTAL SAND
DUNES IN BERRIEN COUNTY, MICHIGAN

By

Iuliegh R. Bookout

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF ARTS

Department of Geography

2006

ABSTRACT
USING DIGITAL ELEVATION DATA TO PREDICT SLOPES OF COASTAL SAND
DUNES 1N BERRIEN COUNTY, MICHIGAN
By

Iuliegh R. Bookout

In 1989 the state of Michigan amended the Sand Dune Protection and Management
Act to include the designation of critical dunes. Some of the most spectacular dunes
along the Lake Michigan shore are also the most vulnerable; therefore, the distinction
of critical dunes is given to these areas in an effort to mitigate the negative impacts of
change. The Michigan Department of Environmental Quality is the agency charged
with regulating all site alterations in these areas. The MDEQ’S decision to approve or
deny a property owner a permit is based primarily on the slope of the dune, which is
collected in the ﬁeld. Using a digital elevation model and land cover data, I believe
that MDEQ agents could quickly and efﬁciently gather the slope measures they need
to complete the permit process. In the past, accuracy issues have hindered the
widespread use of DEMS in management; however, in recent years the accuracy of
the underlying elevation data has Signiﬁcantly improved with the development of
lidar. I propose that lidar used in conjunction with calculated slope and land cover, in
a linear regression model, could enable users to predict true slope more accurately

than a model that uses NED as its source data and those same variables.

This thesis is dedicated to my son Jackson who made the ﬁnal days of my journey
more beautiful than all of the ones that came before.

iii

ACKNOWLEDGEMENTS

First and foremost I would like to thank my advisor, Dr. Alan Arbogast, who
roped me into grad school, nudged me towards studying sand dunes, and then kept
my type A personality in check. I would like to thank my committee members, Dr.
Bruce Pigozzi and Dr. Ashton Shortridge, for their patience, guidance, and invaluable
knowledge. A special thanks to the many people from MSU’S RS&GIS including
Jessica Moy, for providing me with the means to carry out my research, Jeff Schlueter,
for assisting me in the ﬁeld, and Justin Booth and Sarah Acmoody, for continuing to
offer outstanding technical support long after they were being paid to do so. I would
also like to express my gratitude to the Michigan Department of Environmental
Quality, for allowing me to use DEQdata for this study, and Matt Warner, for his
time and expertise.

Although the skills and knowledge of many people took me a long way, I
could not have done any of this without the love and support of my family, especially
my husband Eric. From the moment I applied to graduate school he was willing to do
whatever was necessary to help me accomplish my goal, and never once let me
believe that ﬁnishing my project was impossible. Finally, I want to thank God for

giving me the courage and ability to push ahead even when I thought I couldn’t do it.

iv

TABLE OF CONTENTS

LIST OF FIGURES ....................................................................................................... vii
LIST OF TABLES ........................................................................................................... ix
ABBREVIATIONS .......................................................................................................... x
I. INTRODUCTION ....................................................................................................... 1
Problem Statement ........................................................................................................ 4
Research Purpose ........................................................................................................... 9
II. LITERATURE REVIEW .......................................................................................... 11
Coastal Sand Dune Formation ..................................................................................... 11
Coastal Dunes of Lake Michigan ................................................................................. 15
National Coastal Zone Management ........................................................................... 22
Sand Dune Protection & Management in Michigan .................................................. 25
Digital Elevation Data: Collection, Processing, & Use ............................................... 30
The National Elevation Dataset ............................................................................... 32

The Collection of Lidar Data ................................................................................... 35
Post-Processing of Lidar Data ................................................................................. 38

The Application of Lidar Data ................................................................................. 41

The Comparison of Lidar DEMS to NED DEMs ......................................................... 46
III. STUDY AREA ........................................................................................................ 50
History .......................................................................................................................... 51
Dune Topography ........................................................................................................ 55
Climate .......................................................................................................................... 56
Land Use / Land Cover ................................................................................................. 58
Soils ............................................................................................................................... 59
IV. METHODS ............................................................................................................. 61
Collection of Field Data ............................................................................................... 61

Selection of the Independent Variables ...................................................................... 67

Lidar Elevation Data ................................................................................................ 70
30-meter National Elevation Data .......................................................................... 76
Creating the Lidar and NED Slope Grids ................................................................ 78
Land Cover Data ....................................................................................................... 81
Overview of Multiple Regression ............................................................................... 84
Assumptions of Multiple Regression ...................................................................... 85

V. RESULTS AND DISCUSSION ................................................................................. 87
Univariate Regression .................................................................................................. 89
Multivariate Regression ............................................................................................... 90
Analysis of the Residuals ............................................................................................. 94
Discussion ..................................................................................................................... 96
Discussion of Model Error ......................................................................................... 101
Summary ..................................................................................................................... 106
VI. CONCLUSION ..................................................................................................... 108
Research Problems ..................................................................................................... 1 1 1
Directions for Future Research ............................ I .................................................... 113
APPENDIX A ............................................................................................................. 1 l6
APPENDD( B .............................................................................................................. 118
APPENDIX C ............................................................................................................. 119
BIBLIOGRAPHY ........................................................................................................ 120

vi

LIST OF FIGURES

Figure 1-1 Map of the coastal dunes in lower Michigan and NW Indiana including the
location of the study area (modiﬁed from Arbogast et a1. 2002). .................................... 3

Figure 2-1 Wind movement by saltation and surface creep resulting from the impact
of saltating grains. The wind moves sand up the windward slope of the dune toward

the crest. The sand then slides down the steeper leeward side or slipface, causing the
dune to advance (modiﬁed from Gabler et a1. 2004). ................................................... 14

Figure 2-2 Map of the coastal dunes in Michigan and NW Indiana including the
location of Manistee, which was noted in the text, and the study area (modiﬁed from

Arbogast et a1. 2002). ....................................................................................................... 16

Figure 2-3 Cross section of a typical Lake Michigan dune ﬁeld (modiﬁed from Wilson
2001). ................................................................................................................................ 19

Figure 2-4 Map of the twenty-nine states with CZM programs approved by the
federal government. Illinois, the one state with approval pending, is currently seeking
to reinstate their former program. .................................................................................. 25

Figure 2—5 Map of the areas designated "critical dunes" in Lower Michigan. .............. 28

Figure 2-6 Schematic of lidar data acquisition from a twin engine aircraft (modiﬁed
from Woolard and Colby 2002). ..................................................................................... 36

Figure 2—7 Representative illustration of the three—dimensional and vertical
distributions of lidar returns within a 25-m footprint (from Lefsky et a1. 2002). ........ 40

Figure 2-8 Lidar representation of pre- and post hurricane beach topography (right)
for a transect on Topsail Island, North Carolina (left) (from the ALACE project in
Lefsky et a1. 2002). ........................................................................................................... 45
Figure 3-1 Map of the study area, Lake Township, Berrien County, MI. .................... 51

Figure 4-1 Map of the sample points collected in the northern half of Lake Township,
Berrien County, MI .......................................................................................................... 64

Figure 4-2 Map of the sample points collected in the southern half of Lake Township,
Berrien County, MI .......................................................................................................... 65

vii

Figure 4—3 Photograph showing the method and equipment used to collect slope

measurments in the ﬁeld. ................................................................................................ 66
Figure 4-4 Schematic illustrating the cross validation process. .................................... 73
Figure 4-5 Flowchart illustrating the steps taken to create the lidar variables. ........... 75

Figure 5-1 Graph Showing LDSLOPE plotted against FDSLOPE. With the exception
of a few outlying points, LDSLOPE exhibits a linear relationship with FDSLOPE. 88

Figure 5-2 Graph of NDSLOPE plotted against FDSLOPE. The relationship depicted
in this graph is not linear and therefore the NDSLOPE data does not meet the ﬁrst
assumption. ....................................................................................................................... 88

Figure 5-3 Graph showing the regression estimates plotted against the residuals. ..... 95
Figure 5-4 Graph showing the independent variable LDSLOPE plotted against the

dependent variable FDSLOPE with outlier cases highlighted. The red points note
cases that have a large studentized residual, with the larger red point indicating the

case that also has a large inﬂuence .................................................................................. 96
Figure 5-5 Graph showing FDSLOPE plotted against the residuals; points with the

largest studentized residuals are shown in red ............................................................. 102
Figure 5-6 Graph of the average RMSE by slope class. ................................................ 103

Figure 5-7 Map showing the spatial distribution of the residuals. Points were classiﬁed
by the number of standard deviations the residual at that point fell above or below
the mean. The map was broken into three geographic extents (a. north, b. central,
and c. south) based on the proximity of the points to one another. ........................... 104

Images in this thesis are presented in color

viii

LIST OF TABLES

Table 4-1 A Comparison of the descriptive statistics for the point subset to those of

the complete dataset. ....................................................................................................... 74
Table 4-2 Descriptive statistics of the elevation datasets ............................................... 78
Table 4-3 Error Statistics of the lidar and NED datasets ................................................ 78
Table 4-4 Descriptive statistics of the slope datasets ..................................................... 81
Table 4-5 Error statistics of the slope datasets ............................................................... 81

Table 4-6 Confusion matrix comparing ground truth land cover (observed)
classiﬁcations to the NLCD (expected) classiﬁcations. .................................................. 84

Table 5-1 Summary statistics of the univariate regression model ................................. 90

Table 5-2 Summary statistics of the multivariate regression model employing lidar
source data, and slope, elevation, and land cover as independent variables. ............... 92

Table 5-3 Summary statistics of the multivariate regression model employing NED
source data, and slope, elevation, and land cover as independent variables. ............... 92

Table 5-4 Summary statistics of the multivariate regression model employing lidar
source data, and slope and elevation as independent variables ..................................... 93

Table 5-5 Summary Statistics of the multivariate regression model employing NED
source data, and slope and elevation as independent variables ..................................... 93

Table 5-6 Model error statistics ..................................................................................... 101

ix

ABBREVIATIONS
ALACE: Airborne Lidar Assessment of Coastal Erosion
ALS: Airborne Laser Scanning System
ATM: Airborne Topographic Mapper
yrs BP: Years Before Present
Cal. yrs BP: Calendar Years Before Present
CZM: Coastal Zone Management
CZMA: Coastal Zone Management Act
DEM: Digital Elevation Model
dGPS: Differential Global Positioning System
DTM: Digital Terrain Model
EROS: Earth Resources Observation Systems
F GDC: Federal Geographic Data Committee
GIS: Geographic Information System
GPS: Global Positioning System
IDW: Inverse Distance Weighting
INS: Inertial Navigation System
Lidar: Light Detection and Ranging
LULC: Land Use Land Cover

MAE: Mean Absolute Error

MDEQ: Michigan Department of Environmental Qiality
MDNR: Michigan Department of Natural Resources
MICGI: Michigan Center for Geographic Information

MSU RS&GIS: Michigan State University Remote Sensing 8t Geographic Information
Systems Research and Outreach Services

NAD83: North American Datum of 1983

NASA: National Aeronautics and Space Administration
NAPP: National Aerial Photography Program

NED: National Elevation Data

NGS: National Geodetic Survey

NLCD: National Land Cover Data

NOAA: National Oceanic and Atmospheric Administration
RMSE: Root Mean Square Error

SAR: Synthetic Aperture Radar

SHOALS: Scanning Hydrographic Operational Airborne lidar Surveying System
SRTM: Shuttle Radar Topography Mission

USACE: United States Army Corps of Engineers

USGS: United States Geological Survey

UTM: Universal Transverse Mercator

xi

I. INTRODUCTION

Coastal sand dunes are common along the southeastern shore of Lake
Michigan. These sand dunes collectively form the largest complex of freshwater
dunes in the world and are highly valued for the scenic, recreational, ecological, and
economic opportunities that they provide (Buckler 1979; Lichter 1995; Arbogast and
Loope 1999; VanOort et al. 2001; Arbogast et al. 2002). For this reason, the State of
Michigan has designated nearly 480 km of the shoreline critical dunes (covering
nearly 32,000 hectares) in an effort to mitigate the negative impacts of human-
induced change and prevent irreversible damage to the ecosystem (MDEQAtlas of
Critical Dunes 1989; Bemd-Cohen and Gordon 1999).

The signiﬁcance of the sand dune ecosystem is evident by the presence of
several rare plant and animal species, including the Pitcher’s thistle (C'inlsium
Pitcben), a threatened plant species, and the Piping Plover, a federally endangered
bird species (lake Michigan Federation 1999). From a recreational standpoint,
residents, visitors, and the state and local economy beneﬁt from the many national,
state, and county parks that occur within Michigan’s coastal dunes (lake Michigan
Federation 1999; Arbogast et al. 2002). In addition to the revenue generated from
tourism, the dunes are also highly valued by industry as a source of foundry sand

(Lake Michigan Federation 1999).

Beginning in the early 1900’s, Lake Michigan sand dunes were targeted by
local industries primarily for creating foundry casting molds. Not only were the
physical and chemical properties of Lake Michigan dune sand ideal for this use, it was
also widely available and convenient. Over the next few decades Michigan’s
automobile industry ﬂourished and, in turn, the sand mining industry intensiﬁed. In
the most extreme cases, entire dune systems were completely destroyed by
overzealous mining practices (Buckler 1979; Lake Michigan Federation 1999; Albert
2006). In the early 1950s, Michigan residents began to take notice of the
disappearing dunes. This culminated in an outpour of public concern that lead to the
eventual passing of the Sand Dunes Protection and Management Act in 1976 (Act No.
222, Public Acts of 1976; lake Michigan Federation 1999).

In the years that followed, concerns also grew over other developmental
pressures on the dunes, such as recreation and construction. These new concerns,
combined with the continued destruction of the dunes from mining, lead to
amendments to the act in 1989, which resulted in the critical dune designation. The
1989 amendments also included the addition of a program that established standards
and a permitting program for development in areas designated critical dunes
(Michigan State Legislature Acts No. 146 and 147, Public Acts of 1989). More
recently, Michigan reorganized its environmental acts dividing the 1976 Sand Dune

Protection and Management Act into Part 353, Sand Dune Protection and

Management, and Part 637, Sand Dune Mining (Michigan State Legislature Act No.

451, Public Acts of 1994).

 

 
 
  
   

 

 

 

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Figure 1-1 Map ofthe coastal dunes in lower Michigan and NW Indiana including the location ofthe

study area (modiﬁed from Arbogast et al. 2002).

The administration and management of critical dune policies is divided

between two branches of the Michigan Department of Environmental Qiahty

(MDEQ). Sand dune mining (Act No. 451, Part 637, Public Acts of 1994) is regulated

by the Ofﬁce of Geological Survey, while all other matters concerning critical dunes,

including the permitting process, are handled by the Land and Water Management

Division (Michigan State Legislature Act No. 451, Public Acts of 1994). The focus of
this research is on residential and commercial site alteration, therefore, from hereafter

I will be referring only to the land and Water Management Division unless otherwise

Speciﬁed.

Problem Statement

The decision of the MDEQto deny or reject an application for a permit to alter
a site in critical dunes is based primarily on the slope of the dune that will be affected.
This stipulation requires agents to conduct an onsite inspection, which can be very
time consuming depending on the scope of the project. At present, the State of
Michigan employs eleven agents to cover nearly forty counties. As such, these agents
are constantly pressed for time. Further, the effectiveness of this program has never
been evaluated. It is estimated, however, that of the hundreds of sites permitted
every year, only about 10% of ever receive follow-up visits from permitting staff
(Warner, personal comm., 2002).

The lack of accountability is troubling given the results of a number of studies
assessing the impact of development on natural dune systems in other coastal locales
(Gares 1990; Nordstrom 1994; Nordstrom et al. 2000; Brown and McLachlan 2002;
Nordstrom et al. 2002). Gares (1990) Studied dunes along a stretch of developed shore

in New Jersey and concluded that residential development there is severely altering

the naturally functioning dune system. Overall he found that the dunes had a
gentler slope, lower elevation, and lower sediment transport than their undeveloped
counterparts in the same area. He attributed these differences to less vegetation, the
construction of sand fences, and the presence of houses, all of which are
anthropogenic. Parking lots and roadways are impermeable surfaces that provide
unobstructed pathways for entrained sand, while buildings may alter the local ﬂow of
wind as well as the location of accretion on beaches and dunes (N ordstrom 1994).
With a host of threats facing coastal ecosystems and increasing developmental
pressures increase, there is an urgent need for improved legislation and protection
(Brown and Mclachlan 2002).

Research (Bemd-Cohen and Gordon 1999; Hershman et al. 1999) also shows
that Michigan is not alone in respect to the problems faced managing development in
the coastal zone. Hershman et al. (1999) report that all coastal mangers are
overburdened with implementation tasks and, when combined with the political and
legal pressures of managing a valuable resource, the focus is almost always on the
current decision processes, not monitoring and evaluating past actions (Hershman et
al. 1999). In order for a coastal program to change or improve, program managers
must have the time and resources available to evaluate the state of coastal resources
and make that information available to policy makers (Bemd-Cohen and Gordon

1999; Hershman et al. 1999).

At this time, a majority of states with a coastal zone management (CZM)
program do incorporate digital technology to track permits, however, none of these
states employs a database directly related to the extent to which resources are affected
by permits or policies (Bemd-Cohen and Gordon 1999). In Michigan, the key to
achieving a more objective assessment of the coastal zone may lie in integrating the
use of digital and remotely sensed data, such as a digital elevation model (DEM), with
the current sand dune protection and management program. Much like the current
permitting process, gathering the data necessary to do that using traditional means,
such as ground based surveys or photogrammetry, could become prohibitively time
consuming and expensive. However, remote sensing can provide spatially dense
quantitative data over regional scales. If sufficiently accurate this data, when used in
a Geographic Information System (GIS), could be invaluable in determining and
understanding patterns and magnitudes of dune development (Sallenger et al. 2003).

