Comparing Geomorphometric Pattern Recognition Methods for Semi-Automated

Landform Mapping

A thesis presented to

the faculty of

the College of Arts and Sciences of Ohio University

In partial fulfillment

of the requirements for the degree

Master of Science

Wael Hassan

December 2020

©2020 Wael Hassan. All Rights Reserved.

2

This thesis titled

Comparing Geomorphometric Pattern Recognition Methods for Semi-Automated

Landform Mapping

by

WAEL HASSAN

has been approved for

the Department of Geography

and the College of Arts and Sciences by

Gaurav Sinha

Associate Professor of Geography

Florenz Plassmann

Dean, College of Arts and Sciences 3

Abstract

HASSAN, WAEL , M.S., December 2020, Geography

Comparing Geomorphometric Pattern Recognition Methods for Semi-Automated

Landform Mapping

Director of Thesis: Gaurav Sinha

Landscape regions and hydrological features such as wetlands, rivers, and lakes are frequently mapped and stored digitally as features. Their boundary can be mapped and identified at the physically observable wetland-dryland interface. However, landforms such as mountains, hills, mesas, valleys, which are cognized as component features of or objects attached to the terrestrial surface are not easily delineated due to the lack of clear or unambiguous criteria for defining their boundaries. It is quite challenging to determine where the boundary of the mountain, hill, or valley starts and ends because terrain type, culture, language, and other subjective factors greatly affect how the same portion of the terrestrial surface maybe discretized, classified, labeled, and characterized by people. Cartographers have traditionally used point and line symbols as labels to describe landforms in a map, but this approach ignores the problem of representing the possible physical shape and extension of landforms.

This thesis advanced prior work in the fields of geomorphometry and geographic information science to test the viability of existing semi-automated terrain analysis methods for mesoscale landforms that are easily recognized by people because of local topographic and cultural salience. The focus was on finding methods that can help automate the extraction of three broad categories of landforms: non-linear eminences

(e.g., peak, mount, pillar, mountain, hill, mesa, butte), linear eminences (e.g., ridge and 4

spur) and linear depressions (e.g., channel, valley, and hollow). Three methods proposed by Wood (1996), Jasiewicz and Stepinski (2013), and Weiss (2001) were selected because they are popular in terrain characterization, have shown promising results for mapping discrete terrain features that are intended to resemble landforms recognized intuitively by people, and because they are easily available for experimentation in freely available software. These methods require only an elevation raster as input, and then users must modify a few parameters to derive classified rasters reflecting discrete morphometric features or landform objects.

The three methods were first independently tested by varying their parameters and creating many classified rasters for each method for three study areas in the continental

US (Great Smoky Mountains (NC-TN), White Mountains (NH), and Colorado Plateau

(NM)). These experimental results were then compared in 2D and 3D map views in GIS software, followed by quantitative comparative analysis of a subset of the rasters to answer questions about the impact of input parameters and the terrain type on quality of results. Additional comparative analysis of the methods also helped answer questions about the relative strengths and weaknesses of the methods and the semantic similarity between some of the landform classes recognized in the unique classification system used by each method.

The major finding from this thesis was that only smaller neighborhood scales between 300 to 400 meters are the optimum scales for extracting landform objects that correspond well to expected shapes and extents. Other parameters have similarly specifically narrow ranges for which cognitively plausible results can be obtained.

Identifying these ranges of parameters is the major contribution of this thesis. The impact 5

of terrain type is not as critical as initially assumed, but more careful analysis is warranted for low relief areas which make it harder to detect and delineate landform boundaries.

Despite differences, all three (Wood, Geomorphon and TPI) methods are worthy candidates for mapping all three types of landform categories, with the TPI method producing the most realistic, narrower linear polygons for non-linear eminences and depressions. However, the TPI method lacks a dedicated class for mapping non-linear eminences, leaving only the Wood and Geomorphon methods as candidates for mapping non-linear eminences. The semantic analysis of the classification systems is complicated and preliminary analysis suggests that a much more carefully planned and detailed analysis will be needed.

This thesis clearly shows the potential for automated mapping of landforms, but also raises enough questions that further research must be conducted on parameterization impacts for each method, feasibility of extending GNIS feature representing beyond points to polygons, and creating an automation workflow based on a combination of methods, instead of hoping to rely on one method exclusively. A comprehensive set of findings for each research question and important limitations and recommendations for future research are provided in the concluding chapter. 6

Dedication

To the soul of my Aunts, may Allah rest their souls

To my parents

To my all teachers

To All whom I love

I dedicate this work

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Acknowledgments

I want to give thanks to the almighty God whose grace has brought me this far.

Next, my deepest gratitude goes to my advisor, Dr. Gaurav Sinha, for his guidance, support, advice, encouragement, and great dedication. The successful completion of this thesis would not have been possible without his tremendous contribution. Just saying thank you is not enough to express how grateful I am. I would also like to express my gratitude to Dr. Dorothy Sack and Dr. Timothy Anderson, who sat on my committee and offered invaluable recommendations and generous encouragement.

Additionally, I extend special thanks to Dr. Ryan Fogt and Ms. Ana Myers, and the entire Geography faculty for contributing to my academic life in one way or another in such a new environment. I have learned much from you all. I would also like to thank my family for all their support, endless love, and encouragement. A special thanks to my father, Ali Saleh, and my mother, Wafa Hassan, for their incredible investment in my life in general. Thanks to the Sudanese community in Columbus, Ohio, for their endless support. Your love and support are overwhelming. Finally, I would like to thank the

Muslim Student Association (MSA) in Athens, Ohio University, for their supplication and spiritual support. I cannot conclude without offering appreciation for my fellow graduate students in the Department of Geography. You have been very kind and helpful throughout my study.

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Table of Contents Page

Abstract ...... 3 Dedication ...... 6 Acknowledgments ...... 7 List of Tables ...... 11 List of Figures ...... 15 Chapter 1: Conceptualization and Computational Representation of Landscape ...... 18 1.1 Mapping Landforms ...... 18

1.2 Conceptualization of Landforms...... 22

1.3 Extraction of Terrain Features and Landform Objects from DEMs ...... 24

1.4 Research Questions ...... 27

1.5 Project Significance ...... 29

Chapter 2: Geomorphometric Methods for Mapping Landforms ...... 30 2.1 Geomorphometry Theory ...... 30

2.1.1 Digital Elevation Models (DEMs) ...... 31

2.1.2 General Geomorphometry ...... 32

2.1.3 Segmentation of the Continuous Surface into Geomorphological Units ..... 35

2.1.4 Specific Geomorphometry: Features vs Landforms...... 39

2.2 Semi-Automated Feature Extraction and Mapping of Landforms ...... 41

2.3 Bridging the General-Specific Geomorphometric Divide with Supervised Pattern Recognition methods for Landform Mapping ...... 44

2.3.1 Selection of Pattern Recognition Methods ...... 45

2.3.2 Wood’s Multiscale Quadratic Polynomial Estimation and Six Morphometric Features ...... 47

2.3.3 Geomorphon-Based “Local” Landform Pattern Recognition ...... 52

2.3.4 Topographic Position Index (TPI) Based Landform Mapping ...... 53 9

Chapter 3: Methodology ...... 59 3.1 Chapter Overview ...... 59

3.2 Sources of Data ...... 60

3.2.1 (10-Meters) Resolution DEM ...... 60

3.2.2 Geographic Names Information System (GNIS) ...... 60

3.2.3 National Hydrography Dataset (NHD) ...... 62

3.3 Study Areas ...... 62

3.3.1 Great Smoky Mountains, Tennessee – North Carolina ...... 63

3.3.2 White Mountains, New Hampshire ...... 65

3.3.3 Colorado Plateau, New Mexico ...... 66

3.4 Methodology for Answering Research Questions ...... 69

3.4.1 Parametric Variation ...... 69

3.4.2 Visual Geomorphometric Analysis ...... 70

3.4.3 Quantitative Analysis of Parametric Impacts Using a Confusion Matrix .... 72

Category 1 ...... 73

3.4.4 Quantitative Analysis of Parametric Impacts by Comparison with GNIS Features ...... 75

3.4.5 Quantitative Comparison of Classification Methods Based on Contingency Tables ...... 75

3.5 Software ...... 77

Chapter 4: Results and Discussions ...... 81 4.1 Parametric Variation ...... 81

4.1.1 Overview of Visual Geomorphometric Analysis ...... 82

4.1.2 Mapping Wood Morphometric Features ...... 84

4.1.3 Mapping Geomorphon Landform Classes ...... 91 10

4.1.4 Mapping Topographic Position Index (TPI) Landform Classes ...... 98

4.2 Quantitative Analysis of Rasters from the Same Method Using a Confusion Matrix ...... 104

4.2.1 Wood Method ...... 104

4.2.2 Geomorphon Method...... 107

4.2.3 TPI Method ...... 108

4.3 Using GNIS Features for Cognitive Validation of Extracted Landform Features ...... 119

4.3.1 Process for Calculation and Analysis of GNIS Shortest Distances ...... 120

4.3.2 Analysis of GNIS Shortest Distances for the Wood Method ...... 122

4.3.3 Analysis of GNIS Shortest Distances for the Geomorphon Method ...... 127

4.3.4 Analysis of GNIS Shortest Distances for the TPI Method ...... 132

4.4 Comparison of the Wood, Geomorphon and TPI Landform Mapping Methods 137

4.4.1 Comparing Methods Based on Overall Similarity Measures ...... 138

4.4.2 Wood vis-à-vis Geomorphon Classification Systems ...... 139

4.4.3 TPI vis-à-vis Wood and Geomorphon Classification Systems ...... 142

Chapter 5: Conclusions and Recommendations ...... 153 5.1 Semi-Automated Feature Extraction for Landform Mapping ...... 153

5.2 Discussion: Impact of Parameterization (Research Questions A.i and A.ii) ...... 155

5.3 Discussion: Relative Performance of and Similarity Between Methods (Research Questions B.i and B.ii) ...... 160

5.4 Limitations and Recommendations...... 162

References ...... 166

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List of Tables

Page

Table 2.1 Subset of commonly used geomorphometric continuous field variables. (Source: Bolstad, 2019)...... 36

Table 2.2 Correspondence between the three broad landform categories (non-linear eminence, linear eminence, linear depression) and geomorphometric landform classes for the three geomorphometric feature extraction methods...... 51

Table 3.1 Definitions and frequency of GNIS feature classes corresponding to the three broad landform categories (non-linear eminence, linear eminence, linear depression) of interest in this study...... 61 Table 3.2 GNIS feature counts for the three GNIS feature classes corresponding to the three landform categories (non-linear eminence, linear eminence, linear depression). .... 65

Table 3.3 Parameters and values chosen to conduct experiments with the Wood, Geomorphon and TPI feature extraction methods...... 71

Table 3. 4 Example layout of a confusion matrix...... 73

Table 4.1 Confusion matrix (overlap area percentages for class combinations) analysis for the two best experimental runs for the Wood method (Great Smoky Mountains (NC-TN) study area)...... 110 Table 4.2 Confusion matrix (overlap area percentages normalized for every column) analysis for the two best experimental runs for the Wood method (Great Smoky Mountains (NC-TN) study area)...... 111

Table 4.3 Confusion matrix (overlap area percentages normalized for every row) analysis for the two best experimental runs for the Wood method (Great Smoky Mountains (NC- TN) study area)...... 112

Table 4.4 Confusion matrix (overlap area percentages for class combinations) analysis for the two best experimental runs for the Geomorphon method (Great Smoky Mountains (NC-TN) study area)...... 113 12

Table 4.5 Confusion matrix (overlap area percentages normalized for every column) analysis for the two best experimental runs for the Geomorphon method (Great Smoky Mountains (NC-TN) study area)...... 114

Table 4.6 Confusion matrix (overlap area percentages normalized for every row) analysis for the two best experimental runs for the Geomorphon method (Great Smoky Mountains (NC-TN) study area)...... 115

Table 4.7 Confusion matrix (overlap area percentages for class combinations) analysis for the two best experimental runs for the TPI method (Great Smoky Mountains (NC-TN) study area)...... 116

Table 4.8 Confusion matrix (overlap area percentages normalized for every column) analysis for the two best experimental runs for the TPI method (Great Smoky Mountains (NC-TN) study area)...... 117

Table 4.9 Confusion matrix (overlap area percentages normalized for every row) analysis for the two best experimental runs for the TPI method (Great Smoky Mountains (NC-TN) study area)...... 118

Table 4. 10 Study Area: Great Smoky Mountains (NC-TN). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 20⁰ (Peak); 1⁰ (Ridge/Channel). Curvature: 0.0001...... 124

Table 4. 11 Study Area: White Mountains (NH). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 20⁰ (Peak); 1⁰ (Ridge/Channel). Curvature: 0.0001...... 125

Table 4. 12 Study Area: Colorado Plateau (NM). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 20⁰ (Peak); 1⁰ ...... 126

Table 4. 13 Study area: Great Smoky Mountains (NC-TN). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 1⁰...... 129 13

Table 4. 14 Study Area: White Mountains (NH). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 1⁰...... 130

Table 4. 15 Study area: Colorado Plateau (NM). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 1⁰...... 131

Table 4. 16 Study Area: Great Smoky Mountains (NC-TN). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type...... 134

Table 4. 17 Study Area: White Mountains (NH). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. .. 135

Table 4. 18 Study Area: Colorado Plateau (NM). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. .. 136

Table 4. 19 Contingency table (overlap area percentages for class combinations) analysis for the best experimental runs from the Wood and Geomorphon methods (Great Smoky Mountains (NC-TN) study area)...... 144

Table 4. 20 Contingency table (overlap area percentages normalized for every column) analysis for the best experimental runs from the Wood and Geomorphon methods (Great Smoky Mountains (NC-TN) study area)...... 145

Table 4. 21 Contingency table (overlap area percentages normalized for every row) analysis for the best experimental runs from the Wood and Geomorphon methods (Great Smoky Mountains (NC-TN) study area)...... 146

Table 4. 22 Contingency table (overlap area percentages for class combinations) analysis for the best experimental runs from the Wood and TPI methods (Great Smoky Mountains (NC-TN) study area)...... 147

Table 4. 23 Contingency table (overlap area percentages normalized for every column) analysis for the best experimental runs from the Wood and TPI methods (Great Smoky Mountains (NC-TN) study area)...... 148 14

Table 4. 24 Contingency table (overlap area percentages normalized for every row) analysis for the best experimental runs from the Wood and TPI methods (Great Smoky Mountains (NC-TN) study area)...... 149

Table 4. 25 Contingency table (overlap area percentages for class combinations) analysis for the best experimental runs from the Geomorphon and TPI methods (Great Smoky Mountains (NC-TN) study area)...... 150

Table 4. 26 Contingency table (overlap area percentages normalized for every column) analysis for the best experimental runs from the Geomorphon and TPI methods (Great Smoky Mountains (NC-TN) study area)...... 151

Table 4. 27 Contingency table (overlap area percentages normalized for every row) analysis for the best experimental runs from the Geomorphon and TPI methods (Great Smoky Mountains (NC-TN) study area)...... 152

15

List of Figures

Page

Figure 1.1 Screenshot from the map view of USGS’ The National Map portal showing the query returning a single point whose coordinates represent the location of Grand Canyon in the GNIS...... 20

Figure 2.1 Illustration of the concept of a moving window in raster-based analysis (Source: Bolstad, 2019)...... 34 Figure 2.2 Use of second-degree polynomials (a) to derive six morphometric feature classes (b) in Wood (1996). (Source: Zieger et al., 2009)...... 50

Figure 2.3 Derivation of morphometric features using second derivates (Wood, 1996). . 51

Figure 2.4 Illustration of the 3D search patterns morphologies and their corresponding geomorphons (ternary patterns) for the 10 most common landform elements. (Source: Jasiewicz and Stepinski, 2013)...... 53

Figure 2.5 Illustration of combination of topographic position index (TPI) calculation for a small and a large neighborhood scale to classify locations into landform types. (Source: Jenness, 2006)...... 58

Figure 3.1 Location, elevation patterns, and distribution of GNIS Summit, Ridge and Valley features within the second study area in the Great Smoky Mountains study area, along the Tennessee – North Carolina border...... 64 Figure 3.2 Location, elevation patterns, and distribution of GNIS Summit, Ridge and Valley features within the second study area in the White Mountains study area in New Hampshire...... 67

Figure 3.3 Location, elevation patterns, and distribution of GNIS Summit, Ridge and Valley features within the second study area in the Colorado Plateau study area in New Mexico...... 68

Figure 3.5 Illustration of the concept of the Tabulate Area tool in ArcGIS Desktop 10.6...... 74 16

Figure 3.6 Screenshot from Quantum GIS software showing initial default parameter values for the r.param.scale function based on Wood (1996)...... 79

Figure 3.7 Screenshot from Quantum GIS software showing initial default parameter values for the r.geomorphon function based on Jasiewicz and Stepinski (2013)...... 80

Figure 4.1 Mapping Wood morphometric features for the Great Smoky Mountains (NC-TN) study area...... 87 Figure 4.2 Mapping Wood morphometric features for the White Mountains (NH) study area...... 88

Figure 4.3 Mapping Wood morphometric features for the Colorado Plateau (NM) study area...... 89

Figure 4.4 3D geovisualization of results from one visually appealing (top) and one visually unappealing (bottom) experimental run for the Wood method for the Great Smoky Mountains (NC-TN) study area...... 90

Figure 4.5 Mapping Geomorphon landform classes for the Great Smoky Mountains (NC- TN) study area...... 94

Figure 4.6 Mapping Geomorphon landform classes for the White Mountains (NH) study area...... 95

Figure 4.7 Mapping Geomorphon landform classes for the Colorado Plateau (NM) study area...... 96

Figure 4.8 3D geovisualization of results from one visually appealing (top) and one visually unappealing (bottom) experimental run for the Geomorphon method for the Great Smoky Mountains (NC-TN) study area...... 97

Figure 4.9 Mapping TPI landform classes for the Great Smoky Mountains (NC-TN) study area...... 100

Figure 4.10 Mapping TPI landform classes for the White Mountains (NH) study area. 101

Figure 4.11 Mapping TPI landform classes for the Colorado Plateau (NM) study area. 102 17

Figure 4.12 3D geovisualization of results from one visually appealing (top) and one visually unappealing (bottom) experimental run for the Geomorphon method for the Great Smoky Mountains (NC-TN) study area...... 103

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Chapter 1: Conceptualization and Computational Representation of Landscape

1.1 Mapping Landforms

Some landscape regions such as wetlands and hydrological features such as rivers, lakes are commonly mapped and stored digitally as features since their boundary can be mapped at the physically observable wetland-dryland interface. Other landforms such as mountains, hills, mesas, valleys that dry “parts” of the landscape are not easily delineated due to the lack of unambiguous criteria for defining their boundaries. It is difficult to state where a mountain ends, and a valley begins; or where exactly does a hill ‘melt’ away into the surrounding planar region. Because of this issue of indeterminate boundaries of natural geographic features (Burrough and Frank, 1996), geographic databases and topographic maps rarely support explicit spatial representation of such features. On maps, cartographers have chosen to recognize the presence of landforms only implicitly via point or line symbols and associated labels. The general shape of landforms, such as mountains and valleys, can be interpreted from contours and hill shading, but there is rarely an explicit boundary marker. Similarly, in GIS databases, terrain is represented typically based on the elevation field conceptual model, which is then stored digitally as a raster, TIN or point cloud data model (Bolstad, 2019; Hengl and Reuter, 2009).

Twenty-first century digital topographic mapping involves sophisticated algorithms and complicated workflows, mostly automated, for deriving specialized processing of elevation data into other alternative forms of representation such as contours and hillshades, followed by cartographic symbologization and labeling. Such topographic maps are readily available to everyday users of online web-mapping services such as

Google Maps and Bing Maps. More sophisticated consumers can access more detailed 19

and customizable online topographic maps from the United States Geological Survey’s

(USGS) The National Map (USGS, 2020c) web-mapping portal in the US, or through similar topographic map services supported by the respective national mapping agencies of other countries.

Due to the lack of well-established criteria for identifying and delineating the boundaries of individual landforms national mapping agencies such as the U.S

Geological Survey are still unable to support object-oriented strategies for storing and retrieving information of terrain features. Thus, despite tremendous developments in geospatial technologies, the cartographic representation of landforms and terrain features on topographic maps remains practically unchanged. Today, maps still show a few named landforms, which are drawn from digital gazetteers such as USGS maintained

Geographic Names Information System (GNIS) (USGS, 2020a) and NGA’s Geonet

Names Server (GNS) (NGA, 2020). However, such gazetteers identify features by names and a somewhat arbitrary point location; they do not provide any information about the spatial footprints of the geographic features. For example, as shown in Figure 1.1 the

Grand Canyon, while commonly understood as a massive feature is still represented in the GNIS through a single representative point! There is no officially accepted boundary for the landform known as the Grand Canyon, and probably for good reason, since there can be many interpretations of the boundary or boundaries that could represent the Grand

Canyon. Similarly, all other topographic features in the GNIS lack spatial footprints. This makes geometric and topological queries about landforms impossible unless the service provider chooses to derive landform extents using some preferred method for mapping landform boundaries. 20

Figure 1.1

Screenshot from the map view of USGS’ The National Map portal showing the query returning a single point whose coordinates represent the location of Grand Canyon in the

GNIS.

Gazetteers also differ in the list of feature types and the definitions of those types.

The distinguishing characteristics of a type or the criteria that are used for interpreting a feature’s type are neither well understood, nor consistently applied within or across standards (Feng and Sorokine, 2013). Otherwise, there is no explicit information available about types and the spatial extents of landforms in any topographic information system. People have always been expected to make their own personal interpretation about the size and extent of such features from the contours on maps and perspective views in 3D scene displays.

On the other hand, geoscientists have developed many alternative frameworks for segmenting geomorphological (terrain) units at multiple scales. Several of these 21

frameworks are reviewed in the next chapter (section 2.1). However, geoscientific classification systems developed are intended to help geoscientists study geoscientific processes and landscape impacts and lack the common-sense topographic concepts and categories used by non-experts. The taxonomies and descriptions of landform types in geomorphological textbooks do not correspond well with the naïve geographic (i.e., common-sense) (Egenhofer and Mark, 1995) based landform categories that people develop and use in everyday reasoning and communication (Mark and Smith, 2004).

This is because geomorphology science uses a technical system of classification which most non-experts are unaware of. For example, while geoscientists may classify a landform as a dormant stratovolcano based on its volcanic origin and steeper slopes, the average person is unlikely to be able to infer the volcanic origins, and probably only see a mountain (a more generic landform category) and pay attention only to its perceptual size and shape attributes (Hoffman and Pike, 1995).

Similarly, on maps and in the design of algorithms for mapping landforms and terrain features from digital elevation models (DEMs), only the geomorphometric signature can be relied. Automating how geoscientists infer the origin and evolution of landforms is far more difficult to encode in algorithms, and often impractical or impossible from DEMs alone—substantial ancillary geological data will be needed to make such inferences algorithmically. Since mapping technologies can rely only on geomorphometric information available from DEMs, and common sense based recognition of landforms is also based on visual perception, this thesis relies only on form based geomorphometric segmentation and classification to explore automated landform mapping (Arundel and

Sinha, 2018; Sinha et al., 2018). 22

1.2 Conceptualization of Landforms

Contrary to general conception, landform demarcation and categorization is not independent of human cognition. This thesis is philosophically aligned with the claims of the ethnophysiographic hypothesis that there are well-documented differences in how people from different cultures, languages and landscapes refer to various elements of the landscape, including, even elementary landform and hydrographic feature types (Mark et al., 2007; Mark and Turk, 2003;). Ethnophysiography is a relatively new interdisciplinary research paradigm framework that was conceived to compare and document how the natural landscape and its parts are referred to in various cultures and languages, and how

(dis)similar the meanings of those terms maybe (Turk et al., 2011).

Thus, it would be quite fallacious to assume that there could be an objective and universally applicable system of defining landform categories (Sinha and Mark, 2010b).

