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Library of Congress Cataloging‐in‐Publication Data
Names: Wilson, John P. (John Peter), 1955– author.
Title: Environmental applications of digital terrain modeling / John P. Wilson.
Description: First edition. | Hoboken, NJ : Wiley‐Blackwell, 2018. | Series: New analytical methods in earth and environmental science | Includes bibliographical references and index.
Identifiers: LCCN 2017048368 (print) | LCCN 2018001634 (ebook) | ISBN 9781118936207 (pdf) | ISBN 9781118938171 (epub) | ISBN 9781118936214 (hardback)
Subjects: LCSH: Digital elevation models | Three‐dimensional imaging. | Digital mapping. | BISAC: SCIENCE / Earth Sciences / Geology.
Classification: LCC GA139 (ebook) | LCC GA139 .W55 2018 (print) | DDC 551.410285–dc23
LC record available at https://lccn.loc.gov/2017048368
Cover Design: Wiley
Cover Image: Photograph taken to the north of the main channel looking southward to the highest peak which marks the southeast corner of the Cottonwood Creek, MT catchment. Photograph courtesy of William K. Wyckoff.
For Duncan, Ha and Vanessa who made a project like this all the more meaningful for me and to Richard Bedford, Pip Forer, Kenneth Hare, Bruce Leadley, Michael Hutchinson, Ian Moore, and John Gallant and the many others I have encountered along the way for helping to lead me to this place.
1.1 | Scales at which various biophysical processes dominate calculation of primary environmental regimes. |
1.2 | Map of Cottonwood Creek, MT study site. |
1.3 | NED 10‐m contour and NHD‐Plus streamline data for the Cottonwood Creek, MT study site, with the catchment boundary overlaid. |
2.1 | The main tasks associated with digital terrain modeling. |
2.2 | The three principal methods of structuring an elevation data network: (a) a contour‐based network; (b) a square‐grid network showing a 3 × 3 moving window; and (c) a triangulated irregular network (TIN). |
2.3 | Streamline data in green and (a) initial gridded streamlines at 1‐second resolution in red and (b) adjusted gridded streamlines at 1‐second resolution in red. |
3.1 | Schematic showing site‐specific, local, and regional interactions as a function of time. |
3.2 | A 3 × 3 moving grid used to calculate selected local land surface parameters. |
3.3 | Node numbering convention used for calculation of local land surface parameters. |
3.4 | Percent slope grid derived for Cottonwood Creek, MT study site using the finite difference equation, with the catchment boundary overlaid. |
3.5 | Aspect in degrees from north derived for Cottonwood Creek, MT study site using the finite difference equation, with the catchment boundary overlaid. |
3.6 | Northness derived for Cottonwood Creek, MT study site, with the catchment boundary overlaid. |
3.7 | Eastness derived for Cottonwood Creek, MT study site, with the catchment boundary overlaid. |
3.8 | Profile curvature (radians per 100 m, convex curvatures are positive) derived for Cottonwood Creek, MT study site using the finite difference formula, with the catchment boundary overlaid. |
3.9 | Plan curvature (radians per 100 m, convex curvatures are positive) derived for Cottonwood Creek, MT study site using the finite difference formula, with the catchment boundary overlaid. |
3.10 | Single‐ and multiple‐flow directions assigned to the central grid cell in a 3 × 3 moving window using the D8 and FMFD flow‐direction algorithms. Gray shading represents elevation decreasing with the darkness of the cell. Multiple‐flow directions are assigned in (b) and a fraction of the flow of the central cell is distributed to each of the three cells that the arrows point to. |
3.11 | Concept of flow apportioning in D∞. |
3.12 | Upslope contributing area (ha) derived for Cottonwood Creek, MT study site using the D8 single‐flow direction algorithm, with the catchment boundary overlaid. |
3.13 | Upslope contributing area (ha) derived for Cottonwood Creek, MT study site using the D∞ single‐flow direction algorithm, with the catchment boundary overlaid. |
3.14 | The four mathematical surfaces commonly used for data‐independent assessment of different flow‐direction algorithms. |
3.15 | Concept of flow apportioning in MD∞ based on the construction of triangular facets around one cell. |
3.16 | Distribution of the number of cells that receive accumulated area (i.e. flow) from one cell in a sample DEM for an area in central Sweden. |
3.17 | Flow apportioning between two cardinal neighbors in the Mass Flux method. L1 and L2 denote the projected flow widths into the upper and right neighbor and together equal the projected flow width ω. n1 and n2 are vectors normal to the cell boundaries, q is the flow vector and θ is the flow direction. |