The National Elevation Dataset, or NED, is one digital data source that is
presently available to all potential users on the United States Geological Survey
(USGS) website (Gesch et al. 2002). It is a compilation of many data sources, deemed
the “best available”, including 7.5 minute, 15-minute, 2-arc-second, and 3-arc second
DEMs (Smith and Sandwell 2003). The metadata that accompanies NED allows users
to calculate accuracy statistics based on source DEM characteristics; however, the
actual error in any one dataset may differ from what is stated depending on several

factors including local terrain characteristics, the application for which it is being

6

used, and any parameters besides elevation (Bolstad and Stowe 1994; Gesch et al.
2002; Hodgson et al. 2003). Although NED may be sufﬁcient in some areas and for
some applications, the recent shift has been toward models that require a more
detailed and spatially explicit representation of process, which requires a better
quality source for topographic data (French 2003; Barber and Shortridge 2004).

Light Detection and Ranging, or lidar, is a technology that can produce high-
resolution elevation datasets; it is also the technology that may be able to better meet
the needs of coastal zone managers. This technology can quickly gather spatially
dense elevation data over a large area and is generally regarded as a more accurate,
more efficient, and less expensive collection method for the creation of DEMs than
alternative methods (W oolard and Colby 2002; Sallenger et al. 2003; Barber and
Shortridge 2004).

The decision for any agency to incorporate remotely sensed data into their
current practices and standards and decide between lidar, NED, and any other dataset
for a particular application can depend on any number or combination of factors,
including accuracy requirements, purpose, cost, and availability. In the case of the
MDEQ, the accuracy of the terrain characteristic slope is of primary importance given
that their permit decision is based on this measure and there could be legal
consequences associated with an erroneous decision based on inaccurate

measurements.

Although researchers have recommended using either a lidar or USGS Level 2
digital elevation model over other elevation products if an application requires
accurate slope measures, investigations have been unable to provide evidence that
either product is suitable for such uses, based on study area characteristics (Hodgson
et al. 2003). While research (Barber and Shortridge 2005) has Shown that slope is
particularly sensitive to and greatly affected by resolution and, therefore, a high-
resolution dataset like lidar may be a better choice, the researchers in that case also
stipulate that this is more true in areas of low relief. This added condition begs the
question, “What role do terrain attributes play in the measurement of elevation and
its derivations?”

It has been previously established (Chang and Tsai 1991; Bolstad and Stowe
1994; Bowen and Waltermire 2002; Hodgson et al. 2003) that elevation, land cover,
and slope influence remote collection methods, leading researchers to seek a better
understanding of how in Situ terrain attributes affect the quality of a digital elevation
model and its derivatives. For example, researchers have determined that both
elevation error and modeled slope error increase when slopes on the ground are
steeper (Chang and Tsai I991; Bolstad and Stowe 1994; Hodgson et al. 2003). Bolstad
and Stowe (1994) also determined that, for a USGS Level 1 DEM, the largest errors
were found in areas exhibiting the highest and lowest elevations for the study area.
Further, error in elevation and Slope measurements derived from both lidar and USGS
DEMs increases to varying degrees based on land cover attributes, including forest

8

canopy, stem obstruction, and understory vegetation (Bolstad and Stowe 1994;

Hodgson et al. 2003).

Research Purpose

Given that errors are generally systematic and inﬂuenced by patterns of land
cover, elevation, and gradient, it may be possible to determine actual slope if land
cover, elevation, and calculated slope are known variables. The purpose of my
research, therefore, is to determine:

1.) What terrain variables, or combination of variables, when used in a regression
model, most closely predict true slope?

2.) What is the error in the predicted slope values?

3.) To what degree do the source, or collection method, and/or resolution of the
elevation data inﬂuence the model?

By conducting this research and answering these questions, I am hoping to
better understand how digital data can be used to aid management decisions that
would typically require data collection in the ﬁeld. Further, I hope to explore the
relationships between digital data collection methods, data resolution, and the true
slope values at any given point. Given the fairly recent emergence of lidar technology
in the collection of elevation measures, a greater knowledge of its potential to model

topography and its relationship with terrain characteristics that inﬂuence the

elevation and derived slope values, could be beneﬁcial to agencies like the MDEQaS

well as other environmental applications.

10

II. LITERATURE REVIEW

The topic of this research concerns coastal sand dunes and their management,
as well as remote sensing and terrain modeling, therefore, each of these areas will be
addressed in this review of relevant literature. This chapter can be divided into two
distinct parts. The ﬁrst will cover coastal sand dune formation, focusing speciﬁcally
on the origin of the dunes found in Michigan, and the history of sand dune protection
and management from the national level down to the state level. The latter half of
the chapter is devoted to digital elevation data including its collection, processing,

and use, particularly as it relates to modeling applications.

Comtal Sand Dune Formation

Knowledge of coastal dunes and dune geomorphology is essential to
understanding the spatial relationships between elevation, gradient, and vegetation
on a coastal eolian landscape. Coastal dunes are located above the high water marks
on sandy beaches of oceans and lakes, and can be found across all latitudes. Dunes
range in size from small, transient features to very large, stabilized dune ﬁelds, and

can exist in almost any climate (Nordstrom et al. 1990).

11

Many studies have explored eolian sediment transport and deposition in
relation to the coastal environment. Dune formation is a function of sediment grain
size, the beach proﬁle, and wind regime. In general, the development of coastal
dunes is dependent upon 1) a source of sandy sediments, 2) a prevailing, onshore
wind with a veloCity sufficient to move those sediments, and 3) an area of land
partially protected from wave action (Smith 1988; Nordstrom et al. 1990; Orme 1990;
Sherman and Hotta 1990). Dunes most readily form on gently sloping shorelines
under dissipative wave conditions where the foreshore dries out at low water. Ideal
eolian sands are well-rounded, sand-sized (2 to .2 mm) quartz grains with a speciﬁc
gravity in air of 2.65 g cm‘3 (Nordstrom et al. 1990).

Eolian forces cause sediment movement when shear stress exceeds a threshold
value, or the velocity required to entrain a particle of sand. Momentum is then
transferred from the air to the sand grains and initiates movement by suspension,
saltation, or creep. On beaches and coasts sediments are most often transported by
saltation or creep because sand-sized particles are generally too large to be carried in
true suspension (Sherman and Hotta 1990). Saltation, the dominate process of eolian
sand movement, occurs when sand grains bounce or skip along the ground (s 1 cm
above the surface) by repeated lifting and deposition. As the saltating grains skip
along the surface they dislodge smaller particles, which may then become saltating

grains, and/or larger particles that slowly roll forward along the ground. The latter

12

process, which accounts for a somewhat smaller portion of eolian sand movement, is
called traction or creep (Figure 2-1; Gabler et al. 2004).

Forces that oppose the initial motion include a cohesive agent (moisture) and
gravity. Once in motion, however, with sufﬁcient velocity the sand can continue to
move until it encounters either topographic obstructions or surface obstacles, when it
is deposited and may accumulate in drifts. These drifts, or dunes, create a topographic
barrier that further reduces the winds velocity. A dune will only grow as long as its
size does not impede the wind’s ability to feed sand to the dune (Gabler et al. 2004).

Sand dunes have three main features, a back slope, which is erosional and
faces upwind, a crest, and a slipface or leeward Slope (Figure 2-1). A dune will
migrate as long as winds are strong enough to carry sand up the windward slope to
the crest (Gabler et al. 2004). As sand is deposited over the crest, the angle of the lee
slope continues to build until it reaches the steepest angle dry sand can hold without
falling or the angle of repose (~ 30 -— 35°). Once the angle of repose is met, sand will
slide down the slip face causing the dune to advance downwind (Figure 2-1). A new
slipface is created as the dune advances layer by layer. Small dunes (< 10 m high) can
migrate up to 40 meters in a year while larger dunes move more slowly (Gabler et al.
2004). Sand will continue to move until the net transport rate decreases, which can
be initiated by an increase in slope, decrease in wind velocity, and/or an encounter

with vegetation (Sherman and Hotta 1990). Likewise, dune stability is enhanced by a

13

reduction in the sediment supply or wind velocity, typically reﬂecting changes in the

environment or an increase in vegetation (Gares 1990; Orme 1990).

 

 

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y , {yv’iy”.‘g*¢0-a,wﬁna_ .- 'v-NI-h:...,.. , ‘ "m" ..qq. ...y"... v‘d. ... -_Tq'.m“'ﬂ.~:fw.f‘vfbﬁ‘ _
~~ . -- ~. - - RIppIes on sand surface -._:_. ..

annual- .ALLIJA'L

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Figure 2-1 Wind movement by saltation and surface creep resulting from the impact of saltating grains.
Thewindmovessandupthewindwardslopeofthedunetowardthecrest.Thesandthenslidesdown
thesteeperleewardsideorslipface, cansingthedunetoadvanceﬂnodiﬁed ﬁ'omGableretal. 2004).

Vegetation, if present, acts in three ways, speciﬁcally it 1) reduces wind
velocity, 2) prevents wind from being directed against the land surface, and 3) secures
sediments with its root network (Gabler et al. 2004). Sedimentation in the coastal
environment is often limited by the density and growth rate of vegetation (Nordstrom

et al. 1990). Vegetation serves to encourage deposition (trapping sand) and stabilize

14

deposits by dissipating the energy of the wind and forcing it to deposits its load (Olson
I958c; Orme 1990; Robertson-Rintoul 1990; Sherman and Hotta 1990). Dunes in
more developed areas often have sparse vegetation cover due to heavy pedestrian

trafﬁc and, therefore, little Stability in the long term (Gares 1990).

Coastal Dunes of lake Michigan

Coastal dunes are common along the eastern shore of Lake Michigan, with the
most numerous being those that mantle lake terraces extending south from Manistee,
MI and into Indiana (Figure 2-2). These sand dunes may collectively be the largest
complex of freshwater dunes in the world (V anOort et al. 2001; Arbogast et al. 2002).
The earliest published research on lake Michigan sand dunes focused on ecology,
speciﬁcally the vegetation found in and among the dunes in Indiana Dunes State Park
along the southern shores of lake Michigan (Cowles 1899). While studies of the
plant species and the role of vegetation on the dunes continued (Olson 1958a, 1958c),
a growing number of studies began to focus on dune geomorphology by concentrating
on the processes, controls, and timing of dune development with an emphasis on
lake-level oscillations (Dow 1937; Scott 1942; Olson l958d; Buckler 1979; Thompson
1992; Lichter 1995; Thompson and Baedke 1995, 1997; Arbogast and Loope 1999;
Baedke and Thompson 2000; Loope and Arbogast 2000; VanOort et al. 2001; Arbogast

et al. 2002).

15

 

 
  
  

 

 

 

I I
90° W 85° W
0 Eolian Sand
46° N ""
43° N —‘
Study Area
Indiana 50 “1“
i . J.
50 mm

90°1W 85°l W

 

 

Figure 2-2 Map ofthecoastaldunesinMichiganandNWIndiana including the location ofManistee,
whichwasnotedinthetext,andthestudyarea(modiﬁedfromArbogastetaL2m2).

Both Dow (1937) and Scott (1942) recognized that ﬂuctuations in lake level
were the dominant control of the sand supply to the dunes on the eastern shore of
lake Michigan. Dow’s (1937) work centered on what he called “perched” dunes at
Sleeping Bear Point in Empire, MI. He used the term perched dunes to refer to eolian
bedforms elevated above the present lake—level, often on high headlands, and

overlaying non-eolian sediments. This includes dunes that mantle lacustrine

16

sediments of post-glacial beaches as well as dunes found much higher above the lake
on moraines. He found that when lake levels are high, waves undercut the bases of
the bluffs exposing a fresh supply of sediments that can then be entrained by the wind
and deposited at the top of the bluff.

Olson (l958d) expanded on the idea of lake-level oscillations as the dominant
control of sediment supply, and recognized two basic dune forms on the southern
shore of lake Michigan: primary and secondary (Figure 2-3). This classiﬁcation is
loosely based on positional, morphological, stability, and age factors. Primary dunes
(also called “incipient” or “embryo” dunes) are young and located near the lake, while
secondary dunes, which include established foredunes, parabolic dunes, and
blowouts, are positioned farther inland (Nordstrom et al. 1990).

In 1958, Olson (l958a, 1958b, 1958c, 1958d) published a series of four articles
describing the development of lake Michigan coastal dunes. While the ﬁrst three
articles focus on the role of vegetation in dune building and stability, in the fourth,
Olson (l958d) describes the formation of foredunes on the shore of lake Michigan.
He states that the process is contingent upon periodic ﬂuctuations of the lake level
occurring roughly every 30 years. During periods of low or receding lake levels, the
beach widens and new dune growth begins as colonizing plants intercept eolian sand.
If these primary dunes become sufﬁcient enough to withstand wave erosion, when
average or high lake levels return they become a new foredune ridge. Secondary

dune building, on the other hand, generally occurs when the lake level is high or

17

winds are strong. At this time, the previously established foredune ridges are
destabilized by wave and wind erosion and sediment removed from the ridge can
then be returned to the slope faces of the secondary dunes (Olson 1958d).

The next signiﬁcant study of the geologic characteristics of lake Michigan
coastal dunes was conducted by Buckler (1979) in response to the State of Michigan
Sand Dune Protection and Management Act (Michigan State Legislature Act N o. 222,
Public Acts of 1976). He inventoried and classiﬁed nine dune forms found along the
lake Michigan shore including parabolic dunes, linear dune ridges, dune terraces,
dune platforms, domol dunes, complex dune ﬁelds, dune ﬂats, marginal sand aprons,
and interdune lowlands. The classiﬁcation scheme proposed by Buckler (1979)
combined several dune attributes including dune form, relative relief, orientation,
arrangement, and the stratigraphic relationship of the dune to the underlying
sediments.

The well-developed dune ﬁelds on the southeastern shore of lake Michigan
are large parabolic dunes (> 60 m) that may be separated from the lake by small
foredunes (Figure 2-3; VanOort et al. 2001; Arbogast et al. 2002). Buckler (1979)
described parabolic dunes as non-elevated, with a parallel orientation and high relief,
often occurring in groups and overlapping. Widths, he noted, can be more than
400 m with lengths exceeding 900 m. On its windward side, a parabolic dune has a
concave shape with a gentle slope that becomes steeper closer to the crest. The

convex landward side has a steeper slope that descends abruptly from the crest at the

18

angle of repose. Blowouts, or unvegetated, depressions created by deﬂation, may exist
between the tails of the dune, which are often stabilized by vegetation (Buckler 2001;
Gabler et al. 2004). Two generations of parabolic dunes are frequently found adjacent
to one another with the shoreward group being higher, more individually well-
deﬁned forms while the landward group is lower, more dispersed, and less distinctive.
The sand dune formation, or assemblage of dunes, that separates the present coastal
zone from inland activities is also given the term barrier dune by the Michigan

Legislature (Buckler 1979) .

 

parabolic dune inland boundary
(secondary) of the barrier
dune formation
foredune

(primary)

    

 

 

Figure2-3CrosssectionofatypimllakeMichiganduneﬁeld(modiﬁedﬁomWﬂaon2001).

In the 1990’s several geomorphic Studies of lake Michigan dunes directed at
lake level oscillations and beach ridge development were published (Thompson 1992;

Thompson and Baedke 1995, 1997). Together, these studies focused on ﬁve beach

ridge complexes around lake Michigan, including sites at Toleston Beach, IN,
Sleeping Bear Dunes National Lakeshore, MI, Wilderness State Park, MI, Manistique,
MI, and Ridges Sanctuary, WT, and used vibracores collected from the bases of
wetlands between the ridges to reconstruct four late Holocene (from 200 to 4,700 cal.
yrs. BP) relative lake level curves. In 2000, Baedke and Thompson compared the
radiocarbon dates of samples collected in all ﬁve complexes and determined that,
when isostatic rebound is accounted for, all four curves Show similar variations in
lake-levels. Small beach ridges could be linked to ~ 33-year ﬂuctuations of .5 - .6 m,
while larger groups of ridges (4 - 6) corresponded to ~ l60-year ﬂuctuations of .8 - .9
m.

The most current research on dune geomorphology (Arbogast and Loope 1999;
Loope and Arbogast 2000; VanOort et al. 2001 ; Arbogast et al. 2002) focuses
speciﬁcally on the evolution of some of the largest coastal dunes, many of which are
found along the southeastern shore of lake Michigan. It is signiﬁcant because it
challenges previous beliefs about the timing of dune development (Dorr and Eschman
1970; Buckler 1979; Eschman 1985) as well as the broad applicability of Olson’s
(l958d) foredune model by comparing dates obtained from buried soils to the
historical lake-level curve. Arbogast and Loope (1999) ﬁrst conducted a study of
buried soils at three sites along the lakeshore to test the theory that all of the dunes
along the western coast developed between 6,000 and 4,000 yrs BP during the

Nipissing high stand of ancestral lake Michigan (Dorr and Eschman 1970; Buckler

20

1979; Eschman 1985). The researchers found that although dune building at one of
the sites began during the Nipissing transgression, dune formation at the other two
sites began following the transgression (between 4,300 and 3,900 cal. yr BP and 3,300
and 2,900 cal. yr BP). They concluded that the sand supply to these lake-terrace
dunes originated from bluff destabilization related to minor peaks in lake-level that
occurred post—Nipissing.

A second study conducted by Loope and Arbogast (2000) aimed to distinguish
between the origin of foredunes (~ 5 m thick) on the south and southeastern shore
initially described by Olson (1958d) and that of larger dunes (~ 50 m thick) mantling
lake terraces along the eastern shore, by comparing the dates of buried soils at 32 sites
to a late Holocene lake-level curve (Baedke and Thompson 2000). The smaller
foredunes occur close to the lake, are subject to direct wave action, and, as Olson
(l958d) suggested, form as the lake level falls and the beach widens (the quasi-
periodic ~ 30 yr regressions documented by Baedke and Thompson 2000). The
larger dunes that Sit higher on the landscape and are remote from direct wave action
build as the lake-level rises and waves cut into bluffs and previously established
dunes. Using radiocarbon dating they were able to correlate dominant periods of
sand accumulation at a majority of the sites with ~150 yr lake highstands that have
occurred over the past 1500 years, making the age of many of the larger dunes

younger than previously thought (Loope and Arbogast 2000).