There cannot really be a universal list of landform types or an objective count of the number of instances of any type of landform. Linguistic landform categories have been convincingly been argued to be mind-dependent or fiat (Mark and Smith, 2003) or quasi- objects (Burenhult and Levinson, 2008). The Lokono language presents an especially extreme case since it supports only one scale and size independent general term

“horhorho” for landforms, and all further distinctions for describing landforms are realized through phrases that classify landforms as networks of connected places (Rybka,

2015). Further evidence comes from studies comparing topographic gazetteers (Feng and

Sorokine, 2013) that different countries and agencies in the same country identify feature types that are have only partial semantic similarity. Another study by Wellen and Sieber

(2013) documented how the Cree indigenous tribe in Quebec, Canada, conceive 23

hydrographic features quite differently from English speakers in Canada and elsewhere.

Notably, there were differences in conceptions even between different subsets of the tribe.

Despite such variations in how people conceive of landforms and terrain related feature types and individual instances of such types, there obviously are some fundamental categories and relationships that underlie most people’s common sense

(naïve geographic) conceptualization and reasoning about landforms (Mark and Smith,

2004). However, these fundamental categories cannot be based on popular natural language terms (e.g., mountain, lake, pond, valley, canyon in English; montagne, lac, etang, vallée, canyon) since the interpretation of these categories can vary with geographic region, culture, visual perspective, geographic scale, or any combination of these and other factors. Instead of such higher level contextually dependent categories, it would be strategic to begin with simpler perceptual categories (requiring less cognitive processing) that are much more likely to be perceived similarly by humans of all backgrounds (Sinha et al. 2018; Sinha and Mark, 2010b).

The form of objects is one of the most basic visual discrimination criteria used by humans quite early in their childhood. It is no coincidence that recognizing the shape of the land we exist on and individuating various types of landforms has been a fundamental aspect of human-environment interaction. Geomorphologists have long recognized the principle that, for landform analysis, the genetic, chronologic and dynamic principles can only be applied after a landform is recognized first based on the morphological principle

(Minár and Evans, 2008; Speight, 1974). This idea is at the core of this thesis. It is recognized that landform cognition and classification is contingent on people recognizing 24

a stable, characteristic terrestrial form (shape and size) of, and spatial and mereological relationships between, subaerial or subaqueous parts of the (continuous and solid) surface of the Earth (or of another planetary body). Other physical attributes of landforms such as material, texture, color, and relationships with hydrographic features can only aid and enhance landform cognition and description but cannot be the primary criterion for recognizing a landform.

1.3 Extraction of Terrain Features and Landform Objects from DEMs

The fundamental input for any automated terrain feature extraction is a digital elevation model (DEM), which represents a ground surface using a continuous field model of regular grid cells that embed elevation values. DEMs are available for the whole world now, albeit with varying degrees of accuracy. The USGS provides freely available DEMs for download for the entire US from the data download service of The

National Map website (USGS, 2020c). DEMs are generally stored and shared as rasters, which means that DEMs can be mapped and processed in GIS using standard raster management and analysis tools.

Mapping terrain characteristics and extracting boundaries for landscape elements and terrain features can be conceived and implemented at different levels of geographic scale

(Evans, 2012) and for multiple purposes. Thus, it is important to realize the fundamental difference between general and specific geomorphometry. General geomorphometry is the quantitative spatial characterization of continuous land surface form. The focus in such terrain analysis is to apply mathematical formulas to DEMs to derive fundamental terrain parameters like relief, slope, curvature, and aspect (Bolstad, 2019; Evans, 1972).

Terrain parameters are critical in themselves in many kinds of landscape analyses, 25

including the study of the geometric and topological study of discrete landforms of various types (e.g. drainage networks, mountains, valleys, drumlins, and dunes), which is understood as the knowledge domain of specific geomorphometry.

Over the past few decades, many specific geomorphometry methods have been proposed to extract landscape elements and terrain features from analysis of a combination of terrain parameters. While in some cases, manual delineation methods are still the most efficient, semi-automated methods are, obviously, are far more common. A brief review summary of such semi-automated methods and the general limitations of methods is provided in the next chapter. However, in this thesis, the focus is on only three special methods of land surface segmentation or feature extraction that were found to support simultaneous mapping of multiple types of landforms. These are general purpose supervised pattern recognition geomorphometric analysis algorithms that can be easily customized for multiscale analysis. The appeal of these methods lies in in their ability to support several terrain feature types whose shapes are intended to resemble the shapes of larger meso and macro scale landforms or their parts (e.g., peak, pit, pass, valley, slope, shoulder). These methods are also gaining popularity because no special programming or scripting skills are required to implement them, since all of them are available as ready to use functions in at least one open source GIS software (SAGA or

GRASS).

The first method of interest in this thesis is due to Jo Wood (1996) who proposed an elegant method for extracting six types of terrain features (Peak, Pit, Pass, Ridge,

Channel and Planar), at any scale of analysis by using larger and larger scales (defined by size of processing window imposed on each DEM cell while classifying it). This 26

method has been widely used for almost two decades now to characterize different landscapes in terms of the six constituent features, and to identify the approximate extents of large scale mountains, hills, ridges, and valleys that people notice on topographic maps and in the real world. This method is available as a function in both SAGA and GRASS

GIS.

The second method of interest was proposed much more recently by Jasiewicz and

Stepinski (2013) as a terrain segmented and classification algorithm inspired by pattern recognition methods. Like Wood’s (1996) morphometric features, this method also classifies every cell into one of ten types of landform elements: Flat, Peak, Ridge,

Shoulder, Spur, Slope, Hollow, Footslope, Valley and Pit. This method uses line of sight analysis in the direction of the 8 neighboring grid cells. Each line-of-sight is attributed

‘−’,‘+’ or ‘0’, depending on whether it ends downwards, upwards, or horizontal, respectively. A complex set of rules are used to combine the information from the line of sights toward a decision about which of the ten landscape elements a location is best categorized into. The authors have shown promising results for general geomorphometric classification and physiographic mapping for Poland. This method is currently only implemented in GRASS GIS (Development Team, 2020).

The third landform classification method is based on the intuitive topographic position index (TPI) geomorphometric variable. TPI quantifies the relative vertical position of any location (DEM cell) by comparing its elevation to that of the mean elevation in its neighborhood. Weiss (2001) developed an intuitive multiscale analysis and classification of TPI values to into one of ten landform classes. This method has been 27

implemented in SAGA GIS (Conrad et al., 2015) as a ready to use function. This method was included for testing because of its simplicity and popularity.

Despite being quite popular, these three methods (and many others) have not been extensively tested for national scale geomorphometric landform mapping to identify and delineate meso/macro scale landform categories, which people refer to in natural language, and instances of which they tend to intuitively identify when observing the landscape directly or in representations. The author is aware of only one recent study

(Gruber et al., 2018) that compared the results from the above listed methods to landform delineations and topographic positions surveyed by soil survey experts in the field.

Insights from Gruber et al. (2018) already suggest several limitations of the automated methods. At the very least, the methods must be researched and parameterized before they can produce cognitively plausible results for landform mapping.

1.4 Research Questions

Based on the general background provided above, this thesis is designed to discover the relative strengths and weaknesses of three chosen tertian feature extraction methods

(discussed above) for national scale automated mapping of the three most commonly types of meso/macro scale landforms encountered by people in the United States: i) convex, non-linear eminences (e.g., mountain, hill, plateau, mesa) ii) (convex) linear eminences (e.g., ridge and spur) and iii) (concave) linear depressions (e.g., channel, valley, canyon, gorge, and ravine). The choice of form based categories is intended to minimize bias toward any particular region, language or culture because these are fundamental shape categories that can be easily recognized and understood by people across the world, and, consequently, also cover an extremely of a wide variety of more 28

specialized linguistic landform categories. Moreover, defining the rules for segmenting simple shape categories will be a lot easier than trying to segment instances of more specialized landform categories. The research questions for this thesis are organized as follows, under two larger objectives:

A. Exploring customization of individual software for automated landform mapping.

i.) What are the best values or range of values for parameters necessary to

customize methods proposed Wood (1996), Jasiewicz and Stepinski (2013),

and Weiss (2001) to derive plausible areal extents for (instances of) three

common landform categories: non-linear eminences, linear eminences, and

linear depressions?

ii.) For each of the three methods and landform categories, how sensitive is the

parameterization process to the type of terrain (e.g. mountainous vs. arid

terrain) and what is the implication for creating a national scale workflow for

automated landform mapping?

B. Comparison of methods for automated landform mapping.

i.) Based on an assessment of results from Objective A, what are relative

strengths and weaknesses of the three feature extraction methods for mapping

(linear/non-linear) eminences and linear depressions in the US?

ii.) Based on comparative analysis of individual and overlaid extracted landform

polygons, how much geomorphometric similarity exists between supposedly

corresponding landform categories from the three feature extraction methods?

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1.5 Project Significance

This thesis is a concrete step in advancing our general understanding of how much automated methods of landform mapping for creating cognitively plausible representations of landforms that people intuitively recognize and individuate in the real world and on maps and other geovisual media. The findings of this research will help terrain analysts and topographic cartographers understand the strengths and weaknesses of three popular terrain feature extraction techniques for automated mapping of meso/macro scale landforms. This study reveals the extent to which the three methods are

(dis)similar to each other, since no extensive comparison is available yet in the literature.

The results from this thesis will help national mapping agencies such as the USGS in making decisions about how to complement these three tested methods with other existing and new methods for object-based terrain representation in GIS and cartographic databases.

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Chapter 2: Geomorphometric Methods for Mapping Landforms

2.1 Geomorphometry Theory

The simplest way to define geomorphometry is that it is the science of quantitative land-surface analysis (Pike, 1995, 2000). “Geomorphometry supports earth and environmental science (including oceanography and planetary exploration), civil engineering, military operations, and video entertainment” (Pike et al., 2009). According to Wood (1996), earliest documented quantitative analysis of topography can be attributed to geometric analysis of map data by Glock (1932) and Johnson (1933).

However, the seminal work by Walter F. Wood published in military and industrial reports (Wood and Snell, 1957, 1960) established quantitative terrain analysis as a legitimate geoscientific pursuit (Pike, 1995). At the same time, Chorley, et al. (1957) were the first to write about geomorphometry as a specialization of geomorphology, with its focus being quantitative descriptions of the land surface.

An important distinction in the field of geomorphometry is between general geomorphometry, the quantitative characterization of continuous land surface mostly through the use of quantitative parameters and specific geomorphometry, the study of specific kinds of features (e.g., peak, ridge, channel, saddle or pass) and larger landforms

(e.g. drainage networks, drumlins, dunes etc.) (Evans, 1972). For a summary of the discipline’s scope and applications, readers should consult Pike (1995, 2000) and Hengl and Reuter’s (2009) comprehensive edited book volume for a more thorough review. In this thesis, aspects of both general and specific geomorphometry were used to answer the four research questions.

31

2.1.1 Digital Elevation Models (DEMs)

The operational focus in geomorphometric analysis is the extraction of land-surface parameters and objects from digital elevation models (DEMs), which are the usual input for most computational algorithms in use today for geomorphometric analysis (Pike et al.,

2009). In this thesis, DEMs are inferred following the most common interpretation, as a gridded set of points in Cartesian space, and assigned a single elevation value to approximate the height of the Earth’s ground surface above a chosen vertical datum

(Evans, 2012 ;Wood, 1996). Contours, triangular irregular networks (TINs) and other types of sampled elevations are not DEMs as the term is used here. Currently, global coverage DEMs (with varying resolution and quality) are available from multiple sources

(e.g. SRTM, GLOBE DEM, GTOPO 30, ASTER GDEM). Additionally, for regional or national scale, other DEM products are also available. For the US, the best source of

DEMs for anywhere in the nation is the USGS maintained The National Map portal

(USGS, 2020c), which makes accessible quality controlled DEMs a multiple resolutions and from multiple past and current DEM mapping initiatives.

The quick uptake and continuing popularity of DEMs is because of the simple raster image data model on which it was based. Processing a simple matrix of values assigned to a regular grid of square cells was the most efficient way to model and imagery of continuous surfaces of any kind and at any scale. Therefore, most algorithms for terrain analysis are raster based. However, there are multiple conceptual limitations of the raster- based DEM model (Wood, 1996). The most obvious limitation is that despite being a representation of a continuous surface, the DEM is essentially a discrete model since elevations are assumed to be uniform within the area represented by a grid cell. Thus, the 32

fidelity with which it captures the elevation variation of the true surface will depend on the latter’s surface roughness and DEM resolution. Second, there is also the matter of how to interpret the elevation values—as averages of the area represented by a cell (grid model), or as a single sample value at the center of the cell (lattice model). Most often, it is the latter, which then means the DEM is a matrix of values measured at point locations, and some model of spatial interpolation must be invoked to recreate the continuous surface from the discrete set of points. The spatial interpolation strategy chosen to realize a continuous surface can lead to different elevation estimates at unsampled locations.

This will also affect the values of derived parameters and detection and delimitation of features and objects. Thus, DEM analysis is always going to be accompanied by uncertainty. More specific analytical issues related to general and specific geomorphometry are discussed next.

2.1.2 General Geomorphometry

General geomorphometric analysis focuses on analysis of the continuous land surface form through quantitative variables (also referred to as parameters) such as slope, aspect, curvature, visibility, wetness index. Like the gridded elevation values of a DEM, variables derived from the DEM are also calculated for every cell, and arrayed into a two- dimensional matrix of values, representing a continuous field of that variable (e.g. slope field). Like the DEM, variable fields are almost always stored as a raster image and refer to same area as the source DEM. Variables can be classified or grouped in many ways.

The simplest approach is to distinguish them as primary, if they are derived directly from a DEM (e.g., slope, aspect, curvature, topographic position index) or as secondary, if additional processing steps/inputs are required (e.g., flow accumulation, catchment area, 33

wetness index). A more involved classification of field and object based geomorphometric variables is presented in Evans and Minár (2011).

Derivation of most land surface field variables is based on using the standard raster map algebra concept of a moving window analysis (Bolstad, 2019), which involves defining a neighborhood of some size and shape (default is a 3x3 square window) and using it to define a local support for calculating the surface parameter value, which is then assigned to the center cell on which the neighborhood window is centered.

“Moving” that window successively to adjacent cells of the raster image allows calculation of parameter values for every location. In Figure 2.1 a rectangular window is chosen to define the neighborhood, but several other window definitions are also common (circle, square, wedge, annular ring, irregular). All cells in a neighborhood contribute their values as inputs to a mathematical function to derive a new statistic for the center cell. The window of calculation is then centered to the next adjacent cell, and the process iterates over the new set of window cells. The scale of analysis can be chosen by varying the size of the window, and specialized shape and directional effects can be further introduced by choosing different shapes for the neighborhood definition (square, rectangle, triangle, wedge, annular ring). Moreover, the value of the parameter (e.g., slope, curvature, aspect, visibility) can be calculated using one of many possible computational algorithms and for different sources of DEMs. Thus, variable values derived from DEMs cannot be assumed to be definitive (Pike et al., 2009). The scale and computational method need to be chosen based on multiple criteria related to resolution and quality of source DEM, desired computational efficiency, validation strategy, and analytical purpose. 34

Figure 2.1

Illustration of the concept of a moving window in raster-based analysis (Source: Bolstad,

2019).

The impact of measurement errors must also be understood similarly as a function of

DEM resolution, source and method of DEM production, scale of analysis, and algorithm chosen for computing the variable value (Deng et al., 2007; Florinsky, 1998a, 1998b,

2017; Pike and Hengl, 2009). Based on extensive research, it is generally accepted that, in most cases, a quadratic polynomial-based method produces the best overall accuracy for slope, aspect, and curvature. The quadratic polynomial method involves interpolating a locally continuous surface patch around the point (cell) of estimation; the coefficients of the polynomial are then used to calculate slope and curvature measures (Evans, 1980;

Wood, 1996). For an accessible discussion of the conceptual and mathematical details 35

about the derivation of these and other popular geomorphometric parameters, consult

Wilson and Gallant (2000) and Bolstad (2019). Table 2.1 lists some of the popular geomorphometric variables.

2.1.3 Segmentation of the Continuous Surface into Geomorphological Units

Grid cells, for which continuous field variables are measured, are not “natural” units for geomorphological analysis. The simplicity of a regularly spaced grid also is its weakness since grid cells cannot be adapted to morphological discontinuities—hence, they are not useful as geomorphological units. Yet, there are many geomorphologic and ecological studies that require the continuous land surface to be first segmented into discrete units based on morphological discontinuities between and/or morphological homogeneity within sections of the land surface. Thus, researchers have devised several methods for discretizing the continuous surface in geomorphometric studies (Minár and

Evans, 2008). Several terms such as geomorphological unit, landform unit, landform element, and terrain (mapping) unit are used by authors to refer to the segments. Evans

(2012) also used the term land surface objects to cover all kinds of segments and landforms. This term is also used in this thesis to refer to any kind of discrete part of the continuous surface, since this term it does not imply scale dependence, maintains a clear reference to the source “land surface”, and does not invoke additional concepts such as geomorphology, terrain or landform. 36

Table 2.1

Subset of commonly used geomorphometric continuous field variables. (Source: Bolstad,

2019).

Both the interior properties of segmented units and the boundaries of such units have a crucial role in the definition of units. There are two approaches to segmentation—one in which the boundary is primary (graph-based segmentation) and the other in which the 37

internal area is primary (classification-based segmentation) (Minár and Evans, 2008). In the first approach, segmentation begins with identification of morphological discontinuities based on extrema points (e.g. peak, pit, and saddle) and extrema lines (e.g. inflection and discontinuity lines of elevation and derived fields of slope and curvature) to demarcate a set of small elementary facets/segments/units, without any gaps.

In contrast to boundary driven morphological segmentation, many researchers have instead relied on the classification approach for deriving the elementary forms of a surface (Minár and Evans, 2008), with the boundary only emerging as a consequence of the classification of cells into one of many possible landform classes. With the advent of

DEMs and computing power, this segmentation approach has come to dominate general geomorphometric analysis. Most methods are supervised classification methods since a set of classes are defined based (primarily but not exclusively) on combinations of threshold values or classified ranges of curvature, slope, and topographic position (Dikau,

1989; Irvin et al., 1997; Krcho, 1973; MacMillan et al., 2000, 2004, 2009; MacMillan and Shary, 2009; Schmidt and Dikau, 1999; Schmidt and Hewitt, 2004; Schmidt and

Andrew, 2005; Shary et al., 1995, 2002; Young, 1972).

The segmented units (variously called land elements, landform elements, landform units, terrain objects, relief units, and terrain form units) exhaustively partition the continuous surface at a given scale or spatial resolution, are bounded by topographic discontinuities and characterized by (relatively) uniform morphometry (Pike et al., 2009).

Their shapes can be summarized using mathematical functions or statistically summaries of one or more geomorphometric variables (e.g. statistical zonal summaries of elevation, slope, aspect, curvature, wetness, topographic position, flow length values for each 38

segment) are used instead. Compared to the boundary-based methods, classification methods support use of wide range of criteria of varying complexity and involving multiple criteria. However, that also increases the subjectivity of these methods because the classes are rarely defined explicitly, and their intended semantics are supposed to be intuited from the label used to describe the class (e.g. peak, shoulder, spur, hollow, valley, channel, and pass). The lack of deep and stable semantics renders such classification schemes of limited use beyond the narrow disciplinary scope for which they were invented. Moreover, because the operational philosophy is minimization of intraclass and maximization of interclass differences, there is no explicit control over the shape and extents of individual segments (landform elements) since position and topology are not explicitly considered (Minár and Evans, 2008).

Minár and Evans (2008) have identified commonalities from many segmentation methods to define elementary forms, which are morphometrically uniform and indivisible, and the smallest geomorphometrically meaningful units of analysis. Like the source grid cells, these units also exhaustively cover the part of the Earth’s surface under consideration, but they are not of regular size or geometric shape. The purpose of delimiting such units is to provide geomorphologically meaningful and morphometrically uniform spatio-structural units that are fundamental to any type of geomorphological analysis. These can, therefore, replace the DEM cells which lack geomorphological meaning. The elementary forms method of segmentation is perhaps as close to a “natural” unit of surface analysis that is possible. These units are quite amenable to formal description based on smooth mathematical functions, which is a preferred approach, 39

especially with better computing power and high resolution DEMs allowing finer scale geomorphometric segmentation.

Elementary forms or equivalent morphometrically uniform units still only provide a transformation of the basic data structure element from arbitrary DEM cells, but they generally need to be aggregated into larger, context sensitive, higher order semantic units for decision making. Hierarchical approaches to geomorphological segmentation and classification have been explored for at least two decades, albeit less commonly. While some have used fuzzy logic (MacMillan et al., 2000; Schmidt and Hewitt, 2004), a few others have relied on object based image analysis (OBIA) methods (Castilla & Hay,

2007; Drăguţ and Blaschke, 2006, 2008; Drăguţ and Eisank, 2012; Drăguţ and Verhagen,

2012; Gercek et al. 2011; Hay and Castilla, 2008; Liu and Xia, 2010; Saha et al., 2011;

Seijmonsbergen et al., 2011; Strobl, 2008) based on success from remote sensing and ecological analysis. OBIA methods can also be credited for combining both spatial and thematic criteria.

2.1.4 Specific Geomorphometry: Features vs Landforms

Irrespective of the theoretical and technical sophistication of how land elements and higher-level objects are segmented, they are ultimately tessellation units describing the shape of the continuous surface of the Earth (or another terrestrial planetary body). These methods can only yield computational land surface objects, which have value in mathematical geomorphometric analysis, but the spatial extents of segmented units will often not correspond to that of the landforms that geomorphologists and people tend to recognize in the real world (Arundel and Sinha, 2018; Evans, 2012). If the goal is to map 40

individual landforms such as mountains, hills, drumlins, landslides, drainage networks, islands, using alternative methods is necessary.

Specific geomorphometry is the study of discrete land surface objects, often called terrain features or landforms, and parts of such objects. This kind of mapping can be termed morphologic mapping, in contrast to morphometric mapping that is the essence of general geomorphometric mapping and analysis. For specific geomorphometric analysis, there are at least two types of land surface objects that need to be distinguished: secondary, localized point/line features and larger landforms, which are the primary subjects of interest in specific geomorphometry. Morphometric features are the most basic descriptors of surface shape. Unlike surface parameters, which can be calculated for every location, morphometric features are identified at only a few critical points on the surface. Note that geomorphometric features (e.g., peak, pit, saddle, ridge line, valley line, and channel end/junction) are used even in general geomorphometry for segmentation or physiographic description of landscapes, but, in specific geomorphometry their primary function is to locate, represent and delineate landforms.

Landforms (in specific geomorphometry) are topographically distinct and salient individual entities, and can be adjacent to, disjoint from, overlap with, nested within, or comprise other landform individuals of a different type). (Evans, 2012; Mark and Smith,

2003, 2004; Sinha 2008). There is no requirement that landforms exhaustively cover the entire continuous surface (Evans, 2012; Pike et al., 2009). As asserted in Sinha et al.

(2018), and acknowledged briefly in Evans (2012), landforms are not just surface segments, but fully three-dimensional, volumetric physical entities. The vertical dimensional of landforms is, therefore, critical, to its definition and full 41

characterization—unlike the two-dimensional land surface objects segmented in general geomorphometric analysis. Finally, it should be noted that unlike the general geomorphometric mapping which yield maps with many classes, semi-automated methods for specific geomorphometry have to focus on one type of landform at a time

(e.g. drumlin, dune, bajadas, drainage network, mountain, valley, and eminence), albeit, the landform category could be broad enough to cover many different sub-categories of landforms (Guilbert and Moulin, 2017; Sinha et al., 2018).

2.2 Semi-Automated Feature Extraction and Mapping of Landforms

As noted in Wood (1996), Evan’s (1972) distinction between specific and general geomorphometry should not be seen as an absolute dichotomy but, rather as sort of a continuum, General geomorphometry represents an approach providing a uniform approach to surface characterization anywhere on the surface (uniformity and consistency). On the other hand, specific geomorphometry allows more specialized recognition and characterization of certain characteristic shapes found on the surface, but the methods cannot be applied uniformly to every location and many parts of the surface will be left practically uncharacterized. General geomorphometry is also purely quantitative, but general geomorphometry’s primary goal is extraction of parts of the surface such that they would exhibit a characteristic qualitative form. The review that follows of geomorphometric feature extraction and landform mapping discusses methods which probably lie somewhere between general and specific geomorphometry on the continuum.

