Mercator (UTM) Grid System
and Topographic Maps
—
An Introductory Guide for Scientists and Engineers
Joe S. Depner First edition: 2008 Jun 02 This edition: 2010 Aug 12
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Preface ix
Abbreviations and Symbols xi
1 Introduction 1
1.1 Knowledge Prerequisites . . . 1
1.2 Motivation . . . 2
1.3 History of the UTM Grid System . . . 2
1.3.1 About Map Projections . . . 3
1.3.2 The Mercator Projection . . . 3
1.3.3 The Transverse Mercator Projection . . . 4
1.3.4 A Universal System . . . 5
2 The UTM Grid 7 2.1 Area of Definition . . . 7
2.2 Longitude and Latitude Zones. . . 7
2.2.1 Longitude Zones . . . 7
2.2.2 Latitude Zones . . . 7
2.2.3 Zone Specification . . . 11
2.2.4 Irregular Longitude Zones . . . 14
2.2.5 Points on Zone Boundaries . . . 17
2.3 Easting and Northing Coordinates . . . 18
2.3.1 Easting Coordinates . . . 19
2.3.2 Northing Coordinates . . . 19
2.3.3 Easting and Northing Coordinate Specifications. . . 21
2.3.4 Coordinate Gridlines . . . 22
2.4 UTM Coordinate Specifications . . . 22
2.5 Map Projections, Datums, and the Graticule . . . 25
2.6 Chapter Summary . . . 26
3 The UTM Grid and USGS Topographic Maps 29 3.1 Map Elements Supporting Use of the UTM Grid . . . 29
3.1.1 Horizontal Datum Identifier . . . 29
3.1.2 UTM Longitude Zone Identifier . . . 29
3.1.3 UTM Grid Tick Marks and Coordinate Labels . . . 31
3.1.4 UTM Grid Declination Information. . . 35
3.1.5 UTM Gridlines . . . 35
3.2 Using Topographic Maps Without Preprinted Gridlines . . . 36
3.2.1 Visual Estimation of Gridline Positions . . . 36
3.2.2 Overlaying a UTM Grid Transparency . . . 38
3.2.3 Drawing UTM Gridlines on Maps . . . 39
3.3 Determining the UTM Coordinates of a Point on a Map . . . 40
3.3.1 Basic Procedure . . . 40
3.3.2 Measuring Projected Easting and Northing Distances . . . 43
3.4 Plotting a Point with Known UTM Coordinates on a Map . . . 47
3.5 Software for Using the UTM Grid with Topographic Maps. . . 51
3.6 Chapter Summary . . . 51
4 Horizontal Distance and Bearing Determination 53 4.1 Points in the Same UTM Longitude Zone and Hemisphere . . . 53
4.1.1 Measurement Using a Paper Map. . . 53
4.1.2 Calculation Using Plane Geometry . . . 54
4.2 Points Not in the Same UTM Longitude Zone and Hemisphere . . . 58
4.2.1 Spherical Earth . . . 58
4.2.2 Ellipsoidal Earth . . . 59
4.3 Chapter Summary . . . 59
References 61 Appendices 64 A Approximate Ranges for UTM Easting Coordinates 67 A.1 Crude Approximation, for Nonspecific Latitude . . . 67
A.2 Refined Approximation, for Nonspecific Latitude . . . 68
A.3 Crude Approximation, for Specific Latitude . . . 70
B Approximate Ranges for UTM Northing Coordinates 73 B.1 Northern Hemisphere. . . 73
B.2 Southern Hemisphere. . . 74
C Measuring the Distance from a Point to a Gridline 75 C.1 Introduction. . . 75
C.2 Measuring the Distance from a Point to a Fully Displayed Gridline . . . 75
C.2.1 Direct Method . . . 76
C.2.2 Indirect Method . . . 76
C.2.3 Combined Method for Measuring Easting and Northing . . . 76
C.3 Measuring the Distance from a Point to a Marked-only Gridline. . . 76
D Obtaining an Appropriate USGS Topographic Map 79 D.1 Basic Procedure . . . 79
D.2 Resources for Identifying Relevant Topographic Maps . . . 79
D.3 Selecting an Appropriate Map Scale . . . 80
D.4 Acquiring USGS Topographic Maps . . . 80
1 Examples Illustrating Two Conventions for Grouping Digits . . . x
2.1 UTM Longitude Zones Spanning the U.S. . . 11
2.2 UTM Latitude Zones Spanning the U.S. . . 14
2.3 Minimum and Maximum UTM Easting Coordinates . . . 19
2.4 Minimum and Maximum UTM Northing Coordinates . . . 21
2.5 Summary of UTM Map Projections and Local Coordinate Systems . . . 27
4.1 Data for Distance and Bearing Calculation Example – 1st of 2. . . 55
4.2 Data for Distance and Bearing Calculation Example – 2nd of 2 . . . 57
A.1 Output from NGS Utility, for NAD 83 . . . 69
A.2 Output from NGS Utility, for NAD 27 . . . 70
2.1 Area of Definition for UTM Grid System. . . 8
2.2 Regular UTM Longitude Zones – Equatorial Aspect . . . 9
2.3 Regular UTM Longitude Zones – Oblique Aspect . . . 10
2.4 UTM Latitude Zones – Equatorial Aspect . . . 12
2.5 UTM Latitude Zones – Oblique Aspect . . . 13
2.6 Global Distribution of UTM Longitude Zones and Latitude Zones. . . 16
2.7 Regular UTM Longitude Zone in Northern Hemisphere . . . 20
3.1 UTM Grid Information – Older Map . . . 30
3.2 UTM Grid Information – Newer Map . . . 30
3.3 A Basic Corner Ruler . . . 37
3.4 Using a Corner Ruler with a Topographic Map . . . 43
3.5 Using a Corner Ruler to Measure UTM Coordinates on a Map – 1st of 4 . . . 45
3.6 Using a Corner Ruler to Measure UTM Coordinates on a Map – 2nd of 4 . . . . 46
3.7 Using a Corner Ruler to Measure UTM Coordinates on a Map – 3rd of 4 . . . 48
3.8 Using a Corner Ruler to Measure UTM Coordinates on a Map – 4th of 4 . . . 49
This guide provides a comprehensive introduction to the Universal Transverse Mercator (UTM) grid system (also called the UTM coordinate system or the GPS grid system) and its use with topographic maps. The intended audience is primarily scientists and engineers. It assumes the reader has basic knowledge of the following:
• spatial coordinate systems, including Cartesian (rectangular) and geodetic (geographic) coordinate systems,
• general cartographic principles, and
• topographic maps.
Section 1.1(Knowledge Prerequisites) gives a more detailed list of the prerequisite subjects. Much information about the UTM grid system is available in many forms, including books, reports, articles, and websites. These range from the most basic, which assume little knowledge of mapping and navigation, to the advanced, which assume specialized knowledge in one or more subfields of geomatics (e.g., analytical cartography, geodesy, geographic information systems, global positioning system (GPS)). This guide takes a middle path. It provides more depth than the most basic materials, without requiring as much specialized knowledge as the advanced materials. It attempts to make explicit much of the information that’s implicit in some of the more terse references on the subject, such as Defense Mapping Agency (DMA) [1989].
This guide is intended primarily, but not exclusively, for civilian readers in the United States (U.S.). For instance, it discusses only those topographic maps produced by the U.S. Geological Survey (USGS). However, much of the material presented here, such as the basic description of the UTM grid system, is applicable worldwide. Additionally, the discussion of topographic maps likely applies, to some extent, to topographic maps produced by other agencies (e.g., U.S. Department of Defense) and to maps produced in other countries.
Numerous resources are available for working with the UTM grid system and topographic maps. These range from the technologically primitive (e.g., paper map, straightedge, corner ruler) to the technologically advanced (computer and software, digital dataset, worldwide web, GPS). The current trend is toward the increased use of advanced resources. However, certain fundamental concepts underlie the competent use of even the most primitive resources, and such concepts can be explained quite naturally in terms of paper maps, rulers, and plane geometry. In contrast, explanations in terms of more advanced resources are likely to suffer from the distractions imposed by the complexities of the particular technologies, and to be less universally applicable. For these reasons, and not because of any anti-technology bias, I’ve formulated my explanations primarily in terms of map and straightedge rather than computer and worldwide web.