21

Two studies of buried soils found in sand dunes south of Holland, MI were
conducted by Van Oort et al. (2001) and Arbogast et al. (2002) and found that
deposition of eolian sand began there during the Nipissing high stand (~ 5500 cal. yr
BP) and lasted for ~ 3500 years. Arbogast et al. (2002) found that a dominant period
of rapid dune building occurred between ~ 4000 and 2500 cal. years BP, and was only
punctuated by brief periods of stability. Subsequently, the dunes were stable for
~2000 years before becoming active again between ~1000 and 500 cal. yr BP (similar
to ﬁndings north of the study area). They hypothesize that the increase in sand
supply as lake levels fell immediately following the Nipissing transgression most
likely accounts for the onset of the initial growth period, while later growth
(occurring ~ 3200, 2400, and 900 cal. years BP) is associated with intervals of higher

lake levels and wave destabilization of bluffs.

National Coastal Zone Management

In the early part of the twentieth century, states began recognizing the value
of the shoreline as both a natural resource and an economic commodity. In response
to the rapid development of coastal resources during this time, the United States
Congress enacted the Coastal Zone Management Act (CZMA). The CZMA had two
primary objectives: 1) the protection of natural resources within the coastal zone and

2) the management of coastal development to minimize loss of life and property

22

caused by improper development, including the destruction of natural protective
features such as beaches and dunes (United States Legislature Coastal Zone
Management Act of 1972, Sec. 303). Following the enactment of the CZMA, all
coastal states (including Great Lakes states and island territories) were offered policy
guidance, ﬁnancial resources, and legal tools as incentives to upgrade their capacity
for coastal zone management. By the early 1980’s most state programs had been
approved and implementation began thereafter (Figure 2-4). As of 1999, federal
funding for CZM was approximately $50 million dollars, with a 50% state or local
matching requirement for most programs (Hershman et al. 1999).

Under the CZMA, states determine the coastal zone boundary, key coastal
problems, the policies and laws that will address them, and the state and local
organizations to be involved in enforcement. The federal, state, and local
governments are all given roles in CZM with considerable ﬂexibility given to deﬁning
the extent of those roles, which has lead to many unique management programs
around the country (Hershman et al. 1999). Although there are speciﬁc objectives of
the CZMA, conﬂicting trends and policies are continually challenging the ability of
States to protect natural resources. States are under pressure to balance the need for
public access and recreation, the high economic value of coastal property, the

protection of private property rights, and the preservation of natural resources

(Bemd—Cohen and Gordon 1999).

23

Twelve of the twenty—nine States with CZM programs have amended their
CZM program in the past two decades to increase the protection of beaches, dunes,
bluffs, and rocky shores (Bemd-Cohen and Gordon 1999). For example, several states
including Florida, Hawaii, Michigan, New Hampshire, New Jersey and North
Carolina have expanded CZM jurisdiction landward and extended inland setback
requirements. California, Maine, and New Jersey have all amended their CZM
programs to further limit development on dunes and bluffs, while Connecticut, North
Carolina, and South Carolina all added amendments to reduce the number of
shoreline protection structures built (Bemd-Cohen and Gordon 1999).

In addition to improving their policies, states also use a wide range of tools to
implement CZM. land acquisition, coastal zoning, permit programs, research, and
public education and awareness programs are common methods used in CZM
programs (Bernd-Cohen and Gordon 1999; Hershman et al. 1999). Most States have
also developed and/ or incorporated digital technology to track permits; however no
States employ a database on coastal statistics or resources affected by permits or

policies (Bernd-Cohen and Gordon 1999).

24

 

Coastal Zone Management Program

 

l [:IApproved CZM program
EIPending approval

 

 

 

Figure 2-4 Map of the twenty-nine states with CZM programs approved by the federal government.
Illinois, the one state with approval pending. is currently seeking to reinstate their former program.

Sand Dune Protection & Management in Michigan

Nearly all of the studies mentioned earlier in this chapter (Cowles 1899;
Buckler 1979; Lichter 1995; Arbogast and Loope 1999; Loope and Arbogast 2000;
VanOort et al. 2001; Arbogast et al. 2002) noted the importance of lake Michigan
sand dunes for the unique scenic, recreational, ecological, and economic opportunities
they provide. This section begins with a brief description of those qualities which
increase the value of the dunes, to establish why they deserve and require legislative

protection. It will end with a summary of the current management scheme in place

25

to mitigate the effects of ongoing development, as well as some of the challenges of
coastal zone management in Michigan.

Cowles (1899) was ﬁrst to state the value of the dune habitat in the study of
plant succession and ecology, due to the dynamic and often extreme physical
conditions that exist there, including temperatures, sunlight, and ongoing wave and
wind action. The importance of sand dunes as habitat is evident by the several rare
plant and animal species found there, including the threatened plant species Pitcher’s
Thistle ( Czhlsium Pitcben) and the Piping Plover, a federally endangered bird species
that relies on the shoreline for nesting (lake Michigan Federation 1999). In addition
to the preservation of plant species, the vegetation found in and among the dunes is
an important dune building agent that often dictates the area, shape, and height of a
dune by trapping sand and altering surface roughness (Cowles 1899; Olson 1958c).

From a recreational standpoint the dunes contain many national, state, and
county parks that are enjoyed year-round by visitors (Figure 2-5; Arbogast et al.
2002). For example, P.J. Hoffmaster State Park in Muskegon County, MI attracts
nearly 500,000 visitors each year with miles of hiking and cross country ski trails. A
larger park like the Sleeping Bear Dunes National Lakeshore in Leelanau County, MI
draws an estimated 1 million visitors annually with a ﬁnancial beneﬁt estimated at
more than $39 million since its creation in 1970 (lake Michigan Federation 1999).

In addition to the revenue generated from tourism, the dunes are also highly
valued as a source of foundry sand. Since the early 1900’s lake Michigan sand dunes

26

have been intensively mined, and in some cases completely destroyed, primarily for
use as foundry cores and molding sands in the automobile industry (Buckler 1979;
lake Michigan Federation 1999). Although severe restrictions had been placed on
the mining of coastal dune areas in other states, under the control of local
government, intensive mining continued on the shore of Lake Michigan with little
regulation (Buckler 1979). It was not until the middle of the twentieth century that
residents began to notice the disappearance of some of the highest and most
magniﬁcent dunes, which had once been local landmarks, and in the 1970’s, public
outcry ﬁnally lead to the passing of the Sand Dunes Protection and Management Act
in 1976 (lake Michigan Federation 1999).

Although Michigan’s Sand Dunes Protection and Management Act was
initially enacted to regulate the mining industry, subsequently, concerns grew over
other developmental pressures on the dunes like recreation, silviculture, and
residential and commercial construction (Holt 2002). In response to the continued
destruction of the dunes from mining, and the added pressure of various other uses,
the act was amended in 1989 to include these activities (Michigan State Legislature
Acts No. 146 and 147, RA. 1989). At that time the Michigan State Legislature found
that:

(a) The critical dune areas of this state are a unique, irreplaceable, and fragile resource
that provide signiﬁcant recreational, economic, scientiﬁc, geological, scenic,

botanical, educational, agricultural, and ecological beneﬁts to the people of this
state and to people from other states and countries who visit this resource.

27

(b) Local units of government should have the opportunity to exercise the primary
role in protecting and managing critical dune areas in accordance with this part.

(c) The beneﬁts derived from alteration, industrial, residential, commercial,
agricultural, silvicultural, and the recreational use of critical dune areas shall occur
only when the protection of the environment and the ecology of the critical dune
area for the beneﬁt of the present and future generations is assured (Michigan
State Legislature Acts No. 146 and 147, Public Acts of 1989).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

88'W 86'W 84°W 82'W
r I I 1
- 46'N
46'N '-
44," _ .. 44 N
42'N _ -' 42 N
l J l L
88'W 06°W 84'W 82'W

Figure 2-5 Map ofthe areas designated 'critical dunes' in Lower Michigan.

28

At present Michigan has designated nearly 480 km of critical dunes (covering
nearly 32,000 hectares), 400 km of natural preserves, and 500 km of high risk erosion
areas along its shores (Figure 2-5; Bemd-Cohen and Gordon 1999). However, one of
the biggest imperatives of this legislation is that a permit is required before any of the
included activities can be carried out in an area designated as critical dunes (Holt
2002).

The Michigan Department of Environmental Qiality is the state agency that
administers all activities within critical dune areas. Within the MDEQ, management
responsibilities are shared by two separate branches. Sand dune mining is regulated
by the Office of Geological Survey, while all other matters concerning critical dunes
are handled by the land and Water Management Division (Michigan State Legislature
Act No. 451, Public Acts of 1994). Various means are used to administer CZM
including regulatory and planning tools (permits and restrictions), direct land
management, restoration and acquisition, investment restrictions and incentives,
education outreach programs, and mandated research (Bemd-Cohen and Gordon
1999). At the forefront of sand dune management is a permit program that prohibits
any new development or modiﬁcations in critical dune areas on slopes measuring
33% or greater and on the ﬁrst lakeward facing slope, and requires a variance for
projects affecting slopes greater than 25%. Further, an environmental impact

statement is required for all special use projects such as the building of condominiums

29

or subdivisions (Holt 2002). With the exception of sand mining, the overall

effectiveness of this program has never been evaluated.

Digital Elevation Data: Collection, Processing, 8: Use

Nordstrom et al. (1990) concluded that the management of dunes everywhere
should not be based on subjective assessments, using words like ‘fragile’ and
‘vulnerable’ that have no quantitative meaning to describe a dune system, but rather a
scientiﬁc approach is both possible and necessary. In Michigan, the key to achieving
a more objective assessment may lie in integrating the use of remotely sensed data,
such as digital slope and elevation models, with the current sand dune protection and
management program. Remote sensing provides spatially dense quantitative data over
regional scales that, if sufﬁciently accurate, would be invaluable in determining and
understanding patterns and magnitudes of dune development (Sallenger et al. 2003).

The importance of accurately characterizing topography is well established in
geomorphological research (Krabill et al. 2000; Wise 2000; Spinney 2001; Bowen and
Waltermire 2002; Woolard and Colby 2002; Sallenger et al. 2003; White and Wang
2003; Barber and Shortridge 2004; Nagihara et al. 2004; Barber and Shortridge 2005).
Two areas where topographic models have proved to be an invaluable resource
include quantifying beach morphology and shoreline mapping (Krabill et al. 2000 ;

Woolard and Colby 2002; Sallenger et al. 2003; White and Wang 2003) and drainage

30

network and watershed delineation (\Nise 2000; Spinney 2001). Gathering this data
using traditional means, such as ground based surveys or photogrammetry, can be
prohibitively time consuming, expensive, and sometimes inaccurate based on
environmental conditions (Sallenger et al. 2003). So in response to the need for
reliable and accessible topographic data, in the mid to late-nineties the USGS began
developing a seamless mosaic of the best available elevation data for the conterminous
United States. By the year 2000, work was complete on the National Elevation
Dataset and 30-meter raster elevation ﬁles were available for download free of charge
from the USGS website (Gesch et al. 2002).

Over the past few years, however, the shift has been toward models that
require a more detailed and Spatially explicit representation of process, such as
determining the rate shoreline erosion and the volumetric change of a coastline
(W oolard and Colby 2002; Sallenger et al. 2003; White and Wang 2003), and this has
created the need for greater quality topographic data (French 2003; Barber and
Shortridge 2004). Lidar is a technology that can produce high-resolution elevation
datasets; it is also the technology that may be able to meet that need. Several
collection methods as well as digital elevation products exist, and selecting one may
depend on the application, purpose and/ or availability to the end user. Lidar and
NED are possibly the two most common sources of elevation data available yet they

are considerably different from one another.

31

The National Elevation Dataset

NED is a Seamless elevation model produced and distributed by the USGS that
covers the United States at a 1 arc second (approximately 30-meter) resolution for
most areas. It is a compilation of many data sources, deemed “best available”,
including 7.5 minute, lS-minute, 2-arc-second, and 3-arc second DEMs that, in some
cases, date back to 1978. Further, the production method, horizontal datum, map
projections, and elevation units of the initial elevation data may vary within the
dataset (Smith and Sandwell 2003).

The USGS has used four primary methods of producing the underlying DEMS
including: 1) manual proﬁling, 2) automatic correlation, 3) contour-to-grid
interpolation, and 4) integrated contour-to-grid interpolation. Each method uses a
different combination of source materials and production methods resulting in varied
data quality, artifacts, and accuracy. A DEM is categorized Level 1 or Level 2 based
on the way it was produced (Hodgson et al. 2003). Level 1 DEMS are typically older
and created using automated correlation, while Level 2 DEMS are derived from
manual proﬁling of contours (1:24:000 scale digital line graphs) or aerial photography
and have higher accuracy speciﬁcations (Shortridge 2003).

During assembly, procedures to remove production artifacts and minimize
elevation discrepancies at the transition between different sources are used to

improve the quality of the dataset. Every two months NED is updated and any new

32

source DEMS that have become available are incorporated, which typically means
replacing the oldest and least accurate source data (Gesch et al. 2001; Gesch et al.
2002). NED can be downloaded free of charge or ordered on hard media for the cost
of reproduction from the NED data distribution system on the USGS website.
Spatially referenced metadata included with NED allows users to calculate
accuracy statistics based on source DEM characteristics such as resolution, age, level,
contour interval, and production method (Gesch et al. 2002). While the USGS
encourages the use of Level 2 DEMS for surface modeling, there is not a stated
accuracy standard for parameters such as slope, aspect, and drainage (Hodgson et a1.
2003). Further, when using an elevation dataset for a speciﬁc site or application and
in regions with varying terrain or vegetation, error may differ (Bolstad and Stowe
1994). Investigations of NED include error assessments of the elevation surface and
its impact on the derivative slope and aspect surfaces (Bolstad and Stowe 1994;
Holmes et al. 2000; Gesch et al. 2001). More recently, studies have compared the
accuracy of NED to that of lidar in areas with varying relief during leaf-on conditions
(Hodgson et al. 2003) and for surface hydrologic modeling (Hodgson et al. 2003;
Barber and Shortridge 2005). These studies may provide insight into the strengths
and weaknesses of the different production methods of USGS DEMS, and how an
older dataset with a coarser resolution compares to newer, high resolution lidar

elevation data.

33

Bolstad and Stowe (1994) compared elevation, slope, and aspect derived
from a USGS Level 1 DEM to that of a DEM developed using a proprietary stereo-
correlation technique developed by a private ﬁrm. The Level 1 DEM used was created
using automated Stereo-correlation of a l:40,000-scale leaf-off aerial photographs with
a Gestalt Photomapper (GPM) and has a reported vertical accuracy of 7 In (target
RMSE) with a maximum acceptable RMSE of 15 m. The study compared the DEM
elevation values to those of 40 “ground-truth” values collected from National
Geodetic Survey (NGS) control points and carrier-phase GPS surveys. Slope values
were calculated as a percent using the Horn algorithm, a third-order ﬁnite difference
method, and compared to slope values measured using a hand-held clinometer.

Signiﬁcant ﬁndings from this study include: 1) the USGS DEM meets the
reported accuracy for Level 1 DEMS, with the largest errors found in areas exhibiting
the highest and lowest elevations for the study area, 2) on average, the USGS DEM
under-estimated elevation, 3) a positive correlation between slope errors and slope,
indicates larger errors on steeper slopes. Areas with the steepest terrain are typically
forested and, using photogrammetric techniques, fewer postings are collected in
forested areas. When interpolation is used to calculate elevation values it tends to
smooth microtopography. Bolstad and Stowe (1994) believe that this may be the
reason larger slope errors are associated with more rugged terrain . Further, when the

terrain is more varied with steeper slopes, ﬁeld collection methods may be hampered

34

due to stem obstruction, understory vegetation, and other factors, which also lend to
larger slope errors between sources (Bolstad and Stowe 1994).

Holmes et al. (2000) used geostatistics to evaluate the distribution of error in a
USGS DEM in relation to data collected using a GPS with the intent of determining
the affect of DEM error on a landslide modeling application. The USGS DEM used in
their study is a Level 2 dataset produced by digitizing contours, either
photogrammetrically or from existing topographic maps. In Level 2 DEMS, the
maximum allowable error (RMSE) is up to one half of the contour interval, in this
case 5 In. Their study area includes about 1000 m of relief, including ﬂoodplains, low
rolling hills, and mountains.

The researchers (Holmes et al. 2000) did not ﬁnd a statistically signiﬁcant
correlation between DEM error and terrain attributes, including slope, elevation and
roughness. The strongest correlation value was .325 between slope and error. They
report that the USGS Level 2 DEMS are generally accurate given the reported error
estimates. However, they conclude that accounting for error can greatly enhance the
value of an environmental model given that the error in an elevation surface can

compound in derivative measures such as slope, aspect, and ﬂow accumulation.

The Collection of Lidar Data

Lidar is an advanced remote sensing technology that is widely used to collect

high-resolution terrain data (Lloyd and Atkinson 2002). Mounted to a small aircraft,

35

the lidar instrument uses a fast-ﬁring laser light (typically between 10,000 and 50,000
hertz) to transmit a light pulse to a target on the ground. The round-trip travel time
of the pulse and the arrival of the pulse reﬂection are recorded by the sensor’s
receiver (Bowen and Waltermire 2002; Lefsky et al. 2002; Barber and Shortridge
2004). In 1999, at least 5 companies manufactured lidar systems and roughly 40

private ﬁrms offered lidar data collection services (Baltsavias 1999).

 

Direction of Flight
(parallel to beach)

 

 

 

 

Figure 2-6 Schematic of lidar data acquisition from a twin engine aircraft (modiﬁed from Woolard and
Colby 2002).

