The Global Positioning System (GPS) consists of a set of 24 satellites in Medium Earth Orbit which continually broadcast very accurate timing signals for reception by GPS Units. A GPS Unit first computes its own location in an earth-centered coordinate system and then converts that location either to Lat/Lon coordinates or to equivalent METRIC coordinates expressed in any of the several METRIC GRID REFERENCE METHODS which may be printed on the maps available to the GPS user. The standard GRID REFERENCE METHODS available on maps include both Lat/Lon and those based on the METRIC GRID: UTM (Universal Transverse Mercator), MGRS (Military Grid Reference System), and UPS (Universal Polar Stereographic - not further discussed on this website). While Lat/Lon is the basic grid, it does not promote easy determination of ground distances and directions from grid lines drawn on maps. The UTM system, comprising the METRIC GRID and the UTM REFERENCE METHOD, was devised to overcome this deficiency by providing a GRID composed of two orthogonal sets of straight lines whose distances apart are measured in the Metric System ( Wildi,  Nelson,  comments ). The UTM system allows location addresses to be expressed in various ways, but all are mainly numeric. The MGRS system uses the same METRIC GRID but modifies UTM location addresses by converting two specific UTM digits to letters. The initial design of the UTM system, and hence of the MGRS system, contained one minor flaw and one major flaw, both of which are easily corrected by normalizations described below. The sole raison d'etre for MGRS that I have been able to discern is a desire to allow high-order truncations of location addresses to remain unique over large areas. Use of truncated addresses is patently risky for military personnel in the field, and it is purchased in MGRS at the expense of an obfuscatory address modification. Even if truncated addresses were useful, MGRS is less effective in attaining large areas of truncation unicity than are certain GRID REFERENCE METHODS proposed below which do not involve the address modifications present in MGRS. The NUTM (Normalized Universal Transverse Mercator) is proposed below as an excellent general-purpose METRIC GRID REFERENCE METHOD which is essentially the same as UTM but has a much improved truncation unicity. A new metric grid reference method, the MGPG (Metric Global Positioning Grid) is proposed below for those who insist on high-order truncation with very large areas of unicity. A great variety of other constructible METRIC GRID REFERENCE METHODS (MGRM) is also suggested.

In an email I received at UTC-7 2001.10.14.0809,  Tom Terry of the USNG  (United States National Grid)  conveyed the following.
1.  He objects to my use of the word flaw on this webpage.
2.  He disagrees with my statement that "use of truncated addresses is patently risky for military personnel in the field".
3.  He disagrees with my opinion that the MGRS replacement of the UTM dual-digit designation of 100-kilometer SQUARES by a dual-letter designation constitutes an "obfuscatory address modification".
4.  He effectively stated that the US Military (designed and) adopted the MGRS modification of UTM in 1947 in order not only to allow control over the precision of addresses by low-order (right-end) truncations or extensions, but also to allow control over the length of addresses by high-order (left-end) truncations while simultaneously attaining large areas of unicity of those truncated address. It is clear from page 5 of the  USNG file prepared by Tom Terry (PDF)  that MGRS (on which USNG is based) succeeds admirably in this respect, attaining excellent unicity with a three-character truncation. However, there is available  a two-character truncation which can provide a considerable improvement over MGRS without replacing dual-digits by dual-letters.