Numerous examples are included to illustrate and reinforce the ideas presented here.
Table 1: Examples Illustrating Two Conventions for Grouping Digits
Other U.S. This Documents Document 8, 861 8861 56, 774.0 56 774.0 4, 936.2005 4936.2005 9, 385.70323 9385.703 23 8, 800, 512 8 800 512
In an attempt to appeal to an international audience, this document generally follows the convention recommended by Taylor [1995] for the grouping of digits:
Because the comma is widely used as the decimal marker outside the United States, it should not be used to separate digits into groups of three. Instead, digits should be separated into groups of three, counting from the decimal marker towards the left and right, by the use of a thin, fixed space. However, this practice is not usually followed for numbers having only four digits on either side of the decimal marker except when uniformity in a table is desired.
This convention eliminates potential confusion about interpretation of commas, without sacrific-ing readability of long numeric strsacrific-ings. A period serves as the decimal marker (point). Table1
gives examples.
This convention conforms to the recommendations of the International Union of Pure and Applied Chemistry (IUPAC) [IUPAC, 2006]. A different convention is followed when listing the formal UTM coordinate specification of one or more points. In that case, no commas or spaces are used. See Chapter2 for details.
Symbol Description
a Length of major semi-axis (semimajor axis) of ellipsoid
arccos Inverse cosine function
arcsin Inverse sine function
arctan Inverse tangent function
b Length of minor semi-axis (semiminor axis) of ellipsoid
CI Contour interval
cm Centimeter(s)
cm Central meridian
Co. Company
cos Cosine function
D Distance
DD Degree(s) of arc
DMA Defense Mapping Agency (U.S.)
DOI Digital object identifier
DRG Digital raster graphic
E Easting coordinate identifier
E. East
E-gridline Easting gridline
FGDC Federal Geographic Data Committee (U.S.)
ft Foot (feet)
List of Abbreviations and Symbols (continued)
Symbol Description
GN Grid north
GOI Gridline of interest
GPO Government Printing Office
GPS Global Positioning System
hemis. Hemisphere
in. Inch(es)
IUGG International Union of Geodesy and Geophysics
IUPAC International Union of Pure and Applied Chemistry
km Kilometer(s)
lat. Latitude
lon. Longitude
m Meter(s)
MGRS Military Grid Reference System (U.S.)
MM Minute(s) of arc
mm Millimeter(s)
MN Magnetic north
N Northing coordinate identifier
N. North
NAD 27 North American Datum of 1927
NAD 83 North American Datum of 1983
NATO North Atlantic Treaty Organization
N-gridline Northing gridline
NGS National Geodetic Survey (U.S.)
NIMA National Imagery and Mapping Agency (U.S.)
List of Abbreviations and Symbols (continued)
Symbol Description
NOAA National Oceanic and Atmospheric Administration (U.S.)
NOS National Ocean Service (U.S.)
OMNR Ontario Ministry of Natural Resources (Canada)
PDF Portable Document Format
PLSS Public Land Survey System (U.S.)
POI point of interest
r Radius of Earth
rad Radian(s) of arc
S Length of arc on the surface of the ellipsoid
S. South
SI International System of Units
SS Second(s) of arc
sin Sine function
SPCS State Plane Coordinate System (U.S.)
tan Tangent function
u Map scale
UPS Universal Polar Stereographic
URI Worldwide-web uniform resource indicator
US, U.S. United States
USC&GS United States Coast and Geodetic Survey
USGS United States Geological Survey
USNG United States National Grid
UTM Universal Transverse Mercator
W. West
List of Abbreviations and Symbols (continued)
Symbol Description
WGS 84 World Geodetic System of 1984
x UTM easting coordinate
xcm UTM easting coordinate of central meridian
xE−gridline UTM easting coordinate of UTM easting gridline
xPOI UTM easting coordinate of point of interest
∆x Projected easting distance (as horizontal ground distance)
∆xmap Projected easting distance (as map distance)
y UTM northing coordinate
yN−gridline UTM northing coordinate of UTM northing gridline
yPOI UTM northing coordinate of point of interest
∆y Projected northing distance (as horizontal ground distance)
∆ymap Projected northing distance (as map distance)
β Bearing (angle)
φ Latitude coordinate (angle)
λ Longitude coordinate (angle)
π The mathematical constant, π = 3.14159265 . . .
: (colon separating two integers) Numerical ratio
◦ Degree(s) of arc
Introduction
1.1
Knowledge Prerequisites
To get the maximum benefit from this document, readers should have a basic familiarity with the topics and concepts listed in the following paragraphs. Each paragraph corresponds to a main topic, which is given by the paragraph heading. Keywords corresponding to associated subtopics, concepts, and terms follow in alphabetical order.
Spatial coordinate systems
coordinate axes, coordinate grid, coordinate grid tick mark, coordinate numerical values and units, coordinate origin, coordinate specification, orthogonal coordinates, orthogonal curvilinear coordinates, rectilinear coordinates, spatial coordinates
Cartesian coordinate systems
abscissa, Cartesian coordinates, distance coordinates, easting (or x) coordinate, hori-zontal coordinate, northing (or y) coordinate, ordered pair, ordered triplet, ordinate, vertical (or z) coordinate
Geodetic/geographic coordinate systems
angle, angle coordinates, degrees of arc, equator, geodetic coordinates, geographic coordinates, globe, graticule, great circle, great-circle distance, Greenwich Meridian, hemispheres, International Date Line, latitude, latitude lines (parallels), longitude, longitude lines (meridians), minutes of arc, polar regions, pole, Prime Meridian, ra-dians, seconds of arc, small circle
General cartographic principles
direction, distance, explanatory material, explanatory text, horizontal datum, index map, labels, legend, locator map, map border, map collar, map sheet, map-sheet mar-gin, neatline, orientation indicator, projection information, publication information (publisher name, year, copyright), scale, scale indicator (graphic, numerical, verbal), source note, title and subtitles, vertical datum
Topographic maps
contour interval (CI), CI indicator, contour lines, contour map, declination diagram, elevation, hypsography, magnetic declination, topographic map, topographic map symbols, topography, USGS 7.5-minute and 15-minute series quadrangles
1.2
Motivation
Coordinate systems provide effective means of communicating and analyzing information about position. Multiple coordinate systems have been developed for various uses, each with its own particular advantages. To extract the maximum value from data collection and analysis efforts, it’s important to choose the most appropriate coordinate system for the particular situation. Generally this requires knowing the following about coordinate systems:
• their definitions and basic characteristics;
• their strengths and weaknesses;
• which ones are best suited to particular applications; and
• how to convert coordinate data for one system to coordinate data for another system.
The UTM grid system has advantages over other coordinate systems. For instance, unlike State Plane Coordinate Systems (SPCSs), which are defined over relatively small regions, the UTM grid system is defined worldwide exclusive of the polar regions. Cole [1977] and Grubb and Eakle [1988] summarize some of the advantages of the UTM grid system relative to other existing coordinate systems.
The UTM grid system is conceptually simple to use, effectively requiring one to apply a local Cartesian (xy) coordinate system. This makes it easier to learn and more convenient to use than, say, the Public Land Survey System (PLSS; also sometimes referred to as the Section-Township-Range System, or the Cadastral System).
In the U.S., both military and civilian government agencies use what amount to extended forms of the UTM grid system for georeferencing. Hence, learning the UTM grid system is a logical first step toward learning these extended systems.
The U.S. military’s worldwide georeferencing system is called the Military Grid Reference System (MGRS) [DMA, 1990]. U.S. Air Force [2001] gives a clear description of the MGRS. The MGRS applies two separate coordinate systems to their respective areas of definition. The UTM grid system is defined within the area of the globe between 80◦S. lat. and 84◦N. lat. A companion system, the Universal Polar Stereographic (UPS) grid system, is defined for the polar regions [DMA, 1989]. The MGRS also overlays additional location elements on the UTM grid.
The system used by various local, state, and federal civilian agencies in the U.S. is called the U.S. National Grid (USNG) [Federal Geographic Data Committee (FGDC), 2001]. Like the MGRS, the USNG overlays additional location elements on the UTM grid. Within the U.S., the USNG is interoperable with the MGRS [FGDC, 2001].