An outline of the ground surface can be captured when the vertical distance
between the sensor, located in a level-flying aircraft, and the Earth’s surface is

repeatedly measured along a transect (Lefsky et al. 2002). The laser scans the terrain

36

surface perpendicular to the ﬂight path, gathering up to ﬁve measurements per square
meter, although the density will vary depending upon the local topography and the
scan angle (Adams and Chandler 2002; French 2003). Lidar can quickly gather
spatially dense elevation data within a survey swath hundreds of meters wide

(W oolard and Colby 2002; Sallenger et a1. 2003; Barber and Shortridge 2004). For
coastal mapping applications, the common aircraft altitude is around 700 m, with an
individual swath width of roughly half of the altitude (Figure 2-6). The rotating
mirror has an elliptical swath pattern with an approximately 30° scan angle (W oolard
and Colby 2002; Sallenger et al. 2003).

The lidar system is typically used in combination with instruments for locating
the source of the return signal in three-dimensional space (Baltsavias 1999; Lefsky et
al. 2002). These instruments include a differential Global Positioning System (dGPS)
receivers to obtain the position of the platform, an Inertial Navigation System (INS) to
monitor the pitch, roll, and altitude of the aircraft, and angle encoders for the
orientation of the scanning mirrors (Baltsavias 1999; Adams and Chandler 2002;
Lefsky et al. 2002; Sallenger et al. 2003; Barber and Shortridge 2004). When
combined, they may be referred to as an Airborne Laser Scanning (ALS) system. Since
an AIS has the potential to determine the 3—D location of the target, it is commonly
used for terrain mapping (Adams and Chandler 2002; Barber and Shortridge 2004).
Several application speciﬁc laser scanning systems have been developed in recent
years including the US Army Corps of Engineers’ (U SACE) Scanning Hydrographic

37

Operational Airborne Lidar Surveying (SHOALS) system for surveying bathymetry
and NASA’S Airborne Topographic Mapper (ATM) for global climate change

applications (Sallenger et al. 2003).

Post-Processing of Lidar Data

The data returned using an ALS system is a point cloud represented by a series
of xyz data points, which describes the location of the observations in three-
dimensional space (Figure 2-7). The elevations, or z-values, associated with each
point can represent a myriad of features including the ground, buildings, clouds, the
canopy, or anything else that the laser pulse may come in contact with (Lefsky et al.
2002; Barber and Shortridge 2004). Although lidar appears to be useful in obtaining
data points in leaf- on conditions, a closed canopy can result in signiﬁcantly fewer
ground hits and lower accuracy. Ackerman (1996) estimates an overall penetration
rate of 24-29% for coniferous forests and 22-25% for deciduous forests during the
growing season. While Cowen et al. (2000) report that in canopy closures of 30 -
40%, 80-90 % of lidar pulses will reach the ground, but when forest cover increases to
80-90% the number of bare ground hits Signiﬁcantly decreases to 10%.

For use in applications that require bare-earth results, data must undergo post-
processing to remove points returned from vegetation, buildings, and any other above
the ground component (Lefsky et al. 2002). This process involves a combination of

highly automated processes, typically ﬁltering algorithms, with some manual

38

correction (Kraus and Pfeifer 1998; Bowen and Waltermire 2002; Lefsky et al. 2002;
Barber and Shortridge 2004). Less is known about the affects of a dense understory
on the quality of the data set. Research shows that traditional methods of removing
points that hit trees and buildings may not work with vegetation below the canopy
and a systematic vertical shift may be more appropriate (Pfeifer et al. 2004).

When data are collected by a contractor or engineering ﬁrm, algorithms and
programs used in post-processing are generally proprietary and vary between ﬁrms
(Bowen and Waltermire 2002; Lefsky et al. 2002; Barber and Shortridge 2004). Firms
are often reluctant to describe their methods in detail and this can present problems
for scientists using the data for research (Lefsky et al. 2002). Methods commonly used
include some form of linear prediction and/ or data segmentation. Linear prediction
techniques use knowledge of the terrain to classify points based on their z-values.
Kraus and Pfeifer (2001) developed a method they call robust interpolation or robust
linear prediction. This technique combines a ﬁltering algorithm with surface
interpolation. It uses the residuals, or vertical distance between point values to the
surface, to assign a weight to each z-value. The surface is then re-interpolated using
the weights and if the points fall outside of a certain value, they are thrown out and
the process repeated until all gross errors are eliminated. Lee and Younan (2003)
further modiﬁed the work of Kraus and Pfeifer (2001) combining linear prediction
with adaptive processing to derive bare earth points in vegetated areas. Data
segmentation, on the other hand, separates entire features from ground points as a

39

whole instead of point by point, by generating texture maps to identify the comers of

buildings and trees (Barber and Shortridge 2004).

 

  
    
 

 

 

 

 

 

330 r
5
3
370 g
2‘
r u"
E
g 360
9
2"
N

 

 

 

 

 

///////

 

0‘9

 

 

 

Figure 2-7 Representative illustration of the three-dimensional and
vertical distributions of lidar returns within a 25—m footprint (from
Lefsky et al. 2002).

A second step in post-processing, which is commonly performed by the user of
the data, is interpolation to a raster grid. The data collected via lidar, being a set of

irregularly spaced points, requires interpolation if an elevation surface or digital

40

elevation model is to be derived (Lloyd and Atkinson 2002). Research, typically based
on cross-validation of the data, shows that there is some discrepancy on which
interpolation method of the many available is most accurate. Inverse distance
weighting (IDW), ordinary kriging, and universal kriging have proven to result in a
relatively high degree of accuracy in the interpolated surface (Lloyd and Atkinson
2002; Woolard and Colby 2002; Rosso et al. 2003).

The interpolation method that will work best is usually dependant on the data
itself and terrain characteristics. If large voids exits or the data is generally sparse
interpolation with kriging may be the more suitable method (Lloyd and Atkinson
2002; Barber and Shortridge 2004). However, in most cases the simpler IDW method
is appropriate and may even be preferable (Rosso et al. 2003; Barber and Shortridge
2004). Although the point data may be carefully edited, once interpolated, it is
important to consider that investigations into using lidar for surface modeling show
that features such as elevated roadways, bridges, and railroad grades may remain
leaving large Sinks in the dataset (Barber and Shortridge 2004; Barber and Shortridge

2005).

The Application of Lidar Data

As previously mentioned, the primary disadvantage of ground surveys is the
large time and labor expense, while the alternative photogrammetric methods are

inaccurate when the ground is under a forest canopy and in areas of low relief and

41

texture, like that of wetlands and coastal dune systems (Lefsky et al. 2002). Lidar is
generally regarded as a more accurate, more efﬁcient, and less expensive collection
method for the creation of DEMS than these conventional methods (Hill et al. 2000;
Bowen and Waltermire 2002; Lefsky et al. 2002; Woolard and Colby 2002; Sallenger
et al. 2003; Barber and Shortridge 2004). Published accuracies for lidar data range
anywhere from 5 cm to l m vertically, with some consensus between 15 and 20 cm,
and l m to 2 m horizontally (Hill et al. 2000; Bowen and Waltermire 2002; Woolard
and Colby 2002; French 2003; Sallenger et al. 2003; Barber and Shortridge 2004;
Davenport et al. 2004). The cost of obtaining lidar data ranges from $500 to $1500 per
square mile, which is substantially lower than traditional methods (Bowen and
Waltermire 2002; Sallenger et al. 2003).

Given the beneﬁts of using lidar data, its use has been and continues to be
examined for many purposes. In terms of environmental applications, Lefsky et al.
(2002) broadly divide lidar research into three categories: 1) remote sensing of ground
topography, 2) measurement of the three dimensional structure and function of forest
canopies, and 3) prediction of forest stand attributes. In addition to ecosystem
management there are also several commercial uses of lidar including
telecommunications, transportation, and urban development, all of which use lidar to
map landscape components including buildings, infrastructure, topography, and

vegetation (Hill et al. 2000). While these categories may fall short of describing the

42

actual extent to which lidar technology has been applied, the remote sensing of
ground topography alone covers numerous scientiﬁc ﬁelds and applications.

Speciﬁc topographic applications of lidar data that have been examined
include hydraulic modeling and watershed delineation (Spinney 2001; Bowen and
Waltermire 2002; French 2003; Barber and Shortridge 2004), analysis of the
volumetric change and erosion of the coastal zone (Krabill et al. 2000; Adams and
Chandler 2002; Woolard and Colby 2002 ; Sallenger et al. 2003; White and Wang
2003), near shore bathymetry and seaﬂoor mapping (Irish and White 1998; Irish and
Lillycrop I999; Guenther et al. 2000), mapping the morphology and distribution of
landforms (Rango et al. 2000; Nagihara et al. 2004), land cover classiﬁcation (Jelaska
et al. 2003; Rosso et al. 2003; Davenport et al. 2004), and habitat management (Blott
and Pye 2004).

One of the most prevalent topics in the literature is coastal zone mapping. The
coastal zone is the zone of interaction between land and ocean where the
hydrosphere, lithosphere, and atmosphere are in constant interaction with one
another (White and Wang 2003; Gabler et al. 2004). These interactions make it one
of the most dynamic environments, operating on a variety of time scales ranging from
a few hours to hundreds of years (Krabill et al. 2000). The US. coastline stretches
more than 20,000 km in length, making remotely sensed data an invaluable resource
for monitoring the constant shifts and changes occurring there (Krabill et al. 2000;
Sallenger et al. 2003). Further driving the need for research is the heavy

43

anthropogenic pressure placed on this margin when you consider that over half of the
US. population resides there and the heavy economic cost of severe erosion events
(N ordstrom et al. 1990; Bernd-Cohen and Gordon 1999; White and Wang 2003).
Coastal erosion is a topic well suited for the spatially dense lidar data,
demonstrated by the ALACE (Airborne Lidar Assessment of Coastal Erosion) project,
a joint venture of NOAA’S Coastal Services Center, the USGS Center for Coastal
Geology, and NASA. Using NASA’S ATM, annual surveys of the Atlantic, Paciﬁc,
Great lakes, and Gulf of Mexico shorelines were conducted between the years of
1997 and 2000 primarily to examine and measure coastal erosion (Figure 2-8) (Krabill
et al. 2000; Lefsky et al. 2002; Sallenger et al. 2003). In a ﬁeld experiment called
Sandy Duck, researchers used an extensive set of ground measurements to verify that
the data collected by the ATM was ﬁt for coastal change applications. The researchers
found that the accuracy of the data was sufﬁcient to determine the magnitude of
beach erosion following a severe Storm event (Sallenger et al. 2003). A similar study
was conducted on Assateague Island off the coast of Maryland, to measure the net
change in beach morphology between the fall of 1995 and 1996. With the exception
of areas affected by overwash, the measurements collected by the lidar system were
comparable to those collected using ground survey techniques. Finding a vertical
RMSE of 10 -20 cm, this study shows that lidar data can represent detailed beach

morphology (Krabill et al. 2000).

44

While most coastal studies, like the ones described above, have focused on the
validation of lidar as a mapping tool or its ability to proﬁle erosion rates and trends,
Woolard and Colby (2002) used lidar to assess the volumetric change in sand dunes
between 1996 and 1997. They concluded that lidar (interpolated to a 1-2 m
resolution grid using IDW) is able to accurately represent the topographic variability
found on a dune covered landscape and provides sufficient information to analyze the
net sediment change year over year. They suggest that their methods could be used to
compare volumetric change from season to season in order to better understand the

changes taking place in a dune system.

 

a
34 330“
l b.
‘.o l l I I I I
sept 1997»
Sept 1995A ‘99,
3 9 ‘ :jmune crest
u , ‘.
. 3 . ,
. ' / overwash
34 325°1 31 1 2 o - .

0
Change (at)

9.-
Co
..g
.-W
5:5
a
if
83
O
s
2

Elevation (m)
't
.g

I
l
I
I

 

     

34 320°j Proﬁle Location

A
-300 ~25O -200

_
20° "‘9'“ Distance across beach (m)

 

—I T’ I I I I
283312" 283 316° 283 320°

Figure 2-8 Lidar representation of pre- and post hurricane beach topography (right) for a transect
on Topsail Island, North Carolina (left) (from the ALACE project in Lefsky et al. 2002).

White and Wang (2003) performed a similar study on barrier islands in North

Carolina. Using lidar data from nearly one hundred study sites over three time

45

periods (1997-1998, 1998-1999, and 1999-2000), and grid resolutions ranging from 1
m to 5 111, they were able to assess morphologic changes in the barrier islands from
year to year and at different resolutions. They were also able to relate the differences
in sediment volume to contrasting management techniques (developed, undeveloped,
and nourished). The authors concluded that the increase in development and
different management practices greatly affect the coastline’s response to storm events
from year to year. While both of these studies conﬁrm the value and suitability of
using lidar as a tool for evaluating and managing the coastal zone, there is Still a need

to study the use of lidar derivatives to further characterize topography in this setting.

The Comparison of Lidar DEMS to NED DEMS

Research comparing USGS Level 1 and Level 2 DEMS to lidar datasets is
limited. Two such published studies were done by Barber and Shortridge (2005) and
by Hodgson, Jensen et al. (2003). Barber and Shortridge (2005) initially intended to
compare a 30-m NED dataset to a corresponding lidar dataset for two watersheds in
North Carolina. However, the USGS had used lidar data in an update of the DEM for
the study area, so a comparable 30-m dataset was obtained from a mosaic of USGS 7.5
minute quadrangles and used in lieu of the NED data. The second study, performed
by Hodgson, Jensen et al. (2002), compares elevation data collected by lidar during

leaf-on to that of both Level 1 and Level 2 DEMS in relation to slope and land cover.

46

Barber and Shortridge (2005) were interested in determining whether the use
of lidar over traditional data collection methods improved terrain representation and
hydrologic modeling. In their study three areas of investigation were considered
including: 1) the dense forest cover that is often associated with riparian
environments (although all survey methods may be affected by this, lidar is especially
sensitive to heavily vegetated areas), 2) production artifacts that are present in any
elevation dataset and are of particular challenge to hydrologic modeling; and 3) spatial
scale or the difference in resolution between a lidar-based DEM and a medium-
resolution datasets. They presented three “testing challenges” to resolve the
differences between the two sets of elevation measures in relation to the three areas
of investigation, considering whether lidar elevations were more similar to the USGS
elevations in upland areas, whether lidar surfaces are hindered by manmade
obstructions, and whether the differences between lidar and USGS elevations were a
matter of spatial resolution as opposed to production methods.

The authors (Barber and Shortridge 2005) found that post-processing of the
lidar data, in this case, was successful in removing man-made obstructions from the
data set, and although there were numerous sinks, which are a reﬂection of non-
ground hits, they were very small in area. Findings on the issue of scale versus source
were less conclusive and the authors determined that this is likely dependent upon
the terrain derivative in question. Slope, for example, is greatly affected by resolution

and not as affected by source. The paper concludes that the while the beneﬁts of

47

using lidar rather than DEMS like NED are marginal, some operations may be
sensitive to resolution and therefore lidar may be a better choice, particularly in areas
of low relief (Barber and Shortridge 2005).

The aim of the research conducted by Hodgson et al. (2003) was to determine
the overall accuracy of elevation and slope measures of four different DEMs,
including one derived from lidar and two from NED (Levell and Level 2). One
further goal was to establish if land cover and terrain variability impacted the

accuracy of those measures. Elevations in their study area range from 44 to 136 m,

s10pes range from 0° to 14°, and land cover is primarily deciduous and pine forest

(60%). Sampling took place along 23 transects ranging in length from 100 to 840 m,
and over 1,470 elevation points were collected using GPS and conventional surveying
techniques. Slope was computed as the degree of slape between adjacent transect
points, with the average distance between points being 6.88 In. Land cover data was
collected at 1,195 of the survey points.

Of the four elevation surfaces studied, only the USGS Level 2 DEM fell within
its reported accuracy range of 1 to 2 111. Although, the accuracy of the lidar data
surpassed that of the Level 2 DEM, it more than quadrupled the RMSE that is
generally advertised for the product (93 cm versus 15 to 20 cm). In forested areas the
error jumped to 113 - 122 m, keeping in mind that the data was collected during the

growing season. The researchers found that although elevation errors were less

48

related to Slope than they were to land cover class, error and slope were positively
correlated. However, they conclude that if the environmental application in question
is in an area of rugged terrain, greater elevation errors should be expected. Further,
the authors recommend using either a lidar or USGS Level 2 DEM over other
elevation products if an application requires accurate slope measures but, based on the
topography of their study area, are unable to provide evidence that either product is

suitable for such uses (Hodgson et al. 2003).

49

III. STUDY AREA

The study area for this investigation is a 300-meter wide Strip of land,
approximately 3.25 sq km in total area, spanning the shoreline of lake Michigan in
lake Township ('T6S, R20VV), Berrien County, MI (Figure 3-1). Berrien County marks
the southern reach of the eastern shore of Lake Michigan in Michigan and contains
over 1,600 hectares of the state’s 32,000 hectares designated crin'cal dunes. Of those
1,600 hectares, approximately 900 are in lake Township (MDEQAtlaS of Critical
Dunes 1989). Also located within the township are Warren Dunes State Park,
spanning a little more than 4 km of the shoreline, and Weko Beach recreation area.

land use in the rest of the township is primarily residential with some
industrial development, most notably the Cook nuclear power facility. Combined
there are approximately 340 taxable parcels of land on record, with at least some
portion of the lot contained within the study area. Although the Sand Dunes
Protection and Management Act (Michigan State Legislature Act No. 451, Public Acts
of 1994) allows the local unit of government to assume management of the dunes, at

this time the MDEQ manages all of the critical dune land in Lake Township.

50

 

Lake Township, Berrien County

   

063120

 

 

 

/
I /'
///‘
//
,4
.; J
i i
i/, \ ——
. 5
Berrien County, c
. . ,, U?
Michigan /, l ,0

 

 

>2

 

 

 

 

 

Figure 3—1 Map of the study area, Lake Township, Berrien County, MI.