Over the past few decades, many geomorphometric analysis methods and techniques have been proposed to extract landscape elements and terrain features from analysis of a 42

combination of terrain parameters. While manual delineation methods maybe preferred in some cases, (Clark et al., 2009; Dowling et al., 2015), semi-automated methods are, obviously, are far more common. The simplest strategy for automating the segmentation of continuous DEM based terrain surfaces was to directly operate on small neighborhoods around cells (pixels) and assign each cell to one terrain feature category based on supervised or unsupervised classification system (Bennett & Armstrong, 1996;

Burrough et al., 2000; Chang & Sinha, 2007; Clarke & Archer, 2009; Deng and Wilson,

2007; Fisher et al., 2004; Gallant & Dowling, 2003). These methods represent some of the earliest and some of the most elegant examples of transitioning from general to specific geomorphometry. The underlying motivation of these methods was to support summarization and comparison of different types of landscapes in terms of a standard set of morphological units and, optionally, relating them to landcover, soil, and geomorphological processes.

There also are a special class of specific geomorphometric methods that use a region growing approach from a representative feature known to characterize that type of landform. The rules for choosing a signature feature type and to direct the growth and termination of the region can be specified explicitly, reflecting a specific conceptualization of and GIS based implementation of the semi-automated mapping of the landform. Authors have used this method to extract both eminences (Chaudhry and

Mackaness, 2008; Deng and Wilson, 2008; Graff and Usery, 1993; Miliaresis and

Argialas, 1999, 2002; Podobnikar, 2012; Sinha, 2008; Wood, 2004) and valleys (Dowling and Gallant, 2003; Guilbert and Moulin, 2017; Straumann and Purves, 2008, 2011).

Another approach is to create contour trees from the DEM, and reason with contour 43

network graphs as was done recently for mapping complex hierarchical depressions (Wu et al., 2015), wetland depressions (Wu and Lane, 2016) and sinkholes (Wu, et al., 2016).

The region growing and contour tree methods can target only a specific landform category, not multiple categories simultaneously. In contrast, multiclass OBIA landform mapping methods are quite attractive because they could simultaneously extract instances of multiple types of landforms. This efficiency was the primary reason for Arundel and

Sinha (2018) to investigate the feasibility of applying an OBIA workflow (Drăguţ and

Eisank, 2012) for creating footprints for multiple GNIS (landform) features simultaneously to cut down on the need for a unique method for every landform class.

However, results clearly suggested that the chosen OBIA workflow was only suitable for generalized physiographic segmentation of the surface in terms of a set of prescribed geomorphological classes, when there is no interest in any individual landform. While extracted boundaries seemed plausible for some Summit GNIS features, for many others, there was no plausible corresponding object (determined from visual comparison of contours and relief shaded map layer around the GNIS features. Objects extracted for multiple GEOBIA classes also were found to correspond to GNIS Summit features.

Moreover, most of the GEOBIA classes were not found to have statistically significant spatial overlap relationships with any other type of GNIS feature class.

For specific geomorphometric mapping, one-to-one correspondence between (at least) cognitively salient landforms and extracted map landform objects is necessary. It seems that, to guarantee that level of correspondence, separate OBIA workflows (like most supervised learning methods) will be needed for different landform types. Finally, a significant limitation of GEOBIA methods is that they require a highly specialized 44

software (generally the eCognition suite from Trimble is used) and extensive exploratory parameterization for any study area. Thus, it does not seem like GEOBIA can currently offer much in the way of simultaneous mapping of multiple landform types (i.e., linear/non-linear eminences and linear depressions) that are of interest in this thesis.

Other methods need to be researched to try and bridge the general-specific geomorphometric divide such that a small subset of methods can be easily parameterized to derive at least the common landforms of interest to both geoscientists and non-experts.

2.3 Bridging the General-Specific Geomorphometric Divide with Supervised Pattern

Recognition methods for Landform Mapping

This thesis was conceived to continue more research into the feasibility of using existing popular methods for topographic form characterization for simultaneous mapping of a multiple landform types—specifically, the three extremely common superordinate categories: linear and non-linear eminences, and linear depressions. As mentioned above, there are multiple dedicated methods already available for extracting such landforms, but they require substantial parameter customization for each study area.

This is a major impediment in their formal adoption for national scale mapping since so many landform types would need to be explored interactively for different terrain types and areas of a country as large as the US with many different algorithms. For the sake of cognitive and computational simplicity, it is worth exhausting other existing methods that have the potential for supporting automated mapping of several landforms simultaneously, with just minor modifications to values of the same parameters.

Since specific geomorphometry methods are targeted only for specific landform types, the solution then was to find geomorphometric methods that were not designed as 45

surface segmentation methods, but, instead as (supervised) landform pattern recognition methods for searching and detecting the presence of common land surface forms (e.g., peak, saddle, pit, ridge, valley, slope). Completely, unsupervised classification, like the case of landform element mapping, is highly unlikely to yield land surface objects with common sense interpretation. Due to the need for general purpose use by multiple user communities, the methods should also not require too much exploratory parametrization and must be able to support generalization at multiple scales. Ease of use and availability of software were other secondarily important factors in selection of methods for this thesis.

2.3.1 Selection of Pattern Recognition Methods

The search for pattern recognition landform mapping methods led to several candidate methods, mostly designed as supervised learning methods with pre-defined rules for finding form patterns based on analysis of standard geomorphometric variables

(local relief, slope, curvature, topographic position, openness, and visibility).

Interestingly, all candidate methods for semiautomated and multicategory landform mapping are already popular enough to have been implemented as functions in either

SAGA (v 7.6.3) (Conrad et al, 2015) and/or GRASS (Development Team, 2020; Neteler et al., 2012), which have long been popular free and open source GIS software for geoscientific modeling and analysis. Moreover, even though GRASS has a steep learning curve, Quantum GIS (QGIS) can be used instead to call GRASS functions, through a special plugin. QGIS has a far more intuitive user interface and shorter learning curve,

Thus, ease of use and software availability was not a concern, ultimately, while narrowing down the methods to be tested for this thesis. 46

SAGA offers an impressive collection of functions for geomorphometric analysis and measurement through its Terrain Analysis module. Two methods for joint ridge and valley extraction, the Multiresolution Index for Valley Bottom Flatness (MRVBF)

(Gallant and Dowling, 2003) and the Top Hat approach (Rodriguez et al., 2002) based on fuzzy membership calculations in ridge and valley classes would probably be well suited for mapping the core areas of linear eminences and linear depressions, but cannot yield objects for non-linear eminences. An unsupervised classification method (Terrain

Surface Classification) due to Iwahashi & Pike (2007) was found to be suited only for physiographic characterization of the continuous surface, but the boundaries of the segmented objects did not seem to match well that of individual eminences and depressions. Another sophisticated supervised fuzzy classification method (Fuzzy

Landform Element Classification) due to Schmidt and Andrew (2004) combines and modifies morphometric classifications proposed originally by Dikau (1989) and Wood

(1996). It was decided to leave this method for future work and instead first explore the source methods by Dikau and Wood. Both these methods are also implemented in

SAGA.

Dikau’s method is a curvature focused segmentation scheme and quite inappropriate for the purposes of this thesis. However, the method by Wood (1996) can be customized easily to extract morphometric features that by definition are intended to resemble the characteristic forms of linear and non-linear eminences, and linear depressions. Hence, it was chosen as one of the three methods for intensive comparative analysis. This method is implemented in both SAGA and GRASS. The second method chosen for comparative analysis is based on multiscale analysis of the topographic position index (TPI) (Guisan 47

et al., 1999; Weiss, 2001). A subset of the landform classes corresponds to the three abstract landform categories of interest in this thesis: linear and non-linear eminences and linear depressions. The method is implemented as the Multi-Scale Topographic Position

Index function in the SAGA Terrain Analysis module.

The third method is based on the idea of geomorphons, which the authors (Jasiewicz and Stepinski, 2013) describe as machine vision inspired landform search patterns. Three of the geomorphons are modeled after the characteristic forms of linear eminences, non- linear eminences, and linear depressions. This method is available as a function in

GRASS. The remainder of this chapter presents the theoretical details these three methods, and the next chapter discusses how they were used to conduct experiments to answer the four research questions.

2.3.2 Wood’s Multiscale Quadratic Polynomial Estimation and Six Morphometric

Features

Wood’s (1996) method is based on the well-established idea that of the surface of the

Earth may be conceptualized locally as a smooth patch, represented analytically by a bivariate quadratic polynomial function, such as: z=ax2+by2+cxy+dx+ey+f, wherein x and y are projected geographic coordinates, z is the interpolated elevation of the surface at location with coordinates (x, y), and coefficients of the polynomial (A through F) capture information on relief attributes (Evans, 1979, 1980). If a 3x3 window is set on a central cell for a DEM, the nine cell values can be used to construct the polynomial function by calculating the coefficients to get the best estimate of the overall shape of the underlying continuous surface for a small neighborhood around the central point. The first and second order numerical differentiation of the function can also be used to 48

calculate several other geomorphometric variables (slope, aspect, and several types of curvatures) which together can be seen as a system of parameters characterizing the surface at that location. The process can be repeated for any location, which means the original continuous surface is approximated by a series of locally continuous surface patches.

Wood’s novel contribution to this approach was to generalize the method to allow derivation of the local surface patch’s polynomial coefficients for any window size, rather than just the default 3x3 window. This ushered in the era of multiscale characterization of the surface, since surface patches could be created over spatial extents that are relevant to the analytical scale, rather than the scale dictates by the resolution of the raster. The previous approach was to first resample the raster to a coarser resolution but Wood’s method allows generalization based on the original resolution DEM and maintaining the output geomorphometric raster to be at the same resolution, even if a more generalized and smoother version of the surface is to be realized. Since larger tan 3x3 windows include cells at varying distances from the center cell, there is also the option of using distance decay function to control the relative contribution of elevation values from cells farther away from the center. This corresponds to using a weighted least squares regression model to of the coefficients of the quadratic surface being fitted for that window.

Wood also contributed to geomorphometric science by providing a smooth interpolated surface-based detection of six surface specific forms (morphometric features): Peak, Pass, Pit, Ridge, Channel, and Plain. Peucker and Douglas (1975) first suggested characterizing a surface in terms of these types of features, but they operated 49

directly on the discrete DEM, whereas Wood derives the features based on the locally interpolated smooth surface. He considers using discrete DEM values as less accurate.

Figure 2.2 illustrates the local patterns of elevations for the six morphometric features using a simple 3x3 cell, and the conic form of the quadratic surface patch that would be interpolated centered on and around such features. Figure 2.3 summarizes the mathematical formulas for defining morphometric features based on second order derivatives of elevation (curvatures). These formulas are applied to every DEM cell to decide which of the six features they can be (exclusively) classified into. This classification is made contingent on threshold values for slope and curvature thresholds, and the scale of analysis is controlled by choosing the size of the window for constructing the locally continuous surface patch. Larger the window size, the more generalized the surface patch will be, emphasizing more macro scale landforms and smoothing smaller scale landforms.

Wood’s approach to basic geomorphometric variable calculation is a major theoretical advancement in geomorphometry. Many applications of this method are documented for varied research projects (Bolongaro-Crevenna et al. 2005; Chaudhry and

Mackaness, 2008; Ehsani and Quiel, 2008, 2009; Fisher et al., 2004; Gruber et al., 2017;

Schmidt and Hewitt, 2004) and this thesis became another such project to evaluate this method for automated mapping individual instances of intuitively recognizable landform categories. In this thesis, it is assumed that the Peak, Ridge and Channel morphometric classes are sub-categories of non-linear eminence, linear eminence, and linear depression landform categories, respectively (Table 2.2). 50

Wood originally implemented his method and several other terrain analysis functionalities in his open source Landserf software for terrain analysis (Wood, 2009).

The code for geomorphometric feature classification at multiple scales has also been implemented in GRASS GIS as the r.param.scale function and in SAGA GIS as the

Morphometric Features function in the Terrain Analysis module.

Figure 2.2

Use of second-degree polynomials (a) to derive six morphometric feature classes (b) in

Wood (1996). (Source: Zieger et al., 2009).

51

Figure 2.3

Derivation of morphometric features using second derivates (Wood, 1996).

Table 2.2

Correspondence between the three broad landform categories (non-linear eminence, linear eminence, linear depression) and geomorphometric landform classes for the three geomorphometric feature extraction methods. Conceptual Wood’s landform Morphometr Geomorphons TPI Landform Classes category ic Features Non-linear Peak Summit eminence Linear eminence Ridge Ridge High Ridge, Local Ridge, Midslope Ridge Linear depression Channel Valley U-Shape Valley, Canyon

52

2.3.3 Geomorphon-Based “Local” Landform Pattern Recognition

Jasiewicz & Stepinski (2013) recently introduced an innovative landform element mapping technique based on pattern recognition rather than differential geometry. Their method is built around the concept of geomorphon (geomorphologic phonotypes), which are template ternary form patterns with which to “scan” the entire DEM. For comprehensive and exhaustive set of all possible morphological terrain types, a total of

498 geomorphons are required. Critical to the operational definition and detection of geomorphons is the idea of visibility and openness (Yokohoma, and Pike, 2002) since the designed algorithm performs begins by performing line-of-sight calculations in the direction of the 8 neighboring grid cells. Depending on whether the line-of-sight trends downwards, upwards, or stays approximately horizontal, the direction is encoded with a

‘−’,‘+’ or ‘0’ symbol, respectively. The three parameters of importance in this thesis are the outer and inner search distances up to which the line-of-sight computations are performed, and the slope angle (flat) that constitutes the threshold up to which a direction is classified as flat. Finally, based on this ternary pattern, the following ten common landform shape elements are defined and used as search patterns to scan the DEM: Flat,

Peak, Ridge, Shoulder, Spur, Slope, Hollow, Footslope, Valley and Pit. The pattern of these search landform patterns is illustrated in Figure 2.4.

Another novelty of the method is that it self-adapts to identify the most suitable spatial scale at each location so that only a single scan of a DEM is needed to assign an appropriate geomorphon to every cell (location). The geomorphon based method of detecting and classifying landform elements or morphometric features is, therefore, inherently multiscale and computationally efficient. 53

The authors were the first (obviously) to apply this for a general purpose geomorphometric map of Poland, and then also produced a physiographic map of Poland based on landscape similarity (Jasiewicz et al., 2014). Other researchers are now also realizing the benefits of geomorphon based terrain pattern recognition (Gruber et al.,

2017; Rowley et al., 2018).

2.3.4 Topographic Position Index (TPI) Based Landform Mapping

Like elevation, slope and aspect, the underlying concept for the topographic position index (TPI) geomorphometric variable is quite intuitive and easy to explain to even non- experts. As the name suggests, TPI operationalizes the intuitive idea of the relative vertical height of a location with respect to neighboring locations into a quantitative variable. For any DEM cell, TPI is easily calculated by subtracting the elevation of any location from the mean of all elevations in a specified neighborhood.

Figure 2.4

Illustration of the 3D search patterns morphologies and their corresponding geomorphons (ternary patterns) for the 10 most common landform elements. (Source:

Jasiewicz and Stepinski, 2013). 54

This basic concept was suggested first in Guisan et al. (1999) and in Wilson and

Gallant (2000) and can be calculated in any raster GIS package very easily. For example, in Spatial Analyst extension to ArcGIS Desktop 10.6 (Esri, 2020a) or ArcGIS Pro 2.4

(Esri, 2020b) the mean elevation in a neighborhood is calculated using the Focal

Statistics tool in the. Then TPI is calculated as a simple difference raster between the original elevation and the mean (neighborhood) elevation. The choice of the neighborhood size for the Focal Statistics tool controls the scale of analysis.

Positive TPI values define ridge/peak forms in a neighborhood since such locations are higher than the average elevation in their surroundings and. Negative TPI values define local valley forms since such locations are lower than their surroundings. Areas with negligible or constant steep slope are assigned TPI values near zero. Topographic position is an inherently scale-dependent phenomenon, since the chosen size of the neighborhood determines how a location is classified. As shown in Figure 2.5, the same location can be assigned to different landform classes depending on the scale of analysis.

This aligns well with assertions made earlier in this thesis that landform detection/segmentation and classification/categorization can never be definitive but is always context dependent—for instance, the scale of analysis is the context in Figure 2.5.

The scale for calculating TPI should, therefore, depend on the appropriate analytical scale. TPI can also be used to create multiscale signatures for sites by using a series of incrementally larger neighborhoods for analyzing the change in TPI values, until it stabilizes and exhibits no more changes.

TPI is an extremely popular variable in ecological studies since it correlates with soil and vegetation properties. Although TPI is more popular as a continuous variable in 55

general geomorphometric analysis, it has also been used widely for classification of locations to create landform objects (Barka et al., 2011; Gerçek and Zeydanli, 2010;

Gruber et al., 2017; Reu et al., 2013; Mokarram et al., 2015).

In this thesis, a multiscale TPI landform classification system originally proposed by

Weiss (2001) was chosen to explore if can cognitively appealing linear/non-linear eminences and linear depressions could be derived at multiple scales and for different terrain types. Weiss designed a landform classification system by combining information from two TPI rasters created with a smaller and larger neighborhood (search radius), respectively, standardizing the TPI values into standard deviation units, and then classified all locations into one of ten landform classes: High Ridge, Local Ridge,

Midslope Ridge, Canyon, U-Shape Valley, Upland Drainage, Midslope Drainage, Plain,

Open Slope, and Upper Slope. The definitions and TPI thresholds used to define these classes are available in Weiss (2001).

Unlike the Wood and Geomorphon methods, and as indicated in Table 2.2, no TPI class in the chosen TPI classification system was determined to be a strong candidate for mapping non-linear eminences. TPI has three classes instead to map a combination of linear (primarily) and non-linear (secondarily) eminences. The High Ridge class is designed to map locations that are assigned high TPI scores for both small and large scale window based analysis. Thus, the High Ridge class conceptually overlaps with both the non-linear and linear landform categories, but more so with the latter. In experiments,

High Ridge cells identified the highest parts (peaks/summits/tops) of non-linear eminences, but not exclusively since the cells often also connected to delineate linear 56

eminences. Non-linear eminence summits/peaks in high relief areas generally terminate

(or overlap with) non-linear eminences (ridges).

Apart from the High Ridge class, the Weiss (2001) classification also includes two other classes intended to map local highs with high TPI values: Local Ridge and

Midslope Ridge. However, unlike the High Ridge class, these two classes lose their high

TPI score for large scale window analysis, which means that the classes are intended to detect smaller sized local highs embedded within a valley or in planar areas, respectively.

The Canyon and U-Shape Valley classes are both sub-categories of linear depressions, with the Canyon class corresponding more closely to narrower stream channels and the

U-Shape Valley class corresponding to wider valleys (which can contain stream channels delineated with smaller neighborhood windows).

Calculation of TPI, standardizing it and executing the rules to classify pixels into the landform classes from a DEM is straightforward in any raster GIS but is available as the

Multi-Scale Topographic Position Index function in SAGA’s Terrain Analysis module.

(However, for this research project, the SAGA package was not used since TPI was quite easy to implement independently in ArcGIS Desktop 10.6).

A related approach to landform mapping directly inspired by the concept of relative topographic position analysis at a small and large scale is also implemented in Benthic

Terrain Modeler (BTM) (v 3.0) (Lundblad et al., 2006; Walbridge et al., 2017), which was also evaluated briefly for this thesis. However, this option was not chosen since the underlying concept mirrors the TPI based classification, may require more involved exploration of the inner and outer search radius parameters than TPI based classification, and the default classification system is designed for bathymetric data analysis, not to map 57

landforms on dry land. BTM software code is open source and presents a much more interactive interface than SAGA’s Multi-Scale Topographic Position Index function.

However, BTM is an add-on toolbox to, and, hence, cannot be run without a license for the ArcGIS Desktop (Esri, 2020a) GIS software. Since similar results can be obtained with the TPI classification module in open source SAGA GIS, BTM was not explored further for this thesis. However, future work should include a comparison of the relative computational and cognitive efficiencies of SAGA TPI and BTM based landform mapping.

58

Figure 2.5

Illustration of combination of topographic position index (TPI) calculation for a small and a large neighborhood scale to classify locations into landform types. (Source:

Jenness, 2006).

59

Chapter 3: Methodology

3.1 Chapter Overview

As stated earlier, this thesis was conceived to answer three interrelated research questions to help advance automated landform mapping technology. Several methods were reviewed initially, but it became apparent to the author that only three methods by

Wood (1996), Weiss (2001) and Jasiewicz and Stepinski (2013), respectively, should be chosen for detailed exploration. These methods have been cited numerous times and have been shown to produce reliable results for terrain feature extraction. They are also special because they yield features corresponding to all three landform categories of interest in this thesis: non-linear eminences, linear eminences, and linear depressions. In the rest of this thesis, these three methods will be referred by their assigned experimental code names: Wood (Wood, 1996), Geomorphon, (Jasiewicz & Stepinski, 2013) and TPI

(Weiss, 2001).

The experimental validation of these methods was based on an assessment of the degree to which they can be customized to segment out terrain features that would closely correspond to what people would also intuitively recognize as valid representations of real world landform entities. The relative strengths and weaknesses of the three methods also needed to be extensively tested and summarized from a large series of trial experimental runs. Finally, it was also important to determine the degree of geomorphometric similarity between the instances of the semantically similar eminence and linear depression categories, extracted from the application of the three methods. The rest of this chapter provides the rationale and implementation details for the series of experiments conceived to answer each research objective. 60

3.2 Sources of Data

3.2.1 (10-Meters) Resolution DEM

The primary data for this research were 10-meter resolution digital elevation models

(DEM) rasters available for free download from The National Map website maintained by the USGS (USGS, 2020c). For each study area, multiple elevation raster tiles were downloaded, projected to the appropriate map coordinate system for the study area, and then combined into a single mosaicked raster dataset.

3.2.2 Geographic Names Information System (GNIS)

A subset of the Geographic Names Information Systems (GNIS) database (USGS,

2020a) was also used for validating eminence terrain features extracted by the three methods. The GNIS contains basic descriptive information about 2.28 million (current and historical) named physical and cultural geographic features (excluding roads and highways), located in the United States, associated areas, and Antarctica. GNIS classifies every feature into one of 64 feature classes, with 15 being landform related. GNIS terrain features (or some part of it) are characterized by sufficient topographic saliency to be assigned proper names, the generic part of which often is intended to describe the feature type (e.g., Mount Washington, Presidential Range, Tuckerman Ravine). GNIS is, therefore, a good resource of landmark terrain features that can be used for assessing at least a subset of terrain objects extracted from (semi) automated feature extraction methods (Arundel & Sinha, 2018).

The GNIS feature classes, Summit, Ridge, and Valley correspond quite well to non- linear eminence, linear eminence, and linear depression categories, respectively, which are the only landform categories of interest in this thesis. For general reference, the 61

meanings and total count and percentage for these three GNIS feature classes for the entire US are summarized in Table 3.1.

Table 3.1

Definitions and frequency of GNIS feature classes corresponding to the three broad landform categories (non-linear eminence, linear eminence, linear depression) of interest in this study. GNIS Feature Definition Feature Count Class (%) Summit Prominent elevation rising above the 69,645 (11.49%) (non-linear surrounding level of the Earth's surface; eminence) does not include pillars, ridges, or ranges Ridge Elevation with a narrow, elongated crest 14,937 (2.46%) (linear eminence) which can be part of a hill or mountain Valley Linear depression in the Earth's surface that 69,403 (11.45%) (linear depression) generally slopes from one end to the other

The spatial representation of all GNIS features is limited to points—each feature is represented via a single, strategically chosen, point. According to the USGS FAQ webpage “The primary coordinates for features classified as summit, ridge, and range

(all uplifted features), are recorded at the highest point and for linear features (stream, valley, and arroyo) at the mouth” (USGS, 2020b). The highest point for Summit and

Ridge features must also be completely contained within the larger areal extent of the eminence (even if the boundary is spatially undetermined). Thus, it is reasonable to expect that GNIS Summit and Ridge feature coordinates will be contained within some eminence polygon extracted from application of any of the three feature extraction 62

methods (Wood, Geomorphon, and TPI). Since GNIS Valley features are represented by a point at the mouth, the likelihood of such points falling outside extracted linear depression polygons is much higher.