In addition to its use for military purposes, the UTM grid system is widely used for surveying, mapping, and land and sea navigation [Langley, 1998]. The UTM grid system is used with the Global Positioning System (GPS), and the U.S. Geological Survey (USGS) projects most of its digital products on the UTM grid [Moore, 1997]. This makes the UTM grid system useful for both non-scientific applications (e.g., outdoor recreation, search-and-rescue operations) and scientific applications (e.g., environmental investigation, natural-resource management).
1.3
History of the UTM Grid System
1.3.1 About Map Projections
A map projection is a means by which one graphically represents points on the surface of the earth, a three-dimensional surface, as points on a map, a two-dimensional surface. For any given type of map projection, the particular way in which one projects the points is defined by geometrical construction, mathematical equations, or some combination of the two.
Dana [2007] and Dean [2007] give good introductions to, and overviews of, map projections. For a comprehensive, technical reference on map projections, see Snyder [1987] or Snyder and Voxland [1989].
In practical applications the globe is approximated by an ellipsoid of revolution for which the equator is a great circle. A further simplification sometimes employed is to approximate the globe as a sphere, a particular type of ellipsoid of revolution. In the special case where the ellipsoid is spherical, the corresponding projections are known as spherical forms; otherwise they’re known as ellipsoidal forms.
One family of map projections – the cylindrical projections – is central to the development of the UTM grid system. Conceptually, a cylindrical projection may be viewed as a projection of points onto an elliptical (in some cases circular) cylinder (the projection cylinder ) which is wrapped around the globe.
Two particular subfamilies of cylindrical map projection are especially important in the development of the UTM grid system – the Mercator projection and the transverse Mercator projection. Both of these are defined by mathematical equations.
1.3.2 The Mercator Projection
The Flemish cartographer Gerhardus Mercator was the first to apply the projection that bears his name (i.e., the Mercator projection) when he produced his famous world chart in 1569 [OMNR, 1981].
The Mercator projection can take one of two forms based on the configuration of the pro-jection cylinder. In the tangent form, the cylinder intersects the globe at the equator (i.e., the cylinder is tangent to the ellipsoid at the equator). In the secant form, the cylinder intersects the globe at two parallels of latitude equidistant from the equator (the standard parallels) (i.e., the cylinder is secant to the ellipsoid).
The Mercator projection has the following characteristics:
- The meridians of longitude are represented by straight lines oriented parallel to one an-other. For a given longitude increment, the distance between successive meridians is constant.
- The parallels of latitude are represented by straight lines oriented parallel to one another. For a given latitude increment, the distance between successive parallels increases with their distance from the equator.
- The meridians of longitude are orthogonal to the parallels of latitude.
- The scale is the same in all directions.
- The scale varies with location. In the tangent form, the projection is true to scale only at the equator. In the secant form, the projection is true to scale only at the two standard parallels.
- Any small area is represented in its true shape (i.e., the projection is conformal ).
- Rhumb lines (i.e., lines of constant azimuth, lines of true constant bearing) appear as straight lines.
This last characteristic makes Mercator charts useful for global navigation.
In 1910 the former U.S. Coast and Geodetic Survey (now the National Ocean Service) adopted the Mercator projection as the standard projection for the nautical charts it prepares [Shalowitz, 1964, p. 302].
1.3.3 The Transverse Mercator Projection
Conceptually, the transverse Mercator projection may be viewed as a projection of points onto an elliptical projection cylinder that is wrapped around the globe, with the axis of the cylinder lying in the equatorial plane. Like the Mercator projection, the transverse Mercator projection can take one of two forms based on the configuration of the cylinder. In the tangent form, the cylinder intersects the globe at the central meridian of the mapped area; that is, the cylinder is tangent to the ellipsoid at the central meridian. In the secant form, the cylinder intersects the globe at two arcs (the standard lines) parallel to and equidistant from the central meridian (i.e., the cylinder is secant to the ellipsoid).
The transverse Mercator projection has the following characteristics:
- The equator, the central meridian, and each meridian 90 degrees (90◦) from the central meridian are represented by straight lines.
- Other meridians and parallels are represented by complex curves.
- The meridians of longitude are orthogonal to the parallels of latitude.
- The scale is the same in all directions.
- The scale varies with location. In the tangent form the projection is true to scale only at the central meridian. In the secant form the projection is true to scale only at the standard lines [OMNR, 1981].
- The scale becomes infinite 90◦ from the central meridian.
- Both the spherical and ellipsoidal forms of the projection are conformal [Snyder, 1987].
- Rhumb lines don’t appear as straight lines.
The tangent form maps the central meridian and nearby regions on either side of it with low distortion [Snyder 1987]. Similarly, the secant form maps the two standard lines and the regions near them with low distortion. It follows that if the two standard lines are sufficiently close together, the region between them will have low distortion. Consequently the transverse Mercator projection typically is applied to long narrow bands.
The Alsatian mathematician and cartographer Johann Heinrich Lambert invented the trans-verse Mercator projection in its spherical form [Snyder, 1987]. In 1772 Lambert presented the projection in his classic work, Beitr¨age [Lambert, 1772].
While Lambert only indirectly discussed the ellipsoidal form of the transverse Mercator projection, Johann Karl Friedrich Gauss analyzed it further in 1822 [Snyder, 1987]. In 1912 and 1919 L. Kr¨uger published, for the first time, results for the ellipsoidal form of the transverse
Mercator projection; for this reason it is sometimes called the Gauss-Kr¨uger projection [O’Brien, 1986]. Others, including L.P. Lee of New Zealand, also contributed to the development of the ellipsoidal form [Snyder and Voxland, 1989].
In 1936 the International Union of Geodesy and Geophysics (IUGG) proposed the universal adoption of the transverse Mercator projection in 6◦ bands [OMNR, 1981].
1.3.4 A Universal System
After years of consideration, in 1947 the U.S. Army adopted the Universal Transverse Mercator (UTM) grid system as their standard for designating rectangular coordinates on large-scale military maps throughout the world [OMNR, 1981; Snyder, 1987]. Dean [2007] describes the context and rationale for the U.S. Army’s decision. Dracup [2007] provides details pertinent to the U.S. Army’s adoption and implementation of the UTM grid system.
The UTM grid system applies the ellipsoidal, secant form of the transverse Mercator projec-tion individually to bands 6◦ wide (in longitude), with additional modifications. These include the following [OMNR, 1981]:
• a scale reduction of 1 part in 2500 (i.e., a scale factor of 0.9996) at the central meridian,
• a definition of the area of coverage between 80◦S. lat. and 84◦N. lat., and
• the use of metric units (meters).
Subsequently, the North Atlantic Treaty Organization (NATO) and many other countries have adopted the UTM grid system as their official grid system for military purposes [OMNR, 1981].
The UTM Grid
The UTM grid system is, in effect, a hybrid coordinate system. It combines elements of the geographic coordinate system (i.e., longitude and latitude zones defined in terms of the graticule) with numerous, local Cartesian coordinate systems (i.e., easting and northing coordinates within each UTM longitude zone and hemisphere).
2.1
Area of Definition
The UTM grid system is defined over that portion of the earth’s surface between latitudes 80◦S. and 84◦N. (Figure2.1). The UTM grid system isn’t defined for the polar regions (i.e., latitudes south of 80◦S. and latitudes north of 84◦N.).
2.2
Longitude and Latitude Zones
2.2.1 Longitude Zones
The UTM grid divides the earth into 60 contiguous, non-overlapping longitude zones, each one 6◦ wide (as measured along a parallel). Each longitude zone is bounded on the east and on the west by meridians of longitude (see Figures 2.2and 2.3). This document will refer to these as the zone’s bounding meridians. UTM longitude zones are also called grid zones, longitude zones, UTM zones, or zones.
Each UTM longitude zone is identified by a one- or two-digit integer. The zones are numbered consecutively, beginning with “1” or “01” at the zone corresponding to 180◦W. lon. - 174◦W. lon., and increasing as one moves eastward to “60” at the zone corresponding to 174◦E. lon. -180◦E. lon. Hence, UTM longitude zones 01 through 30 lie in the western hemisphere, while UTM longitude zones 31 through 60 lie in the eastern hemisphere. Consequently, the Prime Meridian (0◦ lon.) separates UTM longitude zones 30 and 31, while the International Date Line (meridian of 180◦ lon.) separates UTM longitude zones 60 and 01. Each longitude zone is bounded on the north by the parallel of 84◦N. lat. and on the south by the parallel of 80◦S. lat.
