May 2004 Topographic Engineering Center

1 ERDC/TEC SR-00-1. Handbook for Transformation of Datums, Projections, Grids, and Common Coordinate Systems James Ackeret, Fred Esch, Chris Gard, Frederick Gloeckler, May 2004. Daniel Oimen, Juan Perez, Justin Simpson, Daniel Specht, Topographic Engineering Center David Stoner, Joe Watts, Tom Witte, and MAJ Harry 1. Rossander 4. Approved for public release; distribution is unlimited. ii ERDC/TEC SR-00-1. Destroy this report when no longer needed. Do not return it to the originator _____. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. _____. The citation in this report of trade names of commercially available products does not constitute official endorsement or approval of the use of such products.

2 ERDC/TEC SR-00-1 iii EXECUTIVE SUMMARY. This document provides Army organizations and agencies with general guidance on select- ing the appropriate methods for shifting between local geodetic datums and the world geodetic System (WGS), and for converting Cartesian and map projection coordinates to and from geo- detic coordinates. This guidance is provided to aid the Army community in selecting datum shift algorithms; developing, selecting, and maintaining software using these algorithms; and imple- menting this software to support operational units. Equations are furnished for map projections and datums commonly used within the Army. References are provided for other, less commonly encountered, map projections and datums.

3 Beneficial comments (corrections, recommendations, additions, deletions) or information that may be of use in improving this document should be addressed to the Army Engineer Re- search and Development Center 's (ERDC), Topographic Engineering Center (TEC), Information Generation and Management Branch (IGMB) of the Topographic , Imagery, and Geospatial Re- search Division. Mail: ERDC, TEC, Bldg. 2592, ATTN: CEERD-TR-G, 7701 Telegraph Road, Alexandria, VA. 22315-3864. FAX: (703) 428-6834; ATTN: Topographic , Imagery, and Geospatial Research Division (IGMB). Telephone: (703) 428-6802. iv ERDC/TEC SR-00-1. PREFACE. This handbook was funded under the Army Topographic Engineering Center 's (TEC) Digi- tal Topographic Data Standards Program and co-authored at TEC by Messrs.

4 James Ackeret, Frederick Gloeckler, Justin Simpson, Daniel Specht, and David Stoner. The handbook is based on a draft of the Military Handbook, Datums, Projections, Grids, and Common Coordinate Systems, Transformation of (MIL-HDBK-600008), and was revised during the period July 1994 through July 1995. This handbook uses material from MIL-HDBK-600008. co-authored by Messrs. James Ackeret, Fred Esch, Chris Gard, Frederick Gloeckler, Daniel Oi- moen, Juan Perez, Justin Simpson, Joe Watts, Tom Witte, and MAJ Harry Rossander. This work was performed under the previous supervision of Messrs. Juan Perez, and Richard A. Herrmann and the supervision of John W. Hale, Chief, Standards Division and Regis J. Orsinger, Director, Digital Concepts and Analysis Center .

5 Mr. Robert Burkhart was the Director of ERDC's TEC at the time of re-publication of this hand- book. TEC is an element of the Army Engineer Research and Development Center (ERDC), Army Corps of Engineers. The Director of ERDC is Dr. James R. Houston and the Deputy to the Commander is Roberto, Jr. DISCLAIMER: The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. All product names and trademarks cited are the property of their respective owners. The findings of this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.

6 DESTROY THIS REPORT WHEN IT IS NO LONGER NEEDED. DO NOT RETURN IT TO THE. ORIGINATOR. ERDC/TEC SR-00-1 v CONTENTS. EXECUTIVE IV. LIST OF FIGURES AND VII. 1 SCOPE ..1. 1. Applicability .. 1. Application 1. 2 REFERENCED DOCUMENTS ..2. Government documents.. 2. Non-Government publications .. 3. 3 DEFINITIONS AND Acronyms .. 5. Terms.. 5. 8. Sign conventions .. 8. Unit conversion factors .. 9. 4 FUNDAMENTAL CONCEPTS .. 10. Introduction .. 10. Reference surfaces ..11. Earth-fixed coordinate systems ..11. Representation of geodetic Coordinates .. 18. Height 18. 5 geodetic SYSTEMS AND DATUMS .. 20. Introduction .. 20. geodetic (horizontal) datums .. 20. Vertical datums and 20. world geodetic System 1984 (WGS 84).. 21.