3.18 | (a) Two triangular facets are formed in a 2 × 2 cell moving window using the spot heights at the center of each grid cell; (b) a 4 × 4 cell moving window is used to estimate elevation at P by fitting a bivariate cubic spline surface. |
3.19 | Flow line over a TFN: the numbers at the nodes of triangles represent elevation, the light lines show the original grid cells, and the flow lines represented by the arrow chains are formed by tracking the movement of flow (i.e. the flow directions). |
3.20 | The decomposition of grid cells into a set of eight triangular facets defined by the nine‐cell kernel nodes (black circles) in Dtrig. The node’s elevations are listed next to each node and facet boundaries are denoted by dashed lines. The surface extent is limited to the central cell so that the only node within this domain is the element‐centered node. The contours and gray scale illustrate the elevation variability within the element and the rounding of the contours adjacent to facet boundaries is an artifact of the contouring algorithm. |
3.21 | Examples of flow partitioning from a triangular facet. (a) A triangular facet, the local coordinates, and the î, ĵ directions. (b) The case where the line oriented in the direction of intersects node [x2, y2, z2] and is plunging toward this node. The dashed lines that bound denote the range of orientations where intersects this node and divides the area into two triangles. In this case, the facet’s drainage area is partitioned proportionally to the area of each of the triangles bounded by the facet’s drainage divide (i.e. the dashed intersecting line) and the facet’s bounding legs. The area is partitioned into the two facets sharing the bold colored facet legs. (c) Same as (b) except that is dipping toward node [x1, y1, z1]. (d) Same as (b) except is plunging away from node [x2, y2, z2]. (e) Same as (d) except that is plunging away from node [x1, y1, z1]. |
3.22 | The center cell in a 3 × 3 grid cell window divided into eight triangular facets (1–8) with each facet formed from three points; one is the center of the central grid cell (M) and the other two are the centers of two adjacent grid cells (e.g. C1 and C2). |
3.23 | Upslope contributing area (ha) derived for the Cottonwood Creek, MT study site using the MD∞ multiple‐flow direction algorithm, with the catchment boundary overlaid. |
3.24 | Upslope contributing area (ha) derived for the Cottonwood Creek, MT study site using the TFM multiple‐flow direction algorithm, with the catchment boundary overlaid. |
3.25 | An idealized stream tube originating at a hilltop and terminating at a contour on a hillslope. The average specific catchment area a along the contour segment is the ratio of contributing area A to flow width w. |
3.26 | Difference from mean elevation for the Cottonwood Creek, MT study site using a 15 × 15 cell moving window, with the catchment boundary overlaid. |
3.27 | Elevation percentile for the Cottonwood Creek, MT study site using a 15 × 15 cell moving window, with the catchment boundary overlaid. |
3.28 | Standard deviation of elevation for the Cottonwood Creek, MT study site using a 15 × 15 cell moving window, with the catchment boundary overlaid. |
3.29 | A comparison of the shape complexity index values for a perfectly oval shape (left) and for different levels of complexity (right). |
3.30 | (a) The local gradient in the original topographic wetness index and (b) with the new slope term proposed by Hjerdt et al. (2004). The dotted lines represent the gradient of the groundwater table that is constant in the original topographic wetness index (a) and variable in the slope‐adjusted topographic wetness index (b). |
3.31 | Steady‐state topographic wetness index derived for the Cottonwood Creek, MT study site using Equation 3.46, with the catchment boundary overlaid. |
4.1 | The modified Dikau (1989) classification of form elements based on the profile and tangential curvatures. The elements have been further classified as positive or negative based on the radius of curvatures (>600 or <600 m) and the planform curvature in the original classification was replaced by tangential curvature based on Shary and Stepanov (1991). |
4.2 | Shary’s complete system of classification of landform elements based on signs of tangential, profile, mean difference, and total Gaussian curvatures. |
4.3 | Landscape elements on a hillslope profile between two interfluves as delineated by Ruhl (1960) and Ruhl and Walker (1968). |