Table2.1summarizes the distribution of UTM longitude zones across the U.S.
2.2.2 Latitude Zones
The UTM grid divides the region of the earth that lies between the latitudes of 80◦S. and 84◦N. into 20 contiguous, non-overlapping latitude zones – 10 in each of the northern and southern hemispheres. Each latitude zone is bounded on the north and the south by parallels of latitude.
Table 2.1: UTM Longitude Zones Spanning the U.S.
Region Longitude Range Longitude Number (approximate) Zones of Zones
Lower 48 124◦ 46’ W. – 66◦ 57’ W. 10 - 19 10
Alaska 172◦ 26’ E. – 130◦ 00’ W. 59, 60, and 1 - 9 11
Hawaii 178◦ 22’ W. – 154◦ 48’ W. 1 - 5 5
Entire U.S. 172◦ 26’ E. – 66◦ 57’ W. 59, 60, and 1 - 19 21
Notes:
(1) “Lower 48” designates the 48 conterminous states and the District of Columbia. (2) “Entire U.S.” designates all 50 states and the District of Columbia.
(3) Sources for longitude information: Wikipedia [2007b, c, d]
All of the latitude zones are 8◦ wide (as measured along a meridian), except the most northerly latitude zone, which is 12◦ wide (see Figures2.4and 2.5). The UTM latitude zones encircle the globe, from the meridian of 180◦W. lon. eastward to the meridian of 180◦E. lon.
Each UTM latitude zone is identified by a single uppercase letter of the Latin alphabet. The latitude zones are lettered consecutively, beginning with “C” at the southernmost zone (i.e., 80◦S. lat. - 72◦S. lat.), and progressing alphabetically as one moves northward to zone “X” (i.e., 72◦N. lat. - 84◦N. lat.). To minimize the potential for confusion with the numerals “1” and “0”, respectively, the letters “I” and “O” aren’t used. Hence, latitude zones C through M, excluding I, lie in the southern hemisphere, while latitude zones N through X, excluding O, lie in the northern hemisphere. The equator separates UTM latitude zones M and N.
Table2.2summarizes the distribution of UTM latitude zones across the U.S.
2.2.3 Zone Specification
When both the UTM longitude zone and the UTM latitude zone of a point are specified, normally their respective designations are combined into a single alphanumeric string consisting of the following elements, written from left to right in the order listed:
• the word “zone” or “Zone”,
• a single space,
• the one- or two-digit numeric designation for the longitude zone, and
Table 2.2: UTM Latitude Zones Spanning the U.S.
Region Latitude Range Latitude Number (approximate) Zones of Zones
Lower 48 24◦ 31’ N. – 49◦ 23’ N. R, S, T, and U 4 Alaska 51◦ 12’ N. – 71◦ 23’ N. U, V, and W 3 Hawaii 18◦ 55’ N. – 28◦ 27’ N. Q and R 2
Entire U.S. 18◦ 55’ N. – 71◦ 23’ N. Q through W 7
Notes:
(1) “Lower 48” designates the 48 conterminous states and the District of Columbia. (2) “Entire U.S.” designates all 50 states and the District of Columbia.
(3) Sources for latitude information: Wikipedia [2007b, c, d]
Example: Formats for Reporting Combined UTM Longitude/Latitude Zones
Problem: Parse each of the following combined UTM longitude/latitude zone designations into its respective UTM longitude zone and UTM latitude zone:
“Zone 01H” (or, equivalently, “zone 1H”) “Zone 17N” (or, equivalently, “zone 17N”) “Zone 51P” (or, equivalently, “zone 51P”)
Solution:
“Zone 01H” (or, equivalently, “zone 1H”) designates UTM longitude zone 1, UTM latitude zone H.
“Zone 17N” (or, equivalently, “zone 17N”) designates UTM longitude zone 17, UTM latitude zone N.
“Zone 51P” (or, equivalently, “zone 51P”) designates UTM longitude zone 51, UTM latitude zone P.
2.2.4 Irregular Longitude Zones
The scheme described above for defining the boundaries of the UTM longitude and latitude zones is valid everywhere between the latitudes of 80◦S. and 84◦N., with the exception of the two areas described below [DMA, 1990].
The first area is on or near the southwest coast of Norway, between latitudes 56◦N. and 64◦N. (i.e., in UTM latitude zone V). UTM zones 31V and 32V are 3◦ and 9◦ wide, respectively, rather than the usual 6◦ wide. UTM zones 31V and 32V extend from 0◦E. lon. to 3◦E. lon., and from 3◦E. lon. to 12◦E. lon., respectively. Normally UTM longitude zones 31 and 32 extend from 0◦E. lon. to 6◦E. lon., and from 6◦E. lon. to 12◦E. lon., respectively.
latitude zone X). Svalbard is an archipelago in the Arctic Ocean north of mainland Europe, approximately midway between Norway and the North Pole [Central Intelligence Agency, 2007]. UTM zones 31X and 37X are 9◦ wide, zones 33X and 35X are 12◦ wide, and zones 32X, 34X, and 36X are undefined. Consequently, the four UTM zones 31X, 33X, 35X, and 37X cover the same area that would have been covered by the seven zones 31X to 37X, had these zones been defined on a regular grid.
The schematic diagram in Figure 2.6 shows the relative positions of UTM longitude zones and latitude zones.
KEY
UTM Grid Code "54F" Denotes:
Longitude Zone 54 Latitude Zone F
© 2008 Joe Depner 25 26 60 28 29 33 32 31
UTM Latitude Zone Regular UTM Zone Irregular UTM Zone
White Fill Gray Fill
Blue Letter 120 21 43 44 45 38 39 60 29 33 150 9 150 180 30 0 30 150 120 90
WEST LONGITUDE (degrees)
EAST LONGITUDE (degrees)