By the GLOBE we mean a nearly spherical oblate spheroidal surface, which serves as a conceptualized idealization of the mean sea level surface of the earth, on which we can draw the grid lines (curves) of the two GRIDS and whose various projections onto flat paper surfaces can serve as maps which represent the surface of the earth for purposes of navigation. A GRID is a pair of sets of grid lines which have the property that the grid lines of the two sets are mutually orthogonal wherever they intersect; the grid lines of each individual set must be non-intersecting (except at possible singular points, such as the two poles). In order to be cartographically useful for purposes of precise navigation, a projection from the GLOBE to a map (and its inverse from the map back to the GLOBE) must be conformal or orthomorphic, meaning that all angles between intersecting lines (grid lines or otherwise) are preserved by the projection (and by its inverse). A DATUM is an encapsulation of cartographically pertinent properties of the earth such as shape and gravitational variations. A DATUM thereby determines an exact shape for the GLOBE and hence specifies the manner in which a GPS Unit interprets the GPS satellite timing signals to calculate its Lat/Lon and METRIC coordinates. Each grid, and hence its associated grid reference methods (GRM), depends on the DATUM used for its specification. The signature of a DATUM-specified GRM is the concatenation of the name of the DATUM and the name of the GRM (e.g., NAD27-UTM).

This website touches on five grid reference methods and three datums. The five grid reference methods are listed below. The first three are in common usage while the last two are being proposed on this website. The last four are METRIC.

The three datums are listed below. The first two datums are quite distinct while the second and third datums are effectively identical for civilian use.

The USGS topo quads generally were prepared using NAD27-UTM while the foto and topo arrays for the Joshua Tree National Park portion of this website were constructed using materials prepared using NAD83-UTM. The address of a location on earth, in terms of a specific DATUM-based grid reference method, is presented as the DATUM-GRM signature coupled with the GRM address of the location, as described in sections on the specific grid reference methods. Many locations on this website will be presented in terms of NAD83-UTM and NAD83MGRS for illustrative purposes, and again in terms of NAD83NUTM and NAD83MGPG in order to illustrate advantages being claimed for NUTM and MGPG.

For an excellent discussion of DATUMS and GRIDS,  the reader is referred to the following fine text by   Noel J. Hotchkiss:  
A Comprehensive Guide to Land Navigation with GPS (Third Edition) Alexis Publishing 1999 ISBN 1-892688-00-X. For a set of excellent maps which illustrate the concepts discussed in this text, the reader is referred to the GPS-Compatible Highway Maps designed by Noel J. Hotchkiss and published by Alexis Publishing.

The Lat/Lon GRID has been well-known and heavily used for centuries. This GRID consists of two mutually orthogonal sets of curves superimposed on the GLOBE, namely the latitude lines which are circles parallel to the equator and the longitude lines which run from the South Pole to the North Pole and are orthogonal to the latitude lines. The latitude of the equator is 0 degrees while the latitude of the South Pole is 90 degrees south latitude and the latitude of the North Pole is 90 degrees north latitude. The longitude of the International Date Line, which is directly opposite the prime meridian passing through Greenwich England, is both 180 degrees west and 180 degrees east. Determining latitude is relatively easy, but determining longitude is a much more difficult problem due to the earth's rotation, one whose solution requires very accurate clocks. The first clock of the required accuracy was invented by John Harrison and successfully tested in 1761. Many websites and books dealing with this fascinating story can be found using an appropriate google search, and a particularly interesting article is found at http://www.oldnewspublishing.com/harrison.htm. Cartographers have invented many conformal projection methods to project either the whole GLOBE or carefully selected portions of the GLOBE onto flat surfaces to make possible the generation and publication of maps on which the projected sets of latitude and longitude lines remain orthogonal. Maps useful for land navigation in particular need to be relatively distortion free. One of the most successful of these projections is the Transverse Mercator, which is the basis for the UNIVERSAL TRANSVERSE MAP (UTMAP), the METRIC GRID superimposed on the UTMAP, and the primary METRIC GRID REFERENCE METHOD discussed in Section 4, Universal Transverse Mercator (UTM).