History

Throughout the Pleistocene, Michigan’s landscape was repeatedly overrun by
glacial ice with initial ice ﬂow into the region controlled by the local geology. In the

southern, lowland region of the Great lakes, which includes the Lake Erie and Lake

Michigan basins and most of the Huron and Ontario basins, the ice was channeled

51

 

over top weaker sedimentary rocks into bedrock valley systems already present in the
region (Larson and Schaetzl 2001). Subsequent ice ﬂows into the area followed a
Similar path and, therefore, a highly lobate front developed each time ice advanced,
scouring and further incising the Great lakes’ basins (Eschman 1985; larson and
Schaetzl 2001). Present day lake Michigan ﬁlls the large depression that was heavily
eroded by the multiple ice advances and retreats, and last occupied by the lake
Michigan lobe of the Laurentide ice sheet (Eschman 1985).

Early in the history of geomorphic studies on the coastal dune complexes of
lake Michigan, researchers (Dow 1937; Scott 1942; Olson 1958d) recognized the
relationship between the elevation of the lake and the adjacent landforms.
Throughout the Pleistocene and into the Holocene, the level of Lake Michigan has
ﬂuctuated in response to ice advances, retreats, and isostatic changes in elevation.
Some have even reported differences of as much aslS m higher and 61 m lower than
the mean present day lake level of 177 m (Chrzastowski and Thompson 1992). On a
smaller scale, lake level may also vary from year to year depending on temperature
and precipitation and over time, patterns develop given that any year’s water balance
is dependant upon that of the preceding years (Olson 1958d). Both Dow (1937) and
Scott (1942) hypothesized that ﬂuctuations in lake level were the dominant control of
the sand supply to the dunes on the eastern shore of Lake Michigan. Olson (l958d)
further expanded this idea, and developed a cycle of dune development controlled

primarily by the rising and falling of the lake level.

52

Although Olson’s (1958d) work remains the foundational model of foredune
development in the region, work by Arbogast and Loope (1999) and Van Oort et a1.
(2001) provided evidence in the form of radiocarbon dates from buried soils within
the dunes that the evolution of the massive dunes located atop lacustrine sediments is
directly linked to the historical lake level curve. Prior to this research, Dorr and
Eschman (1970) and Eschman (1985) hypothesized that major dune development
along the lake largely occurred during the Nipissing Phase of the Great Lakes (~ 6000
to 4000 years B.P.) when lake levels peaked at 184 In. More recent studies of Lake
Michigan dune ﬁelds (Arbogast and Loope 1999; Loope and Arbogast 2000; VanOort
et al. 2001; Arbogast et al. 2002), however, provide evidence that dune building began
during that high stand, but that the most signiﬁcant growth occurred later at episodic
intervals. Van Oort et al. (2001) studied large parabolic dunes at Van Buren State
Park approximately 60 km north of the study area, and their results also indicate that
there were several periods of dune growth marked by intervals of Stability when soils
developed. A rapid decline in lake level following the Nipissing transgression led to
an increase in sand supply and to a dominant period of dune building between ~ 4000
and 2500 years B.P. This time of rapid growth was followed by a long period of
Stability sufficient for soil development until the dunes remobilized again between
1140 and 790 cal. yr B.P.

In studies conducted elsewhere on the eastern shore it seems that while

receding lake levels account for the onset of the initial growth period, later periods of

53

dune growth (~ 3200, 2400, and 900 years B.P.) are often associated with intervals of
higher lake levels (Figure 3-2; Arbogast et al. 2002). One hypothesis is that the
presence of a broad beach and foredunes during lower lake levels protect the large
parabolic dunes and a narrow beach and the absence of foredunes during high lake
levels subject the dunes to increased wave erosion (V anOort et al. 2001). Given the
Similarities of dunes in Van Buren State Park and those found in the study area, this
research can be used to infer a history of the large parabolic dunes found in the study

area.

 

 

‘r

 

Lake Michigan , .
130 b” —LakaLevel i” """1"

  
  
    
  

 

 

 

’Historical 1 I , t . ' '
179 —-record-—- ---——:-- —-- --- -. - -~-----t-—~------

,(annual avg) , I
178

L——-——--]— -—-

177 _ - - . I» - _ . .L-——-—»—-—«>—-—-—-—¢

 

 

 

I Historical average
- 1' ---— (1819-1999)---

ALAleJI 41111;

-500 ' 4500 5000 5500 6000
Calendar year BP

IGLD 1985 Elevation (m)

 

 

 

 

 

 

 

 

 

 

Figure 3-2 Graph showing the residual lake level curve of Lake Michigan as determined by Baedke
and Thompson (2000), plotted with the historical average. A. marks the dominant time period of
dune building along the eastern shore, while a, b, and c are used to note times of dune growth
associated with higher lake levels (Arbogast et al. 2002; modified from Baedke and Thompson 2000).

54

Dune Topography

Dunes within the township are classiﬁed as barrier dunes by the MDEQ
(1994), a term ﬁrst deﬁned by the MDNR (1976) and later reﬁned by Buckler (197 9)
to describe an assemblage of dunes that form a physiographic boundary marked by
great relief between the aesthetically pleasing shore zone and the interior. In more
speciﬁc terms, Arbogast et al. (2002) noted that the dunes along the Lake Michigan
shoreline can generally be divided into two universal categories 1) foredunes (~ 5m
high), which are relatively small sublinear dunes, and 2) large dunes (> 20 m high),
which tend to be parabolic in form and occur within many well-developed dune
ﬁelds along the lake. The largest dunes in the study area are parabolic dunes over
50 m high. Other dune features that exist within the study area include but are not
limited to blowouts, dune ﬂats, and interdune lowlands (Buckler 1979). The margin
of the study area is lined by small hills and low ridges of glacial till that are part of the
Lake Border morainic system (Figure 3-3; Schaetzl 2006). Dunes are absent in areas
where moraines approach the lake or where the shore is composed of glacial till or
outwash (V anOort et al. 2001).

Where not altered by development, foredunes, parabolic dunes, blowouts,
dune ﬂats, and interdune lowlands are found throughout the study area and give dune
ﬁelds the distinction of having very diversiﬁed topography. Elevation in Lake

Township ranges from a low of 176 m at the shoreline to a high of 233 m on the

55

largest dunes. The mean elevation of the study area is near 190 In, with most heights
not varying more than 10 m from the mean (0 = 9.04 m). The gradient ranges from
ﬂat (0% or 0°), typically near the shore, on dune ﬂats, and interdune lowlands, to
>300% (70°) on the steepest slopes (all values were calculated using Arc Info and lidar

elevation data).

 

 

. I— - r-‘- " I ‘
. Lake .Boiderfmgr
.43.’ _ y, "a";

f )(l’v

 

 

 

 

Figure 3—3 Physiography of Berrien County as depicted in the Soil Survey of Berrien County. The
inset highlights the landforms found within and around the study area including the dunes, Lake
Border morainic system, and glacial lake plain that underlies most of the study area (Larson 1980).

Climate
A unique characteristic of coastal locales to the east of Lake Michigan is a
maritime inﬂuence on climate despite the continental location. In these areas,

climate is classiﬁed as mixed marine, continental, whereas areas further inland are

56

classiﬁed as humid continental, hot summer, which is noted for its large range in
temperature (Eichenlaub et al. 1990; Gabler et al. 2004). Average annual
temperatures for the area range from about -5° C in January to 21° C in July, and
annual precipitation totals are near 81 cm (Eichenlaub et a1. 1990). The closest
coastal weather station to the study area is located approximately 20 km to the north
in Benton Harbor, MI. In the 30-year period from 1951 to 1980, average daily
temperatures ranged from — 4° C in January to 23° C in July. The annual precipitation
average during this time was 92.7 cm with a little more than half falling as rain in the
spring and summer (Andresen et al. 2005).

Winds are multidirectional and follow a seasonal pattern, with winter and
summer winds being northwesterly and southwesterly, respectively (Eichenlaub et al.
1990). Near the study area, south-south-westerly winds tend to dominate and
average wind speeds are near 10 mph (Andresen et al. 2005). Prevailing westerly
winds coming off the lake are a key factor in the development of large sand dunes on
the eastern and southern shore of the lake (Cowles 1899; Gabler et al. 2004). Climate
reconstruction during the time of major dune building episodes shows both a slight
decrease in precipitation and an increase in seasonality from that of the early
Holocene, however, when compared to climate reconstruction elsewhere in the

region, this climate change is negligible (Davis et al. 2000).

57

Land Use / Land Cover

According to the most recent available data (MDNR land use / land cover
(LULC) classiﬁcation of 1978), LULC in the study area includes areas of deciduous
forest (code 41), residential (code 11), transportation, communication and utilities
(code 14), and barren land (code 7) (level 11 categories). These classiﬁcations are
based on the dominant LULC type in an area no smaller than one hectare.

An on the ground inspection of LULC classes at individual sample sites also
revealed areas of dune grass and mixed forest including pines, however, there was no
attempt to determine whether or not these areas met the minimum mapping unit of
one hectare. Further, the limited width of the study area from the shore (300 m)
combined with the selection of 46 sample points from within that area greatly limited
the number of possible LULC classiﬁcations found at any of the sample locations.

In general, the distribution of land cover types moving from the shore inland
is beach, barren land (including sand other than beaches), and forest (both hardwoods
and pine), which is the dominant land cover on many of the largest and most well
established dunes. land use outside of the state park and recreation area includes
many single family homes, which are scattered throughout, and a large nuclear power

facility located in the northern half.

58

Soils

The predominant soil series within the study area is Oakville ﬁne sand, which
is found primarily in forested dune areas. A narrow margin of gently sloping beach
stretches along the coast with projections of dune land extending back into the
forested areas (Larson 1980). Areas mapped as beach remain in the swash zone and
are repeatedly overrun by wave action. The primary use of the beach is recreation and
that, combined with the absence of notable relief, made the areas mapped as beach an
unfavorable choice for sampling.

The Oakville series corresponds with the deciduous forest land cover and
developed areas (mainly residential). The Oakville series is well drained with rapid to
very rapid permeability and weakly developed with A / E / B / C horizonation. In
some areas, this soil is prone to instability and its best use is for woodland and wildlife
habitat. In those places where it has been used for building construction, slope
instability can be controlled with retaining structures (Larson 1980). Further, when
compared to areas mapped dune land, in places where Oakville is found, it is
generally safe to assume that the soil is older than its bare sand counterpart and has
moderate to fairly stable (slopes < 18%; Arbogast 2004).

The sediment found in areas classiﬁed as dune land was derived largely from
glacial drift and is composed chieﬂy (~90%) of quartz sand, which is extremely

resistant to erosion (Santer 1993). Due to the sorting ability of wind, the dune sand is

59

remarkably uniform in size when compared with beach sand. The sand is still
actively shifting and has little to no protective vegetation cover and, therefore, soils
are yet to develop (Larson 1980; Santer 1993). Vegetation where present is primarily
dune grass with some trees and woody shrubs. In the areas with stabilizing

vegetation, it is likely too recent for a soil proﬁle to develop (Larson 1980).

60

IV. METHODS

The methods used in this study are designed to determine which digital terrain
attributes, or combination of attributes, when used in a linear regression model will
most closely predict true slope. Further, I will use data from two different sources,
lidar and NED, to determine whether the source of the data inﬂuences the outcome of
the model. My hypothesis is that lidar, when used in conjunction with calculated
slope and land cover, will more accurately predict true slope than a model that uses
NED and the same variables.

The ﬁrst steps toward answering my research questions and testing my
hypothesis are the collection of ﬁeld data, primarily slope, and processing of digital
data, including elevation, slope, and land cover. Once prepared, variables from each
data set will be used in the design of multiple regression models. This chapter begins
with an account of the methods used to collect ﬁeld data, followed by a description of
each digital data set and its preparation. Once this discussion is complete, I will

conclude with an overview of multiple regression.

Collection of Field Data

Perhaps the most important variable in the regression equation is the set of

observations (or the sample) that is used to construct the model. Generally a large

61

sample size representative of the entire population creates an equation that is more
stable or replicable across samples from that same population (Osborne 2000). While
there are many different opinions on what number of observations is the appropriate
amount for creating a model, several authors (Park and Dudycha 1974; Cohen and
Cohen 1983; Tabachnick and Fidell 1996) agree that the size of the sample should be
based on the number of independent variables used. The sample size used in this
research is 46, which is a small number by some standards, but based on the literature
should be suﬁicient to create a model using up to three predictor variables
(Tabachnick and Fidell 1996; Osborne 2000).

Sites selected for ﬁeld sampling needed to accurately represent the entire study
area, which includes everything from expanses of level ground to near vertical slopes,
but at the same time be suitable for the purpose of this study (to predict slope). Prior
to entering the ﬁeld 100 sample points were generated using a random point
generator in Arc Map. Once in the ﬁeld, a point was discarded if it was not accessible
due to property rights or terrain conditions, such as dense vegetation combined with
steep slopes, too close to the water line (in the swash zone), or within 5 meters of
another sampling point.

Property rights were a much bigger issue than expected, speciﬁcally with
respect to private roads that limited access. As a result I was unable to select points
distributed over the entire study area. Given the ﬁeld limitations encountered, I was

ultimately able to sample 46 sites. At each of these sites, I collected three terrain

62

attributes: slope, land cover, and elevation. Slope is the dependant variable in the
multiple regression model, while elevation and land cover were collected only for
assessing the accuracy of their respective digital data sets.

Figures 4-1 and 4-2 are maps showing the locations of the sample points in the
northern and southern extents of the township. A majority of points in the
northernmost cluster (Figure 4-1) were collected in a private residential area where I
was granted access by a property owner. All points to the south of this area (Figures
4-1 and 4-2) are located either on publicly owned Weko Beach in the central part of
the study area or on state land in the south, which includes Warren Dunes State Park.
large gaps represent areas were access was restricted by land ownership or terrain
conditions (i.e., dense forest and/or understory combined with slopes too steep to
traverse).

Vertical and horizontal measurements were collected with a Trimble
Pathﬁnder Pro XRS GPS unit, which uses both point averaging and built-in, real-time
differential correction. When point averaging of approximately 100 observations and
real-time differential correction are used, the documented error of both

measurements is reduced to sub—meter (T rimble Navigation Limited 2005).-

63

 

 

0 0 25 0 5 1 Kilometers

[1111111111

 

l

81

Bridgman

 

 

 

 

 

 

 

 

 

 

Figure 4—1 Map of the sample points collected in the northern halfof Lake Township, Berrien County,
MI.

64

 

 

 

 

 

 

 

 

 

 

Figure +2 Map of the sample points collected in the southern halfof lake Township, Berrien Cmmty,
MI.

65

When conducting a ﬁeld inspection, a MDEQagent locates visual breaks in
the affected dune and uses a clinometer to measure slope across the distance of each
discemable slope. Given the resolution of the digital slope grid (2 m), slope values
collected in the ﬁeld had to be measured across a more precise distance than the
method currently employed by the MDEQ (Shortridge 20043; Warner 2005). Instead,
slope measurements were collected using a 2-meter piece of ﬂat, wood trim and a
compass with an internal level and slope measuring device (Figure 4—3). After loose
debris such as branches and leaves were cleared, the piece of trim was laid on the
ground parallel to the steepest gradient at the geographic location (point) being
sampled. The slope measuring device was then placed on the center of the board and,

with the aid of the internal level, a percent slope value was obtained.

 

Figure 4—3 Photograph showing the method and equipment used to collect slope
measurments in the ﬁeld.

66

The horizontal (point locations) and vertical (elevation) measures collected
with the GPS were tabulated and projected from the unit into a database using
Pathﬁnder software. As a projected database of values, the elevation measures were
converted to a point coverage in Arc Toolbox and the corresponding slope and land
cover values collected in the ﬁeld entered into the attribute table manually. The ﬁeld
data was then joined to the attribute table containing the NED and lidar slope and

elevation measures and the NLCD based on geographic location.

Selection of the Independent Variables

Osborne (2000) stated that, when a multiple regression equation is designed
for prediction, the goal is to arrive at the model that best estimates the value of the
dependant variable at unsampled locations, regardless of the relationship it has with
the independent variables. Although the variables are not required to make
conceptual sense, theory is quite helpful for identifying which predictor variables
should be included in the equation (Osborne 2000). I chose to go with the latter
approach and chose three independent variables, elevation, calculated slope, and land
cover, based primarily on the potential relationship each has with the dependant
variable.

The inﬂuence of land cover on remote collection methods has long been and

will continue to be the subject of much research (Hodgson et al. 2003). However,

67

more recent studies (Bolstad and Stowe 1994; Bowen and Waltermire 2002; Hodgson
et al. 2003) have tended to focus more speciﬁcally on the relationship that the
collection method has with elevation, land cover, and slope to gain a better
understanding of how in situ terrain attributes affect the quality of a digital elevation
model and its derivatives.

For example, research has found that both elevation error and modeled slope
error increase when slopes on the ground are steeper (Chang and Tsai 1991; Bolstad
and Stowe 1994; Hodgson et al. 2003). If the terrain surface is variable, then any
horizontal errors in position created by the lidar instrument will typically result in
vertical (elevation) errors (Hodgson et al. 2003). A major part of post-processing raw
points collected with lidar includes identifying ground returns to weed out those from
other objects. This typically involves a combination of highly automated processes,
such as ﬁltering algorithms, with some manual correction (Kraus and Pfeifer 1998;
Bowen and Waltermire 2002; Lefsky et al. 2002; Barber and Shortridge 2004). In
addition to affecting the instrument, sloping terrain can also make it difﬁcult for
automated weeding algorithms to reliably identify ground returns, which will result
in increased error in the lidar dataset. If rugged terrain is found in conjunction with
multi-story vegetation, the increase in error can be even more signiﬁcant (Hodgson et
al. 2003).