60 90 GREENWICH MERIDIAN 30 60 30 15 16 16 08 00 08 24 32 90 120 64 72 80 40 48 150 10 90 120 14 11 12 13 14 15 13X V U T S W 1 2 3 1W 2W 3W 8 180 19 20 11 12 4 5 6 7 18 54 46 47 42 49 26 27 28 M 55 50 51 52 53 40 41 37 17 2 3 64 56 48 40 32 00 08 L J 80 1 C D 64 1E 1D 1C H 13 59 72 40 48 56 G F E K 58 72 84 X 33X 30 22 23 24 25 45X D GREENWICH MERIDIAN 35 G 60 56 57 48 36 16 X 31X 35X 37X 38X 39X 40X 43X 44X 24 56 W V U T S N F E 34 32V 31 32 31V 32W 33W 34W 31W 33V 34 35 36 33Q 34Q 35Q 36Q 33P 34P 35P 37 44 45 38 39 40 41 8 9 10 54 46 47 48 49 42 43 4 5 6 7 58 59 60 C 59F 60F 59E 60E 59D 55 56 57 55D 56D 57D 58D 55C 56C 50 51 52 53 16 180 180 M L K J H 0 30 08 16 24 R Q R Q P N P 24 32 84 72 64 56 48 40 32 24 30X 29X 28X 27X 26X 23X 22X 19X 20X 21X 12X 41X 42X 17X 16X 15X 14X 18X 25X 24X 46X 47X 48X 49X 50X 51X 52X 53X 54X 55X 56X 57X 58X 59X 60X 2X 3X 4X 5X 6X 7X 8X 9X 10X 11X 1X 4W 5W 6W 7W 8W 9W 10W 11W 12W 13W 14W 15W 16W 17W 18W 19W 20W 21W 22W 23W 24W 25W 26W 27W 28W 29W 30W 31U 29V 30V 29U 30U 28V 35W 36W 37W 38W 39W 40W 41W 42W 43W 44W 45W 46W 47W 48W 49W 50W 51W 52W 53W 54W 55W 56W 57W 58W 59W 60W 32U 34V 35V 36V 37V 38V 39V 40V 41V 42V Red Number 41U 42U 41T 42T 41S 42S 43V 44V 45V 46V 47V 48V 49V 50V 51V 52V 53V 54V 55V 56V 57V 58V 59V 60V 33U 34U 35U 36U 37U 38U 39U 40U 43U 44U 45U 46U 47U 48U 49U 50U 51U 52U 53U 54U 55U 56U 57U 58U 59U 60U 33T 34T 35T 36T 37T 38T 39T 40T 43T 44T 45T 46T 47T 48T 49T 50T 51T 52T 53T 54T 55T 56T 57T 58T 59T 60T 33S 34S 35S 36S 37S 38S 39S 40S 43S 44S 45S 46S 47S 48S 49S 50S 51S 52S 53S 54S 55S 56S 57S 58S 59S 60S 33R 34R 35R 36R 37R 38R 39R 40R 41R 42R 43R 44R 45R 46R 47R 48R 49R 50R 51R 52R 53R 54R 55R 56R 57R 58R 59R 60R 37Q 38Q 39Q 40Q 41Q 42Q 43Q 44Q 45Q 46Q 47Q 48Q 49Q 50Q 51Q 52Q 53Q 54Q 55Q 56Q 57Q 58Q 59Q 60Q 36P 37P 38P 39P 40P 41P 42P 43P 44P 45P 46P 47P 48P 49P 50P 51P 52P 53P 54P 55P 56P 57P 58P 59P 60P 31T 32T 31S 32S 31R 32R 31Q 32Q 31P 32P 31N 32N 33N 34N 35N 36N 37N 38N 39N 40N 41N 42N 43N 44N 45N 46N 47N 48N 49N 50N 51N 52N 53N 54N 55N 56N 57N 58N 59N 60N 1V 2V 3V 4V 5V 6V 7V 8V 9V 10V 11V 12V 13V 14V 15V 16V 17V 18V 19V 20V 21V 22V 23V 24V 25V 26V 27V 1U 2U 3U 4U 5U 6U 7U 8U 9U 10U 11U 12U 13U 14U 15U 16U 17U 18U 19U 20U 21U 22U 23U 24U 25U 26U 27U 28U 1T 2T 3T 4T 5T 6T 7T 8T 9T 10T 11T 12T 13T 14T 15T 16T 17T 18T 19T 20T 21T 22T 23T 24T 25T 26T 27T 28T 29T 30T 1S 2S 3S 4S 5S 6S 7S 8S 9S 10S 11S 12S 13S 14S 15S 16S 17S 18S 19S 20S 21S 22S 23S 24S 25S 26S 27S 28S 29S 30S 1R 2R 3R 4R 5R 6R 7R 8R 9R 10R 11R 12R 13R 14R 15R 16R 17R 18R 19R 20R 21R 22R 23R 24R 25R 26R 27R 28R 29R 30R 1Q 2Q 3Q 4Q 5Q 6Q 7Q 8Q 9Q 10Q 11Q 12Q 13Q 14Q 15Q 16Q 17Q 18Q 19Q 20Q 21Q 22Q 23Q 24Q 25Q 26Q 27Q 28Q 29Q 30Q 1P 2P 3P 4P 5P 6P 7P 8P 9P 10P 11P 12P 13P 14P 15P 16P 17P 18P 19P 20P 21P 22P 23P 24P 25P 26P 27P 28P 29P 30P 1N 2N 3N 4N 5N 6N 7N 8N 9N 10N 11N 12N 13N 14N 15N 16N 17N 18N 19N 20N 21N 22N 23N 24N 25N 26N 27N 28N 29N 30N 31M 31L 30L 29M 30M 29L 32M 32L 33M 34M 33L 34L 35M 36M 37M 38M 39M 40M 41M 42M 43M 44M 45M 46M 47M 48M 49M 50M 51M 52M 53M 54M 55M 56M 57M 58M 59M 60M 60L 35L 36L 37L 38L 39L 40L 41L 42L 43L 44L 45L 46L 47L 48L 49L 50L 51L 52L 53L 54L 55L 56L 57L 58L 59L 31K 32K 33K 34K 35K 36K 37K 38K 39K 40K 41K 42K 43K 44K 45K 46K 47K 48K 49K 50K 51K 52K 53K 54K 55K 56K 57K 58K 59K 60K 31J 32J 33J 34J 35J 36J 37J 38J 39J 40J 41J 42J 43J 44J 45J 46J 47J 48J 49J 50J 51J 52J 53J 54J 55J 56J 57J 58J 59J 60J 31H 32H 33H 34H 35H 36H 37H 38H 39H 40H 41H 42H 43H 44H 45H 46H 47H 48H 49H 50H 51H 52H 53H 54H 55H 56H 57H 58H 59H 60H 31G 32G 33G 34G 35G 36G 37G 38G 39G 40G 41G 42G 43G 44G 45G 46G 47G 48G 49G 50G 51G 52G 53G 54G 55G 56G 57G 58G 59G 60G 31F 32F 33F 34F 35F 36F 37F 38F 39F 40F 41F 42F 43F 44F 45F 46F 47F 48F 49F 50F 51F 52F 53F 54F 55F 56F 57F 58F 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E 58E 31D 32D 33D 34D 35D 36D 37D 38D 39D 40D 41D 42D 43D 44D 45D 46D 47D 48D 49D 50D 51D 52D 53D 54D 60D 60C 31C 32C 33C 34C 35C 36C 37C 38C 39C 40C 41C 42C 43C 44C 45C 46C 47C 48C 49C 50C 51C 52C 53C 54C 57C 58C 59C 2C 3C 4C 5C 6C 7C 8C 9C 10C 11C 12C 7M 8M 9M 10M 3M 4M 5M 6M 30F 30E 25C 26C 26F 27F 28F 29F 29C 30C 30K 30J 30H 30G 1M 2M 2L 1L 11M 12M 13M 14M 15M 16M 17M 18M 19M 20M 21M 22M 23M 24M 25M 26M 27M 28M 3L 4L 5L 6L 7L 8L 9L 10L 11L 12L 13L 14L 15L 16L 17L 18L 19L 20L 21L 22L 23L 24L 25L 26L 27L 28L 1K 2K 3K 4K 5K 6K 7K 8K 9K 10K 11K 12K 13K 14K 15K 16K 17K 18K 19K 20K 21K 22K 23K 24K 25K 26K 27K 28K 29K 1J 2J 3J 4J 5J 6J 7J 8J 9J 10J 11J 12J 13J 14J 15J 16J 17J 18J 19J 20J 21J 22J 23J 24J 25J 26J 27J 28J 29J 1H 2H 3H 4H 5H 6H 7H 8H 9H 10H 11H 12H 13H 14H 15H 16H 17H 18H 19H 20H 21H 22H 23H 24H 25H 26H 27H 28H 29H 1G 2G 3G 4G 5G 6G 7G 8G 9G 10G 11G 12G 13G 14G 15G 16G 17G 18G 19G 20G 21G 22G 23G 24G 25G 26G 27G 28G 29G 1F 2F 3F 4F 5F 6F 7F 8F 9F 10F 11F 12F 13F 14F 15F 16F 17F 18F 19F 20F 21F 22F 23F 24F 25F 2E 3E 4E 5E 6E 7E 8E 9E 10E 17E 18E 11E 12E 13E 14E 6D 7D 8D 23E 19E 20E 21E 22E 15E 16E 2D 3D 4D 5D
WEST LONGITUDE (degrees)
EAST LONGITUDE (degrees)
26D 27D 28D 29D 22D 23D 13D 14D
NORTH LATITUDE (degrees) EQUATOR SOUTH LATITUDE (degrees)
17D 27E 28E 29E 24E 25E 26E
SOUTH LATITUDE (degrees)
NORTH LATITUDE (degrees) EQUATOR
24D 15D 16D 9D 10D 11D 12D 25D 18D 19D 20D 21D 30D 21C 22C
UTM Longitude Zone
Notes: 27C 28C 23C 24C 17C Example: 54F 18C 19C 15C 16C 16 17 18 19 20C
UTM Grid Zones 32X, 34X, and 36X are not defined.
Equirectangular projection of the graticule.