In preparation for the discussion of the METRIC GRID REFERENCE METHODS, we note that two mutually orthogonal partitions can be usefully applied to the GLOBE. First, the GLOBE can be partitioned into 60 vertical longitude bands called ZONES (Cylindrical Mercator Projection) whose boundaries are the longitude lines at integer multiples of six degrees of longitude. These ZONES should be numbered from 00 to 59 starting at 180 degrees west and proceeding eastward around to 180 degrees east. (We must note that UTM and MGRS number these ZONES from 01 to 60. This is the minor flaw I mentioned earlier and is easily corrected by normalizing to the range 00 to 59. Despite their lacking a symbol for zero, the Babylonians were aware of this normalization by about 2000BC. We will see in Section 4 that the UTM designers themselves were aware of a similar situation when they established the south-to-north equatorial rollover from 9,999,999 to 0,000,000 in northings. A more closely related example is provided by 24-hour time, in which the hours run through the sequence from 00 to 23, inclusive, rather than from 01 to 24, inclusive. Even in the ridiculous 12-hour time used in the United States, the hours run through the sequence from 00 to 11, inclusive, rather than through the sequence from 01 to 12, inclusive, except that the numeral 12 is used in place of the more appropriate numeral 00.) Second, the GLOBE (from 80 degrees south latitude to 80 degrees north latitude) can be partitioned into 20 horizontal latitude bands whose boundaries are the latitude lines at integer multiples of eight degrees of latitude. Note that these 20 latitude bands extend only from 80 degrees south latitude to 80 degrees north latitude, leaving the polar areas to be treated separately (by the UPS grids). We could label the 10 latitude bands from south to north within each hemisphere with the indexes 0 through 9, but since there are 20 latitude bands altogether, it is common practice to name them, in order from the South Pole region to the North Pole region, with the successive letters of the two sequences

but note that latitude band X is commonly extended to 84 degrees in order to accommodate certain areas in northern Europe. The 1200 (60x20) intersections of ZONES with latitude bands are called REGIONS. The obvious name to use for a REGION which is the intersection of a particular ZONE with a particular latitude band is the concatenation of the name (numeral) of the ZONE and the name (letter) of the latitude band (sometimes called a Zone Designator). For example, Joshua Tree National Park in Southern California is located in  REGION  11S  according to NAD83-UTM.

A marvelously informative article by Robert A. Nelson states that during the French Revolution, a commission of the French Academy of Sciences, including J. L. Lagrange and Simon Laplace, proposed that a new unit of length be defined as one ten-millionth of the quarter polar circumference of the earth. The proposal was accepted by the French National Assembly on 26 March 1791, and the new unit was given the name meter in 1793. According to the table  The Earth according to WGS84, the distance from either pole to the equator is 10,001.966 km, ##################################################### Fortunately for cartographers and others dealing with the various grid reference methods associated with GPS units and precise land navigation (UTM, MGRS, UPS, etc.), the effort made between 1792 and 1798 to determine the distance from the equator to the North Pole along the meridian through Paris was slightly in error, leading to an oversized meter and a quarter polar circumference which is about 15 km short of the intended 10,000km. According to D. G. Leahy, the Year 2000 International Astronomical Union estimated the earth's polar circumference to be 39940.67142790km and the earth's equatorial circumference to be 40075.0355351km (the degree of precision seems to far exceed the possible degree of accuracy). This leads to a quarter polar circumference of about 9985.17km, as noted above. In preparation for discussion of the UTM GRM, we note now that 1/60-th of the equatorial circumference is about 667.92km, well short of 800km.

We may note here that the partitioning of the UTMAP of Section 4 into just 20 metric bands from the South Pole to the North Pole, each 1000km tall (except for the two closest to the poles, which are shorter by about 15km), would not be possible if the earth's polar circumference were equal to the earth's equatorial circumference (or even exceeded 40,000km).