Research has found a positive relationship between true elevation and
elevation error and true slope and slope errors in USGS level 2 DEMS as well (Bolstad

68

and Stowe 1994). During the production process, level 2 DEMS, like the one used in
this study, are checked for consistency in slope and often smoothed. This process can
remove naturally occurring high frequency terrain variability (Hodgson et al. 2003).

land cover may also play a role in the accuracy of both data sources for a few
different reasons. First, terrain is generally more varied and rugged on steeper
mountain- and hillsides, making point estimation more difﬁcult, which leads to error
in the interpolated elevation surface. This error then propagates in the derivative
slope calculations. Second, larger errors are expected in forested terrain due to a
lower posting density. For example, in the lidar data set, many of the returns (2-
values) that would be present on barren land would be removed because they hit the
canopy, and if not they would remain in the dataset. In USGS DEMs, a dense forest
cover makes stereo-correlation more difﬁcult due to the lack of clearly deﬁned
features such as roads and buildings, resulting in fewer or less accurate elevation
measures (Bolstad and Stowe 1994). Land cover patterns in the study area may also
play a role, as some of the oldest and largest dunes tend to be forested, while many of
the younger, smaller dunes are colonized by dune grass if at all. While collecting
ﬁeld measurements, land cover was documented at each site and any attenuating
conditions such as nearby elevated roadways that could affect the accuracy of
elevation or slope measures were noted for further analysis.

It is known that DEM errors generally exhibit a distinct spatial distribution or

pattern, and in most cases are not random (Fisher 1998; Liu and Jezek 1999;

69

Shortridge 2003; Pfeifer et al. 2004). Given that errors are systematic and inﬂuenced
by patterns of land cover, elevation, and gradient, it may be possible to determine
actual slope if land cover, elevation, and calculated slope are known variables.
Based on the source of the data, either lidar or NED, the elevation and slope
data will be used to construct separate models. Further, from each of these sources
slope was calculated in two different ways, the Horn algorithm and maximum
gradient. The result being two models (lidar and NED) with four potential
independent variables for each model: elevation, Horn slope, maximum gradient
slope, and land cover. All of the independent variables in the model were obtained
by remote sensing, reducing the time and cost of data collection and with the
exception of lidar data, each dataset is available at present in a digital format to all
potential users. In the near future it is highly probable that lidar elevation data will
also be widely available to users. The following sections outline the steps taken to
obtain and, where necessary, modify the source data of the independent variables

used in the multiple regression models.

Lidar Elevation Data

The lidar point data was collected and processed in April of 2001 by Woolpert
LLP, a private ﬁrm that specializes in the collection of spatial data, for distribution by
the Detroit District, USACE. In its raw form, the data was three individual text ﬁles

in an x,y,z format with a documented horizontal accuracy between 1 and 2 meters

70

and a vertical accuracy of approximately 15 cm, suitable for use in applications that
require bare-earth elevation measures (lidar F GDC metadata). The data was
converted from the text ﬁle tables to point shapeﬁles in Arc Toolbox and merged into
one ﬁle in Arc Map. It was then reprojected from the Universal Transverse Mercator
(UTM) projection into the Michigan GeoRef projection based on the North American
Datum of 1983 (NAD83).

In contrast to the 30.meter NED data, which comes in the appropriate format
(raster grid) for calculating terrain derivatives such as slope, the lidar data are a cloud
of irregularly spaced points and interpolation is required to create a continuous
elevation surface (Lloyd and Atkinson 2002 ; Barber and Shortridge 2004).
Interpolating to create a grid involves the selection and use of an interpolation
algorithm. Given a set of discrete points, the most appropriate spatial interpolation
algorithm will be the one that best represents the known values and is able to predict
the elevation values where they are unknown (Lam 1983). For this study I selected
inverse distance weighting (IDW'). It is a relatively simple approach that has been
shown to result in minimal error in the interpolated surface (Lloyd and Atkinson
2002; Rosso et al. 2003; Barber and Shortridge 2004). The formula used to interpolate

the value at an unsampled location is expressed as:

1 zwdz.
a, Wd = — . =_I_I.
’ d" M Z zwd

71

The ﬁrst equation, a., is used to calculate the weight given to each known
point where wd is the weighting factor applied to the known value, dis the distance
from the known value to the unknown value, and k is a user-selected power factor.
Equation b. uses Wd to determine the value of the interpolated point, where Z is the
known value and Z is the value of the interpolated point.

IDW is an exact interpolator, meaning that all known elevation values remain
in the output surface (Lam 1983; Shortridge 2004b). The IDW equation requires that
the user select two variables: I: and n. The variable denoted k is equal to the power of
the weight as a function of distance and the variable 11 is equal to the number of
nearby known elevation values that will be used to compute the unknown elevation
at the center of a grid cell. As the value of 1: increases, the inﬂuence of nearby points
also increases and that of distant points decreases. likewise, as the number of
neighbors increases, the resulting elevation surface becomes smoother or less variable.
Both 11 and I: have a large impact on the output surface and therefore each must be
chosen carefully. Cross validation was used to determine the power and number of
neighbors that would minimize the RMSE in the interpolated grid (Figure 4-4; Lloyd
and Atkinson 2002; Shortridge 2004b). In essence, the error introduced during the
interpolation process can be ascertained using only the dataset. This method is
favorable when working with a data source for which no other available dataset is

known to be more accurate (Shortridge 2004a).

72

 

 

Cross Validation

Original Surface
0 O O
0 Process Point' 0 °
1 as
0 El 0 __. Rmegﬁown _. o o . Surfaceoislnterpo. lated(without
o / Interpolation o pl'oocssmg pomt) using IDW
O 0

Processing Point (2 = 205.5)

Error Equals the difference in the 0
original point and the interpo- ‘—_—" E] °
Isted value (2055—2062 = -0.7) o /

0

Estimates Value at location of Removed
Processing point

lnterpolated Point (2 = 206.2)

 

Figure 4—4 Schematic illustrating the cross validation process.

 

In order to use the cross validation algorithm, a representative sample of the

dataset had to be selected due to limitations on computing power and time. A sample

of 20,000 points was selected based upon a comparison of maximum elevation,

minimum elevation, mean elevation, and standard deviation across the point sets

(Table 4—1). The points selected depict a small, but representative area of the 400,000

total data points.

Next, using an R—GUI (Chambers 1991) source code written by Shortridge

(2004a), I created a matrix in which the x—axis represents the power and the y—axis the

number of neighbors used by the IDW algorithm. In R-GUI statistical software, I ran

the code on the subset of points using a sequence of powers from .05 to 4.05, in

73

increments of .50, and a sequence of neighbors from 1 to 10. The output was a 9 x 10
matrix of values equal to the RMSE of each combination. In this case, the resulting
matrix showed that using a power of 3.05 and 9 neighbors would minimize the

combined RMSE in the surface interpolated with IDW (RMSE = 39.2 cm).

Table +1 A Comparison of the descriptive statistics for the point
subset to those ofthe complete dataset.

 

 

 

 

 

 

 

 

 

 

Subset Dataset
No. ofcases 25,107 334,861
Range 175.7—232.8 m 1783-2328 In
Mean 190.86 In 194.57 In
Standard Dev. 9.04 m 10.43 m
Variance 81.78 m 108.79 In

 

In addition to the weight and number of neighbors, interpolation also requires
the user to select the appropriate cell resolution of the output raster grid. As with the
interpolation method, the level of error in a surface can vary greatly with different
grid sizes (Smith et al. 2003). I employed a second code written by Shortridge
(2004a) in R— GUI (Chambers 1991) to compute the nearest neighbor statistics of the
point subset. This enabled me to determine an appropriate cell size based on the
frequency interval of each data point within the representative sample. The results of
the nearest neighbor operation showed that the distance between the points ranged
from .326 m to 10.73 m, with a mean spacing of 1.85 m. Smith et al. (2003) suggest

that the optimal resolution for minimizing error is that which is closest to the original

74

point spacing. Therefore, based on the nearest neighbor statistics and data presented
in that study as well as data storage and computation requirements, I selected a 2 x 2
m cell resolution.

The ﬁnal interpolation from a point shape ﬁle to a raster grid was performed in
Arc Map and the three individual grids were combined using the merge command in
Arc Info. Figure 4—5 shows the steps taken to process the lidar data beginning at data

collection and ending with the creation of the slope grids.

 

 

 

 

  
 

 

 

 

 

 

 

 

 

 

 

[Durham
L
f
Automatic
4 Stratiﬁcation of
[: UdarData ]<Kﬁrsttolastreurmsj
Collection r l x
( Filtering of lag
Returns for
“Bare Earth"
L
Horn Max.
§.Algonthm ..Gradlent
”...... [aw] [ WW]
Collection and Processing

 

 

 

 

 

Fignre4-5Flowchmﬂlusuaﬁngthestepsmkentocreatethelidarvariables.

75

30-meter National Elevation Data

The 30-meter elevation data was collected by the USGS EROS Data Center and
originally came from the USGS NED website. It is classiﬁed as a level 2 dataset, .
comprised of the best available elevation data (7.5 minute resolution). The data,
which is available for all Michigan counties on the Michigan Center for Geographic
Information (MICGI) website, underwent post-processing at MSU’s RS&GIS for use in
their proprietary mapping software, Michigan Maplmage Viewer. Processing steps
included clipping the dataset to match the extent of Michigan counties, merging the
county data to create a statewide mosaic, and projecting the data in the Michigan
GeoRef projection, NAD83 datum. After processing, the most recent publication date
for the data is 2002.

Although the use of NED is widespread, one big disadvantage of using pre-
processed DEMs is that, in general, little information is provided to the end user in
terms of data collection, processing, and error distribution (Holmes et al. 2000). It is
known from the metadata that the DEM used in this study was produced using
manual proﬁling of photogrammetric stereomodels, derived from either digitized
cartographic map contour overlays or scanned National Aerial Photography Program
(NAPP) photographs. No estimate of accuracy is given apart from the USGS level 2
global accuracy standard of one half of the contour interval of the source DEM, which

could not be found (Berrien County —NED FGDC metadata). A spot check of vertical

76

accuracy at the 46 points sampled using a Trimble Pro XRS GPS unit revealed that,
while the lidar dataset fell within its reported accuracy range, the error in the NED
DEM was much higher than what is expected even in a level 1 DEM (Table 4-3).
Overall, the NED elevation values at these points consistently overestimated the
elevation by more than 10 m compared to both the GPS data and the lidar data.
Based on the production method and the terrain, there are several possible reasons
why the DEM error is larger than expected. These reasons, as well as the implications
for the derivative slope values, will be discussed further in the following chapter.

The decision was made to use NED as the primary source of 30-meter
elevation data over elevation data collected more recently (2001) by the Shuttle Radar
Topography Mission (SRTM). For the end user, there are potential beneﬁts of using
SRTM data including its newness (although NED employs the “best available” data
upon upgrades), an increase in vertical accuracy, and one common collection method
(Gesch et al. 2001). However, one of the objectives of this research is investigate the
relationship between land cover and two different collection methods and while
SRTM technology is different than that of lidar, the reﬂection of the SRTM radar
signal off of a tree canopy is reminiscent of the reﬂection of the lidar laser. Further,
the systems used for lidar and SRTM data collection, ALS and Synthetic Aperture
Radar (SAR), are complimentary to one another when used in conjunction (Sun et al.

2003).

77

Radar (SAR), are complimentary to one another when used in conjunction (Sun et a1.

 

 

 

 

 

 

2003).
Table 4—2 Descriptive statistics ofthe elevation datasets
Elevation Lidar NED
Elevation Elevation

Minimum 176.87 In 177.74 111 189.38 m
Maximum 218.16 in 213.81 in 221.71 in
Mean 192.15 111 191.44 in 206.55 m
Standard Dev. 9.45 m 8.48 m 7.47 m
Variance 89.28 71.97 55.80

 

 

 

 

 

Table 4-3 Error statistics of the lidar and NED datasets

 

 

 

 

 

 

 

 

Lidar NED
Elevation (m) Elevation (m)
RMSE 1.66 m 17.91 m
MAE 1.18 m 15.09 m
MAX 5.43 m 36.75 m
MIN 2.7 cm 35.4 cm

 

 

Creating the lidar and NED Slope Grids

 

On a natural landscape, slope is commonly measured in the direction of the
maximum perceived elevation gradient. In contrast to calculating slope in nature,
however, modeling slope using a digital raster model is a bit more complicated. The
direction of the steepest slope on a landscape and the straight line slope between grid
cell centers most often do not match up. The fastest and simplest approach in Arc

Info determines the maximum change in elevation between the processing cell and its

78

eight surrounding neighbors, and divides this difference by the distance between the
centers of the two cells (Shortridge 2003). The maximum gradient approach is not
commonly used in applications that require slope measures because it is sensitive to
error, creates a rough surface, and generally achieves poorer results than alternate
methods.

In this study, the slope values for both elevation surfaces were calculated using
both maximum gradient, the drop option when using the ﬂowdirection command in
Arc Info, and the Horn algorithm or slope command in Are Info. The Horn algorithm
calculates slope as the average change in elevation from north to south (rise) and east
to west (rise), divided by the distance between cell centers in a 3 x 3 cell
neighborhood (Figure 4-6). Although other methods of calculating slope exist, studies
have shown that using a third-order ﬁnite difference approach like the Horn
algorithm is best in variable terrain (Bolstad 2002). The output is a grid of slope
values measured as percent slope (the unit used by the MDEQ) where values can
range from 0 where elevation is constant across all cells, to values that approach
inﬁnity (or 90°). At 100% slope, the rise is equal to the run and the angle of
inclination is 45°. Values measured as a percent do not have a linear relationship and
a difference in values may not accurately depict the difference in on the ground slope,

likewise, a difference in 1% does not equal a 1° change in gradient (Bolstad 2002).

79

 

 

A B c M ,Ax=(Z..+2-Z.+Z,>—(Z.+2-Z,+z,-)

 

 

 

 

x 8-cellraduiim
D E F Z +22 +2 — Z +2-Z +Z.
AZy/Ay=( 8 b C) ( g b I)

8-oellimohtim

 

 

 

 

 

QMW/o= J(Az, /AX)2 +(Az, /Ay)2

 

e Azx is the change in elevation in the x direction
0 AZ), is the change in elevation in the y direction

0 AX is the distance in the x direction (8-cell resolution)
a A}; is the distance in the y direction (8-cell resolution)

 

 

 

Figure4-61nthisiﬂustrationoftheHomA1gorithm,slopeforthecenterceﬂ
EiscomputedfromthesurroundingeightcellslabeledA,B,C,D,F,G,H
andI.

In one ﬁnal processing step, the values of the two slope grids were rounded to
the nearest whole percent. This step reduces the precision of values; however, whole
values are more comparable to those obtained in the ﬁeld (also measured to the
nearest whole percent). The descriptive statistics of each slope dataset at the 46
sample points, including the measures collected in the ﬁeld and those calculated from
the DEMs, are shown in Table 4-4. Table 4-5 presents the error statistics of each of
the digital slope datasets compared to the actual slope measurements obtained in the

ﬁeld.

80

Table 4—4 Descriptive statistics of the slope datasetsl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sl lidar NED lidar NED
ope Slope Slope Drop Drop
Minimum 0 1% 2% 1% 17%
Maximum 79% 87% 36% 45% 67%
Mean 30.5% 29.3% 13.2% 13.9% 30.7%
Standard Dev. 21.6% 19.3% 7.8% 9.1% 13.9%
Variance 464.6 372.5 61.5 82.8 193.3
Table 4—5 Error statistics of the slo datasets
Lidar Slope NED Slope lidar Drop NED Drop
RMSE 14.9% 27.8% 16.2% 27.2%
MAE 9.9% 21.6% 12.4% 21.8%
MAX 44% -67% 42% -69%
MIN 1% 0 0% 0
Land Cover Data

 

As previously mentioned, many studies (Lefsky et al. 2002; Rosso et al. 2003;
Chasmer et al. 2004) have examined the presence of vegetation in the return signal
and resultant dataset of an ALS. In some instances the goal may be to measure
biomass (Lefsky et al. 2002) or map vegetation (Rosso et al. 2003), and therefore bare-
earth returns are not desirable. In other applications, however, particularly those that

require accurate elevation measures, such as surface hydrology, landform, or slope

 

‘ The second column, labeled “slope”, is the dependent variable in the subsequent models, while the
remaining four columns represent the independent slope variables.

81

mapping, bare-earth returns are necessary and feature removal is key (Bowen and
Waltermire 2002; Woolard and Colby 2002; French 2003; Barber and Shortridge
2004). In either case it is clear that the presence or absence of vegetation may
interfere with the collection of lidar data, inﬂuencing the accuracy of both elevation
and derivative slope values, and to some degree affect USGS level 2 DEMs as well.
For this reason I included land-cover, more speciﬁcally a categorical dummy variable
for presence (1) or absence (0) of forest cover, as a possible variable in the multiple
regression model Although herbaceous or understory vegetation can also intercept
the laser signal, lower vegetation tends to have a much smaller standard deviation of
height than trees and, therefore, these types of ground covers are less likely to
inﬂuence slope measurements (Pfeifer et al. 2004). likewise, it does not interfere
with stereo-correlation or affect the posting density of Level 2 elevation measures.
The land cover data used in this study was adapted from the USGS National
Land Cover Data (NLCD 1992) set. It uses a 21-class classiﬁcation scheme and was
derived from the early to mid-19908 Landsat Thematic Mapper satellite data. It is
freely available from the USGS as a 30-meter raster data set for the conterminous
United States (NLCD F GDC metadata). The NLCD for the state of Michigan is also
available from the MICGI. It is essentially the same data except that it has been
repackaged for each county as a shape ﬁle projected in the MI GeoRef projection,

NAD83.

82

I reclassiﬁed the original land cover classes of the study area, which included
Barren (31), Forested Upland (41, 42), Shrub land (51), Herbaceous Upland
Natural/Semi-natural Vegetation (71), Herbaceous Planted/Cultivated (81, 82), and
Wetlands (91, 92), into the forest (1)/non—forest (0) variable for the purposes of this
study. Forested Upland (41, 42) and Wetlands (91 Woody Wetlands) were
reclassiﬁed as forest while all other classes were considered non-forest (Figure 4—8).
Table 4-6 is a land cover confusion matrix that summarizes how often the
classiﬁcations of the NLCD dataset correctly matched those observed in the ﬁeld.
The overall accuracy of the dataset, as noted in the table, is 85%, which means that of
those 46 sites sampled, 39 sites were correctly classiﬁed as forest/non—forest by the
NLCD. Also noted in the table is the number of sites that have a canopy (28),

compared to those without (18).