13C 14C 27 20 21 22 23 Figure 2.6: Global Distribution of UTM Longitude Zones and Latitu de Zones
2.2.5 Points on Zone Boundaries
The UTM zone specifications for points on the boundaries between adjacent zones are non-unique. These points fall into one of the following categories:
• points on the boundaries (meridians) between two adjacent UTM longitude zones;
• points on the boundaries (parallels) between two adjacent UTM latitude zones, including
- points not on the equator (this case is only relevant in those situations where the latitude-zone form of the UTM coordinate specification is used);
- points on the equator (i.e., the boundary between the northern and southern hemi-spheres); and
• points where two of the above boundaries intersect.
Every point on the boundary between two or more adjacent zones can be considered a mem-ber of all of the corresponding adjacent zones. In these cases, the UTM zone specification corresponding to any of the adjacent zones can be used without introducing positional ambigu-ity. The following examples illustrate the concept.
Example: Point on Boundary between Two Adjacent Longitude Zones
Problem: Determine the UTM latitude and longitude zones corresponding to the point whose geographic coordinates are 19◦S. lat. and 120◦W. lon.
Solution: Refer to Figure2.6. The point is in both of UTM zones 10K and 11K because it lies at their intersection.
Example: Point on Boundary between Two Adjacent Latitude Zones
Problem: Determine the UTM latitude and longitude zones corresponding to the point whose geographic coordinates are 72◦N. lat. and 86◦E. lon.
Solution: Refer to Figure 2.6. The point is in both of UTM zones 45W and 45X, because it lies at their intersection.
Example: Point on Boundary between Three Adjacent Zones
Problem: Determine the UTM latitude and longitude zones corresponding to the point whose geographic coordinates are 72◦N. lat. and 33◦E. lon.
Solution: Refer to Figure2.6. The point is in all three of UTM zones 36W, 35X and 37X, because it lies at their intersection.
Example: Point on Boundary between Four Adjacent Zones
Problem: Determine the UTM latitude and longitude zones corresponding to the point whose geographic coordinates are 24◦S. lat. and 162◦W. lon.
Solution: Refer to Figure 2.6. The point is in all four of UTM zones 3J, 3K, 4J, and 4K, because it lies at their intersection.
Example: Point(s) with Apparently Different UTM Zone Specifications
Problem: Field notes by one field technician report the location of a particular monitoring station as UTM zone 11S. Field notes by a second technician report the location of the same monitoring station as UTM zone 12T. The station has not been moved. Is it possible that both technicians are correct?
Solution: Refer to Figure 2.6. UTM zones 11S and 12T intersect at a corner point, which therefore lies in both zones. Therefore, it’s possible that both technicians are correct.
Example: Point(s) with Apparently Different UTM Zone Specifications
Problem: Field notes by one technician report the location of a particular monitoring station as UTM zone 12S. Field notes by a second technician report the location of the same monitoring station as UTM zone 12U. The monitoring station has not been moved. Is it possible that both technicians are correct?
Solution: Refer to Figure 2.6. UTM zones 12S and 12U do not intersect, so no points lie in both zones. Thus, in this case it’s not possible that both technicians are correct; either one or both are incorrect.
2.3
Easting and Northing Coordinates
Every UTM longitude zone has a particular Cartesian coordinate system associated with it (i.e., a local xy coordinate system). The UTM easting and northing coordinates are the x and y coordinates, respectively, of this system.
UTM easting and northing coordinates are numerical, and are reported as base-ten integers (Arabic numerals, no decimals or fractions). The numerical values are written without commas, spaces, or decimal points; and in non-exponential notation (e.g., neither in engineering notation nor in scientific notation). The coordinate definitions (see below) imply that the numerical values are nonnegative. Therefore, the coordinates are written as unsigned numbers (i.e., without “+” or “−” signs).
UTM easting and northing coordinates are reported in units of meters. Some non-technical publications on civilian navigation and the GPS use a nonstandard convention in which the easting and northing coordinates are reported in kilometers, but the use of kilometers doesn’t conform to the standard defined by DMA [1989] and therefore isn’t recommended.
Table 2.3: Minimum and Maximum UTM Easting Coordinates
Latitude
Horizontal UTM Easting Coordinates
Datum (meters)
Minimum Maximum Difference
NAD 27 166 018 833 982 667 964 0◦N./S. NAD 83 166 022 833 978 667 956 NAD 27 441 866 558 134 116 268 80◦N./S. NAD 83 441 868 558 132 116 264 NAD 27 465 004 534 996 69 992 84◦N./S. NAD 83 465 006 534 994 69 988
Source: Decimal values of minimum and maximum easting coordinates were obtained from National Geodetic Survey [2007], and then were rounded up and down, respectively, to the nearest integer coordinate corresponding to points within a UTM longitude zone.
2.3.1 Easting Coordinates
The easting (x) coordinate increases continuously as one moves eastward. Each longitude zone has a central meridian midway between its two bounding meridians (See Figure2.7). The central meridian of each longitude zone is assigned the easting coordinate 500000m (i.e., x = 500 000 m). Consequently, the easting coordinate has the following characteristics:
• It’s local to the corresponding particular longitude zone; • It’s non-negative; and
• It’s also referred to as false easting.
Table2.3 lists the minimum and maximum UTM easting coordinates for regular (6◦ wide) UTM longitude zones, at various latitudes and for the two most commonly used datums in the U.S. The full range is realized only at the equator, where the UTM longitude zones are widest. At higher latitudes the range generally is narrower, because the UTM longitude zones narrow with increasing latitude due to convergence of the meridians.
The ranges in Table2.3correspond to regular UTM longitude zones; for irregular zones the ranges differ from these. From these results it follows that the UTM easting coordinate of every point within every regular UTM longitude zone is a six-digit integer. It turns out that this is also true for irregular UTM longitude zones (see Appendix A).
2.3.2 Northing Coordinates
The northing (y) coordinate increases continuously as one moves northward. In the northern hemisphere the equator is assigned the northing coordinate 0mN (i.e., y = 0 m). In the southern
Table 2.4: Minimum and Maximum UTM Northing Coordinates
Hemisphere
Horizontal UTM Northing Coordinates
Datum (meters)
Minimum Maximum Difference
NAD 27 0 9 328 895 9 328 895 Northern NAD 83 0 9 329 005 9 329 005 NAD 27 1 117 046 10 000 000 8 882 954 Southern NAD 83 1 116 916 10 000 000 8 883 084
Source: Decimal values of minimum and maximum northing coordinates were obtained from National Geodetic Survey [2007], and then were rounded up and down, respectively, to the nearest integer coordinate corresponding to points within a UTM longitude zone.
hemisphere the equator is assigned the northing coordinate 10000000mN (i.e., y = 10 000 000 m). Consequently the northing coordinate has the following characteristics:
• It’s local to the corresponding particular hemisphere.
• It’s non-negative.
• It’s also referred to as false northing.
Table2.4 lists the minimum and maximum UTM northing coordinates for any given UTM longitude zone, for the two most commonly used datums in the U.S. The full range isn’t realized near the bounding meridians of each zone, due to meridian convergence. From these results it follows that the UTM northing coordinate of every point within every UTM longitude zone is a one- to seven-digit integer (see Appendix Balso).
2.3.3 Easting and Northing Coordinate Specifications
The conventional format for reporting UTM easting and northing coordinates is rather specific. The numerical value of the coordinate is written first (leftmost), immediately followed by the lowercase “m” abbreviation for meters, with or without a single space separating the two. An uppercase “E” or “N” immediately follows the “m”, to indicate whether the coordinate is an easting or a northing, respectively. The following examples illustrate the convention.
Examples: Conventional Format for Reporting UTM Easting Coordinates
“500000mE” or “500000 mE” (e.g., the central meridian)
“566785mE” or “566785 mE”
“177003mE” or “177003 mE”
“792324mE” or “792324 mE”
Examples: Conventional Format for Reporting UTM Northing Coordinates
“0mN” or “0 mN” (e.g., the equator)
“353mN” or “353 mN”
“8315466mN” or “8315466 mN”
“10000000mN” or “10000000 mN” (e.g., the equator)
2.3.4 Coordinate Gridlines
Within each UTM longitude zone, two sets of gridlines are defined – a set of UTM easting gridlines and a set of UTM northing gridlines. The easting gridlines are orthogonal to the northing gridlines. Each set is described below.