3.2.3 National Hydrography Dataset (NHD)

Since the point locations for GNIS Valley features are not deemed appropriate for validating the linear depression polygons, mapped water courses (streamlines) were chosen instead. The assumption made was that most (if not all) linear depressions would also support a stream of water flowing through them, provided enough precipitation is available in the region. Streamline data for the US are available from the National

Hydrography Dataset (NHD). “The National Hydrography Dataset (NHD) represents the water drainage network of the United States with features such as rivers, streams, canals, lakes, ponds, coastline, dams, and streamgages.” (USGS, 2020d). NHD data specific for the three study areas were also downloaded from the USGS’ The National Map (USGS,

2020c) data viewing and download service.

3.3 Study Areas

Three separate study areas were chosen so that the three feature extraction methods could be tested in a variety of terrain types. All three study areas are in uninhabited areas, and used in previous feature extraction studies (Sinha, 2008; Arundel et al., 2020; Sinha

& Arundel, 2020) that informed this thesis. An important purpose of this thesis is to inform future studies that are being planned at the USGS for automated feature extraction. Thus, it was prudent to continue with study areas that have been used before and will continue to be used for collaborative projects between Ohio University and the

USGS. A brief description of the three study areas is provided in this section. 63

3.3.1 Great Smoky Mountains, Tennessee – North Carolina

The first study area overlaps considerably with the Great Smoky Mountains, which are a subrange of the Blue Ridge Mountains in the famous Appalachian Mountain system in eastern USA. As shown in Figure 3.1, the northern part of the study area overlaps three counties in Tennessee (Cocke, Sevier, and Blount), while the southern part overlaps with four counties (Graham, Swain, Jackson, and Haywood) in North Carolina. Following

Fenneman’s popular hierarchical physiographic mapping system (Fenneman, 1917;

Fenneman & Johnson, 1946) that classifies the continental US into 8 divisions, 25 provinces and 85 sections, this study area falls within the Appalachian Highlands province, with most of the area within the Blue Ridge province’s Southern section. A small northwestern corner of the area crosses over to the neighboring Tennessee section of the Valley and Ridge province.

This study area (90 km by 70 km) is a subset of a larger study area used in the automated extraction of non-linear eminences (Sinha and Arundel, 2020). This subset area was created to reduce the computational burden of processing a large study area, but still maintaining the number of terrain features that could be extracted by the automated feature extraction methods. As shown in Figure 3.1, the study area supports relief of approximately 1,800 meters, with the highest and lowest elevations being 2,023 and 204 meters. There are many notable mountain peaks with high elevations and prominence found in this area.

As listed in Table 3.2 and mapped in Figure 3.2, this study area supports a substantially large number (1,197) of GNIS features corresponding to all three feature types of interest (528 Summit, 385 Ridge and 284 Valley features). The other two study 64

areas do not have as large a total or such an equitable distribution of GNIS features across all three feature types. This study area was, therefore, chosen to be the primary reference for validating the three feature extraction algorithms, while the other two study areas were used for comparative purposes arising from moderate to extreme changes in terrain type.

Figure 3.1

Location, elevation patterns, and distribution of GNIS Summit, Ridge and Valley features within the second study area in the Great Smoky Mountains study area, along the

Tennessee – North Carolina border. 65

Table 3.2

GNIS feature counts for the three GNIS feature classes corresponding to the three landform categories (non-linear eminence, linear eminence, linear depression).

Study Area GNIS Feature Class Feature Count (%) Summit 528 (44%) Great Smoky Mountains, NC-TN Ridge 385 (32%) (90 km X 70 km) Valley 284 (24%) Total 1,197 Summit 545 (86%) White Mountains, NH Ridge 67 (11%) (90 km X 105 km) Valley 24 (4%) Total 636 Summit 43 (43%) Colorado Plateau, NM Ridge 3 (3%) (90 km X 110 km) Valley 55 (54%) Total 101

3.3.2 White Mountains, New Hampshire

The second study area (90 km by 105 km) is situated in the White Mountains area in

New Hampshire and includes the famous Presidential Range mountain range (center of

Figure 3.2) which supports the highest peaks of the White Mountains. The entire White

Mountains region is heavily glaciated and characterized by mountainous landforms with high relief and steep slopes. Thus, geologically, this part of the US is somewhat different from the more heavily eroded Great Smoky Mountains area. This study area, therefore, offers a moderate change in terrain type, compared to the primary study area in Great

Smoky Mountains. Following Fenneman’s physiographic classification, this chosen study area lies in the White Mountain section of the New England province within the northeastern edges of the Appalachian Highlands division. A small part of the study area 66

in the west crosses over from the White Mountain section to the adjacent New England

Upland section.

This second study area is a subset of the larger reference study used in a comprehensive study of eminence feature extraction in Sinha (2008). The smaller area was created as a subset to increase computational efficiency, to maintain a similar extent compared to the first study area, and to keep the Presidential Range in the center, since several well-known terrain features are to be found within and around the range. This study area also exhibits a relief of approximately 1,800 meters, with the highest elevation

(1,917 meters / 6,288 feet) attributed to the famous peak of Mount Washington, the second highest mountain peak on the eastern coast of the United States. As listed in Table

3.2 and mapped in Figure 3.2, this study area supports a similarly large number (545) of

Summit GNIS features, but substantially fewer instances of Ridge (67) and Valley (27)

GNIS feature classes. This area was chosen, therefore, to test how moderate change in terrain type affects the number, spatial extents, and geomorphometric signatures extracted features obtained from the three feature extraction methods.

3.3.3 Colorado Plateau, New Mexico

The third study area is in western San Juan County in New Mexico (Figure 3.3). The northwest corner of the study area is adjacent to the famous Four Corners intersection of the boundaries of the states of Utah, New Mexico, Colorado, and Arizona. Close to the center of the study area is the famous “Shiprock” formation, in the Navajo reservation in

New Mexico. The spatial extent of this area is 90 kilometers by 110 kilometers. This study area in the Colorado Plateau area was chosen originally in Sinha (2008), and forthis 67

study, because of the starkly different physiographic characteristics compared to the mountainous study areas in the Great Smoky Mountains and the White Mountains.

Figure 3.2

Location, elevation patterns, and distribution of GNIS Summit, Ridge and Valley features within the second study area in the White Mountains study area in New Hampshire.

Following Fenneman’s physiographic classification, this study area lies in the Navajo section of the Intermontane Plateau province of the Colorado Plateaus division. A small part along the north central edge of the study area crosses over to the adjacent Canyon

Lands section. Since the area lies in the high-desert plateau area of volcanic origin, it is 68

characterized mostly by slopes of less than two degrees, with some scattered portions exhibiting with slopes under five degrees.

Figure 3.3

Location, elevation patterns, and distribution of GNIS Summit, Ridge and Valley features within the second study area in the Colorado Plateau study area in New Mexico.

There is only a scattering of a few, well-formed, but relatively isolated higher elevation eminence features. In contrast to the sharp mountain peaks, most of the eminences and ridges are best described as mesas with characteristic flat tops, whose highest points may not be as salient as mountain peaks. As listed in Table 3.2 and 69

mapped in Figure 3.3, only 43 Summit and 3 Ridge GNIS features are officially recognized on USGS topographic maps of this area, reflecting the lack of mountainous peaks and flat terrain. Unlike the other study areas, Valley GNIS features (55) are most common in this study area, and most of them are concentrated in the northeast. Based on this description of the study area, it should be obvious that this study area offers an extreme contrast from the eroded tectonic terrain of the Great Smoky Mountains, and the heavily glaciated, rugged terrain of the White Mountains.

3.4 Methodology for Answering Research Questions

The overall methodology used to answer the four research questions listed in Section

1.3 is presented in this section. The general approach was to run a large number of experimental runs and results were compared visually and statistically. All research questions could be answered by focusing on different combinations of map layers and summary statistics generated from each experimental run.

3.4.1 Parametric Variation

As mentioned earlier, three study areas in different parts of the US were chosen to explore the impact of terrain type on the choice of optimal parameter values for customizing the Wood, Geomorphon and TPI methods such that they would yield delineated areas that would correspond to what people would also intuitively recognize as topographically distinct and salient landforms.

First, the three input DEMs corresponding to the three study areas, respectively, were smoothed once using a mean filter. Since the goal in this project is to automatically map meso and macro scale landform features, smoothing was assumed to help by masking small range variations (noise) and enhancing the spatial autocorrelation signal necessary 70

to detect topologically connected, larger features. The Focal Statistics tool in the Spatial

Analyst extension to ArcGIS Desktop 10.6 was used for smoothing. A 3x3 rectangular window and the mean statistic type was chosen as parameters.

For each study area, the analysis was performed at six scales for 10-meter resolution

DEM, where scale control was operationalized by varying the neighborhood kernels

(windows) used for classifying cells into a single terrain feature class for any method.

Table 3.3 lists the 6 neighbor window sizes chosen for all three methods of terrain feature extraction. In addition, for both the Wood and Geomorphon methods, five slope threshold values were tested for each window size. Additionally, for only the Wood method, two different curvatures were also tested for each window size and slope threshold combination. The last row in Table 3.3 lists the total number of experimental runs executed for each method and study area. For both the Wood method, there were 60 experimental runs implemented for each study area, leading to a total of 180 runs. For the Geomorphon method, there were 80 experimental runs for each study area, leading to a total of 240 runs. For the TPI method, the chosen combination and inner and outer thresholds required only 16 experimental runs, leading to a total of 48 runs for all three study areas. Thus, a total of 468 experimental runs were implemented for this thesis.

3.4.2 Visual Geomorphometric Analysis

Given the large number of parameters and resulting map layers that needed to be evaluated, it was important to first gain a generalized sense of how changing a parameter’s value affected the overall quality of the feature classification. Visual analysis of results was the most intuitive way to begin the analysis. For visual analysis, a few 71

reference layers were added to provide physiographic context: topographic basemaps, 2D hillshade relief maps, and 3D views of satellite imagery draped over an elevation layer.

Table 3.3

Parameters and values chosen to conduct experiments with the Wood, Geomorphon and

TPI feature extraction methods.

Parameter Wood Method Geomorphon Method TPI Method

Outer Inner search Window size search Large radius Small scale (#cells) radius scale (#cells) (#cells) 11 11 0, 5 11 0, 5 21 21 0, 10 21 0, 10 Neighborhood 31 31 0, 10, 15 31 0, 10, 15 Size 41 41 0, 10, 15 41 0, 10, 15 (# cells) 51 51 0, 15, 25 51 0, 15, 25 61 61 0, 15, 25 61 0, 15, 25 Slope threshold 1, 5, 10, 15, 20 1, 5, 10, 15, 20 N/A N/A Curvature 0.001, 0.0001 N/A N/A N/A Total # experimental 60 80 16 runs

Visual analysis of classified rasters from 468 experimental runs was obviously a time- intensive task, but there is no better way to understand the cognitive plausibility of extracted objects than to visually assess the objects against the topographic setting. After the extensive, painstaking visual assessment, a small set of optimal parameters for each 72

category was identified based on the author’s assessment of which values tended to produce the most plausible shapes and extents of features.

3.4.3 Quantitative Analysis of Parametric Impacts Using a Confusion Matrix

Visual exploratory analysis clearly has limits since it is impossible to manually assess all parts of such large study areas for so many raster pairs. While the analysis presented earlier is reliable and robust, it still needs to be complemented with quantitative summaries of areas classified into the same or different morphometric types/ or landform classes area as experimental parameters are changed for the same method. As discussed in the next chapter, these summaries further underscored the patterns observed by the painstakingly done visual analysis and as expected, revealed some new patterns not determined from visual analysis.

The quantitative comparison of results from different experiments can be undertaken by deriving a confusion matrix (also known as error matrix when one source can be considered as a reference dataset). A confusion matrix is a square matrix with rows and columns representing the same variables but from two different sources, while the cells of the matrix contain values measuring the frequencies of co-occurrence or agreement

(Figure 3.4). The confusion matrix can be derived only for categorical data—and only if two datasets to be compared are classified using the same classification system. If two different classification systems need to be compared, that is a more general case of contingency table analysis (section 3.4.5 below).

The comparison of categorical rasters can be done by overlaying them and tabulating the areas observed for every (cross)pair of categories from the two rasters (Figure 3.4).

All raster overlay analyses were implemented in ArcGIS Desktop 10.6 using the Tabulate 73

Area tool available in the Zonal toolbox available within the Spatial Analyst extension.

The Tabulate Area tool takes as input two categorical datasets and outputs a M*N cross- table, where M and N are the number of categories coded in the two rasters, respectively

(Figure 3.5). The values in the cells of the M*N cross-table represent the amount of overlap area for each possible categorical combination between the two rasters. The overlap areas can be normalized by converting to percentages by dividing cell areas by the sum of all cell values (i.e., the total area of overlap under the two input rasters). Note that Figure 3.5 illustrates the more general case of contingency table creation, since the two rasters map different variables, but if they were to map the same variable, the number and labels for the classes from both rasters would be identical, creating a square table, which can be interpreted as a confusion matrix.

Table 3. 4

Example layout of a confusion matrix. Variable 1 (Raster 1)

Category 1 Category 2 Category 3

Variable 2 Category 1 Area11 Area12 Area13

(Raster 2) Category 2 Area21 Area22 Area23

Category 3 Area31 Area32 Area33

The overall similarity between identically classified categorical datasets can be measured simply by calculating the ratio of area in the diagonal cells of the confusion matrix to the total area of all cells, since only the diagonal cells identify areas classified 74

identically in both datasets (rasters). A better summary measure is the Kappa index which also uses only diagonal values (similar category matches only) but adjusts for chance agreement by comparing observed to expected agreement values in the diagonal cells from row and column marginal totals for each category (Congalton et al. 1983; Congalton

1991). Another popular summary measure that adjusts for chance is the Chi-Square statistic that

Figure 3.4

Illustration of the concept of the Tabulate Area tool in ArcGIS Desktop 10.6.

uses all values (not just diagonal cell values) (Wikipedia, 2020a). However, since the

Chi-Square value depends on the units of measurement, it can evaluate to unwieldy large numbers. Thus, in most cases, when the goal is only to summarize association values, the normalized Cramer's Coefficient V and Contingency Coefficient C (Wikipedia, 2020b) 75

indexes are preferred. Finally, for confusion matrix analysis, overall summary measures can also be complemented with analysis of class specific errors of exclusion (omission) and errors of inclusion (commission) (Congalton et al. 1983; Congalton 1991). These measures help understand how a class from one dataset (raster) is “confused” with a non- equivalent class in another dataset (raster).

3.4.4 Quantitative Analysis of Parametric Impacts by Comparison with GNIS Features

As discussed above, in this study, GNIS features serve as an external source of reference to test the cognitive validity of extracted objects from the various experimental runs. Since GNIS features are represented only as points, the best approach is to overlay them against extracted objects and measure the nearest distance between GNIS features and the region of the corresponding type of landform object. Only if the distances are zero or at least within a chosen threshold depending on raster resolution and inherent positional accuracy of GNIS features, can the features be assumed to be contained within the region of a corresponding landform object. The numeric frequency of contained

GNIS features for each object type was primarily used for complementary diagnosis after the extensive visual geomorphometric analysis. More details about how this analysis was undertaken are provided in the next chapter before the discussion of experimental results.

3.4.5 Quantitative Comparison of Classification Methods Based on Contingency

Tables

The methods described so far in this chapter helped directly answer the first subset of research questions (A.i and A.ii) outlined in section 1.4. These relate to the impact of choice of parameters for the three methods and the degree of variation induced due to changes in terrain type or physiographic context. These methods also indirectly helped 76

answer the second set of research questions (B.i and B.ii) outlined in section 1.4, since visual and quantitative geomorphometric analysis and GNIS shortest analysis for the three different methods for three study areas already reflect many differences between the methods. These indirect comparisons were also supplemented with direct comparisons of classified rasters based on contingency table analysis.

There is no work known to the author from an extended search of available literature that provides a systematic comparison of the Wood, Geomorphon and TPI methods. The semantics and equivalencies between feature types or landform classes from these methods cannot merely be assumed from the assigned category labels. To what degree are such supposedly similar categories equivalent? While some categories could be assumed to be somewhat equivalent between the methods (e.g., Ridge-Ridge, Channel-

Valley, Peak-Summit for the Wood and Geomorphon methods, respectively), each method also has categories that do not seem to have a direct equivalent in other methods. Even for seemingly similar and equivalent feature types and landform classes, the correspondence between such classes or between all possible pairs of classes from two input datasets needs to be clearly measured. In an ideal case, there should be a mutually exhaustive overlap pattern observed if landform feature types or classes were perfectly equivalent. However, this is unlikely since the methods are reliant on substantially different conceptual categories and use different parameters as well. Thus, what needs to be evaluated is to what extent do the areas allocated to one class in one method overlap with the areas allocated to an equivalent class in the other method.

For a more direct comparison of results from two different methods for the same study area, rasters from different methods were also overlaid to create contingency cross- 77

tables, similar to what was done for calculating confusion matrices for comparing results from the same method (section 3.4.2). When two different categorical classification systems are compared (e.g., from the Wood, Geomorphon and TPI methods), the cross- table is conceptualized as a more general contingency table, with rows and columns representing different variables. Since the process of overlaying categorical rasters and creating cross-tables is identical for both contingency tables and confusion matrices, the

Tabulate Area tool was again used for creating contingency tables just like it was used for confusion matrices. Figure 3.5 illustrates the concept of contingency table derivation from raster overlays.

Overall accuracy and Cohen’s Kappa are not valid summary measures for contingency table summarization since the categories from the two datasets (rasters) are not equivalent. Only Cramer's Coefficient V and Contingency Coefficient C were calculated, therefore, to measure the overall spatial association patterns between the morphometric features and/or landform classes from the Wood, Geomorphon and TPI methods. As with analysis of the confusion matrix, overall summary measures were complemented with analysis of class specific column and row normalized percentages.

These measures cannot be interpreted help understand how a class from one dataset

(raster) is “confused” with a non-equivalent class in another dataset (raster).

3.5 Software

All cartographic mapping and map-based analyses were done with ArcGIS Desktop

10.6 (Esri, 2020a) or ArcGIS Pro 2.4 software (Esri, 2020b). The TPI method (Weiss,

2001) was implemented in ArcGIS Desktop 10.6 as an automated script developed using the Model Builder graphical scripting tool. The details of the model for classifying 78

features based on TPI and slope threshold values have already been discussed in the previous chapter.

The methods proposed by Wood (1996) and Jasiewicz and Stepinski (2013) require extensive GIS programming if implemented from scratch. However, both methods are available now as ready to use functions in the well-known GRASS GIS software package

(Development Team, 2020). The Wood method can be accessed via the r.param.scale function (Figure 3.6), while the Geomorphon method can be accessed via the r.geomorphon function (Figure 3.7) in GRASS. These functions (along with most other

GRASS functions) can also be accessed through the open source Quantum GIS software, which was the option chosen to implement all experimental runs with the Wood and

Geomorphon methods.

For the r.param.scale, all possible combinations of window size, slope and curvature parameter values, as listed in Table 3.3, were varied one at a time to generate 60 alternative terrain feature classifications for each study area, based on the Wood method.

Similarly, for the r.geomorphon function, all possible combinations of the outer search, inner search, and flatness threshold parameter values, as listed in Table 3.3, were varied one at a time to generate 60 alternative terrain feature classifications based on the

Geomorphon method. All output TIFF format rasters were then imported into the ArcGIS

Desktop 10.6 software for the mapping and spatial analysis tasks summarized above.

79

Figure 3.5

Screenshot from Quantum GIS software showing initial default parameter values for the r.param.scale function based on Wood (1996).

80

Figure 3.6

Screenshot from Quantum GIS software showing initial default parameter values for the r.geomorphon function based on Jasiewicz and Stepinski (2013).

81

Chapter 4: Results and Discussions

4.1 Parametric Variation

The foremost question that served as the inspiration for this thesis was to discover the ranges of parametric values for three popular geomorphometric analysis methods proposed by Wood (1996), Weiss (2001), and Jasiewicz and Stepinski (2013) for the specific purpose of deriving plausible areal extents for (instances of) three common landform categories: non-linear eminences, linear eminences, and linear depressions.

Since this research is largely motivated by the USGS research agenda on national scale terrain feature extraction and landform mapping, the experiments were planned for three study areas in different physiographic regions to assess if the best parametric values for feature extraction from DEMs vary considerably with type of terrain (physiographic and geological context). Depending on the findings about how much the best parametric choices for the three methods varied across the three study areas, recommendations could be made about the possibility and challenges in national or regional standardization of parametric values and the use of one or more methods for national scale semi-automated terrain mapping.

The summary of the range of parametric values tested for the Wood, Geomorphon, and TPI feature extraction and/or landform classification methods for three study areas is available in Table 3.3. Each method is characterized by a different, if not altogether unique, set of parameters. The only common parameter was the use of a range of neighborhood window sizes to assess feature extraction at multiple scales. Overall, this extensive range of parameter values tested led to 468 experimental trial runs, each yielding a separate classified raster dataset representing areas classified as belonging to 82

the feature/landform element type automatically extracted by the corresponding method.

The large number of experimental configurations and rasters created substantial data management and processing challenges. For ensuring future scientific validation and repeatability, considerable time and resources were spent in workflow automation. Thus, all experiments were automated with the help of several workflow automation models created with the Model Builder visual scripting functionality available in ArcGIS

Desktop 10.6. This also ensured that all experimental datasets were automatically created, named and stored systematically in geodatabases which will be available permanently for further validation and extension of this research in the future.

4.1.1 Overview of Visual Geomorphometric Analysis

Because there was such a large number of output classified rasters to evaluate and visual assessment of results must be the starting point since the goal is to produce maps that would correspond to people’s intuitive assessments in the field, the first step was to engage in visual pattern analysis to select a smaller set of candidate parameter values for each method. The findings from this manually intensive process was to identify a small subset of parameters that were deemed to create the best terrain features as determined by comparison with topographic basemaps, GNIS Summit, Ridge and Valley features, and the size and shape of extracted features. The smaller subset of output rasters was then subjected to a more comprehensive and rigorous visual and quantitative analysis. This two-phased approach was considered better than running just a few experiments based on a few combinations of parameter values, since there does not exist any reliable way to determine which sets of parameter values can lead to acceptable results. The following 83

sections summarize the findings from the visual analysis of each method for each study area.

A common methodology was used to standardize the visual assessment of hundreds of rasters obtained for each method for each study area. For each method, all raster map layers were symbologized identically using the same color scheme for the morphometric feature or landform element categories to standardize the visual representation for comparison of the rasters. The author then spent several days combing through and examining many different parts of each study area while comparing the results from the different experimental runs. For the benefit of readers, 2D map panels and 3D scenes were created (Figures 4.1 – 4.12) for illustrating the impact of choice of parameters for one strategically chosen part of each study area. The same region for a study area was used to construct the map panel for all three methods. The region was selected such that there were enough instances of all types of linear/non-linear eminences and linear depressions across all methods.

Based on the comprehensive visual analysis, the general patterns of results for most parts of the study areas were found to be quite similar. The map panels can, therefore, be considered representative of the overall study area. It needs to be stressed here that this initial visual assessment was used only to narrow down the range of parameter values whose maps could then be examined visually in more detail. It was also necessary because visual assessment is essential and crucial for assessing the cognitive validity of the results. Although visual assessment of maps is subjective and harder to describe objectively, the overall Gestalt perceptual assessment of mapped features is only possible from assessment of map displays. This subjectivity is not a limitation of this thesis 84

though since extensive quantitative summaries of the shapes and sizes of extracted features and how they overlap with GNIS features were also generated and are analyzed in detail in later sections of this chapter. However, it is worth noting that such summaries can only provide supplementary evidence and are still secondary to the much more intuitive visual shape pattern analysis necessary for cognitive validation.

4.1.2 Mapping Wood Morphometric Features

For the Wood method, classified terrain feature rasters from 60 experimental runs were evaluated. Figures 4.1 – 4.3 are map panels illustrating the impact of slope, curvature, and window size parameters for strategically chosen parts of the three study areas. The maps were designed to show only three types of morphometric features, Peak,

Ridge, and Channel because they, respectively, correspond to non-linear eminence, linear eminence, and linear depression landform categories. The other categories (Plane, Pass, and Pit) were not mapped to simplify map patterns and their interpretation, but all feature types were included in the analysis of confusion tables (section 4.2) used for intra-method comparisons and contingency tables (section 4.4) for inter-method comparisons.

