Basic GIS coordinates

209 Pages·2017·23.667 MB·English

by  Jan Van Sickle

Basic GIS Coordinates
Third Edition

Basic GIS Coordinates

Third Edition

Jan Van Sickle
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2017 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
International Standard Book Number-13: 978-1-4987-7462-8 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC,
a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Names: Van Sickle, Jan, author.
Title: Basic GIS coordinates / Jan Van Sickle.
Description: Third edition. | Boca Raton : Taylor & Francis, 2017. | Includes
bibliographical references and index.
Identifiers: LCCN 2016059466 | ISBN 9781498774628 (hardback : alk. paper)
Subjects: LCSH: Grids (Cartography)--Data processing. | Geographic
information systems.
Classification: LCC GA116 .V36 2017 | DDC 910.285--dc23
LC record available at https://lccn.loc.gov/2016059466
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface ......................................................................................................................ix
CRC Press Author ......................................................................................................................xi
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
1. Foundation of a Coordinate System ...........................................................1
Boca Raton, FL 33487-2742
Uncertainty .......................................................................................................1
© 2017 by Taylor & Francis Group, LLC
Datums to the Rescue ......................................................................................1
CRC Press is an imprint of Taylor & Francis Group, an Informa business
René Descartes .............................................................................................2
No claim to original U.S. Government works
Cartesian Coordinates ................................................................................2
Printed on acid-free paper Attachment to the Real World ...................................................................4
Cartesian Coordinates and the Earth .......................................................4
International Standard Book Number-13: 978-1-4987-7462-8 (Hardback)
The Shape of the Earth ...............................................................................8
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts Latitude and Longitude ................................................................................11
have been made to publish reliable data and information, but the author and publisher cannot assume
Between the Lines .....................................................................................12
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to Longitude ...................................................................................................13
copyright holders if permission to publish in this form has not been obtained. If any copyright material has Latitude .......................................................................................................15
not been acknowledged please write and let us know so we may rectify in any future reprint.
Categories of Latitude and Longitude ...................................................16
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- The Deflection of the Vertical ..................................................................17
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, Directions ........................................................................................................22
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
Azimuths ....................................................................................................22
without written permission from the publishers.
Bearings ......................................................................................................22
For permission to photocopy or use material electronically from this work, please access www.copyright. Astronomic and Geodetic Directions .....................................................23
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
North ...........................................................................................................25
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, Magnetic North .........................................................................................25
a separate system of payment has been arranged. Grid North ..................................................................................................26
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used Polar Coordinates ..........................................................................................27
only for identification and explanation without intent to infringe. Summary ....................................................................................................30
Exercises ..........................................................................................................32
Library of Congress Cataloging‑in‑Publication Data
Names: Van Sickle, Jan, author. 2. Building a Coordinate System ...................................................................41
Title: Basic GIS coordinates / Jan Van Sickle. Legacy Geodetic Surveying ..........................................................................41
Description: Third edition. | Boca Raton : Taylor & Francis, 2017. | Includes
Ellipsoids .........................................................................................................43
bibliographical references and index.
Identifiers: LCCN 2016059466 | ISBN 9781498774628 (hardback : alk. paper) Ellipsoid Definition ...................................................................................43
Subjects: LCSH: Grids (Cartography)--Data processing. | Geographic Ellipsoid Orientation ................................................................................47
information systems.
The Initial Point ..............................................................................................47
Classification: LCC GA116 .V36 2017 | DDC 910.285--dc23
LC record available at https://lccn.loc.gov/2016059466 The North American Datum 1927...........................................................47
Ground-Based Realization .......................................................................49
A Systematic Change ................................................................................49
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com The North American Datum of 1983 .....................................................51
Space-Based Realization ...........................................................................52
and the CRC Press Web site at
http://www.crcpress.com
v
vi Contents
The Terrestrial Reference Frame ..................................................................53
Comparing Terrestrial Reference Systems and Terrestrial
Reference Frames ......................................................................................53
World Geodetic System 1984 ...................................................................53
TRANSIT ...............................................................................................54
Global Positioning System Weeks ......................................................54
The International Earth Rotation and Reference Systems Service ..........55
The Conventional Terrestrial Reference System ...................................55
International Earth Rotation and Reference Systems Service
Reference Pole .......................................................................................56
The International Terrestrial Reference Frame Realizations ..........58
The North American Datum of 1983, World Geodetic System
1984, and International Terrestrial Reference Frame ...........................59
International Global Navigation Satellite Systems Service 08 .......61
Replacement of the North American Datum of 1983 ......................62
Transforming Coordinates .......................................................................65
Transformations versus Coordinate Conversions ...........................65
Integrity .................................................................................................66
Molodenski Transformation ...............................................................67
Seven-Parameter Transformation ......................................................68
Surface Fitting .......................................................................................69
Exercises ..........................................................................................................70
3. Heights ............................................................................................................79
Ellipsoid Height .............................................................................................79
Trigonometric Leveling .................................................................................81
Spirit Leveling ................................................................................................83
Sea Level ..........................................................................................................85
Evolution of the Vertical Datum ..................................................................87
The Zero Point ................................................................................................88
The International Great Lakes Datum ...................................................88
The North American Vertical Datum 1988 ............................................89
Geoid ................................................................................................................90
Dynamic Heights ...........................................................................................92
Measuring Gravity .........................................................................................94
Gal ...............................................................................................................95
Orthometric Correction .................................................................................96
Ellipsoid, Geoid, and Orthometric Heights ...............................................98
NGS Geoid Models ........................................................................................99
Two Categories of Geoid Models ..........................................................101
Replacement of NAVD88 ............................................................................104
References .....................................................................................................105
Exercises ........................................................................................................106
Contents vii
4. Two Coordinate Systems ...........................................................................111
State Plane Coordinates ..............................................................................111
Map Projection .........................................................................................111
Polar Map Projections .............................................................................114
Choices ......................................................................................................119
State Plane Coordinate Systems 27 to State Plane Coordinate
Systems 83 ................................................................................................123
Geodetic Lengths to Grid Lengths ........................................................125
Geographic Coordinates to Grid Coordinates ....................................133
Conversion from Geodetic Azimuths to Grid Azimuths .............134
State Plane Coordinate Systems to Ground Coordinates ..................139
Common Problems with State Plane Coordinates .............................140
Universal Transverse Mercator Coordinates ...........................................140
Exercises ........................................................................................................146
5. The Rectangular System ............................................................................155
The Initial Points ..........................................................................................156
Quadrangles .................................................................................................158
Townships .....................................................................................................161
Sections ..........................................................................................................164
The Subdivision of Sections........................................................................167
Township Plats .............................................................................................168
Fractional Lots ..............................................................................................169
Naming Aliquot Parts and Corners ..........................................................172
References .....................................................................................................179
Exercises ........................................................................................................179
Index .....................................................................................................................185