4.4 | Schematic showing the derivation of fuzzy memberships using (a) the definition of thresholds and (b) the definition of class centers. |
4.5 | D8 (O’Callaghan & Mark, 1984) flow direction derived for the Cottonwood Creek, MT study site with the catchment boundary overlaid. |
4.6 | Contour maps showing the results of using three methods to predict channel head locations for a catchment in Indian Creek, Ohio. The circles indicate mapped channel heads and the contour intervals are 10 m. The stream networks resulting from the (a) Passalacqua et al. (2010) method, (b) Pelletier (2013) method, and (c) DrEICH (Clubb et al., 2014) methods are shown in the three maps as well. |
4.7 | Schematic showing how the morphometric class at the point indicated by the vertical arrow varies as shown with the scale over which it is measured. |
4.8 | Comparison of major landform types between the Sayre et al. (2014) and Karagulle et al. (2017) maps. |
4.9 | Schematic showing local variance (LV) method applied to the grid cells in a DEM. |
5.1 | Number of papers focused on DEM error and uncertainty cited in Section 5.1 by year of publication. |
5.2 | Composition of the rule set for the scale adaptive digital elevation model (S‐DEM) algorithm. |
5.3 | Data structure for S‐DEM: (a) the original DEM (the number in each cell represents elevation); (b) the index array using DOI (the number in each cell represents the largest adaptable cell size in meters). |
6.1 | Schematic showing some of the capabilities and how the elevation and hydrology tools are accessed in Esri’s ArcGIS Online platform (as of February 2017). |
2.1 | List of key characteristics of elevation data sources described in this chapter. |
2.2 | Horizontal National Map Accuracy Standards (NMAS) used in the USA since 1947. |
2.3 | SRTM‐3 versions produced and distributed by CGIAR‐CSI. |
2.4 | Elevation data sources included in the US National Elevation Dataset (NED) as of August, 2015. |
3.1 | List of primary land surface parameters and their significance. |
3.2 | List of single‐ and multiple‐flow direction algorithms. |
3.3 | Rankings of RMSEs for the TFM and eight other flow‐direction algorithms on the four mathematical surfaces illustrated in Figure 3.14 (with 1 assigned to the flow‐direction algorithm with the lowest RMSE and 9 to the flow‐direction algorithm with the largest RMSE). |
3.4 | List of secondary land surface parameters and their significance. |
4.1 | Conceptual landform units defined by Conacher and Dalrymple (1977). |
4.2 | Morphologic type (i.e. topographic position) classes of Speight (1990). |
4.3 | List of channel attributes and their significance. |
4.4 | List of basin attributes and their significance. |
4.5 | Landform classification criteria used by Dikau et al. (1991). |
4.6 | Landform classes and subclasses used by the Dikau method. |
4.7 | Comparison of landform classes used by the Dikau and Karagulle methods and their assignment to landform types. |
4.8 | Comparison of global Hammond landform classes and types modeled by Sayre et al. (2014) and Karagulle et al. (2017). |
5.1 | Land surface parameters calculated and tested for correlation with GLOBE data. |
5.2 | Model experiments for different parameterization schemes and corresponding DEM products used by Zhang et al. (2016). |
6.1 | List of Spatial Analyst toolsets and tools. |
6.2 | List of Interpolation tools. |
6.3 | List of Surface tools. |
6.4 | List of Hydrology tools. |
6.5 | List of Solar Radiation tools. |
6.6 | List of 3D Analyst toolsets and tools. |
6.7 | List of the Data Management – Terrain Dataset tools. |
6.8 | List of the Data Management – TIN Dataset tools. |
6.9 | List of the Data Management – LAS Dataset tools. |
6.10 | List of Triangulated Surface tools. |
6.11 | Terrain analysis and modeling functions included in ArcGeomorphometry. |
6.12 | Class limits used in QGIS to classify ruggedness index values into categories that describe different types of terrain. |
6.13 | List of SAGA module libraries and modules focused on calculation of terrain parameters and objects. |
7.1 | List of 25 influential digital terrain analysis and modeling papers. |
I started writing this book in January 2015 and the journey that produced the book you see now proved to be both an exhilarating and humbling one. My primary goal from start to finish has been to write a book that describes the typical digital terrain modeling workflow that starts with data capture, continues with data preprocessing and DEM generation, and concludes with the calculation of land surface parameters and objects.