From the overall visual analysis of experimental results, the impact of slope, curvature and window size parameter choices were quite similar in the White Mountains

(NH) and the Great Smoky Mountains (NC-TN) study areas because of their similar physiographic characteristics. Both areas are characterized by high elevations and elevation ranges, steep slopes, ridges, spurs, valleys, gorges, ravines etc. (based on generic parts of named features recorded in GNIS and shown on topographic maps of the area). Thus, the choice of the best parameter values for mapping any of the three types of landforms of interest is similar in both regions, which is not surprising. Interestingly, 85

even the third study area in the Colorado Plateau, despite its greatly different terrain type seemed to yield the best results for similar parameter values, with only a slight exception for the case of mapping non-linear eminences as discussed below. The following are the general observations that can be made from the visual analysis of all the 60 rasters (also observable in Figures 4.1 – 4.4) across all study areas.

• Study area: The best parameter values tend to be the same across all three study areas

for mesoscale specific geomorphometric mapping of landforms using the Wood

method.

• Window size: Because of the expected scale effect, small window sizes below 300

meters produce noisy classified images with too many small-extent landform

instances that appear more arbitrarily segmented features than corresponding to whole

landforms that people may recognize in the field or by examining looking at

topographic maps or interactive 3D geovisualizations (Figures 4.4) supported in GIS

software. In contrast, larger window sizes beyond 400 meters tend start yielding

considerably fewer instances for all types. At neighborhood scales of 500 meters or

more, extracted Ridge and Channel feature instances become too broad to be

considered linear, while for Peak features the area becomes much larger and the

number of features decreases considerably.

• Slope: The choice of best slope values tends to be noticeably different for linear and

non-linear landforms. For non-linear landforms (Peak features), slope threshold

values between 5° to 10° yield plausible results, whereas for linear eminences and

depressions, the best slopes are between 10° to 15°. 86

• Curvature: As for the slope parameter, the choice for best curvature value is

substantially different for the non-linear and linear landforms. Curvature threshold

values of 0.0001 are needed to extract plausible shapes and sufficiently high

frequencies of non-linear eminences (Peak features) but for non-linear eminences and

depressions the curvature threshold needs to be 0.001 to yield more linear shaped than

broader shaped features. This is quite clearly interpretable if the map panels for the

three study areas are examined for the two sets of curvature values across all window

sizes and slope thresholds.

• Landform categories: As can be inferred from the discussion above on how

parameters affect results, for this method, parameter values for extracting non-linear

convex shaped landforms differ from those needed to extract linear landforms.

However, both convex (eminence) and concave (depression) linear landform

categories can be extracted with similar parameter values for all three study areas.

87

Figure 4.1

Mapping Wood morphometric features for the Great Smoky Mountains (NC-TN) study area.

88

Figure 4.2

Mapping Wood morphometric features for the White Mountains (NH) study area.

89

Figure 4.3

Mapping Wood morphometric features for the Colorado Plateau (NM) study area.

90

Figure 4.4

3D geovisualization of results from one visually appealing (top) and one visually unappealing (bottom) experimental run for the Wood method for the Great Smoky

Mountains (NC-TN) study area.

91

4.1.3 Mapping Geomorphon Landform Classes

Following the analysis of the impact of variation of parameters for the Wood method, similar parametric variations were implemented for testing the Geomorphon method for the three study areas. This method too requires choice of a slope threshold, and for setting the scale of analysis, users need to select an inner and an outer search radius, which controls the minimum and maximum size of landform elements, respectively. The outer search radius is primary and equivalent to the window size parameter of Wood’s method.

The inner search radius acts like an additional filter to control the smallest size landform element that can be extracted. Unlike the Wood method, the Geomorphon method does not use the curvature geomorphometric parameter.

As listed in Table.3.3, for the Geomorphon method 80 classified rasters from experimental runs were for generated for each study area (240 rasters total). The overall patterns of the impact of parameters and the stability across all study areas corresponded well with the findings made from experiments with the Wood method. As for Wood’s method, map panels were created (Figures 4.5 – 4.7) for a strategically chosen portion of each study area to illustrate the impact of the variation in the values of the three parameters. The maps were designed to show only three landform classes, Summit, Ridge, and Valley since their shape description most closely correspond to the non-linear eminence, linear eminence, and linear depression landform categories, respectively. The other seven categories were not mapped to simplify map patterns and their interpretation, but all classes were included in the analysis of confusion tables (section 4.2) used for intra-method comparisons and contingency tables (section 4.4) for inter-method comparisons. 92

• Study area: Like the Wood method, the best parameter values tend to be the same

across all three study areas for mesoscale specific geomorphometric mapping of

landforms using the Geomorphon method.

• Outer/Inner window size: The outer search radius (akin to window size parameter in

the Wood method) was also found to work best for a scale of 31x31 to 41x41 cells

(approximately 300 meters to 400 meters), which is the same as inferred for the Wood

method. Smaller values of outer search radius of (11x11 and 21x21) lead to thinner

and small extents that seemed to lie scattered across the study area and did not

correspond well to cognitively plausible “whole” landforms. Using a larger scale

(outer search) of (51x51) or (61x61) creates larger and uncharacteristic shapes, so

those are also not desirable, like what was observed for the Wood method and as

evident from Figures 4.5 – 4.7. For the inner search radius, choosing a radius of

around 15 cells seemed to produce the best results, and not eliminate the good

candidates for landform instances.

• Slope: The best slope value for extracting the three landform categories of interest in

all study areas was around 1°. Thus, the best results can be observed in the first

column of in from Figures 4.5 – 4.7. The slope threshold value has much narrower

range or, in other words, the Geomorphon method is much more sensitive to the slope

parameter than the Wood method. Increasing slope values to beyond 5° substantially

limits the number of Summit (non-linear eminence) and starts disrupting the

topological connectivity of non-linear eminences. Beyond a slope threshold of 10°,

the map looks almost empty with very few landform objects extracted for any

landform category. 93

• Landform categories: Based on the discussion above, it can be concluded that, unlike

the Wood method, the Geomorphon method perform equally well for both non-linear

and linear landform categories for the same choice of best parameter values.

94

Figure 4.5

Mapping Geomorphon landform classes for the Great Smoky Mountains (NC-TN) study area.

95

Figure 4.6

Mapping Geomorphon landform classes for the White Mountains (NH) study area.

96

Figure 4.7

Mapping Geomorphon landform classes for the Colorado Plateau (NM) study area.

97

Figure 4.8

3D geovisualization of results from one visually appealing (top) and one visually unappealing (bottom) experimental run for the Geomorphon method for the Great Smoky

Mountains (NC-TN) study area.

98

4.1.4 Mapping Topographic Position Index (TPI) Landform Classes

The TPI method was the simplest to analyze because it has only the two large scale and small-scale window size parameters that control, respectively, the upper and lower size limits of extracted objects. There were only 16 rasters for each study area allowing for a much faster visual analysis. As for the other two methods, map panels were created for the same portion of the study area as used for the other two methods. Since TPI was determined to lack a reliable class for mapping non-linear landforms, only the five landform classes corresponding closely to linear eminences and depressions categories are mapped. High Ridge, Midslope Ridge and Local Ridge all were determined to correspond to the non-linear eminence category, while both Canyon and U-Shape Valley were determined to correspond to the linear depression category.

• Study area: Like the Geomorphon method, the best parameter values for the TPI

method were the same across all three study areas for mesoscale specific

geomorphometric mapping of landforms. However, as can be seen from the broad

shapes of extracted landform objects in Figure 4.11, for the Colorado Plateau study

area, the TPI method tends to perform much worse in low relief and gently sloped

areas than the other two methods.

• Large/Small scale window size: As for the Wood and Geomorphon methods, the best

primary neighborhood size window was judged to be between 31x31 to 41x41

(approximately 300-400 meters) across all landform categories for all study areas.

Moreover, as was the case with the Geomorphon method, the best choice for the

smaller scale window size was determined to be 15x15 (150 meters). 99

• Landform categories: Compared to the other two methods, the TPI method fails to

detect many instances of non-linear eminences. This was especially noticeable for the

Colorado Plateau study area in New Mexico which hosts many smaller sized, isolated

non-linear eminences. This was expected since the TPI method lacks a dedicated

class for mapping non-linear eminences (section 2.3.4). The map panels in Figures

4.9 – 4.11 illustrate this quite well. The High Ridge class cells overlap with tops of

several non-linear eminences mapped by the Wood and/or Geomorphon methods, but

those cells tend to connect with other cells to delineate linear eminences, rather than

identify localized non-linear eminences. Thus, as expected, the maps lack clear

representation of isolated cell clusters that would correspond to the non-linear

eminences, unlike what was observed for the Wood and Geomorphon maps which

have dedicated classes for mapping non-linear eminences. Also, for the same scale

(window sizes) of analysis, the High Ridge class yields much narrower and linear

looking landforms than the wider shapes of the linear eminences obtained for the

Wood and Geomorphon methods. Local Ridge and Midslope Ridge cells that are

supposed to correspond to other linear eminences at lower elevations within broader

valleys or in planar areas comprised a negligible portion of the study area and hard to

detect except at very large scales. The non-linear depression landform types (Canyon

and U-Shape Valley) are extracted more reliably as topologically continuous objects,

with the U-Shape Valley being the most consistently delineated type for almost all

experiments.

100

Figure 4.9

Mapping TPI landform classes for the Great Smoky Mountains (NC-TN) study area.

101

Figure 4.10

Mapping TPI landform classes for the White Mountains (NH) study area.

102

Figure 4.11

Mapping TPI landform classes for the Colorado Plateau (NM) study area.

103

Figure 4.12

3D geovisualization of results from one visually appealing (top) and one visually unappealing (bottom) experimental run for the Geomorphon method for the Great Smoky

Mountains (NC-TN) study area.

104

4.2 Quantitative Analysis of Rasters from the Same Method Using a Confusion

Matrix

Since the best range of parameter values for each method were already determined based on visual analysis, confusion matrix analysis was used to compare a small subset of experiments to complement the visual assessment with a simple quantitative summary analysis. The analysis was also repeated for all three study areas. Several Excel sheets for each set of method and study area were generated. However, since every confusion matrix analysis yielded three tables, tabulations from only one analysis for each method and only for one study area (the Great Smoky Mountains) are presented for illustrative purposes in this section. Even though cross tabulation details are not provided from other confusion matrix analyses, insights from those analyses also informed the analysis below.

In future analyses, more detailed graphs should help add more nuance to the results discussed below.

4.2.1 Wood Method

Tables 4.1 – 4.3 summarize results from the comparison of rasters from two experiments for the Wood method. These two experiments were run with identical window size (41x41) and curvature threshold (0.0001) values but differed only in the choice of slope thresholds (15°and 10°). The overall similarity measures (overall similarity, Kappa, Cramer’s V, Contingency C) suggest considerable degree of similarity, which is not surprising since visual geomorphometric analysis revealed that slopes of 10°

15° produce similarly good results. With the confusion matrix analysis, it becomes possible to provide an overall quantitative assessment of the (dis)similarity caused by a slight change in the slope threshold value. The row and column total percentage values 105

reveal the relative proportions of each category’s coverage across the entire study area for the two methods. From this analysis, it appears that increasing the slope threshold from

10° – 15°, the amount of area classified as Channel and Ridge increased but the area classified as Peak decreased.

Also, if the curvature threshold was changed from 0.0001, the proportion of Peak cells decreases drastically to less than 1%, while the proportion of Ridge and Channel cells also decreases by 40%-50%, and the proportion of the ‘catch-all’ Planar cells increases to about 60%. One example of study area percentages for a Wood method experiment run curvature threshold of 0.001 (and window size 41x41 and a slope threshold of 15°) is presented later in Table 4.19 in section 4.4.1, which is focused on comparing the semantic similarity between the Wood and Geomorphon classification systems. This observation about the impact of curvature threshold values is consistent with the assessment from visual analysis which also clearly suggested that a curvature of

0.0001 is needed to extract more linear shaped than broad and wide linear eminences

(which also explains the increase in Planar cell percentage).

Table 4.2 was created to compare areas under each morphometric type for the raster with a slope threshold of 10° (Raster 10°) are classified by the raster generated with a slope of 15° (Raster 15°). Each column’s percentage values add up to 100% in this table.

Within any column, the row specific percentage values specify what percentage of the total (100%) area under that feature type for Raster 10° was classified as the same

(diagonal cell) or different feature type (non-diagonal cells) in Raster 15°. Ridge and

Channel cells from Raster 10° seem to be almost perfectly classified in Raster 15°

(99.26%, and 98.14% agreement, respectively), but 36% of the Peak cells from Raster 106

10° got classified as Ridge cells, providing a more specific explanation of why there was a decrease in overall proportion of Peak cells when the slope threshold was changed from

10° to 15°. Similarly, about 38% of Pit cells and 13% of Pass (Saddle) cells got classified as Channel cells, and 19% of Pass cells got classified as Ridge cells, thereby explaining the increase in the coverage of those morphometric feature types when the slope threshold was increased from 10° to 15°. These changes suggest that with increase in slope threshold, all non-linear, localized feature types (Peak, Pass and Pit) tend to become absorbed by the topologically and semantically related linear feature types (Peak to Ridge and Pit to Channel, and Pass to both Ridge and Channel).

Table 4.3 presents a similar analysis, but the focus is instead on Raster 15° and how its features are classified in the Raster 10°. This table adds more insights about the impact of the slope parameter because only 73% of Ridge cells were classified as Ridge cells and only 77% of Channel cells were classified as Channel cells, but 100% of Peak cells were classified as Peak cells in Raster 10°. This suggests that decreasing the slope threshold from 15° to 10° is unlikely to cause a loss of Peak cells, but causes some

Channel cells to be classified as Pit or Pass cells, and some Ridge cells to be classified as

Peak and Pass cells. This is consistent with information from Table 4.2 and visual geomorphometric analysis of the map panels in Figures 4.1-4.3 which clearly show fragmentation of Channel and Ridge cells with decreasing slope threshold values (and with decreasing window sizes).

In contrast to these similarly parameterized experiments, when rasters from dissimilarly parameterized experiments for the same window size of 41x41, but different slope and curvature values (slope=1°; curvature=0.0001 and slope=15°;curvature=0.001) 107

were compared, the overall similarity plummeted substantially to only 30%. This confirmed the observations made from visual analysis that slopes less than 10° produced substantially inferior classification results. Several other comparisons made for the Wood method across the three study areas confirmed the general findings of the visual analysis method.

4.2.2 Geomorphon Method

The analysis conducted for the Wood method was repeated for the Geomorphon method, with several raster pairs overlaid and compared in terms of overall similarity measures to understand how parameter changes could affect the relative spatial distribution of the ten major landform categories recognized in the Geomorphon method.

Based on the visual analysis, the confusion matrix for two experiments run for the Great

Smoky Mountains area with a fixed slope threshold of 1° and the outer search radius of

41x41 cells, but different inner search radii of 10x10 and 15x15 cells was selected for illustration of the impact of change of the inner search radius parameter on landform categorical coverage areas (Tables 4.4 – 4.6).

The relative proportions of the categories as can be obtained from the row and column totals suggest that changing the inner radius from 10x10 to 15x15 did not appreciably alter the relative percentages of areas covered by each category. This is somewhat in contrast to what was observed for the two best experimental runs for the

Wood method. The overall similarity and Kappa measures of overall similarity observed for this confusion matrix are about 10% lower than what was observed for the confusion matrix presented above for the Wood method analysis. In general, even for other confusion matrices not presented here, similarity values between Geomorphon method 108

produced rasters tended to be lower than for the Wood method. This is likely because of the higher likelihood of classification shifts between Geomorphon classes, because there are ten of them (compared to only six morphometric feature types in the Wood method) and there are more similar classes to be “confused” with when a parameter value is altered to create a new classified raster.

The classification shifts in Tables 4.5 – 4.6 clearly suggest that the Spur class is most like the Ridge class, and the Hollow class to the Valley class. Thus, both these

Geomorphon classes need to be included in future analyses of linear eminences and depressions, respectively. The Shoulder areas can also become classified as Ridge areas, so that class too deserves inclusion as a linear eminence category. If such areas are combined, then about 35% of this study area would be classified as linear eminence, and

36% as linear depressions. This would be appreciably more than the relative coverage area percentages of corresponding feature types defined in the Wood method.

The analysis of other confusion matrices further revealed that changing the slope threshold created more dissimilarity than with inner window sizes. Overall, the confusion matrix analysis again underscored the findings from visual analysis that there is a small range of parameter values that are produce the best results and higher similarities.

4.2.3 TPI Method

When the TPI method’s rasters from a smaller scale window size of 10x10 and 15x15 were compared (for a fixed larger scale window size of 41x41) were compared, the overall similarity values were extremely high (Table 4.7). This suggests that the classification is not as sensitive to small changes to the small scale window size. This is 109

further confirmed by Tables 4.8 – 4.9 which show high levels of classification stability with only a small proportion of the study area experiencing classification shifts.

As also observed previously from visual analysis, the TPI method tends to outline much narrower linear eminences and depressions. This is supported from the row and column totals for the corresponding classes in Table 4.7. The TPI method tends to allocate much lower overall percentages to linear eminences (~14%) and depressions

~(12%), compared to the Wood and Geomorphon methods. The need for only window size parameters, the lower sensitivity to variation in window size values, and ability to extract more plausible, narrower linear eminences and depressions makes TPI method more attractive than the other two methods for delineation linear landforms. However, it must also be kept in mind that the method cannot be used for mapping non-linear eminences, and its performance also is degraded substantially in flat or low relief areas. 110

Table 4.1

Confusion matrix (overlap area percentages for class combinations) analysis for the two best experimental runs for the Wood method

(Great Smoky Mountains (NC-TN) study area).

WOOD METHOD (Window size: 41x41) Slope: 15° / Slope: 10° / Curvature: 0.0001 Curvature: 0.0001 PL PT CH PS RI PK Study Area % PL 3.51 0.00 0.47 0.91 0.17 0.00 5.06 PT 0.00 5.86 0.00 0.00 0.00 0.00 5.86 CH 0.00 3.55 24.59 3.80 0.00 0.00 31.94 PS 0.00 0.00 0.00 19.46 0.00 0.00 19.46 RI 0.00 0.00 0.00 5.53 23.48 3.13 32.13 PK 0.00 0.00 0.00 0.00 0.00 5.54 5.54 Study Area % 3.51 9.41 25.06 29.69 23.65 8.67 100 Overall accuracy: 0.82 / Kappa: 0.77 / Cramer's Coefficient V:1.04 / Contingency Coefficient C: 0.87

Note: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak.

111

Table 4.2

Confusion matrix (overlap area percentages normalized for every column) analysis for the two best experimental runs for the Wood method (Great Smoky Mountains (NC-TN) study area).

WOOD METHOD (Window size: 41x 41) Slope: 15° / Slope: 10° / Curvature: 0.0001 Curvature: 0.0001 PL PT CH PS RI PK Study Area % PL 100.00 0.00 1.86 3.05 0.74 0.00 5.06 PT 0.00 62.28 0.00 0.00 0.00 0.00 5.86 CH 0.00 37.72 98.14 12.79 0.00 0.00 31.94 PS 0.00 0.00 0.00 65.53 0.00 0.00 19.46 RI 0.00 0.00 0.00 18.63 99.26 36.06 32.13 PK 0.00 0.00 0.00 0.00 0.00 63.94 5.54 % Total 100 100 100 100 100 100 Study Area % 3.51 9.41 25.06 29.69 23.65 8.67 100

Note: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak.

112

Table 4.3

Confusion matrix (overlap area percentages normalized for every row) analysis for the two best experimental runs for the Wood method (Great Smoky Mountains (NC-TN) study area).

WOOD METHOD (Window size: 41x41) Slope :15° / Slope: 10° / Curvature: 0.0001 Curvature: 0.0001 PL PT CH PS RI PK % Total Study Area % PL 69.42 0.00 9.23 17.91 3.44 0.00 100 5.06 PT 0.00 100.00 0.00 0.00 0.00 0.00 100 5.86 CH 0.00 11.12 77.00 11.89 0.00 0.00 100 31.94 PS 0.00 0.00 0.00 100.00 0.00 0.00 100 19.46 RI 0.00 0.00 0.00 17.21 73.06 9.73 100 32.13 PK 0.00 0.00 0.00 0.00 0.00 100.00 100 5.54 Study Area % 3.51 9.41 25.06 29.69 23.65 8.67 100

Note: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak.

113

Table 4.4

Confusion matrix (overlap area percentages for class combinations) analysis for the two best experimental runs for the Geomorphon method (Great Smoky Mountains (NC-TN) study area). GEOMORPHON METHOD (Outer search radius: 41x41)

Inner search Inner search radius: 10x10 / Slope: 1° radius: 15x15 FL SU RI SH SP SL HO FS VA DP Study Area % / Slope: 10° FL 0.22 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.22

SU 0.00 3.32 0.70 0.00 0.01 0.00 0.00 0.00 0.00 0.00 4.03 RI 0.00 0.86 14.73 0.08 2.04 0.39 0.05 0.00 0.01 0.00 18.15

SH 0.02 0.00 0.01 0.15 0.00 0.02 0.00 0.00 0.00 0.00 0.20 SP 0.00 0.02 2.89 0.04 9.72 2.82 0.42 0.00 0.06 0.00 15.99

SL 0.01 0.00 0.59 0.06 3.16 14.05 2.97 0.13 0.51 0.00 21.47 HO 0.00 0.00 0.06 0.00 0.43 2.85 9.58 0.08 2.50 0.01 15.52

FS 0.04 0.00 0.00 0.00 0.00 0.02 0.00 0.76 0.01 0.00 0.82 VA 0.00 0.00 0.01 0.00 0.05 0.39 2.12 0.15 17.21 0.41 20.34

DP 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.71 2.54 3.26 Study Area % 0.29 4.20 18.99 0.33 15.41 20.54 15.16 1.12 21.01 2.96 100 Overall accuracy: 0.72 / Kappa: 0.66 / Cramer's Coefficient V:1.27 / Contingency Coefficient C: 0.91

Note: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat Slope, VA= Valley, DP=

Depression.

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Table 4.5

Confusion matrix (overlap area percentages normalized for every column) analysis for the two best experimental runs for the

Geomorphon method (Great Smoky Mountains (NC-TN) study area).

GEOMORPHON METHOD (Outer search radius: 41x41) Inner search Inner search radius: 10x10 / Slope: 1° radius: 15x15 FL SU RI SH SP SL HO FS VA DP Study Area % / Slope: 10° FL 76.6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.22 SU 0.00 78.91 3.67 0.26 0.08 0.01 0.00 0.00 0.00 0.00 4.03 RI 0.24 20.48 77.55 22.90 13.2 1.91 0.34 0.04 0.03 0.00 18.15 SH 6.17 0.00 0.05 45.37 0.00 0.09 0.00 0.31 0.00 0.00 0.20 SP 0.18 0.54 15.23 12.56 63.0 13.72 2.78 0.43 0.30 0.00 15.99 SL 2.83 0.06 3.13 17.65 20.4 68.40 19.57 11.14 2.45 0.03 21.47 HO 0.18 0.00 0.34 0.85 2.79 13.87 63.24 7.25 11.88 0.21 15.52 FS 13.1 0.00 0.00 0.28 0.00 0.08 0.00 67.54 0.05 0.00 0.82 VA 0.61 0.00 0.03 0.12 0.31 1.92 14.00 13.19 81.93 13.76 20.34 DP 0.00 0.00 0.00 0.00 0.00 0.01 0.07 0.10 3.36 86.00 3.26 % Total 100 100 100 100 100 100 100 100 100 100 Study Area % 0.29 4.20 18.99 0.33 15.41 20.54 15.16 1.12 21.01 2.96 100

Note: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat Slope, VA= Valley, DP=

Depression.

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Table 4.6

Confusion matrix (overlap area percentages normalized for every row) analysis for the two best experimental runs for the

Geomorphon method (Great Smoky Mountains (NC-TN) study area).