 

 

 

   

a. b.

Figure 4-8 Photographs showing two land cover types found on Lake Michigan sand dunes. Photo a. is
an .mple of the Herbaceous Upland Natural/Semi-natural Vegetation (71) land cover class, which
would be reclassiﬁed as non-forest in contrast to photo b. an example of Forested Upland (41. 42).

83

Table 4—6 Confusion matrix comparing ground truth land cover (observed)
classifications to the N LCD (expected) classifications.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed Class

Forest Non-forest Row Total
5 Forest 25 4 29
E Non-forest 3 l4 l7
Column Total 28 18 46

Producer Accuracy 89% 78%

User Accuracy 86% 82%

Overall Accuracy 85%
Overview of Multiple Regression

Multiple regression is a statistical method designed in most cases to either
predict or explain a variable of interest in order to reach one of two research goals,
either: 1) to make valid projections concerning an outcome (prediction), or 2) to make
an attempt to understand a phenomenon by examining a variable’s correlates on a
group level (explanation; Osborne 2000). The aim of this study is to predict an actual
or true slope measurement based on variables that can be obtained from or calculated
in a GIS. In order to do this, a multiple regression model was constructed in SYSTAT
statistical software package to predict the dependant variable (Y ), in this case actual

slope, based on the value of at least one independent variable (X l ,. . . , X n ).

84

The multiple regression equation takes the form of:
n
Y]. =a+2f b1. oXI. +8
1:

Where,

' Y] is the value of the dependent variable;

° a is the constant or intercept;

' b). is the standardized regression coefﬁcient for Xi;

’ X1. is the independent variable (accounting for the variance in Y ); and
' 8 is the error, resulting from the effect of unspeciﬁed independent

variables and/or a totally random element.

Assumptions of Multiple Regression

In order to achieve reliable results with a regression model, Poole and
O’Farrell (1971) state that six “critical assumptions” must be met. Of these six
assumptions, they note, any one can be either more or less important depending on
the research purpose. While it is not essential to meet the assumptions of
measurement error and multicollinearity, when the research goal is prediction, the
authors say that it is most important that: 1) The relationships between Y, and each

of the independent variables X I. are linear; 2) the variance of the conditional

distribution of 8 is constant for all such distributions (homoscedastic); and 3) the

values of 8 are not autocorrelated (Poole and O'Farrell 1971).

85

If the relationship between the dependent and independent variable(s) is non-
linear, it is likely that the regression equation will not correctly estimate the
relationship between variables. A graph of each independent variable plotted against
the dependent variable can indicate whether or not the relationship is linear. It is
also important to plot the standardized residuals to identify extreme
heteroscedasticity, which can distort ﬁndings and seriously weaken the analysis

(Osborne and Waters 2002).

86

V. RESULTS AND DISCUSSION

This chapter will begin with a discussion of the independent variables as they
relate to the assumptions of regression. Next, I will present the summary statistics
for each model, which will determine if my hypothesis is correct, followed by an
analysis of the residuals. I will then conclude the chapter with a discussion of the
results, including the error in the best model.

As ﬁrst noted in the previous chapter, the variables used in a multiple
regression model need to meet certain key assumptions for the results to be reliable.
Again, when the research goal is prediction the most important assumptions are: 1)

the relationships between Y, and each of the independent variables X I. are linear; 2)

the variance of the conditional distribution of 8 is constant for all such distributions
(homoscedastic); and 3) the values of 8 are not autocorrelated (Poole and O'Farrell
1971). Of these three, only the ﬁrst assumption can be tested prior to generating the
model. To do this I plotted each of the independent variables including calculated
slope (LDSLOPE, NDSLOPE, LDDROP, and NDDROP) and elevation (LDELEV and

NDELEV), against the dependent variable true slope (FDSLOPE). Figures 5-1 and 5-2
show a regression line superimposed on scatterplots of LDSLOPE and FDSLOPE and

NDSLOPE and FDSLOPE. The remainder of the graphs can be seen in Appendix A.

87

FDSLOPE

FDSLOPE

 

O
H
O
N
O
8

40 50 60 70 80 90
LDSLOPE

Figure 5-1 Graph showing LDSLOPE plotted against FDSLOPE. With the exception of a
few outlying points, LDSLOPE exhibits a linear relationship with FDSLOPE.

 

0 10

20 30 40 50

N DS LOPE
Figure 5—2 Graph of NDSLOPE plotted against FDSLOPE. The relationship depicted in this
graph is not linear and therefore the NDSLOPE data does not meet the first ass-uption.

When plotted with the dependent variable, only LDSLOPE and LDELEV
displayed a linear relationship with FDSLOPE. A comparison of the LDSLOPE graph
to the NDSLOPE graph in Figures 5-1 and 52 illustrates the very different
relationship each has with the dependent variable. If the relationship between the
dependent and independent variable(s) is non-linear, it is likely that the regression
equation will not correctly estimate the actual relationship between variables (Poole
and O'Farrell 1971). In some cases a data transformation can correct this issue. I
performed a log transformation on the FDSLOPE, NDSLOPE, and NDELEVATION
data sets, yet their respective relationships remained non-linear. Similar data issues

arose with the LDDROP and NDDROP datasets’.

Univariate Regression

Testing the ﬁrst assumption ruled out all potential regression models with the
exception of those that employ lidar slope (LDSLOPE), lidar elevation (LDELEV), and
the dummy variable, land cover (NLCD_92). Since the independent variable slope is
used to estimate the actual slope at a location on the ground, the ﬁrst thing I did was

regress the dependent variable true slope (FDSLOPE) against the independent slope

 

2 Both slope datasets were calculated using the maximum gradient This method determines the maximum
change in elevation between the processing cell and its eight surrounding neighbors and divides that
difference by the distance between the centers of the two cells. Using a raster grid, the distance is
always the same, so unless there are extreme elevation diﬂerences across cells and throughout the
dataset, the result is a limited number of slope measurements.

89

variable (LDSLOPE). The summary statistics of the univariate analysis are shown in

Table 5-1 .

Table 5—1 Summary statistics of the univariate reggssion model.

 

 

 

 

 

 

Variable Constant (a) (13:18!“ t—value P (l-tail) Adj. R2
LDSLOPE 6.476 0.822 1.621 0.000 0.530

 

 

 

 

The R72 value is an indicator of how well the model ﬁts the data (e.g., R2 close
to 1.0 indicates that the model accounts for nearly all of the variance in the
independent variables). The adjusted R2 is a good statistic to summarize the ﬁt of the
regression model because it corrects for the number of coefﬁcients and sample size, as
well as a small degree of error, to more closely ﬁt the model estimated from a sample
to the entire population (Wilkinson et al. 1996). The univariate model in this study

produced an adjusted R2 of .530, or 53%.

Multivariate Regression

My initial hypothesis was that lidar elevation data used in conjunction with
calculated slope and land cover would more accurately predict true slope than the
same model that used NED as its source. Since the NED data did not meet the

assumption of a linear relationship it may not yield a reliable model; however, I

90

decided to proceed with the NED data for the sole purpose of comparing the two
models and evaluating my hypothesis. In the second phase of my analysis, I
performed a standard multivariate analysis regressing true slope against, elevation,
calculated slope, and land cover for each data source. The regression equation for

both the lidar and NED models can be stated as:

Y FDSLOPE = a + bISLOPE + szLEV + b3NLCD_92

The summary statistics of these models are presented in Table 5-2 and 5-3. The
adjusted R2 for the lidar model is equal to .595, meaning that slope, elevation, and
land cover account for 59.5% of the variation in true slope, compared to only 14.2%
for the NED model. Tolerance values for all variables are above .60, which indicates
that there is little co-linearity among the variables.

In both the lidar and NED models, land cover was not a signiﬁcant variable in
the equation at the 95% conﬁdence level; therefore I removed this variable and
generated the models again using only slope and elevation. Again, the NED model
yielded poor results, with an adjusted R2 value of .127. Further, NDSLOPE was not
found to be a signiﬁcant variable. Of the three models presented, the best model for
predicting true slope was one that used LDSLOPE and LDELEV, with an adjusted R2

value of .603 (Table 5-4).

91

Tables-2 Summarymdsﬁaofthemulﬁvaﬂateregradonmoddemployingﬁdarwurcedammd
slope, elevation, and land cover as independent variables.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dep Var: F DSLOPE N: 46
Muﬁple R: 0.789 Squared multiple R: .622
Adjusted squared multiple R: 0.595 Standard error of estimate: 13.713
Variable “‘3?” Std Error 3 SE? , t Tolerance T P (l-Tail)
CONSTANT -146.229 51.206 0 . -2.856 0.004
LDSLOPE 0.688 0.1 16 0.616 0.829 5.916 0.000
LDELEV 0.824 0.277 0.325 0.754 2.972 0.003
NLCD_92 -1.967 4.567 -0.045 0.841 —0.431 0.335
Analysis ofVariance
Source Ssum-of- Df :13 F-ratio P
Mession 13007 .548 3 4335.849 23.058 0.000
Residual 7897.865 42 188.044

 

Table 5-3 Summary statistics of the multivariate regression model employing NED source data, and

slope, elevation, and land cover as independent variables.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dep Var: FDSLOPE N: 46
Multiple R: 0.446 Squared multiple R: 0.199
Adjusted squared multiple R: 0.142 Standard error of estimate: 19.969
Variable Coeﬂicient Std Error Std: Tolerance T P (1 -Tail)
Coefﬁcient
CONSTANT -137.914 83.139 0.000 0.000 —1.659 0.053
NDSLOPE 0.696 0.382 0.253 0.986 1.822 0.038
NDELEV 0.746 0.407 0.259 0.958 1.833 0.037
NLCD_92 8.096 6.191 0.183 0.971 1.308 0.099
Analysis of Variance
Source siu‘Mf’ Df :23; F-ratio P
Mession 4157.208 3 1385.736 3.475 0.024

Residual 16748.205 42 398.767

 

92

 

 

 

Table 5-4 Summary statistics ofthe multivariate regression model employing lidar source data. and
slope and elevation as independent variables.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dep Var: FDSLOPE N: 46
Multiple R: 0.788 Squared multiple R: 0.621
Adjusted squared multiple R: 0.603 Standard error of estimate: 13.582
Variable Coeﬁcient Std Error Std' Tolerance T P (1 —Tail)
Coeﬁcient
CONSTANT -139.989 48.645 0.000 . —2.878 01116
LDSLOPE 0.682 0.1 14 0.61 1 0.840 5.963 0.000
LDELEV 0.786 0.260 0.309 0.840 3.019 0.1112
Analysis of Variance
Sum-of— Mean-
Source Df F-ratio P
Squares Square
Regression 12972.676 2 6486.338 35.16 0.000
Residual 7932.737 43 184.482

 

Table 5-5 Summary statistics of the multivariate regression model employing NED source data, and
slope and elevation as independent variables.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dep Var: FDSLOPE N: 46
Multiple R: 0.788 multiple R: 0.621
Adjusted squared multiple R: 0.603 Standard error of estimate: 13.582
Variable Coefﬁcient Std Error Std' Tolerance T P (1-Tail)
Coeﬁcient
CONSTANT -151 .446 83.170 0.000 . -1 .821 0.076
LDSLOPE .701 0.385 0.255 0.986 1.820 0.076
LDELEV .836 0.405 0.290 0.986 2.067 0.045
Analysis of Variance
Sum-of- Mean-
Source Df F—ratio P
Squares Square
Regression 3475.422 2 1737.71 1 4.287 0.020
Residual 17429.991 43 405.349

 

 

 

 

 

 

 

93

 

 

Analysis of the Residuals

The section above provided an assessment of each model based on key
statistics such as the adjusted R2. These numbers are useful for model validation, but
it is also important to employ graphical methods. Graphical methods have one
advantage over numerical methods in that they are able to show the relationship
between the model and the data. A graph of the residuals can also uncover trends in
the data that are not apparent in the statistical output (NTST/SEMATECH e-
Handbook of Statistical Methods 2006). Further, the last two critical assumptions, the
variance of the conditional distribution of 8 is homoscedastic and the values of 8 are
not autocorrelated, rely solely on the residual values.

If the model’s ﬁt to the data is correct, the residuals should approximate the
random errors that make the relationship between the explanatory variables and the
response variable a statistical relationship. Therefore, if the residuals appear to behave
randomly, it suggests that the model ﬁts the data well. A scattergram of the
regression residuals plotted against the regression estimates is shown in Figure 5-3.
While there are several outlier cases, the residuals appear to be homoscedastic, which
means the variance of the error values does not appear to be related to the size of the
estimate. Graphs of the residuals plotted against each independent variable can also
reveal patterns of heteroscedasticity. An examination of these two plots also revealed

no obvious patterns (Appendix C).

94

501

20—

101 Q '

Resrdual
o
l

O
0
O
O
O
O

\
O
O

-10 - o . ° ,0 0 °
-20 _
—30 ~ ' °
-40 _
-50 lmm

0 15 30 45 60 75 90

 

 

Estimate

Figure 5-3 Graph showing the regression estimates plotted against the residuals.

The regression output can indicate if there are any outliers including large
residuals, high leverage points, and inﬂuential points, all of which can distort the
regression model. The studentized residuals, leverage, and Cook’s distance are three
statistics that can identify if any of these problems are present in the data. In general,
95% of the studentized residuals should fall between 1 2, and 99% between :t3
(Wilkinson et al. 1996). There were ﬁve points that fell outside of this range. An
examination of the Cook’s D statistic showed one case that was inﬂuential at the 95%
level (compared to an F—distribution), while there were no cases that had unusually

high leverage (Figure 5—4).

95

90 1V" __ ,v,,,,,

 

 

 

FDSLOPE

 

 

100

LDSLOPE

Figure 5-4 Graph showing the independent variable LDSLOPE plotted against the dependent variable
FDSLOPEwithoutliercaseshighlighted. Theredpoints notewesthathavealarge studentized
residuaLwiththelargerredpointindicatingtheeasethatalsohasalargeinﬂnence.

Discussion

The ﬁrst conclusion that can be drawn from the results of this research is that
the NED level 2 DEM for the study area is not ﬁt for use in applications that require
accurate slope measurements. While the sampling method used to collect the ﬁeld
slope measurements was more comparable to the resolution of the lidar data, it is still
reasonable to expect that the relationship between the two datasets, which represent

the same variable, to be linear with a fairly strong positive relationship. A graph of

F DSLOPE and NDSLOPE showed that this was not the case3.

 

3 The Pearson correlation coefﬁcient further conﬁrmed the lack of a positive linear relationship
between the two variables.

96

There is a large difference in the resolution of the lidar data (2 m) versus the
NED data (30 m) and in a study comparing lidar data to NED, Barber and Shortridge
(2005) found that slope in particular is more affected by resolution and less affected
by source. To test this theory on my data, I resampled the NED dataset to a ﬁner
resolution (5 m), calculated the slope variables, and plotted the resampled NED slope
variable against true slope to see if there were any obvious improvements. An
examination of the resampled NED data and the new graph (Appendix B) showed no
improvement whatsoever, nor did the models that employed this data. This leads me
to conclude that the resolution of this dataset is inherently tied to its source and,
therefore, the source of the data, in this case, is as important as the resolution.

Although some researchers (Holmes et al. 2000; Gesch et al. 2002) have found
USGS Level 2 DEMs to be generally accurate, the elevation measures used in this
research on average were in error by more than 10 m. Compounding this problem,
the error that exists in the elevation surface typically propagates in derivative
measures such as slope (Holmes et al. 2000). While I cannot determine why the NED
data was of such poor quality or conclude anything about the overall accuracy of the
entire DEM, terrain attributes within the study area (i.e. slope and land cover), and
the resolution (posting density) of the source data may account for the lack of
correlation between FDSLOPE and NDSLOPE.

Research has found that USGS Level 2 production methods can be hampered
when the ground is under a forest canopy. A dense forest makes stereo—correlation

97

more difﬁcult due to the lack of clearly deﬁned features such as roads and buildings
and when using photogrammetric techniques, fewer postings are collected in forested
areas (Bolstad and Stowe 1994; Lefsky et al. 2002). A positive correlation has been
shown between true elevation and elevation errors and true slope and slope errors‘.
Areas with the steepest terrain are often times forested, which further compounds
this issue (Bolstad and Stowe 1994).

One ﬁnal problem is post-processing. If interpolation has been used to
calculate elevation values, it tends to smooth microtopography and this could be the
reason why such large slope errors are associated with more variable terrain. Most of
the sample points were collected on the sides of dunes and point estimation in these
areas is very difﬁcult. Again, this leads to error in the interpolated elevation surface,
which then propagates itself in the derivative slope (Bolstad and Stowe 1994).

The results of the regression analysis showed that the best model for
predicting true slope employs slope (calculated using the Horn algorithms) and
elevation. The land cover dummy variable was found to be insigniﬁcant and did not
improve the model. I found this surprising because larger errors are expected in
forested terrain due to a lower posting density. Many of the returns that would be
present on barren land would be removed from forested areas because they hit the

canopy and if not, they would remain in the dataset (Bolstad and Stowe 1994).

 

‘ The Pearson correlation coefﬁcient for FDSLOPE and slope error indicated a very strong positive
correlation between the two variables. I found a strong negative correlation between elevation error and
true elevation, indicating that as elevation increased, error decreased.

5 For a review of the Horn Algorithm, see chapter IV.

98

In this particular data set, it is probable that post-processing was successful in
removing man-made obstructions from the data set, similar to ﬁndings made by
Barber and Shortridge (2005). When you consider the collection method, a lower
posting density for lidar is still much greater than that of NED. So while similar
issues with terrain attributes and error persist in lidar data, the collection method
(source), posting density (resolution), and post-processing of the raw data points could
explain why land cover was not a signiﬁcant variable as well as the difference
between lidar and NED.