Within each UTM longitude zone, the UTM easting gridlines form a set of contour lines. Each UTM easting gridline connects those points on the earth’s surface that have the same UTM easting coordinate. The easting gridline corresponding to 500 000 mE (i.e., the central meridian) extends from 80◦S. lat. to 84◦N. lat. As one moves poleward from the equator, each longitude zone becomes narrower, so the easting gridlines corresponding to the more extreme easting coordinates don’t extend as far poleward as the central meridian does (see Figure2.7). Rather, these easting gridlines only extend northward to the points where they intersect the zone’s bounding meridians. Within any particular UTM longitude zone, the easting gridlines never intersect.
Within any particular UTM longitude zone, the UTM northing gridlines also form a set of contour lines. Each UTM northing gridline connects those points on the earth’s surface that have the same UTM northing coordinate. The northing gridlines within each longitude zone extend from one bounding meridian to the other, across 6◦ of longitude. As one moves poleward from the equator, the longitude zones become narrower, so the northing gridlines become shorter (see Figure2.7). Within any particular UTM longitude zone, the northing gridlines never intersect.
2.4
UTM Coordinate Specifications
Unambiguous determination of position using the UTM grid system generally requires specifi-cation of the following five elements:
• horizontal datum,
• UTM longitude zone,
• UTM easting coordinate, and
• UTM northing coordinate.
Example: Conventional Format for UTM Coordinate Specification
Problem: Consider the following UTM coordinate specification for a point: NAD 83, UTM Zone 11, N. hemis., 450300mE, 5291192mN
What is the horizontal datum?
In which UTM longitude zone is the point located? In which hemisphere is the point located?
Solution:
The horizontal datum is the North American Datum of 1983 (NAD 83). The location is within UTM longitude zone 11.
The location is in the northern hemisphere.
In some situations it may be acceptable to omit the datum, zone or hemisphere from the speci-fication, but only if the omitted elements are clearly implied by the context.
Why is it necessary to specify all five elements of the UTM coordinate specification? Let’s consider each element in turn.
The horizontal datum effectively defines the position and orientation of the graticule, relative to which each UTM grid system is defined. Therefore, the horizontal datum is an essential element in the definition of the UTM grid system. UTM coordinates defined with respect to one horizontal datum differ from those defined with respect to another horizontal datum. For instance, the UTM grid system defined with respect to the North American Datum of 1927 (NAD 27) and that defined with respect to NAD 83 are different grid systems. The two grid systems bear a superficial resemblance to one another because they’re structured similarly (i.e., both use 6◦ longitude zones and 8◦ latitude zones, etc.). However, they’re different grid systems because the positions and orientations of the graticules for the two systems differ. This distinction isn’t a mere technicality. For instance, according to the Department of the Army [2001], UTM coordinates for the same point, but corresponding to different horizontal datums, may differ by as much as 900 m.
If the hemisphere designation (or latitude-zone designation) is omitted from the UTM co-ordinate specification, then the point’s position is effectively determined only to within two possible locations – one in each of the northern and southern hemispheres. The one exception to this is points that lie on the equator. The northing coordinates of such points will be either 0 mN (if referenced to the northern hemisphere) or 10 000 000 mN (if referenced to the southern hemisphere). In either case, it would be clear that the point lies on the equator because the minimum UTM northing coordinate in the southern hemisphere is greater than 0 mN and the maximum northing coordinate in the northern hemisphere is less than 10 000 000 mN. Therefore, locations of points on the equator can be specified as either northern hemisphere or southern hemisphere without introducing ambiguity.
If the longitude zone is omitted from the UTM coordinate specification, then the point’s longitudinal position is effectively determined only to within 60 possible locations – one in each longitude zone.
If the easting coordinate is omitted from the UTM coordinate description, then the point’s easting position is effectively determined only to within a longitude zone. Refer to Table2.3. Each UTM longitude zone is almost 668 000 m wide at its widest part (i.e., at the equator). In the northern hemisphere, each UTM longitude zone is almost 70 000 m wide at its narrowest part (i.e., at 84◦N. lat.). In the southern hemisphere each longitude zone is over 116 000 m wide at its narrowest part (i.e., at 80◦S. lat.). That’s a lot of imprecision.
If the northing coordinate is omitted from the coordinate description, then the point’s nor-thing position is effectively determined only to within a hemisphere. As shown in Table 2.4, UTM longitude zones in the southern hemisphere are over eight million meters long, while those in the northern hemisphere are over nine million meters long (measured from northern to south-ern boundaries). Again, that’s a great deal of imprecision. The precision can be increased substantially by specifying the latitude zone (see example below).
Example: Increasing the Precision of the Northing Coordinate by Specifying the UTM Latitude Zone
Problem: How imprecise (roughly) is the UTM northing coordinate if the UTM latitude zone is included in the coordinate specification, but the numerical value of the northing coordinate is omitted? Assume the earth is spherical.
Solution: If the shape of the earth is approximately spherical, then each minute of latitude is approximately equivalent to one nautical mile, or 6076 feet [U.S. Air Force, 2001]. Actually the length of a minute of latitude varies somewhat with latitude, because the earth is more closely approximated by an ellipsoid than by a sphere. However, to model the earth as an ellipsoid requires substantially more mathematical effort than this example requires.
Latitude zones C through W are 8◦ wide in the direction of the northing coordinate, so within those zones the imprecision of the northing coordinate is approximately
(8◦ lat.) 60’ lat. 1◦ lat. 6076 ft 1’ lat. 0.3048 m ft ≈ 890 000 m
UTM latitude zone X is 12◦ wide in the direction of the northing coordinate, so within zone X the imprecision of the northing coordinate is approximately
12◦ lat. 60’ lat. 1◦ lat. 6076 ft 10 lat. 0.3048 m ft ≈ 1 300 000 m
Example: Preliminary Screening of UTM Coordinate Specifications for Out-of-Bounds Errors
Problem: Quickly check each of the following UTM coordinate specifications for out-of-bounds errors:
NAD 27, UTM Zone 10, N. hemis., 150300mE, 9951192mN NAD 83, UTM Zone 12, S. hemis., 751334mE, 1116907mN NAD 83, UTM Zone 19, N. hemis., 833980mE, 192mN NAD 27, UTM Zone 17, N. hemis., 150300mE, 34602mN NAD 27, UTM Zone 18, N. hemis., 237811mE, 9328904mN NAD 83, UTM Zone 63, N. hemis., 623300mE, 9328904mN
Specify which element or elements, if any, are incorrect and explain why.
Solution: For a quick, preliminary screening of UTM coordinate data, use the “0◦N./S.” section of Table 2.3, and Table 2.4. Beware, however, that this approach will detect only extreme cases of out-of-bounds errors. More refined screening may be required to detect all out-of-bounds errors.
“NAD 27, UTM Zone 10, N. hemis., 150300mE, 9951192mN” is incorrect. The easting coordinate is lower than the lower limit given in the “0◦N./S.” section of Table2.3, and the northing coordinate exceeds the upper limit listed in Table2.4. “NAD 83, UTM Zone 12, S. hemis., 751334mE, 1116907mN” is incorrect. The northing coordinate is out of range (too low).
“NAD 83, UTM Zone 19, N. hemis., 833980mE, 192mN” is incorrect. The easting coordinate is out of range (too high).
“NAD 27, UTM Zone 17, N. hemis., 150300mE, 34602mN” is incorrect. The easting coordinate is out of range (too low).
“NAD 27, UTM Zone 18, N. hemis., 237811mE, 9328904mN” is incorrect. The northing coordinate is out of range (too high).
“NAD 83, UTM Zone 63, N. hemis., 623300mE, 9328904mN” is incorrect. The zone number is too high (i.e., UTM zone 63 does not exist).
2.5
Map Projections, Datums, and the Graticule
The UTM grid system applies the secant form of the transverse Mercator projection to each UTM longitude zone. The two standard lines (also called lines of secancy) within each longitude zone are approximately 180 000 m east and west of the central meridian; these have coordinates of approximately 320 000 mE and 680 000 mE, respectively [DMA, 1990].
The scale factor of the projection varies with latitude and longitude within each UTM lon-gitude zone; for mathematical details see DMA [1989]. The spatial variation of the scale factor within each UTM longitude zone can be summarized as follows [DMA, 1990]:
• The scale factor is 1.000 00 at both of the standard lines.
the central meridian, where it’s equal to 0.9996.