GEOMORPHON METHOD (Outer search radius: 41x41) Inner search Inner search radius: 10x10 / Slope: 1° radius:15x15 FL SU RI SH SP SL HO FS VA DP % Total Study Area % / Slope: 1° FL 100 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100 0.22 SU 0.00 82.35 17.28 0.02 0.30 0.04 0.00 0.00 0.00 0.00 100 4.03 RI 0.00 4.74 81.11 0.42 11.2 2.16 0.29 0.00 0.03 0.00 100 18.15 SH 8.94 0.00 4.91 75.21 0.00 9.21 0.00 1.74 0.00 0.00 100 0.20 SP 0.00 0.14 18.09 0.26 60.8 17.63 2.63 0.03 0.39 0.00 100 15.99 SL 0.04 0.01 2.77 0.27 14.70 65.42 13.82 0.58 2.39 0.00 100 21.47 HO 0.00 0.00 0.42 0.02 2.77 18.36 61.78 0.53 16.09 0.04 100 15.52 FS 4.60 0.00 0.00 0.11 0.00 1.96 0.00 92.14 1.19 0.00 100 0.82 VA 0.01 0.00 0.03 0.00 0.23 1.94 10.43 0.73 84.63 2.00 100 20.34 DP 0.00 0.00 0.00 0.00 0.00 0.04 0.30 0.03 21.67 77.95 100 3.26 Study Area % 0.29 4.20 18.99 0.33 15.41 20.54 15.16 1.12 21.01 2.96 100

Note: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat Slope, VA= Valley, DP=

Depression.

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Table 4.7

Confusion matrix (overlap area percentages for class combinations) analysis for the two best experimental runs for the TPI method

(Great Smoky Mountains (NC-TN) study area).

TPI METHOD (Large scale window: 41x41) Small scale Small scale window: 10x10 window: CA MSD UD U-SV PL OS US LR MSR HR Study Area % 15x15 CA 10.18 0.00 0.00 0.09 0.00 0.00 0.00 0.00 0.00 0.00 10.28 MSD 0.00 2.10 0.00 0.00 0.01 0.33 0.00 0.00 0.00 0.00 2.44 UD 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U-SV 0.44 0.00 0.00 3.51 0.00 0.00 0.00 0.00 0.00 0.00 3.95 PL 0.00 0.00 0.00 0.00 8.97 0.00 0.00 0.00 0.00 0.00 8.98 OS 0.00 0.12 0.00 0.00 0.00 56.84 0.00 0.00 0.14 0.00 57.10 US 0.00 0.00 0.00 0.00 0.00 0.00 4.22 0.00 0.00 0.56 4.78 LR 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.01 MSR 0.00 0.00 0.00 0.00 0.01 0.43 0.00 0.00 2.22 0.00 2.65 HR 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.00 0.00 9.74 9.80 Study Area % 10.62 2.23 0.00 3.61 8.99 57.60 4.29 0.00 2.36 10.3 100

Overall accuracy: 0.98 / Kappa: 0.96 / Cramer's Coefficient V:1.53 / Contingency Coefficient C: 0.94 Note: CA = Canyon, MSD = Mid Slope Drainage, UD= Upland Drainage, U-SV= U-Shape Valley, PL = Plain, OS= Open Slope,

US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

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Table 4.8

Confusion matrix (overlap area percentages normalized for every column) analysis for the two best experimental runs for the TPI method (Great Smoky Mountains (NC-TN) study area). TPI METHOD (Large scale window: 41x41)

Small scale Small scale window: 15x15 window: CA MSD UD U-SV PL OS US LR MSR HR Study Area % 15x15 CA 95.88 0.00 0.00 2.57 0.00 0.00 0.00 0.05 0.00 0.00 10.28 MSD 0.00 94.23 0.00 0.00 0.14 0.58 0.00 0.00 0.00 0.00 2.44 UD 0.00 0.00 97.11 0.00 0.00 0.00 0.04 0.00 0.00 0.00 0.00 U-SV 4.12 0.00 0.00 97.29 0.00 0.00 0.00 3.42 0.00 0.00 3.95 PL 0.00 0.22 0.00 0.00 99.7 0.00 0.00 0.00 0.08 0.00 8.98 OS 0.00 5.56 0.00 0.00 0.00 98.68 0.00 0.00 5.95 0.00 57.10 US 0.00 0.00 2.89 0.00 0.00 0.00 98.47 0.00 0.00 5.43 4.78 LR 0.00 0.00 0.00 0.14 0.00 0.00 0.00 96.53 0.00 0.00 0.01 MSR 0.00 0.00 0.00 0.00 0.07 0.74 0.00 0.00 93.97 0.00 2.65 HR 0.00 0.00 0.00 0.00 0.00 0.00 1.49 0.00 0.00 94.5 9.80 % Total 100 100 100 100 100 100 100 100 100 100 Study Area % 10.62 2.23 0.00 3.61 8.99 57.60 4.29 0.00 2.36 10.3 100

Note: CA = Canyon, MSD = Mid Slope Drainage, UD= Upland Drainage, U-SV= U-Shape Valley, PL = Plain, OS= Open Slope,

US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

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Table 4.9

Confusion matrix (overlap area percentages normalized for every row) analysis for the two best experimental runs for the TPI method

(Great Smoky Mountains (NC-TN) study area).

TPI METHOD (Large scale: 41x41) Small scale Small scale: 10x10 window: CA MSD UD U-SV PL OS US LR MSR HR % Total Study Area % 15x15 CA 99.10 0.00 0.00 0.90 0.00 0.00 0.00 0.00 0.00 0.00 100 10.28 MSD 0.00 85.86 0.00 0.00 0.53 13.62 0.00 0.00 0.00 0.00 100 2.44 UD 0.00 0.00 49.29 0.00 0.00 0.00 50.41 0.00 0.00 0.30 100 0.00 U-SV 11.09 0.00 0.00 88.90 0.00 0.00 0.00 0.00 0.00 0.00 100 3.95 PL 0.00 0.05 0.00 0.00 99.9 0.00 0.00 0.00 0.02 0.00 100 8.98 OS 0.00 0.22 0.00 0.00 0.00 99.54 0.00 0.00 0.25 0.00 100 57.10 US 0.00 0.00 0.00 0.00 0.00 0.00 88.30 0.00 0.00 11.7 100 4.78 LR 0.14 0.00 0.00 61.82 0.00 0.00 0.00 38.04 0.00 0.00 100 0.01 MSR 0.00 0.00 0.00 0.00 0.24 16.04 0.00 0.00 83.73 0.00 100 2.65 HR 0.00 0.00 0.00 0.00 0.00 0.00 0.65 0.00 0.00 99.3 100 9.80 Study Area % 10.62 2.23 0.00 3.61 8.99 57.6 4.29 0.00 2.36 10.3 100

Note: CA = Canyon, MSD = Mid Slope Drainage, UD= Updland Drainage, U-SV= U-Shape Valley, PL = Plain, OS= Open Slope,

US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

4.3 Using GNIS Features for Cognitive Validation of Extracted Landform Features

As mention earlier in chapter 3, all GNIS features represent culturally important features with names officially recognized by the US Federal government. GNIS features representing named landforms must represent natural topographically and culturally salient landforms, since people chose to name such features. Thus, GNIS landform features can be used to test the cognitive validity of extracted features by assessing their proximity to computationally extracted features. The rationale for and the summary of the results of the analysis conducted with GNIS features for all 468 experimental runs is presented in this section.

As summarized earlier in Table 3.1, GNIS has one corresponding feature class for each of the conceptual landform categories of interest. The correspondence between the conceptual landform categories and the extracted feature types or landform classes from the

Wood, Geomorphon and TPI methods is shown in Table 2.2 Thus, combining information from these two tables, the correspondence between GNIS feature classes and the feature types or landform categories from the three methods is as follows: GNIS Summit corresponds to Peak (Wood), Summit (Geomorphon), and High Ridge (TPI), GNIS Ridge

(GNIS) corresponds to Ridge (Wood), Ridge (Geomorphon), and Local Ridge and

Midslope Ridge (TPI), and GNIS Valley corresponds to Channel (Wood), Valley

(Geomorphon), and Canyon and U-Shape Valley (TPI).

First, all instances for GNIS feature classes corresponding to the three landform categories were mapped for each study area. GNIS features were first used for visual reference and then for quantitative assessment of the shortest distance from each GNIS feature to the nearest extracted feature of the corresponding type (e.g., from GNIS Summit 120

point features to the nearest Peak (Wood), Summit (Geomorphon) and High Ridge (TPI) features). For measuring distance from GNIS points to extracted features, it was necessary to convert all the categorical rasters from all 468 experimental runs to polygon datasets so that each feature could be mapped as a discrete polygon. This allowed using the Near function in ArcGIS Desktop 10.6 to measure the shortest distance from a GNIS feature to the nearest extracted feature of the corresponding type. For computational efficiency reasons, the raster to polygon conversion was restricted to only cells classified into one of the three morphometric features or landform types that are of interest in this thesis (Table

2.2).

4.3.1 Process for Calculation and Analysis of GNIS Shortest Distances

For easier interpretation and analysis, the measured shortest distances were classified into four distance bands: 0 meters (inside), 0 – 10 meters (size of one raster cell), 10 – 30 meters, and > 30 meters. Ideally, all GNIS features should have a 0-meter distance since they would overlap with an extracted feature of the corresponding type. The next best case would be if they were outside but at least within the eight immediately adjacent raster cells

(0 – 10 meters distance). The next band, 10 – 30 meters was chosen to account for errors in the locations of GNIS features most of which were found to be within 30 meters (Arundel et al., 2020). Thus, in this analysis, it is assumed that if a GNIS feature is at least within 30 meters of an extracted feature, it is possible that the topographically and culturally salient landform represented by the GNIS feature is represented by at least one discrete feature in the set of features of the corresponding type extracted from the experimental run under consideration.

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All distances between GNIS features and the nearest feature of the corresponding type were reclassified into one of the four distance categories. Then the absolute counts and relative percentages of GNIS features in each distance category were calculated, where the reference for a GNIS feature class (Summit, Ridge, Valley) was the total number of GNIS features available for that feature class within each study area (see Table 3.2). Due to the large number of raster conversions and polygon datasets that had to be processed, the entire analysis from the conversion to polygon datasets to calculations was automated in ArcGIS

Desktop 10.6 using its Model Builder functionality to ensure accuracy and efficiency.

Visual analysis clearly suggests that only a small subset of experiments produced results worth exploring further. Neighborhood scale (primary window size) is the most important parameter that affects the size and shape of extracted features, and then other parameters such as slope (Wood and Geomorphon methods only) or curvature (Wood method only) played a secondary role. Thus, to focus on the best cases again, a decision was made to limit the focused analysis of classified GNIS feature shortest distances to a single best case (chosen from results obtained across all other secondary parameters) for each GNIS feature class and for each of the six primary window sizes evaluated for each method. The best case is defined as the experiment that maximized the percentage of GNIS features in the lowest distance category (0 meters). This was determined for each GNIS feature class separately.

For each method and for each study area, results were cross tabulated for the six window sizes (rows) and the three GNIS feature classes (columns) leading to nine cross- tables (Tables 4.10 – 4.18). The values of the secondary parameters that maximized

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percentages of GNIS features within extracted feature polygons is mentioned in the table captions.

4.3.2 Analysis of GNIS Shortest Distances for the Wood Method

Results from GNIS shortest distance analysis for the Wood method for the three study areas are presented in Tables 4.10 – 4.12. After a comparative analysis of these tables, it emerges that the best experimental parameters suggested from GNIS distance analysis do not match closely enough with those identified from visual geomorphometric analysis. As noted in the table captions, for all window sizes, slope thresholds of 20⁰ for Peak features and 1⁰ for Ridge and Channel features, and the same curvature of 0.0001 for Peak, Ridge, and Channel features was found to yield the highest number of GNIS point features within

(distance = 0 meters ) an extracted feature of a corresponding type. Window sizes of

31x31were found to be marginally best for GNIS Valley features for all study areas.

However, for GNIS Ridge and Valley features, the window size choice did not seem to matter all that much.

For reference, based on visual analysis, the best parameter values for the Wood method were judged to be as follows: i) window sizes of 31x31 to 41x41 for all landform categories; ii) slope threshold of 5° for non-linear eminences and 5° -- 10° for linear eminences/depressions, and iii) curvature of 0.0001 for non-linear eminences and 0.001 for linear eminences/depressions. When the percentages of GNIS features inside (i.e., distance

= 0 meters) extracted features of the corresponding type were calculated, the highest percentage values were always observed for the Great Smoky Mountains study area.

The highest percentages of GNIS features found within an extracted feature (of a corresponding type) exceeded 90% for GNIS Summit features for multiple larger window

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sizes for the Great Smoky Mountains and White Mountains study areas (Tables 4.10 and

4.11). For GNIS Ridge features, only the Great Smoky Mountains study area yielded percentages exceeding 90%. For GNIS Valley features, the highest percentages were only

83% and 82% for the Great Smoky Mountains and White Mountains study areas, respectively. Thus, even in the best-case scenario, 18% to 25% of GNIS Valley features could not be found contained within an extracted feature (however, they could still be nearby, even if not inside). Still, it is clear from this analysis that the experiments that maximized GNIS features contained within an extracted feature polygon were not judged visually to yield the best shape and sizes of features.

Finally, it must be noted that the Colorado Plateau study area, with low slopes, smaller and isolated non-linear eminences, and much smaller proportions of the area occupied by linear eminences and depressions made it difficult for GNIS features of all types to be contained within extracted features of the corresponding type. There are only three GNIS

Ridge, 43 Summit and 55 Valley features in this third study area. Thus, analysis of GNIS

Ridge feature shortest distances is moot for this study area (for any method). However, even for GNIS Summit features, the highest percentage observed was 67% for the window size of 31x31, and for GNIS Valley features, it was 60% for the window size of 61x61

(Table 4.12). This means that even in the best case scenarios, one-third of the GNIS features were found to be not within an extracted feature polygon.

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Table 4. 10

Study Area: Great Smoky Mountains (NC-TN). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 20⁰

(Peak); 1⁰ (Ridge/Channel). Curvature: 0.0001.

WOOD METHOD Nearest GNIS Summit GNIS Ridge GNIS Valley Distance Class to Peak (%) to Ridge (%) to Channel (%) Window size: 61x61 0m 88 91 74 >0m – 10m 1 1 5 >10m – 30m 2 3 4 > 30m 9 5 17 Window size: 51x51 0m 89 94 76 >0m – 10m 2 2 5 >10m – 30m 2 1 7 > 30m 7 3 12 Window size: 41x41 0m 91 94 80 >0m – 10m 1 2 8 >10m – 30m 2 2 5 > 30m 6 3 7 Window size: 31x31 0m 94 94 82 >0m – 10m 0 3 8 >10m – 30m 2 1 6 > 30m 4 2 5 Window size: 21x21 0m 93 95 82 >0m – 10m 3 3 10 >10m – 30m 2 2 6 > 30m 2 1 2 Window size: 11x11 0m 85 95 80 >0m – 10m 6 3 12 >10m – 30m 7 2 6 > 30m 2 0 1

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Table 4. 11

Study Area: White Mountains (NH). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 20⁰ (Peak); 1⁰

(Ridge/Channel). Curvature: 0.0001.

WOOD METHOD Nearest GNIS Summit GNIS Ridge GNIS Valley Distance Class to Peak (%) to Ridge (%) to Channel (%) Window size: 61x61 0m 90 88 79 >0m – 10m 1 1 0 >10m – 30m 3 4 8 > 30m 7 6 12 Window size: 51x51 0m 93 82 75 >0m – 10m 1 7 0 >10m – 30m 1 3 17 > 30m 5 7 8 Window size: 41x41 0m 91 79 79 >0m – 10m 1 6 4 >10m – 30m 2 9 4 > 30m 6 6 12 Window size: 31x31 0m 89 81 83 >0m – 10m 2 7 4 >10m – 30m 3 6 4 > 30m 5 6 8 Window size: 21x21 0m 85 75 79 >0m – 10m 5 7 8 >10m – 30m 6 12 8 > 30m 4 6 4 Window size: 11x11 0m 70 76 83 >0m – 10m 13 9 17 >10m – 30m 13 12 0 > 30m 5 3 0

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Table 4. 12

Study Area: Colorado Plateau (NM). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 20⁰ (Peak); 1⁰

(Ridge/Channel). Curvature: 0.0001.

WOOD METHOD Nearest GNIS Summit to GNIS Ridge to GNIS Valley to

Distance Class Peak (%) Ridge (%) Channel (%) Window size: 61x61 0m 58 67 60 >0m – 10m 0 0 2 >10m – 30m 2 0 5 > 30m 40 33 33 Window size: 51x51 0m 63 67 49 >0m – 10m 5 0 4 >10m – 30m 5 0 9 > 30m 28 33 35 Window size: 41x41 0m 67 67 53 >0m – 10m 5 0 7 >10m – 30m 7 0 11 > 30m 21 33 29 Window size: 31x31 0m 67 33 55 >0m – 10m 7 33 9 >10m – 30m 9 33 13 > 30m 16 0 24 Window size: 21x21 0m 58 33 55 >0m – 10m 16 0 18 >10m – 30m 7 33 15 > 30m 19 33 13 Window size: 11x11 0m 44 67 42 >0m – 10m 19 33 29 >10m – 30m 16 0 25 > 30m 21 0 4

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4.3.3 Analysis of GNIS Shortest Distances for the Geomorphon Method

Results from GNIS shortest distance analysis for the Geomorphon method for the three study areas are presented in Tables 4.13 – 4.15. For this method, the best slope threshold was found to be 1° for all three GNIS feature classes, which matches with the best determined slope threshold for visual analysis. This is expected because, for the

Geomorphon method, higher slope values tend to drastically reduce the number of extracted features, which would also increase GNIS distances to the nearest object of the corresponding type. When the larger outer search radius was at least 31x31, the best inner search radius matched that chosen from visual analysis (15x15). Thus, the best parameter values for minimizing GNIS feature distances to the nearest extracted object of the corresponding type also lead to shapes and sizes of features that were judged to be the most cognitively plausible from visual analysis.

Like for the Wood method, the best percentages are observed for the GNIS Summit features for all study areas. For outer search radius of 31x31 or larger, the Great Smoky

Mountains study area (Table 4.14) consistently yielded percentages exceeding 90%, but the

White Mountains study area yielded lower percentages between 81% to 86%. However, for

GNIS Ridge and Valley features, the highest percentages were substantially lower, quite unlike the Wood method. For the Great Smoky Mountains study area, only 51% to 60% features, and for the White Mountains study area, only 54% to 57% GNIS Ridge features were found to be within (distance = 0) an extracted object of the corresponding

Geomorphon landform class. Thus, between 20% to 30% of GNIS features were at least 30 meters or farther away for all outer search radii.

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For GNIS Valley features, the highest percentages ranged between 75% to 88% for the

White Mountains study area but dropped substantially to 27% to 32% if only GNIS Valley features within an extracted object were examined for an outer search radius of at least

31x31. Thus, for the Great Smoky Mountains study area, between 56% to 67% of GNIS

Valley features were farther than 30 meters from the nearest extracted (Geomorphon)

Valley object.

While there is some agreement between GNIS and the Geomorphon classes, further analysis will be needed to assess how much of a spatial mismatch exists between instances of linear eminence/depression landform objects from Geomorphon and GNIS. From this preliminary analysis, it can be said that even for the best configured experiments, the

Geomorphon method does not yield enough linear eminence and depression objects to be able to contain all GNIS Ridge and Valley point features. The Wood method performs better in this regard.

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Table 4. 13

Study area: Great Smoky Mountains (NC-TN). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 1⁰.

GEOMORPHON METHOD Nearest Distance GNIS Summit GNIS Ridge to GNIS Valley to Class to Summit (%) Ridge (%) Valley (%) Outer: 61x61 Inner (Summit): 15x15 Inner (Ridge/Valley): 25x25

0m 93 65 28 >0m – 10m 1 5 4 >10m – 30m 1 6 4 > 30m 5 23 64 Outer: 51x51 Inner (Summit): 15x15 Inner (Ridge/Valley): 25x25 0m 93 64 25 >0m – 10m 1 7 2 >10m – 30m 1 6 6 > 30m 5 23 67 Outer: 41x41 Inner (Summit): 10x10 Inner (Ridge/Valley): 15x15 0m 94 63 32 >0m – 10m 1 10 7 >10m – 30m 2 9 5 > 30m 3 19 56 Outer: 31x31 Inner (Summit): 10x10 Inner (Ridge/Valley): 15x15 0m 93 61 27 >0m – 10m 2 10 7 >10m – 30m 2 10 6 > 30m 3 19 60 Outer: 21x21 Inner (Summit): 10x10 Inner (Ridge/Valley): 10x10 0m 92 61 30 >0m – 10m 2 11 7 >10m – 30m 3 13 8 > 30m 4 15 54 Outer: 11x11 Inner (Summit): 5x5 Inner (Ridge/Valley): 5x5

0m 85 56 19 >0m – 10m 7 16 6

>10m – 30m 3 12 11 > 30m 4 16 64

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Table 4. 14

Study Area: White Mountains (NH). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 1⁰.

GEOMORPHON METHOD Nearest Distance GNIS Summit to GNIS Ridge to GNIS Valley to Class Summit (%) Ridge (%) Valley (%) Outer: 61x61 Inner (Summit): 15x15 Inner (Ridge/Valley): 15x15 0m 86 54 75 >0m – 10m 1 1 17 >10m – 30m 3 15 0 > 30m 10 30 8 Outer: 51x51 Inner (Summit): 15x15 Inner (Ridge/Valley): 15x15 0m 86 54 75 >0m – 10m 2 1 17 >10m – 30m 2 15 0 > 30m 10 30 8 Outer: 41x41 Inner (Summit): 10x10 Inner (Ridge/Valley): 10x10 0m 83 57 88 >0m – 10m 3 9 0 >10m – 30m 4 9 0 > 30m 9 25 12 Outer: 31x31 Inner (Summit): 10x10 Inner (Ridge/Valley): 10x10 0m 81 55 83 >0m – 10m 5 7 4 >10m – 30m 5 12 0 > 30m 10 25 12 Outer: 21x21 Inner (Summit): 10x10 Inner (Ridge/Valley): 10x10 0m 75 54 83 >0m – 10m 5 10 0 >10m – 30m 7 13 0 > 30m 12 22 17 Outer: 11x11 Inner (Summit): 5x5 Inner (Ridge/Valley): 5x5 0m 50 28 50 >0m – 10m 13 25 33 >10m – 30m 15 22 8 > 30m 22 24 8

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Table 4. 15

Study area: Colorado Plateau (NM). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type. Slope: 1⁰.

GEOMORPHON METHOD Nearest Distance GNIS Summit to GNIS Ridge to GNIS Valley to Class Summit (%) Ridge (%) Valley (%)

Outer: 61x61 Inner (Summit): 15x15 Inner (Ridge/Valley): 0x0 0m 60 33 38 >0m – 10m 7 0 20 >10m – 30m 9 33 16 > 30m 23 33 25 Outer: 51x51 Inner (Summit): 15x15 Inner (Ridge/Valley): 0x0 0m 58 33 38 >0m – 10m 5 0 20 >10m – 30m 9 33 15 > 30m 28 33 27 Outer: 41x41 Inner (Summit): 15x15 Inner (Ridge/Valley): 10x10 0m 53 33 36 >0m – 10m 9 0 16 >10m – 30m 9 33 13 > 30m 28 33 35 Outer: 31x31 Inner (Summit): 15x15 Inner (Ridge/Valley): 10x10 0m 51 33 36 >0m – 10m 12 0 22 >10m – 30m 9 33 4 > 30m 28 33 38 Outer: 21x21 Inner (Summit): 10x10 Inner (Ridge/Valley): 10x10

0m 42 33 31 >0m – 10m 19 0 24

>10m – 30m 5 33 7 > 30m 35 33 38

Outer: 11x11 Inner (Summit): 5x5 Inner (Ridge/Valley): 5x5 0m 21 33 31 >0m – 10m 21 33 15 >10m – 30m 16 0 16 > 30m 42 33 38

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4.3.4 Analysis of GNIS Shortest Distances for the TPI Method

Finally, results from GNIS shortest distance analysis for the TPI method are presented in Tables 4.16 – 4.18. for the three study areas. The percentage values for GNIS features inside extracted landform objects is almost always lower than those observed for the other two methods for the corresponding scales of analysis for each GNIS feature type. Since there is no dedicated TPI landform class for non-linear eminences, the High Ridge class was used instead to test the GNIS Summit features. The highest percentage of GNIS

Summit features inside an extracted landform object was only 68% for the Great Smoky

Mountains study area and only 50% for the White Mountains study area. Moreover, these percentages were observed for the largest window size of 61x61, not 41x41 which was found to yield the best results.