The second point to address is why LDELEV was a signiﬁcant variable and
improved the equation. Research has found that both elevation error and modeled
slope error increase when slopes on the ground are steeper, suggesting that there is a
connection between true slope and elevation (Chang and Tsai 1991; Bolstad and
Stowe 1994; Hodgson et al. 2003). Further establishing that relationship, both
FDSLOPE and absolute slope error (equal to |FDSLOPE - LDSLOPEI) were strongly
correlated with LDELEV at the 99% conﬁdence level. This means that steeper slopes
are associated with higher elevations in the study area and the difference between
FDSLOPE and LDSLOPE is at least in part explained by LDELEV, as the regression
equation would suggest. Although I found that land cover did not have an impact on
the model, based on past research it still may be reasonable to expect that certain land
cover attributes are associated with increase in error in the digital data sets. Forest is

the dominant land cover on many of the highest and most well established dunes,

99

which could explain the positive linear relationship between elevation and error in
the 'slope dataset.

One ﬁnal point to address is the problems that could arise by using elevation
and one of its derivatives, slope, in the same model. Slope, as discussed in the methods
section, is calculated as the average change in elevation from north to south and east
to west, across a nine cell neighborhood. Although the tolerance statistics of the
model that used LDSLOPE and LDELEV indicated that there was not a statistical
relationship between the two variables, they certainly are interdependent. When two
variables are collinear, or providing the same information to the regression equation,
the standard errors may be inﬂated and, therefore, the estimated coefﬁcients may not
be representative of the population coefﬁcients Wilkinson et al. 1996).

Conceptually speaking, slope, as it is calculated, is dependent on the difference
in elevation values, not the actual elevation values. For example, the gradient from 10
m to 12 In over a distance of l m and the gradient from 100 m to 102 m over a
distance of l m are the same; however, the elevation at each of those points is very
different. Aside from the model’s tolerance values, there is no way to know if the
relationship between elevation and slope has affected the model apart from

conducting further research from the same population.

100

Discussion of Model Error

Like graphical methods, analysis of the error terms including describing,
classifying, and mapping the residuals, can uncover trends in the data. The error in
remotely sensed data sets and models derived from them is as important, if not more
important, than the data itself, which is made evident by previous research (Chang
and Tsai 1991; Bolstad and Stowe 1994; Fisher 1998; Liu and Jezek 1999; Holmes et al.
2000; Lefsky et al. 2002; Woolard and Colby 2002; Hodgson et al. 2003; Rosso et al.
2003; Sallenger et al. 2003; White and Wang 2003; Nagihara et al. 2004). Key
statistics of the model’s error values are found in Table 5-6 shown below. While some
error values were very high, the RMSE for the model was 13% with over half of the
residuals below 7%. As noted in the previous chapter, values measured as a percent
do not have a linear relationship and a difference in values may not accurately depict
the difference in on the ground slope, likewise, a difference in 1% does not equal 3 1°
change in gradient (Bolstad 2002). Consequently it is difﬁcult to quantify the error

terms“.

Table 5-6 Model error statistics
Minimum Maximum Mean MAE RMSE Standard Dev.

0.007 38.009 0.00 9.38 13.132 9.29

 

 

 

 

 

 

 

 

 

 

 

6 I will address this point again in the “Research Problems” section of Chapter 6.

101

Three of the ﬁve largest studentized residuals are associated with slopes

greater than 40% (Figure 5-5). This ﬁnding is similar to previous research which

found that modeled slope error increases when slopes on the ground are steeper

(Chang and Tsai 1991; Bolstad and Stowe 1994; Hodgson et al. 2003). The two

remaining outliers are found where on the ground slope is less than 5%. Collectively

these ﬁndings suggest that the model is more accurate when true slopes are moderate

and less accurate when slopes are either gentle or steep. A graph of the average root

mean square error broken down by slope class illustrates this point (Figure 5-6).

Residual

 

 

 

 

l 5 30 45 60 75 90

F DSLOPE

Figure 5-5 Graph showing FDSLOPE plotted against the residuals; points with the largest studentized
residuals are shown in red.

102

memiﬂf‘ﬁ IEMHRMIB

 

 

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16 1
a 1176 12.97
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4:
4
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0-8% 9-17% 18-25% 26-34% 35-43% >43%

Slope
Figure 545 Graph of the average RMSE by slope class.

A map of the residuals shown in Figure 5-7 revealed that several larger
residuals are clustered in the northern portion of the study area (inset a.). Here, more
than half of the points have error values that are more than one standard deviation
above the mean. However, an investigation revealed that there is no spatial
autocorrelation between the residuals here or elsewhere in the study area.

The two northernmost points were collected off of a utility access road
beneath a forest canopy. One of these points had a residual value of 27.44%, with the
model signiﬁcantly underestimating the slope of this point. The cluster of points to
the immediate south was collected in a residential area and within highly variable,
forested terrain. Given the number of houses present there, this area is perhaps the
most representative of sites inspected by the MDEQ. The mean absolute error (MAE)

in this area was 10.88%, which is slightly higher than the overall average of 9.38%.

103

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1
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b. I c.
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, 9 250 500 m 190 380 m
l e l l

 

 

 

 

 

Figure 5-7 Map showing the spatial distribution of the residuals. Points were classiﬁed by the number

of standard deviations the residual at that point fell above or below the mean. The map was broken

into three geographic extent: (a. north, b. central, and c. south) based on the proximity of the points to

one another.

104

rm mikﬁﬂilﬂmi

Three of the four largest residuals (> 3 Standard Deviations) are all located in
the same geographic extent (Figure 5-7, inset b.). Based on the surrounding points
and my ﬁeld notes, this is likely the result of site speciﬁc characteristics rather than
spatial autocorrelation. Two of the three points are located within 200 meters of one
another near Weko Beach. Of those, one was collected on a large dune bordering the
lake. The front of the dune is primarily dune grass, while the slipface is forested. The
dune is also topped by an elevated boardwalk, which runs the length of its crest. The
other point was taken just south of that dune in a deﬂation hollow, surrounded on
three sides by forest. Both points are classiﬁed by the NLCD as having a canopy, but
neither is located under a canopy. Both are also ﬂat or near ﬂat areas and lie near
steeper slopes. The three points closest to them all have slopes greater than 23%, yet
have small residuals.

The southernmost extent had the lowest overall error and only one large
residual value out of the twelve points collected there (Figure 5-7, inset c.). It is also
important to note that of those twelve points, nine were classiﬁed as bare sand and
dune grass. The one point that exceeded the mean error by more than three standard
deviations (32.02%) was collected on the side of an exceptionally steep dune
(FDSLOPE = 79%), beneath a forest canopy. In this case the lidar dataset and the
model both underestimated the slope. That being said, the estimate of a nearby point

with nearly identical slope and terrain characteristics was in error by less that 1%.

105

This indicates that the problem with the lidar dataset may be inconsistency as

opposed to terrain characteristics.

Summary

The results of my study revealed several ﬁndings that are both interesting and
relevant. The lack of a linear relationship between NDSLOPE and FDSLOPE
indicated that slope derived from the NED DEM for the study area does not
accurately depict true slope. To a degree this could be a reﬂection of the method used
in this study to collect slope measurements. However, the production method of
USGS level 2 DEMS, resolution (posting density), post-processing, and terrain
characteristics within the study area are most likely the cause of this discrepancy.

The univariate model, which employed lidar slope, and the multivariate
model, which employed lidar slope and lidar elevation, produced adjusted R2 values of
.530 and .603 respectively. While the elevation variable improved the model, the
land cover dummy variable was not found to be a signiﬁcant part of the regression
equation and therefore discarded. The strong positive correlation between elevation
and slope error is likely the reason that elevation improved the model. However,
given the collection method and past research (Bolstad and Stowe 1994; Bowen and
Waltermire 2002; Hodgson et a1. 2003), it is unclear why land cover did not account
for a greater part of the variance. I believe this is due to a superior resolution, even

when taking into account fewer postings, and successful post-processing methods.

106

Based on the studentized residuals, six points were classiﬁed as outliers. While
some of the terrain characteristics at these locations were described, the reason for
these large errors cannot be determined. It is plausible that there may be greater
inconsistencies in the lidar data based on certain terrain characteristics. It is also
interesting to note that the largest errors occurred on slopes less than 5% or greater
than 40% and on average, error was larger for these two slope classes than for any
other. Slope error is expected to increase when slopes are steeper and terrain is more
variable, but ﬁnding two of the largest errors at places on the landscape with little or

no slope is unusual.

107

VI. CONCLUSION

Collectively, the State of Michigan contains what may be the largest complex of
freshwater dunes in the world (V anOort et al. 2001; Arbogast et al. 2002). The
conditions that existed at the time these sand dunes formed were unique and led to
the development of some of the most magniﬁcent parabolic dunes. Since the early
1900’s, dune sand has been prized for its use as foundry cores in the automobile
industry. From that time on, the sand dunes found along the eastern shore of lake
Michigan have been threatened by sand mining and, in some cases, completely
destroyed by intensive mining practices (Buckler 197 9; i lake Michigan Federation
1999).

Initially it was the public’s concern over mining that led to the passing of the
Sand Dunes Protection and Management Act (Act No. 222, Public Acts of 1976), but
as human and developmental pressures increased, the act was amended to include the
critical dune designation (Lake Michigan Federation 1999; Michigan State Legislature
Acts No. 146 and 147, Public Acts of 1989). These amendments also established
standards and a permitting program for development in areas designated critical
dunes (Michigan State Legislature Acts No. 146 and 147, Public Acts of 1989). At
present, the MDEQis charged with the management and administration of critical

dune policy and employs eleven agents to implement the permitting program in

108

nearly forty counties (Warner, personal com., 2002). Today, the sand dunes that
those agents work to protect are highly valued for the scenic, recreational, ecological,
and economic opportunities that they provide (Buckler 1979; Lichter 1995; Arbogast
and Loope 1999; VanOort et al. 2001; Arbogast et al. 2002).

Intrigued by the management issues surrounding Lake Michigan’s sand dunes
and inspired by their evolution, I designed a research project that could potentially be
beneﬁcial to agencies like the MDEQas well as other environmental applications. In
Michigan, the key to achieving a more objective assessment of the coastal zone may
lie in integrating the use of digital and remotely sensed data with the current sand
dune protection and management program. While the results of this study were
focused on one regression model, the research I conducted fell directly at the juncture
of several different disciplines including geomorphology, terrain modeling, and
environmental policy and management.

I began by selecting a study area that was both suitable for what I intended to
study and for which two different sources of digital data were available, including low
resolution NED and high resolution lidar data. I found both of these attributes in
lake Township, which is located along the southern extent of the lakeshore in
Berrien County, Michigan and contains 2,200 acres of the state’s critical dunes.

Next, I outlined several research questions that I intended to explore in the
hope of better understanding how digital data could be used to aid management

decisions that typically require data collection in the ﬁeld. The ﬁrst question I

109

considered was: What terrain variables, or combination of variables, when used in a
regression model, most closely predict true slope? Of the three models I presented in
the Results and Discussion chapter, the best model for predicting true slope was one
that used lidar as the source data and calculated slope and elevation as the
independent variables. This model had an adjusted R2 value of .603.

The next question I planned to address was: What is the error in the predicted
slope values? While some error values were very high, the RMSE for the model was
about 13% with over half of the residuals below 7%. The MAE was equal to 9.38%,
with a minimum error value of .007 and a maximum error value of 38.009. The
RMSE and MAE as well as a majority of the individual errors seem to be reasonable,
but there were several residuals in excess of 25 %. This indicates that the model is not
consistent at predicting slope.

lastly, I hoped to determine to what degree the source, or collection method,
and/ or resolution of the elevation data inﬂuenced the model. I originally planned to
use both lidar and NED as the source of the elevation and slope variables and compare
the models generated from each. After plotting the slope values calculated using NED
against the ﬁeld slope values, I discovered that the relationship was not linear and
therefore violated one of the critical assumptions of multiple regression. Despite this
violation, I generated two models using the NED data strictly for comparison.
However, in the end, the lack of a linear relationship as well as the results of those

models led me to the conclude that the NED level 2 DEM for the study area is not ﬁt

110

for use in applications that require accurate slope measurements. Further, since the
resolution of the data is inherently tied to its source and collection method, I also

concluded that the source of the data is as important as the resolution.

Research Problems

Over the course of conducting and documenting my research I encountered
several problems that I could not overcome. I discovered the ﬁrst major obstacle to
my research the day I entered the ﬁeld to collect sample points. Prior to entering the
ﬁeld, I generated 100 random sampling points across the entire study area. Although I
knew that I would need to eliminate some of those points due to their proximity to
one another or site-speciﬁc characteristics, I had no idea just how many of them
would be inaccessible. Primarily due to private ownership, there were large portions
of the study area that I could not even get close to. Moreover, many of these areas
were residential and therefore perhaps the most representative of sites visited by the
MDEQ.

The second problem is one of measurement. I chose to measure slope as a
percent, both in the ﬁeld and digitally, because I felt that I needed to use the same
scale used by the MDEQwhen measuring slope in the ﬁeld. Unfortunately calculating
it as a percent eventually led to issues in the analysis. Measured as a percent, slope

has an upper limit of inﬁnity and the difference between an 8% and 9% slope and a

111

70 and 71% slope may not be the same. On the other hand, when measured in
degrees, the difference between an 8° and 9° slope and a 70° and 71° slope is an equal
difference. Once I recognized the problem I could have converted all of my data
from percent slope to degree slope, but at that point I chose not to. For future
research I would recommend using degree slope from start to ﬁnish.

The next research problem I encountered was bureaucratic. No matter what
the outcome of my research was, there is no way to judge whether or not it is good
enough to be used by the MDEQ, or even what good enough is. Regardless, given
my results, I would not recommend that agents replace measures obtained in the ﬁeld
with those from digital data sources. However, with that said, it is possible that there
is an alternate use of lidar for predicting whether or not slope measures are above or
below a certain threshold, which may be more useful to an agency like the MDEQ.

The last issue I will discuss is not so much of a problem as it is a reality. While
some dunes exist within large, stabilized dune ﬁelds, dunes are transient features that
can migrate up to 40 meters in a year and a dune will continue to migrate as long as
winds are strong enough to carry sand up the windward slope to the crest (N ordstrom
et al. 1990; Gabler et al. 2004). In addition to the wind, when working near the
shoreline, water is also a factor in destabilizing the coast. What this means is that, on
a variety of time scales, what is true of the coastal zone today may not be true

tomorrow, and slopes that are present today may not be present in the future.

112

Directions for Future Research

The goal of this study was to determine which terrain attributes, or
combination of attributes, when used in a regression model would most closely
predict true slope. Predictability, in this context, also refers to the replication of the
regression results (such as the R2) for other samples from the same population. In an
ideal situation, a second sample would exhibit nearly identical results. More often,
however, the test sample’s results are very different (usually worse, not better) than
those for the model’s sample, because the regression model is data dependent
(Osborne 2000). This may also suggest that the sample used to build the model is not
representative of the population in question. Neter et al. (1996) state that, “By far the
preferred method to validate a regression model is through the collection of new
data.” While gathering additional data to test the models’ predictive ability was
desirable, given the considerable time and effort required to collect more data, it was
not possible. Future research would beneﬁt from collecting a much larger dataset
that could be used to test this model or generate a new model.

Although lidar appears to be useful in obtaining data points in leaf-on
conditions, a closed canopy can result in signiﬁcantly fewer ground hits and lower
accuracy. Ackerman (1996) estimates an overall penetration rate of 24-29% for
coniferous forests and 22-25% for deciduous forests during the growing season.

While Cowen et al. (2000) report that in canopy closures of 30 - 40%, 80-90% of lidar

113

pulses will reach the ground, but when forest cover increases to 80-90% the number
of bare ground hits signiﬁcantly decreases to 10%. The results of this study did not
show conclusive evidence that a canopy or lack there of had any inﬂuence on the
quality of the lidar data; however, I did not measure the forest cover. Future studies
may beneﬁt from classifying the forest by the degree of canopy closure.

While I ruled out NED as a potential data source for the model, every two
months NED is updated and any new source DEMs that have become available are
incorporated (Gesch et al. 2001; Gesch et al. 2002). In a study conducted by Barber
and Shortridge (2005), the researchers sought to compare lidar data to its NED
counterpart. Once they had access to the NED data they discovered that the source of
the NED DEM was lidar. There may come a time when all NED DEMs use higher
resolution source data, thereby eliminating the need to compare lidar to NED. While
this may not be a direction for future research, it is certainly something that future
research should take into consideration.

The US. coastline stretches more than 20,000 km in length, making remotely
sensed data an invaluable resource for monitoring the constant shifts and changes
occurring there (Krabill et al. 2000; Sallenger et al. 2003). Further driving the need
for research is the heavy anthropogenic pressure placed on this margin, considering
that over half of the US. population resides near the coast (Nordstrom et al. 1990;

Bernd-Cohen and Gordon 1999; White and Wang 2003). Lidar has proven potential

114

 

as a valuable a tool for evaluating and managing the coastal zone, yet there is still a

need to study using lidar derivatives to further characterize topography in this setting.

115

F DSLOPE

APPENDIX A

Graphs of the independent variables plotted against the dependent variable
FDSLOPE.

 

F DSLOPE

 

 

 

0 10 20 30 40 50 60 70 80

LDDROP

 

 

 

 

 

 

NDDROP

116

 

w a. w
$8.52

215

205

195

185

NDELEV

m

a
$3QO

 

w

215

205

195

185

175

LDELEV

117

APPENDIX B

Graphs ofthe independent variables derived from the resampled, 5-m NED data
plotted against the dependent variable FDSLOPE.

40
35
30
25
20

FDSLOPE

15
10
5

 

0
0 10 20 30 40 50 60 70 80

NDSDROP

FDSLOPE

 

0 10 20 30 40 50 60 70
NDSSLOPE

118

Residual
888::88888

Residual

APPENDIX C

Graphs of the residuals plotted against each independent variable.

 

—50

O
pa
Ln
8

45 60 75 90
LDSLOPE

 

119

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