• The scale factor increases as one moves outward from either of the two standard lines to-ward the nearest bounding meridian. Where the bounding meridians intersect the equator, the scale factor is approximately equal to 1.0010.
The projection parameters are based on the particular horizontal datum chosen. The hori-zontal datums most commonly used in North America are the following:
• the North American Datum of 1927 (NAD 27); • the North American Datum of 1983 (NAD 83); and • the World Geodetic System 1984 (WGS 84).
All three of these are based on an ellipsoidal, rather than spherical, representation of the globe. For most practical purposes then, the UTM grid system uses the ellipsoidal form of the transverse Mercator projection. DMA [1989] gives mathematical equations for ellipsoid parameters.
The UTM grid declination (i.e., convergence of the meridians) varies with both latitude and longitude within each UTM longitude zone; for mathematical details see DMA [1989]. The spatial variation of grid declination within each UTM longitude zone can be summarized as follows [DMA, 1989]:
• The grid declination is zero at the central meridian.
• The (absolute) grid declination increases with distance from the central meridian.
• For those areas on either side of the central meridian, the (absolute) grid declination increases with distance from the equator.
Because UTM grid north has a slight easterly or westerly declination, except right at the central meridian of each longitude zone, one should never use map neatlines or the graticule (meridians of longitude and parallels of latitude) as a substitute for UTM gridlines. Doing so introduces error.
2.6
Chapter Summary
Refer to Table 2.5. Each of the 60 regular UTM longitude zones has a separate UTM map projection associated with it, giving a total of 60 separate UTM map projections. Each regular zone has two local Cartesian (xy) coordinate systems associated with it – one for each of the northern and southern hemispheres – giving a total of 120 separate member coordinate systems. Each of the six irregular UTM zones (31V, 32V, 31X, 33X, 35X, 37X) has a separate UTM map projection associated with it, giving a total of six additional map projections. Each irregular zone has one local Cartesian coordinate system associated with it, giving a total of six additional member coordinate systems.
Finally, consider the entire set of UTM longitude zones, both regular and irregular, collec-tively. The UTM grid system uses 66 separate UTM projections and comprises 126 member coordinate systems.
The UTM grid system is, in effect, a hybrid system. It combines elements of the geographic coordinate system with numerous local Cartesian coordinate systems. For instance, both the UTM longitude zones and the local easting/northing coordinate system within each longitude zone are defined in terms of the graticule. This is why it’s important to master the principles of geographic and Cartesian (xy) coordinate systems before learning the UTM grid system.
Table 2.5: Summary of UTM Map Projections and Local Coordinate Systems
Number Number Number of Local
Zone Member of of Map Coordinate
Group Zones Zones Projections Systems
Per Group Per Group Zone Total Zone Total
Regular 01 - 60 60 1 60 2 120 Irregular 31V, 32V, 31X, 6 1 6 1 6 33X, 35X, 37X All 01 - 60, 31V, 32V, 31X, 66 1 66 – 126 33X, 35X, 37X
The UTM Grid and USGS
Topographic Maps
In this chapter we occasionally refer to the publication date for a particular map product (e.g., paper map, digital map). The publication date is the date on which the map product was released to the public. If a map has been revised, then the publication date of the original edition is earlier than that of the revised edition. If the map has been revised more than once, then each revision will have its own publication date.
3.1
Map Elements Supporting Use of the UTM Grid
The U.S. Geological Survey (USGS) produces topographic quadrangle maps and related products for public distribution. The maps have various elements that facilitate use of the UTM grid system, including the following:
• horizontal datum identifier,
• UTM longitude zone identifier,
• UTM grid tick marks and coordinate labels,
• UTM grid declination information, and
• UTM gridlines (some maps).
3.1.1 Horizontal Datum Identifier
The horizontal datum is specified in the explanatory text on the map collar, typically on the left-hand side of the lower margin (see Figures 3.1and 3.2).
3.1.2 UTM Longitude Zone Identifier
The UTM longitude zone is specified in the explanatory text on the map collar, typically on the left-hand side of the lower margin (see Figures 3.1and 3.2).
Figure 3.1: UTM Grid Information – Older Map. Source: USGS [1986]
3.1.3 UTM Grid Tick Marks and Coordinate Labels
In general, a grid tick mark is a short, straight-line segment that marks the location of a gridline. Typically, grid tick marks are placed at points where gridlines intersect other lines, such as orthogonal gridlines (e.g., where an easting gridline crosses a northing gridline) or map neatlines.
UTM grid tick marks are displayed on USGS quadrangle topographic maps published since 1959, and on many quadrangles published before 1959 [Cole, 1977]. The UTM grid tick marks are displayed on the map collar adjacent to the neatline. Each tick mark indicates the point where a UTM gridline intersects the map neatline.
The distance between adjacent grid tick marks is called the grid-tick interval. On each map sheet the grid-tick interval is constant (uniform). All USGS quadrangles use either 1000-meter or 5000-meter grid-tick intervals [USGS, 2001]. In addition, on USGS quadrangles the UTM grid tick mark coordinates are positive integer multiples of 1000 m. The grid-tick interval is specified in the explanatory text displayed on the map collar (see Figures3.1and3.2). On some maps, but not all, the color of the grid tick marks also is specified in the explanatory text on the map collar (e.g., compare Figures 3.1 and 3.2). Typically, UTM grid tick marks are displayed in blue on USGS quadrangle topographic maps.
Example: Interpretation of Displayed Explanatory Text
Background:
The following explanatory text is displayed on the left-hand side of the lower margin of the Nine Mile Falls Quadrangle, Washington, 7.5-minute topographic map [USGS ; 1973b, photorevised 1986]:
Mapped, edited, and published by the Geological Survey Control by USGS and NOS/NOAA
Topography by photogrammetric methods from aerial photographs taken 1972. Field checked 1973
Underwater contours by Washington Water Power Co. Projection and 10,000-foot grid ticks: Washington coordinate system, north zone (Lambert conformal conic)
1000-meter Universal Transverse Mercator grid ticks, zone 11, shown in blue. 1927 North American datum To place on the North American Datum 1983, move the projection lines 15 meters north and 80 meters east as shown by dashed corner ticks
There may be private inholdings within the boundaries of the National or State reservations shown on this map
Problem:
What is the horizontal datum? What is the UTM longitude zone? What is the UTM grid-tick interval? What color are the UTM grid tick marks?
Solution:
The horizontal datum is NAD 27. The UTM longitude zone is 11. The UTM grid-tick interval is 1000 m. The UTM grid tick marks are blue.
Example: Explanatory Text
Background:
The following explanatory text is displayed in the lower margin of the Eagle Cap Quadrangle, Oregon, 15-minute topographic map [USGS, 1954]:
Mapped, edited, and published by the Geological Survey Control by USGS and USC&GS
Topography from aerial photographs by multiplex methods Aerial photographs taken 1953. Advance field check 1954 Polyconic projection. 1927 North American datum 10,000-foot grid based on Oregon coordinate system, north zone
1000-foot Universal Transverse Mercator grid ticks, zone 11, shown in blue
To place on the North American Datum 1983 move the projection lines 17 meters north and 79 meters east
There may be private inholdings within the boundaries of the National or State reservations shown on this map
Problem:
What is the horizontal datum? What is the UTM longitude zone?
What UTM grid-tick interval is reported in the explanatory text?
Measure the map distance between adjacent UTM grid tick marks, and use the map scale to convert the map distance to the corresponding horizontal ground distance. What is the measured grid-tick interval?
What UTM grid-tick interval is reported in the USGS UTM fact sheet [USGS, 2001]?
Are the three results obtained above for the UTM grid-tick interval consistent? If not, suggest a possible explanation for any discrepancies.
Solution:
The horizontal datum is NAD 27. The UTM longitude zone is 11.
The grid-tick interval reported in the explanatory text is 1000 feet. The measured UTM grid-tick interval is 1000 meters.
The UTM grid-tick interval reported in the fact sheet is 1000 meters [USGS, 2001].
The UTM grid-tick interval reported in the explanatory text differs from both (1) that measured on the map and (2) that reported in the fact sheet. Apparently the grid-tick interval specification “1000-foot Universal Transverse Mercator grid ticks, . . . ” is a misprint.