The book itself consists of seven chapters The first introduces digital elevation models, the role of scale in this work, the applications that have exploded in number and sophistication during the past 30–40 years, and a study site that is used throughout the remainder of the book to illustrate key concepts and outcomes. The second chapter describes some of the ways in which LiDAR and radar remote sensing technologies have transformed the sources and methods for capturing elevation data. It next discusses the need for and various methods that are currently used to preprocess DEMs along with some of the challenges that confront those who tackle these tasks. The third and largest of the seven chapters describes the subtleties involved in calculating the primary land surface parameters that are derived directly from DEMs without additional inputs and the two sets of secondary land surface parameters that are commonly used to model the energy and thermal regimes and accompanying interactions between the land surface and the atmosphere on the one hand and water flow and soil redistribution on the other hand. The fourth chapter examines how the primary and secondary land surface parameters have been adopted and used to extract and classify landforms and other kinds of land surface objects from digital elevation data. The role of error pops up in various guises in the second, third and fourth chapters and this state of affairs motivated Chapter 5, which explores the various errors that are embedded in DEMs, how these may be propagated and carried forward in calculating various land surface parameters and objects, and the consequences of this state of affairs for the modern terrain analyst. The sixth chapter introduces the software and services that can be used to implement and execute the digital terrain modeling workflows illustrated in the first five chapters. The seventh and final chapter reviews how terrain analysis got started, where things stand today, and what will likely happen to digital terrain modeling in the future.
This was an exciting and exhilarating project for me once I realized how much had changed since I had published my first journal article on the topographic factor in the Universal Soil Loss Equation (Wilson, 1986) and the terrain analysis book I had helped to write and co‐edit with John Gallant in 2000 (Wilson & Gallant, 2000a). The methods and data have changed tremendously along with the numbers and kinds of scholars and practitioners working with terrain and the results have exceeded my wildest expectations if I compare where things stand nowadays with the status quo in the early 1980s (when I was a PhD student at the University of Toronto in Canada). This book took me two years to write as I worked simultaneously to familiarize myself with all that has been accomplished thus far, which made it both the exhilarating and humbling journey it was for me.
Given this state of play, I would be remiss if I did not thank all those scholars who have shared their knowledge and showed me the way forward over the past four decades. Some I have come to know personally because I have been afforded the opportunity and pleasure to work with them directly – this group includes John Gallant, Michael Hutchinson, Ian Moore and Tian‐Xiang Yue, among others – but there are many more whose work I have come to know and appreciate from afar. You will see the works of some of these individuals listed in Table 7.1 towards the end of the book because I have taken the opportunity to list the 25 works that both guided and inspired the contents and layout of the book that you now see.
A group of institutions and people have helped me with the preparation of the book itself. I owe thanks to all those connected with the Spatial Sciences Institute at the University of Southern California and the Institute of Geographic Sciences and Natural Resource Research at the Chinese Academy of Sciences for giving me the time and freedom to devote the many months it took me to write this book. Three people, in particular, deserve special thanks. The first is Petter Pilesjö who graciously shared the code for his TFM algorithm that I used to construct Figure 3.24; the second is Beau MacDonald who helped me to prepare the many maps and diagrams you will find scattered throughout the book and who graciously read the manuscript from start to finish and helped to identify numerous omissions and errors; and the third is my partner and confidant, Ha Nguyen, without whom none of what I have accomplished here would have been possible.
This said, I hope you will find something of value as you read this book and that you will remember that any shortcomings, blunders and errors you find were completely of my own making.