Since there are only three GNIS Ridge features for the Colorado Plateau study area, only the other two study areas (Tables 4.16 – 4.17) were used for exploring the patterns of distances from GNIS Ridge features to the TPI linear eminence classes (High Ridge, Local

Ridge, or Midslope Ridge). Given the extremely low occurrence rates of Local Ridge and

Midslope Ridge areas, almost all the distances reported in the tables below were for High

Ridge objects, even though reference is made broadly to all three types of TPI linear eminence classes in the discussion below and in Tables 4.16 – 4.18). It is also worth noting that for the smallest window sizes (large scale = 11x11, small scale = 5x5), no TPI linear eminence polygons could be found within 30 meters of GNIS Ridge features for all three study areas.

For the other window sizes, overall, results were somewhat more favorable for the

Great Smoky Mountains study area compared to the White Mountains study area. For the

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former, depending on the window size, about 46% – 53% of the GNIS Ridge features were inside, 30% – 36% outside but within 30 meters, and 17% – 18% farther 30 meters from a

TPI linear eminence polygon. In comparison, for the White Mountains study area, only about 22% of the GNIS Ridge features were inside TPI linear eminence polygons, with another 55% outside but within 30 meters, and 21% – 25% farther than 30 meters of a TPI linear eminence polygon.

For GNIS Valley features results improved with increase in the larger scale window size, suggesting the wider valleys made it more likely for GNIS Valley features to be inside or within 30 meters of TPI Valley objects. In this case, results were slightly more favorable for the White Mountains study area. Depending on the window sizes, 21% – 42% of GNIS

Valley features found inside and 12% – 25% farther than 30 meters of a corresponding TPI

Valley object for the White Mountains study area. In comparison, for the Great Smoky

Mountains study area, 18% – 27% GNIS Valley features were inside and 33% – 42% farther than 30 meters of a TPI Valley object. For the Colorado Plateau study area, 13% –

27% GNIS Valley features were inside, but 56% – 65% of GNIS Valley features were farther than 30 meters from a TPI Valley feature.

Based on this analysis, it can be summarized that for according polygon representations to GNIS features, the Wood method tends to outperform the Geomorphon method, but both methods outperform TPI consistently, raising interesting questions about the efficacy of the

TPI method in providing reliable polygonal representations for GNIS landform features.

TPI does not have a dedicated class corresponding to GNIS Summit features, and its narrower, linear eminence and depression polygons, while appearing most accurate from visual analysis, also decrease proximity of GNIS landform features.

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Table 4. 16

Study Area: Great Smoky Mountains (NC-TN). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type.

TPI METHOD Nearest Distance GNIS Summit GNIS Ridge to High GNIS Valley to Class to High Ridge Ridge (HR) / Local Canyon (C) / U- (HR) (%) Ridge (LR)/Mid-slope Shape Valley Ridge (MSR) (%) (UV) (%) Large scale: 61x61 Small scale (HR): 25x25 Small scale (LR/MR/UV/C): 15x15 0m 68 53 27 >0m – 10m 16 20 14 >10m – 30m 8 10 15 > 30m 8 17 42 Large scale: 51x51 Small scale (HR): 25x25 Small scale (LR/MR/UV/C): 15x15 0m 68 53 23 >0m – 10m 16 20 20 >10m – 30m 8 10 17 > 30m 8 17 39 Large scale: 41x41 Small scale: 15x15 0m 59 47 20 >0m – 10m 23 24 23 >10m – 30m 9 11 19 > 30m 10 18 38 Large scale: 31x31 Small scale (HR): 10x10 0m 57 46 18 >0m – 10m 23 24 24 >10m – 30m 9 12 21 > 30m 10 18 37 Large scale: 21x21 Small scale: 10x10 0m 57 46 18 >0m – 10m 23 24 25 >10m – 30m 9 12 21 > 30m 10 18 35 Large scale: 11x11 Small scale: 10x10 0m 0 0 19 >0m – 10m 0 0 25 >10m – 30m 0 0 22 > 30m 0 0 33

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Table 4. 17

Study Area: White Mountains (NH). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type.

TPI METHOD Nearest GNIS Summit to GNIS Ridge to High GNIS Valley to Distance High Ridge (HR) Ridge (HR) / Local Canyon (C) / U- Class (%) Ridge (LR)/Mid-slope Shape Valley (UV) Ridge (MSR) (%) (%) Large scale: 61x61 Small scale: 25x25 0m 50 22 42 >0m – 10m 25 25 17 >10m – 30m 16 31 25 > 30m 10 21 17 Large scale: 51x51 Small scale:25x25 0m 50 22 33 >0m – 10m 25 24 25 >10m – 30m 16 31 25 > 30m 10 22 17 Large scale: 41x41 Small scale:15x15 0m 43 22 21 >0m – 10m 29 16 29 >10m – 30m 18 36 29 > 30m 11 25 21 Large scale: 31x31 Small scale (HR): 10x10 0m 41 22 21 >0m – 10m 29 16 29 >10m – 30m 19 39 25 > 30m 11 22 25 Large scale: 21x21 Small scale (HR): 10x10 0m 41 24 21 >0m – 10m 30 18 25 >10m – 30m 18 37 42 > 30m 10 21 12 Large scale: 11x11 Small scale (HR): 5x5 0m 0 0 25 >0m – 10m 0 0 21 >10m – 30m 0 0 42 > 30m 0 0 12

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Table 4. 18

Study Area: Colorado Plateau (NM). Percentages of GNIS features within and beyond 30 meters from the nearest extracted polygon of the corresponding type.

TPI METHOD Nearest Distance GNIS Summit to GNIS Ridge to High GNIS Valley to Class High Ridge Ridge (HR) / Local Canyon (C) / U- (HR) (%) Ridge (LR)/Mid- Shape Valley slope Ridge (MSR) (UV) (%) (%) Large scale: 61x61 Small scale: 25x25 0m 37 33 27 >0m – 10m 21 33 11 >10m – 30m 21 0 5 > 30m 21 33 56 Large scale: 51x51 Small scale: 25x25 0m 37 33 20 >0m – 10m 21 33 16 >10m – 30m 21 0 7 > 30m 21 33 56 Large scale: 41x41 Small scale: 15x15 0m 30 33 18 >0m – 10m 19 33 11 >10m – 30m 19 0 13 > 30m 33 33 58 Large scale: 31x31 Small scale: 10x10 0m 28 33 18 >0m – 10m 23 33 11 >10m – 30m 16 0 13 > 30m 33 33 58 Large scale: 21x21 Small scale: 10x10 0m 28 33 13 >0m – 10m 23 33 7 >10m – 30m 16 0 16 > 30m 33 33 64 Large scale: 11x11 Small scale: 5x5 0m 0 0 13 >0m – 10m 0 0 9 >10m – 30m 0 0 13 > 30m 0 0 65

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4.4 Comparison of the Wood, Geomorphon and TPI Landform Mapping Methods

The results discussed so far will help answer the first set of research questions (A.i and

A.ii) conceived to characterize the impact of choice of parameters for the three methods and the degree of variation induced due to changes in terrain type or physiographic context.

The second set of research questions (B.i and B.ii) were conceived to directly compare all three methods to each other in a systematic way so that the semantic overlap between their prescriptive feature types or landform classes can also be ascertained. As has already become apparent from the analysis of results presented thus far, there are indeed some similarities, but also many dissimilarities in how these methods are designed to classify

DEM cells into one landform related class. In this section, additional results are presented and analyzed from the spatial overlays of classified rasters from different methods.

The analysis is mostly based on the derived contingency tables for the three overlays that maximized the overall similarity for each method-pair: Wood – Geomorphon (Tables

4.19 – 4.21), Wood – TPI (Tables 4.22 – 4.24), and Geomorphon – TPI (Tables 4.25 –

4.27). Unlike the confusion matrix tables, the contingency tables compare different sets of categories, so only the Cramer’s V and Contingency C overall similarity measures were calculated. As for the analysis of confusion tables in section 4.2, each comparison is supported by three tables—the overall overlap area percentage between the classes of the two classification systems, and then column and row normalized percentage value tables were also derived to tabulated the relative percentage distribution of the cells identified for one class in one method across all classes of the other method. A high percentage of column or row percentage value in the normalized tables suggests that two classes correspond to each other or have a substantial semantically similarity. Finally, it should be

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noted that the relative percentages of areas for different classes were found to be quite similar even for other pairs of overlays across all study areas. Although results here are being discussed from only one comparison for each method, comprehensive comparisons with differently parameterized experiments across all the three study areas suggest that the overall patterns remain the same. Thus, the broad findings reported below and in the next chapter are to be taken as general statements about these methods, not specifically about just these best performing experiments.

4.4.1 Comparing Methods Based on Overall Similarity Measures

Table 4.19 is the contingency table showing overlap percentage obtained from an overlay of the rasters from the experimental runs chosen to maximize overall similarity measures for the Wood and Geomorphon methods. Similarly, Table 4.20 is the contingency table yielding the highest overall similarity results for comparing the Wood and TPI methods, and Table 4.21 is the corresponding contingency table with the highest overall similarity measure for comparing the Geomorphon and TPI methods. The two overall association measures Cramer’s V and Contingency C suggest that there is a substantially higher degree of overall similarity between the results from the Wood and Geomorphon classification systems, than for results obtained from comparisons of the Wood and TPI

(Table 4.22) and Geomorphon and TPI (Table 4.25) methods. Also, all the inter-method similarity measures are also substantially lower than those observed for intra-method confusion tables in section 4.2.

The overall similarity between Wood and TPI methods is quite low and this is to be expected since the Wood method’s morphometric features are conceptually quite different from the TPI method’s landform classes. Results confirm the expectation that the TPI

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landform classes would resemble the landform classes in the Geomorphon methods more than they would the Wood morphometric feature types, inspired by the critical points and lines from surface network theory (the inspiration for the Wood method’s classes).

However, as the following discussion also suggests, the similarity of the TPI linear eminence and depressions landform classes have a very weak correspondence with the equivalent classes in the Wood and Geomorphon classification systems.

4.4.2 Wood vis-à-vis Geomorphon Classification Systems

The column percentages in Table 4.20 reveals how the six Wood morphometric feature types overlapped with the ten Geomorphon landform classes. Peak, Ridge and Channel feature types from the Wood method and the Summit, Ridge, Spur, Valley and Hollow classes from the Geomorphon methods were the pertinent classes for this thesis.

The experiment chosen to represent the Wood method for maximizing overall similarity with the Geomorphon and TPI methods was run with the curvature threshold of 0.001, which is much better suited for Wood Ridge and Channel cells, but not Peak cells. Thus, the relative percentage of Peak cells is only 0.5%, compared to 5.5% when the curvature was set to 0.0001 (Table 4.1). Moreover, the Planar feature type, which was limited to only about 5% of the study area for a curvature value of 0.0001 for the same slope threshold of

15°, occupies a dominant 59% of the study area when the curvature is set to 0.001.

Table 4.20 column percentages, large proportion of the for the Peak feature type, 80% of Wood Peak cells were classified as Geomorphon Summit cells and almost all the rest as

Geomorphon Ridge cells. This is quite in contrast to what is observed from the row percentage for the for the Geomorphon Summit class in Table 4.21. Only 9% Summit cells overlapped with the Wood Peak cells, but 60% of Summit cells overlapped with the Wood

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Ridge cells, and 30.5% with the ‘catch-all’ Wood Planar cells. This is because only 0.5% of the study area was classified as Peak cells, but 4.2% as Summit cells. More careful analysis of individual cell clusters will be needed to determine if this difference is because more distinct non-linear eminences are detected by the Geomorphon method or it tends to extract larger areas for eminences than the Wood method for individual Peak features, or both.

In contrast, the Wood Ridge feature type, and the Geomorphon Ridge class both covered about 19% of the study area, with an additional 15.5% classified as Geomorphon

Spur cells. 56% of Wood Ridge cells were classified as Geomorphon Ridge cells, 24.5% as

Geomorphon Spur and 13% as Summit cells. Conversely, 58% of Geomorphon Ridge cells were classified as Wood Ridge cells, and almost of the rest as Wood Planar cells. Similarly,

31% of Geomorphon Spur cells were classified as Wood Ridge and 66% as Wood Planar cells. Thus, as previously inferred from confusion table analysis for the Geomorphon method (section 4.2.2), these inter-method results also underscore that the Geomorphon

Ridge and Spur classes are both sub-categories of non-linear eminences. The Wood Ridge feature type is primarily like the Geomorphon Ridge class, but also has strong secondary similarity to the Geomorphon Spur class. The 13% areal overlap of the Wood Ridge and

Geomorphon Summit class also fit expectations of tertiary similarity since both represent local convexities.

Similarly, the Wood Channel class exhibited 59% overlap with the Geomorphon Valley class and 23% overlap with the Geomorphon Hollow class, confirming the findings in section 4.2.2 about the similarity between these two Geomorphon classes. About 9.5% is of

Channel classes are also classified as Geomorphon Depression cells. Conversely, 59% of

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Geomorphon Valley and 30% Geomorphon Hollow cells were classified as Wood Channel cells, with the rest classified as Wood Planar feature type cells.

Interestingly, although Wood Pit cells constitute a negligible proportion (0.09%) of the study area, and hence not worth focusing on, still it is worth observing that 61% of Wood

Pit cells were classified as Geomorphon Valley, 36% as Geomorphon Depression cells and only 2% as Geomorphon Hollow cells. This suggests a strong spatial co-occurrence relationship between Pit and Valley cells, but almost negligible connection between Pit and

Hollow cells. This suggests that that the shape differences between the Valley and Hollow classes cannot be disregarded because they can exhibit distinctive and exclusive association patterns. Conversely, 63% of Geomorphon Depression cells were classified as Wood

Channel cells, 35% as Wood Planar cells and only 1% as Wood Pit cells (since there are very few Pit cells).

Overall, these comparisons clearly suggest that the ten Geomorphon classes offer a more diverse and nuances set of landform search patterns, compared to the Wood method, which assigns a lot of the area to the Planar feature type, precluding analysis of much of the study area. Thus, if only one classification system were to be chosen, the Geomorphon method is recommended over the Wood method. For a more detailed analysis of the two systems, topological assessments of polygons representing discrete instances of feature types and landform classes from the two classified rasters is necessary. This was not attempted for this thesis for lack of time but is recommended for future research.

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4.4.3 TPI vis-à-vis Wood and Geomorphon Classification Systems

As indicated by the overall similarity measures, the TPI landform classification system seems to be quite different from the Wood classification system, and only somewhat like the Geomorphon classification system. For the TPI experiment chosen for comparison with the other two methods, 54% study area was classified as Open Slope, 10% as Canyon, and another 10% as High Ridge. In other TPI experiments the observed relative percentages were similar as well, suggesting that just like the Planar feature type for the Wood method, the TPI method also has a catch-all class called Open Slope. Moreover, while for the Wood

– Geomorphon comparison, the largest overlap percentage was still observed between similar classes, in the case of TPI, for all Wood feature types and Geomorphon classes the largest overlap percentage is always with Open Slope. Thus, there is a lack of a strong preferential semantic association of any TPI class with a corresponding class from the

Wood or Geomorphon classification system.

Still, if the row and column normalized percentages are compared from Tables 4.23 –

4.24 and Tables 4.26 – 4.27, a few weak relationships can be observed. As expected, both non-linear and linear eminence classes from the Wood and Geomorphon methods correspond best with the TPI High Ridge class, with 28% Wood Peak and 29%

Geomorphon Summit cells overlapping with the TPI High Ridge class. The overlapping percentages are approximately 20% for the Wood Ridge, 18% for the Geomorphon Ridge and 13% for the Geomorphon Spur classes. The TPI Local Ridge and Midslope Ridge cells were practically non-existent not just for this chosen best experiment, but for all other 15

TPI experiments as well, so not much can be said about those classes based on experimental results. The complementary analysis of row percentages reveals that overlap

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percentages of TPI High Ridge class (Table 4.24) were almost double the column percentages. 37% and 48% of High Ridge cells overlapped with Wood Ridge and Planar cells, respectively, and 33%, 20% and 18% with the Geomorphon Ridge, Spur and Slope cells, respectively.

Similarly, if the Open Slope class is excluded from consideration, the Wood Channel feature type and Geomorphon Valley and Hollow classes overlap most often with the TPI

Canyon class, but the percentages do not exceed even 18%, just like the overlap of the linear eminence classes. The overlap with the TPI U-Shape Valley class is even lower ranging between 5% – 8%. Conversely, when examining the row percentages for the TPI

Canyon and U-Shape Valley classes, as was observed for the linear eminences, the percentages almost double. The row percentages for overlap of the TPI Canyon and U-

Shape Valley classes with the Wood Channel feature type were 33% and 40%, respectively.

The overlap row percentages of both these TPI classes was about 34% with the

Geomorphon Valley class, and only 21% – 22% with the Geomorphon Hollow class.

The overall analysis of class specific column and row overlap percentages clearly explains the reason for the substantially lower overall similarity measure of either method’s classification system with that of the TPI method. While the overlap for the Wood –

Geomorphon comparison did not reveal extremely strong associations, the best overlap percentages for TPI classes did not exceed 35% but were around 50% or more for the

Wood – Geomorphon comparison.

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Table 4. 19

Contingency table (overlap area percentages for class combinations) analysis for the best experimental runs from the Wood and

Geomorphon methods (Great Smoky Mountains (NC-TN) study area).

GEOMORPHON WOOD METHOD (Window size: 41x41 / Slope: 15° / Curvature: 0.001) . METHOD (Slope: 1° / Outer search radius: 41x41 / PL PT CH PS RI PK Study Area % Inner search radius: 15x15) FL 0.28 0.00 0.00 0.00 0.00 0.00 0.28 SU 1.29 0.00 0.00 0.02 2.54 0.38 4.24 RI 7.50 0.00 0.09 0.33 11.04 0.10 19.06 SH 0.17 0.00 0.00 0.00 0.00 0.00 0.17 SP 10.28 0.00 0.25 0.19 4.82 0.00 15.54 SL 17.93 0.00 1.22 0.14 1.12 0.00 20.40 HO 10.44 0.00 4.58 0.11 0.15 0.00 15.28 FS 0.88 0.00 0.06 0.00 0.00 0.00 0.94 VA 9.36 0.05 11.47 0.15 0.06 0.00 21.10 DP 1.05 0.03 1.87 0.03 0.00 0.00 2.98 Study Area % 59.17 0.09 19.55 0.96 19.74 0.49 100 Cramer's Coefficient V= 0.48 / Contingency Coefficient C= 0.64

Note: Wood Features: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak.).

Geomorphon Features: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat Slope,

VA= Valley, DP= Depression.

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Table 4. 20

Contingency table (overlap area percentages normalized for every column) analysis for the best experimental runs from the Wood and

Geomorphon methods (Great Smoky Mountains (NC-TN) study area).

GEOMORPHON WOOD METHOD (Window size: 41x41 / Slope: 15° / Curvature: 0.001) METHOD (Slope: 1° / Outer search radius: 41x41 / PL PT CH PS RI PK Study Area % Inner search radius: 15x15) FT 0.47 0.00 0.01 0.01 0.00 0.00 0.28 SU 2.19 0.00 0.01 1.92 12.89 79.05 4.24 RI 12.67 0.01 0.47 34.38 55.90 20.62 19.06 SH 0.29 0.00 0.00 0.00 0.00 0.00 0.17 SP 17.37 0.09 1.29 19.43 24.42 0.29 15.54 SL 30.29 0.41 6.24 14.08 5.69 0.04 20.40 HO 17.65 2.16 23.41 11.18 0.78 0.00 15.28 FS 1.48 0.05 0.33 0.05 0.00 0.00 0.94 VA 15.82 61.3 58.66 16.06 0.30 0.00 21.10 DP 1.77 35.96 9.58 2.88 0.01 0.00 2.98 % Total 100 100 100 100 100 100 Study Area % 59.17 0.09 19.55 0.96 19.74 0.49 100

Note: Wood Features: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak.).

Geomorphon Features: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat Slope,

VA= Valley, DP= Depression.

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Table 4. 221

Contingency table (overlap area percentages normalized for every row) analysis for the best experimental runs from the Wood and

Geomorphon methods (Great Smoky Mountains (NC-TN) study area).

GEOMORPHON WOOD METHOD (Window size: 41x41 / Slope: 15° / Curvature: 0.001) METHOD (Slope: 1° / Outer search radius: 41x41 / PL PT CH PS RI PK % Total Study Area % Inner search radius: 15x15) FL 99.16 0.00 0.78 0.02 0.04 0.00 100 0.28 SU 30.48 0.00 0.04 0.44 59.98 9.06 100 4.24 RI 39.35 0.00 0.48 1.74 57.91 0.53 100 19.06 SH 99.94 0.00 0.01 0.00 0.05 0.00 100 0.17 SP 66.14 0.00 1.62 1.20 31.03 0.01 100 15.54 SL 87.85 0.00 5.98 0.66 5.51 0.00 100 20.40 HO 68.32 0.01 29.95 0.70 1.01 0.00 100 15.28 FS 93.05 0.00 6.78 0.05 0.10 0.00 100 0.94 VA 44.38 0.25 54.35 0.73 0.28 0.00 100 21.10 DP 35.13 1.05 62.79 0.93 0.09 0.00 100 2.98 Study Area % 59.17 0.09 19.55 0.96 19.74 0.49 100

Note: Wood Features: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak.).

Geomorphon Features: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat Slope,

VA= Valley, DP= Depression.

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Table 4. 22

Contingency table (overlap area percentages for class combinations) analysis for the best experimental runs from the Wood and TPI methods (Great Smoky Mountains (NC-TN) study area).

TPI METHOD WOOD METHOD (Window size: 41x41 / Slope: 15° / Curvature: 0.001) (Large scale window: 41x41 / Study Area % PL PT CH PS RI PK Small scale window: 15x15) CA 5.54 0.01 3.44 0.12 1.28 0.02 10.41 MSD 1.87 0.00 0.54 0.03 0.72 0.01 3.17 UD 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U-SV 2.10 0.01 1.72 0.06 0.43 0.00 4.31 PL 7.16 0.01 1.54 0.01 0.09 0.00 8.81 OS 33.25 0.04 9.97 0.50 10.72 0.22 54.71 US 2.26 0.00 0.40 0.08 2.12 0.09 4.94 LR 0.00 0.00 0.00 0.00 0.00 0.00 0.00 MSR 1.94 0.00 0.79 0.03 0.47 0.01 3.24 HR 5.06 0.01 1.13 0.15 3.91 0.14 10.40 Study Area % 59.17 0.09 19.55 0.96 19.74 0.49 100 Cramer's Coefficient V= 0.18 / Contingency Coefficient C= 0.30 Note: Wood Features: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak).

TPI Features: CA = Canyon, MSD = Mid Slope Drainage, UD= Upland Drainage, U-SV= U-Shape Valley, PL = Plain, OS= Open

Slope, US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

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Table 4. 23

Contingency table (overlap area percentages normalized for every column) analysis for the best experimental runs from the Wood and

TPI methods (Great Smoky Mountains (NC-TN) study area). TPI METHOD WOOD METHOD (Window size: 41x41 / Slope: 15° / Curvature: 0.001) (Large scale window: 41x41 / Study Area % PL PT CH PS RI PK Small scale window: 15x15) CA 9.36 16.56 17.60 12.81 6.49 3.37 10.41 MSD 3.16 3.32 2.77 2.87 3.63 2.80 3.17 UD 0.00 0.01 0.00 0.00 0.01 0.01 0.00 U-SV 3.55 7.69 8.80 5.96 2.16 0.88 4.31 PL 12.09 11.63 7.89 0.94 0.47 0.64 8.81 OS 56.20 45.50 51.03 51.41 54.32 44.76 54.71 US 3.82 2.24 2.06 7.82 10.73 17.59 4.94 LR 0.00 0.02 0.01 0.00 0.00 0.00 0.00 MSR 3.28 4.41 4.04 2.76 2.37 1.13 3.24 HR 8.55 8.62 5.79 15.42 19.82 28.82 10.40 % Total 100 100 100 100 100 100 Study Area % 59.17 0.09 19.55 0.96 19.74 0.49 100

Note: Wood Features: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak).