Preface
A fundamental change is coming. Two datums at the foundation of the
current geographic information system (GIS) work will be replaced: the
North American Datum 1983 and the North American Vertical Datum 1988.
This book provides some of the information necessary to cope with that
change. It is a book about coordinates.
Coordinates? Press a few buttons on a computer and they are automatically
imported, exported, rotated, translated, collated, annotated, and served up
in any format you choose with no trouble at all. There is really nothing to it.
Why have a book about coordinates?
It is a good question really. Computers are astounding in their ability to
make the mathematics behind coordinate manipulation transparent to the
user. This book is not much about that sort of mathematics. However, it is
about coordinates and coordinate systems. It is about understanding how
these systems work and how they sometimes do not work. It is about how
points that should be in New Jersey end up in the middle of the Atlantic
Ocean even if the computer has done nothing wrong. And that is, I suppose,
the answer to the question from my point of view. Computers are currently
very good at repetition and very bad at interpretation. People are usually not
so good at repetition. We tend to get bored. However, we can be very good
indeed at interpretation, that is, if we have the information in our heads to
understand what we are interpreting. This book is about providing some of
that sort of information on the subject of coordinates and coordinate systems.
Coordinates are critical to GIS, cartography, and surveying. They are their
foundation. Points, lines, and polygons form the geometry. Lines define
the polygons, points define the lines, and coordinates define the points.
Therefore, at bottom, it is the coordinates that tie the real world to their elec-
tronic image in the computer.
There are more than 1000 horizontal geodetic datums and over 3000
Cartesian coordinate systems sanctioned by governments around the world
and currently in use to describe our planet electronically and on paper.
ix