7 WGS 84 referenced 22. 6 DATUM 23. Introduction .. 23. Seven-parameter geometric 24. vi ERDC/TEC SR-00-1. Three-parameter( X, Y, Z) geometric transformation .. 25. WGS 72 to WGS 84 transformation .. 30. Approximating geodetic heights for datum transformation .. 33. Multiple regression equations (MRE) .. 33. Vertical datum 34. Unlisted 34. 7 MAP PROJECTIONS .. 35. Introduction .. 35. Mercator 36. Transverse Mercator (TM) projection .. 39. Universal Transverse Mercator (UTM) 44. Lambert Conformal Conic 47. Polar Stereographic projection .. 51. Universal Polar Stereographic (UPS) projection .. 55. The Military Grid Reference System (MGRS) .. 58. The world Geographic Reference System (GEOREF) .. 65. Non-standard grids.

8 65. Modifications to map projections .. 65. 8 SELECTION OF TECHNIQUES, SOFTWARE DEVELOPMENT, AND TESTING .. 67. The general conversion process.. 67. Choosing a datum shift 73. Error 77. Numerical examples .. 84. List of test 99. APPENDIX A: REFERENCE ELLIPSOID 101. APPENDIX B: X, Y AND Z DATUM SHIFT PARAMETERS .. 103. APPENDIX C: COUNTRIES AND ASSOCIATED LOCAL geodetic 121. APPENDIX D: WGS 84 GEOID SEPARATION 130. APPENDIX E: SEVEN-PARAMETER GEOMETRIC DATUM 134. APPENDIX F: OLD HAWAIIAN DATUM WITH INTERNATIONAL ELLIPSOID .136. INDEX .. 139. ERDC/TEC SR-00-1 vii LIST OF FIGURES AND TABLES. Figures The relationship between the reference ellipsoid, the geoid, and the physical surface of the earth. 12. The geometric relationship between Cartesian and geodetic coordinates 14.

9 Relationship between coordinate axes in a seven-parameter geometric transformation 24. Relationship between coordinate axes in a three-parameter geometric transformation 26. Meridians (longitude) and parallels (latitude) in the Mercator projection 37. Meridians and parallels in the Transverse Mercator Projection. 0 is the central meridian 39. Meridians and parallels (dashed) and a Universal Transverse Mercator Grid 45. Meridians and parallels in the Lambert Conformal Conic Projection 47. Meridians and parallels in the Universal Polar Stereographic Projection, Left: South Zone, Right: North Zone 52. Meridians and parallels imposed on a Universal Polar Stereographic grid (north zone) 56. MGRS 100,000 meter square identification, in the UTM region, for the Bessel 1841, Clarke 1866 Ellipsoid (North American 1927 datum, only), and Clarke 1880 ellipsoids 60.

10 MGRS 100,000 meter square identification, in the UTM region, for the Australian National, Clarke 1866 (UTM zones 47 50, only), Everest, geodetic Reference System 1980, International, South American 1969 (GRS 67), WGS 1972 and WGS. 1984 Ellipsoids 61. MGRS 100,000 meter square identification, in the northern UPS region 62. MGRS 100,000 meter square identification, in the southern UPS region 63. MGRS grid zone identification 64. Map projection to geodetic coordinate conversion; height information for H and h is not included in the conversion 67. Coordinate conversions within a datum 68. Datum shifts; note elevation values (H) do not generally change when changing datums 69. The general conversion process 70. System model 83.