TPI Features: CA = Canyon, MSD = Mid Slope Drainage, UD= Upland Drainage, U-SV= U-Shape Valley, PL = Plain, OS= Open

Slope, US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

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Table 4. 24

Contingency table (overlap area percentages normalized for every row) analysis for the best experimental runs from the Wood and

TPI methods (Great Smoky Mountains (NC-TN) study area). TPI METHOD WOOD METHOD (Window size: 41x41 / Slope: 15° / Curvature: 0.001) (Large scale window: 41x41 / PL PT CH PS RI PK % Total Study Area % Small scale window: 15x15) CA 53.17 0.14 33.04 1.19 12.31 0.16 100 10.41 MSD 58.91 0.09 17.07 0.87 22.62 0.43 100 3.17 UD 24.43 0.33 7.79 1.83 63.52 2.10 100 0.00 U-SV 48.66 0.16 39.88 1.33 9.87 0.10 100 4.31 PL 81.19 0.12 17.50 0.10 1.06 0.04 100 8.81 OS 60.79 0.07 18.23 0.91 19.60 0.40 100 54.71 US 45.69 0.04 8.15 1.52 42.87 1.73 100 4.94 LR 31.41 0.56 60.10 1.30 6.63 0.00 100 0.00 MSR 60.05 0.12 24.39 0.82 14.44 0.17 100 3.24 HR 48.63 0.07 10.89 1.43 37.63 1.35 100 10.40 Study Area % 59.17 0.09 19.55 0.96 19.74 0.49 100

Note: Wood Features: PL= Planar, PT= Pit, CH= Channel, PS= Pass (Saddle), RI= Ridge, PK= Peak).

TPI Features: CA = Canyon, MSD = Mid Slope Drainage, UD= Upland Drainage, U-SV= U-Shape Valley, PL = Plain, OS= Open

Slope, US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

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Table 4. 25

Contingency table (overlap area percentages for class combinations) analysis for the best experimental runs from the Geomorphon and TPI methods (Great Smoky Mountains (NC-TN) study area). TPI METHOD GEOMORPHON METHOD (Slope: 1° / Outer search radius: 41x41 / Inner search radius: 15x15) (Large scale window: 41x41 / FL SU RI SH SP SL HO FS VA DP Study Area % Small scale window: 15x15) CA 0.00 0.06 0.81 0.01 1.08 1.99 2.18 0.04 3.64 0.81 10.62 MSD 0.00 0.05 0.36 0.00 0.34 0.48 0.37 0.01 0.52 0.08 2.23 UD 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U-SV 0.00 0.01 0.24 0.00 0.35 0.70 0.78 0.01 1.25 0.27 3.61 PL 0.28 0.22 0.91 0.16 0.55 1.20 0.72 0.87 3.34 0.76 8.99 OS 0.01 2.02 11.33 0.12 9.83 13.04 9.30 0.17 10.80 0.98 57.60 US 0.00 0.56 1.56 0.01 0.85 0.72 0.36 0.00 0.22 0.00 4.29 LR 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 MSR 0.00 0.05 0.33 0.00 0.36 0.55 0.45 0.01 0.56 0.04 2.36 HR 0.00 1.23 3.45 0.02 2.04 1.86 1.00 0.01 0.68 0.01 10.30 Study Area % 0.29 4.20 18.99 0.33 15.40 20.50 15.16 1.12 21.01 2.96 100 Cramer's Coefficient V= 0.29 / Contingency Coefficient C= 0.45 Note: Geomorphon Features: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat

Slope, VA= Valley, DP= Depression.TPI Features: CA = Canyon, MSD = Mid Slope Drainage, UD= Upland Drainage, U-SV= U-

Shape Valley, PL = Plain, OS= Open Slope, US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

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Table 4. 26

Contingency table (overlap area percentages normalized for every column) analysis for the best experimental runs from the

Geomorphon and TPI methods (Great Smoky Mountains (NC-TN) study area). TPI METHOD GEOMORPHON METHOD (Slope: 1° / Outer search radius: 41x41 / Inner search radius: 15x15) (Large scale window: 41x41 / FL SU RI SH SP SL HO FS VA DP Study Area % Small scale window: 15x15) CA 0.47 1.50 4.24 2.56 7.01 9.70 14.37 3.20 17.34 27.57 10.62 MSD 0.27 1.22 1.92 1.34 2.22 2.34 2.44 1.03 2.47 2.71 2.23 UD 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U-SV 0.11 0.35 1.24 0.83 2.29 3.40 5.13 1.04 5.93 9.09 3.61 PL 95.68 5.19 4.77 47.04 3.55 5.83 4.72 77.84 15.89 25.74 8.99 OS 3.25 48.07 59.67 37.69 63.81 63.49 61.34 15.36 51.40 33.01 57.60 US 0.00 13.31 8.21 2.84 5.53 3.50 2.39 0.21 1.06 0.11 4.29 LR 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.01 0.01 0.00 MSR 0.22 1.15 1.76 1.48 2.35 2.68 2.97 0.76 2.69 1.27 2.36 HR 0.01 29.22 18.18 6.21 13.23 9.06 6.62 0.55 3.22 0.50 10.30 % Total 100 100 100 100 100 100 100 100 100 100 Study Area % 0.29 4.20 18.99 0.33 15.40 20.50 15.16 1.12 21.01 2.96 100

Note: Geomorphon Features: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat

Slope, VA= Valley, DP= Depression.TPI Features: CA = Canyon, MSD = Mid Slope Drainage, UD= Upland Drainage, U-SV= U-

Shape Valley, PL = Plain, OS= Open Slope, US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

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Table 4. 27

Contingency table (overlap area percentages normalized for every row) analysis for the best experimental runs from the Geomorphon and TPI methods (Great Smoky Mountains (NC-TN) study area). TPI METHOD GEOMORPHON METHOD (Slope: 1° / Outer search radius: 41x41 / Inner search radius: 15x15) (Large scale window: 41x41 / Study Area % FL SU RI SH SP SL HO FS VA DP % Total Small scale window: 15x15) CA 0.01 0.59 7.58 0.08 10.16 18.75 20.51 0.34 34.30 7.67 100 10.62 MSD 0.04 2.30 16.40 0.20 15.41 21.60 16.63 0.52 23.31 3.60 100 2.23 UD 0.00 7.83 39.32 2.21 19.74 19.74 7.15 0.09 3.91 0.00 100 0.00 U-SV 0.01 0.41 6.54 0.08 9.78 19.34 21.57 0.32 34.51 7.44 100 3.61 PL 3.07 2.43 10.08 1.73 6.09 13.32 7.96 9.72 37.13 8.46 100 8.99 OS 0.02 3.51 19.67 0.22 17.07 22.63 16.14 0.30 18.75 1.69 100 57.60 US 0.00 13.04 36.34 0.22 19.87 16.76 8.44 0.06 5.20 0.07 100 4.29 LR 0.00 0.46 3.38 0.46 5.79 16.50 25.51 0.92 40.93 6.05 100 0.00 MSR 0.03 2.04 14.15 0.21 15.35 23.31 19.07 0.36 23.90 1.59 100 2.36 HR 0.00 11.92 33.51 0.20 19.80 18.07 9.74 0.06 6.56 0.14 100 10.30 Study Area % 0.29 4.20 18.99 0.33 15.40 20.50 15.16 1.12 21.01 2.96

Note: Geomorphon Features: FL = Flat, SU = Summit, RI = Ridge, SH = Shoulder, SP = Spur, SL= Slope, HO = Hollow, FS = Flat

Slope, VA= Valley, DP= Depression.TPI Features: CA = Canyon, MSD = Mid Slope Drainage, UD= Upland Drainage, U-SV= U-

Shape Valley, PL = Plain, OS= Open Slope, US= Upper Slope, LR = Local Ridge, MSR= Mid Slope Ridge, HR= High Ridge.

Chapter 5: Conclusions and Recommendations

5.1 Semi-Automated Feature Extraction for Landform Mapping

This thesis was inspired by the lack of semi-automated methods for mapping landforms, especially for national scale mapping, a core mission of national mapping agencies such as the U.S. Geological Survey (USGS). The lack of such methods is not merely a technical problem, but also conceptual one since there is no completely objective process by which to decide how to represent landforms as discrete objects.

Terrain type, culture, language, and other subjective factors greatly affect how the same portion of the terrestrial surface maybe discretized, classified, labeled, and characterized by people. Despite obvious challenges, there also is clearly enough commonality across all contexts since people do communicate about landforms, because they share the same biological perceptual systems which conditions all humans to perceive the physical aspects of the landscape to some degree of universality. The simplest perceptual characteristics such as form, material, color, spatial relationships etc. are most likely factors that people perceive similarly. The more complex the descriptors get, the more likely they are to be limited to a smaller group of people.

Based on this general idea, and because form remains the most fundamental perceptual characteristic used to recognize landforms in the landscape, this thesis was designed to conduct fundamental research on comparison of existing terrain surface characterization methods to test their capability to support general purpose terrain feature extraction that could underlie semi-automated workflows for mesoscale landform mapping at regional and national scales. These methods have not been compared extensively for such a purpose and this thesis filled that intellectual niche. Two broad 154 research questions were proposed which then guided the selection of three methods for comparison, the design of the experiments, and analysis of results from the experiments.

Three methods proposed by Wood (1996), Jasiewicz and Stepinski (2013), and Weiss

(2001) were selected because they are popular in terrain characterization, have shown promising results for mapping discrete terrain features that are intended to resemble landforms recognized intuitively by people, and because they are easily available for experimentation in freely available software. All these methods have a simple data elevation rasters which are the only input dataset needed for these methods For this thesis, three broadly scoped landform categories: non-linear eminences, linear eminences and linear depressions were chosen to enable comparisons across these methods. These three categories had corresponding landform types in the classification schemes of the three chosen methods. However, the methods rely on substantially different classification schemes and methods for classifying, and they are intended to classify raster pixels, not detect large meso-scale features. Yet, aggregations of such pixels can and have been show in this thesis to correspond to mesoscale landforms that people tend to recognize and name. The labels of the classes and overlaying classified raster cells on 2D topographic map layers and in 3D terrain views is the only realistic way to get an empirical understanding of the type(s) of terrain features or landform objects each class could correspond to.

All three methods (Wood, Geomorphon, and TPI) are sensitive to multiple parameters and as the results show, results can vary appreciably depending on the choice of the parameter values. Thus the first research question (A.i and A.ii) was chosen to study the

155 impact of these parameters for each method for three different study areas which were chosen strategically based on past research and to be able to both compare results from similar (similar mountainous terrain in the Great Smoky Mountains and White Mountains study areas) and starkly different terrain types (arid, low relief Colorado Plateau study area) in the continental US. Much of this research project and the chosen methodology was dedicated to answering this important research question. In addition, a secondary goal of this thesis as capture in the second research question (B.i and B.ii) was to compare how the methods compare to each other for the same study areas and to get a preliminary sense of the semantic similarity between some of the supposedly similar landform categories from the three methods.

5.2 Discussion: Impact of Parameterization (Research Questions A.i and A.ii)

Results from sections1` 4.1, 4.2 and 4.3 helped answer the impact of choice of parameters for each method. Painstaking visual analysis of results of hundreds of rasters became the basis for much of the findings and guided the small number of quantitative comparisons attempted to quantify and cross-check the findings from the visual assessment. While specific findings for each method are available in chapter 4, a summary of the findings is provided below to highlight the primary insights gained from the comprehensive experimental data analysis.

• It is important to continue to use and promote the concept of using abstract categories

such as non-linear eminences, linear eminences, and linear depressions for comparing

landform classes from different methods. Classes defined in one classification system

will typically share only partial or no (but never perfect) semantic similarity with

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classes in another classification system. Yet, based on the labels of classes and shape

correspondence of extracted landform objects from different systems, there is clearly

an attempt to find similar types of features. This is why using a small set of reference

categories, defined based only on form distinctions, can help anchor the comparison

of landform classes from different classification systems.

• Visual geomorphometric analysis is extremely important in assessing the value and

validity of any classification system. It provides important overall context and initial

hypotheses that can be verified with quantitative analyses of raster overlays for intra

and inter method comparisons. Even though visual analysis can be quite subjective,

with sufficient effort and extensive comparisons, it can offer a richer understanding of

landform mapping, than possible with quantitative analysis alone.

• While not used extensively for this thesis, the value and potential of using 3D scene

based terrain visualization and geomorphometric analysis is immense. The intuitive

appeal of exploring overlays of extracted features and landform objects in 3D scenes

with satellite imagery draped over an elevation basemap cannot be overstated.

Observing the landscape from different vantage points not only leads to more holistic

evaluations of the mapped patterns, but sometimes also prevents incorrect

assessments that sometimes can result from examination of only 2D topographic map

views.

• On the other hand, visual analysis is, ultimately, never enough because it is hard to

make strong generalizable claims merely based on visual examination. It is not

possible to explore large study areas with equal detail, so sampling becomes

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inevitably necessary. This can lead to blind spots in the analysis. On the other hand,

quantitative analysis helps summarize findings for large study areas and for many

experiments. The cross-table based methods used in this thesis were simple and

appropriate for this first phase of analysis. However, more advanced

geomorphometric measurements of extracted objects, graphical plots and summaries

from all possible experimental comparisons, and statistical hypothesis testing should

be used in the next phase of analysis.

• After testing a wide range of parameter values, for all methods, it seems clear that

only a narrow range of values can yield results that would help identify discrete

representations of landforms that will match people’s intuitive identification of

landforms and approximate extents either in the field or based on topographic maps

and other forms of geovisual displays. The experiments undertaken for this thesis

identify the possible acceptable ranges of parameter values for each method.

• The choice of the primary window size for each method was found to be the most

important factor in delineating visually appealing landform objects and a very narrow

neighborhood size of 31x31 to 41x41 (approximately 300-400 meters) was found to

be optimal from visual and quantitative analysis. Smaller window sizes led to thin and

topologically discontinuous linear eminences and depressions and often caused

elimination of many non-linear eminences. On the other hand, larger window sizes

lead to broad landform extents, which often do not match with expected shape

patterns for any of the three landform categories.

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• Both visual and confusion matrix analysis from raster overlays clearly shows that

varying parameter values beyond small intervals can cause substantial changes in

mapped patterns of landforms. The pattern of classification shifts is quite predictable

however since the feature types or landform classes tend to shift only to semantically

(e.g., shifts between Ridge and Spur classes for the Geomorphon method) or

morphometrically related classes (e.g., shifts between Pit and Channel and between

Pass and both Ridge and Channel classes for the Wood method).

• Both Wood and Geomorphon methods show much more promise to map all three

landform categories of interest: non-linear eminences, non-linear eminences, and

linear depressions. The TPI method was found to offer the most appealing narrow

non-linear landform shapes. However, it lacks a dedicated class for mapping non-

linear eminences and it also tends to perform poorly in low relief areas.

• There seems to be much similarity in the parameters needed to extract linear

eminences and depressions, but there still seems to be sufficiently different level of

sensitivity to parameter values that it would be fallacious to assume that mapping of

linear eminences and features can always be done with the same parameters.

• In general, for identifying mesoscale landforms from these methods, the

parameterization was not found to be as sensitive to terrain type since values were

found to be relatively constant across all three study areas (research question A.ii).

Even if the TPI method yielded extremely wide linear landforms in the Colorado

Plateau, the best small and large scale window sizes were the same as those

determined for the other study areas.

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• Even the methods are parameterized with the same analytical window sizes, the

curvature and slope thresholds for the Wood method and the slope threshold for the

Geomorphon method can lead to substantial impacts on the classification of locations

in the study area. Moreover, even with comparable parameters, there are substantial

differences in the frequencies of and shapes and size of individual landform objects

delineated by the method.

• Automated mapping in arid, low slope areas such as the Colorado Plateau study area

chosen for this thesis will prove to be more challenging than for other high relief

areas. In such areas, there is a much higher likelihood of not being able to detect

enough instances of desired landform categories and there is much more sensitivity to

parameter values than in high relief areas.

• GNIS features can be used to validate extracted landform objects and complement

visual analysis, but only to some extent. Their use is limited to areas with sufficient

instances of named features. Low frequencies of GNIS features was a limitation for

the Colorado Plateau area, for example. GNIS features only represent named

landforms, which is a small subset of topographically and culturally salient

landforms, so testing with human subjects to validate results is necessary. GNIS can

only serve as a preliminary surrogate for, not a replacement for, human subjects.

• While this thesis relied on high resolution (10 meters) DEMs, the results are not

likely to change as much if a 30-meter size DEM were to be used instead. This can be

inferred from the finding that a neighborhood size of at least 300 meters is needed to

detect cognitively plausible landform objects. Thus, even if a 30-meter DEM were to

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be used, results will be similar. This can also substantially reduce the computational

complexity, which is critical for mapping large areas. This also bodes well for parts of

the world for which 10-meter resolution DEMs are not available.

5.3 Discussion: Relative Performance of and Similarity Between Methods (Research

Questions B.i and B.ii)

The secondary goal in this thesis was to provide a preliminary assessment of how the three methods perform vis-à-vis each other and to what extent can some of the morphometric features and landform classes corresponded across the three methods.

• Visual and quantitative geomorphometric analysis conducted to stud impacts of

parameterization provided a lot of information about how much the methods were

similar or differed in the conceptualization and operational identification of

morphometric features and landform objects. As summarized above, the most obvious

equivalence in the three methods comes from the most important parameter: primary

window size which seems to impact all methods similarly. This is an important

confirmation since this relates directly to scale issues at the heart of any kind of

mapping of natural landscape phenomena. Landforms can be mapped at multiple

scales and it is important to note that all methods support multiscale landform

mapping.

• The Wood method is special in its use of curvature threshold and only one

neighborhood processing window, whereas the Geomorphon and TPI methods need

to be parameterized at two scales simultaneously.

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• From GNIS feature proximity analysis in section 4.3, it seems that the Wood method

is slightly better than the Geomorphon method, and both methods yield results better

than TPI method consistently. TPI does not have a dedicated class corresponding to

non-linear eminences, so it is obvious that it cannot be used for creating areal

representations for GNIS Summit features. However, it does tend to provide mor

realistic, narrower linear eminence and depression polygons than the Wood and

Geomorphon methods, for comparable primary window sizes of analysis. Yet, the

thinner linear polygons also make it much more likely that GNIS Ridge and Valley

features are not found inside a TPI landform object. However, it is still worth noting

that even for the worst performing TPI method, GNIS features are quite likely to be

within 30 meters of a landform object of the corresponding type.

• As can be easily determined from their classification systems, the three methods offer

some similar but also sufficiently different landform classes, reflecting the diversity

of landform classes that can be detected and mapped. This presents a challenge for

selection and comparison of these methods because a lot more work needs to be done

to assess their specialties and limitations. The results reported in section 4.4 suggest

that at least for the Wood and Geomorphon methods, meaningful similarities also

exist for the classes corresponding to non-linear eminences (Wood Peak to

Geomorphon Summit), linear eminences (Wood Ridge to Geomorphon Ridge

(primary) and Geomorphon Spur (secondary), and linear depressions (Wood Channel

to Geomorphon Valley (primary) and Geomorphon Hollow (secondary). However,

even in the best case, the overlap percentages average 50%, which suggests a only a

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moderate level of similarity between the corresponding classes. Results could

possibly be improved for each of the three landform categories separately by more

careful parameterization, which is left for future work. However, the TPI class

definitions are sufficiently different to have a much lower (20% to 35%) level of

overlap with the corresponding classes of the Wood and Geomorphon classification

systems.

• The impact of the primary window size across methods seems to be similar across

methods. However, what was not explored in this thesis is the equivalence between

the slope threshold parameters of the Wood and Geomorphon methods, for different

primary window sizes. The analysis conducted for this thesis the role and impact of

the slope threshold parameters are quite different. Similarly, the impacts of the inner

search radius parameter for the Geomorphon method and the small cale window size

for the TPI method also need to be compared carefully.

5.4 Limitations and Recommendations

As with any research project, several assumptions and limitations become apparent by the end of the project. For this thesis too several such insights emerged after analysis of the results.

• For both the Geomorphon method, the relationship between the Ridge and Spur

classes needs to be explored since they are not equivalent but are both examples of

linear eminences. Their definition is obviously available in the original paper by

Jasiewicz and Stepinski (2013), but an analysis of their relative frequencies, shapes

and sizes in different terrain types needs to be explored for (semi) automated mapping

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of linear landforms. Similar analysis also needs to be done for the Geomorphon

Valley and Hollow classes.

• The TPI method’s classification system proposed in Weiss (2001) can be easily

customized by changing the thresholds for standardized TPI values used to define

landform classes. It will be painstaking work but understand the sensitivity of the TPI

classification to those thresholds is critical for clearly establishing which definitions

of classes are most optimal for mapping mesoscale linear landforms. Given the lack

of a dedicated class for mapping non-linear eminences, it also is important to explore

if a class similar to the Wood Peak feature type or Geomorphon Summit class can be

defined based on standard TPI values using only one primary window size or a

combination of small and large scale windows. More experiments could also reveal a

way to adjust the definition of the High Ridge class that it yields higher frequencies

and more cognitively plausible forms of non-linear eminences.

• There are several other analytical methods that can be used for quantitative

characterization of the types of experiments. For example, for this thesis, extra work

not presented here was undertaken to extensively measure the shape and size of

extracted polygons which was then supposed to be analyzed statistically. However, it

proved to be beyond the scope of this thesis. That work needs to be carried out, much

like the analysis presented in Miliaresis and Argialas (2002) and Sinha (2008) since it

will provide a much better understanding of the impact of parameter choices on the

geomorphometric characteristics of extracted landform objects.

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• The processing of DEMs for geomorphometric analysis is computationally

demanding, especially for high resolution DEMs and large study areas. Therefore,

this kind of project should be done on more advanced desktop computers, with added

graphic cards to reduce the processing times.

• The ability of one or a combination of methods to offer areal approximations of

individual landforms, especially locally well known landforms (e.g. those recorded in

GNIS and other similar gazetteer databases of the world) is an important problem that

should be explored in a parallel research project.

• Although this study was done with three study areas in the US, the methods and

findings should be generalizable to all countries. However, the rate of failure will

likely be higher in low relief places. The relative performance of the three methods

can differ depending on terrain type, so similar research projects with DEMs from

other countries should be tested to verify the findings of this thesis.

• Although most of the experimental runs and data management was done using

automated Model Builder based workflows in ArcGIS Desktop 10.6, there still was a

lot of data processing that had to be done manually. That limited the types of

quantitative analysis that could be undertaken. It is highly recommended, therefore, to

learn and apply more general-purpose scripting approaches using Python and the R

statistical package. Such a technical analysis framework can allow automated

graphing and parameterization analysis that would be nearly impossible to do

manually. It also helps avoid errors that are almost inevitable when lots of files need

to be managed and results manually imported into spreadsheets for analysis.

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Moreover, Python scripts are critical for creating workflows that can invoke functions from multiple software systems including ArcGIS Pro 2.4, QGIS, SAGA GIS and

Whitebox, all of which offer some unique functions which can be useful in geomorphometric analysis. For the benefit of open science and building a shared community of researchers interested in semi-automated and automated landform mapping, using open source software, and sharing the code is highly encouraged.

The work done for this thesis confirms the theoretical assertions made by researchers that the nature of landform conceptualization and mapping is complex and inherently subjective. Contrary to what maybe assumed about physical landscape features, especially landforms, there are several ways to conceptualize and represent landforms It is critical (and an ethical obligation) to support multiple perspectives of landforms and offer at least a few alternative versions of extracted landform objects to support the diversity of perspective. This kind of research cannot be justified only with software simulated experiments and comparisons of methods. Validation of results must also be done with human subjects from diverse linguistic, cultural and education backgrounds.

This will all be obviously quite challenging but necessary. The challenges are not impediments, but only point to the immense complexity and potential for implementing a flexible and customizable national scale mapping workflow for automated mapping of landforms.

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