The following sentence is just a small part of a fine article on the origin of the UTM system. During World War I, the French military found that they had significant problems in rapidly and accurately calculating pointing angles for their artillery when using maps based on the Lat/Lon system. To overcome the problem by producing maps on which direct measurements yield very accurate distances and azimuth settings, the French invented and developed a brilliant concept - the Universal Transverse Mercator Grid (UTM), which is still very much in use today and which serves as the primary metric grid upon which are based all other metric grids (at least for the non-polar portions of the GLOBE). The conformal Transverse Mercator projection is applied to each of the 60 ZONES defined in Section 2 to produce a flat nearly distortion-free "orange-peel-segment" drawn on a tall skinny rectangular map. One may now imagine these 60 rectangular maps joined together to form the single rectangular UTMAP (short for UTM MAP) partitioned into 60 ZONES drawn just touching at the equator. The equator is the sole latitude line which is straight on the UTMAP; all other latitude lines are convex toward the equator within each ZONE. The central meridian of each ZONE is a straight line perpendicular to the equator and is the sole longitude line of the ZONE which is straight; all other longitude lines are concave toward the central meridian. (Compare MGPG COLUMN 1 of the UTMAP [4 megabyte download] with the Cylindrical Mercator Projection. Also, see  Table 1  prepared by  Andrew and Lesley .)

On the UTMAP is now drawn a metric grid composed of two mutually orthogonal sets of straight lines, one set of horizontal metric grid lines (parallel to the equator) and one set of vertical metric grid lines (perpendicular to the equator and parallel to the central meridians). The grid spacing, the distance between adjacent parallel grid lines, may be set to whatever resolution is desired: 1000km, 100km, 10km, 1km, 100m, or any other desired spacing. (On USGS 7.5 minute topo quads, UTM grid lines are spaced 1km apart.) By convention, the vertical central meridian of each of the 60 ZONES is defined to have a horizontal coordinate (called an easting) of 500km; vertical grid lines west of the central meridian have eastings less than 500km, while vertical grid lines to the east of the central meridian have eastings greater than 500km. The maximum horizontal extent of vertical grid lines clearly occurs at the equator, where their eastings run from about 166km to about 834km (recall Section 3). By convention, the vertical coordinates (called northings) of horizontal grid lines run from 0km at the equator toward 10,000km (but reaching only about 9985km) at the North Pole, and from 10,000km at the equator toward 0km (but reaching only about 0015km) at the South Pole. UTM eastings and northings are sometimes called false because they are very close to, but not exactly equal to, true ground distances. Note that eastings are specific to each ZONE. Note also that while northings apply to the whole UTMAP they are duplicated in the southern and northern hemispheres, running in the Southern Hemisphere from about 0015km at the South Pole to just short of 10,000km at the Equator, and running in the Northern Hemisphere from exactly 0000km at the Equator to about 9985km at the North Pole.

The horizontal metric grid lines on the UTMAP are analogous to the latitude lines on the GLOBE. On the GLOBE, the UTM Grid system defines 20 latitude bands, each having a vertical extent of 8-degrees of latitude, which span the GLOBE from 80 degrees south latitude to 80 degrees north latitude (extended for political reasons to 84 degrees north latitude). In an analogous manner, we can define on the UTMAP 20 metric bands as follows. Each metric band on the UTMAP lies between two horizontal metric grid lines whose northings are adjacent integer multiples of 1000km, with due allowance being made for the metric bands adjacent to the two poles. Note that the 20 metric bands cover the entire UTMAP whereas the 20 latitude bands do not quite cover the entire GLOBE. In order to be able to refer easily to the 20 metric bands we label them in order from the South Pole to the North Pole with the successive letters of the two sequences

much as we did with the latitude bands in Lat/Lon. We now define a DOMAIN of the UTMAP to be the intersection of a ZONE and a metric band, and note that there are exactly 1200 (60x20) DOMAINS which cover the entire UTMAP.

On the UTMAP, DOMAINS are areas having straight lines for their horizontal boundaries and curved lines (the projections of longitude lines) for their vertical boundaries. On the GLOBE, REGIONS are actually curvilinear rectangles (four curved sides with right-angle corners) and their projections to the UTMAP remain curvilinear rectangles. The projected REGIONS on the UTMAP have vertical boundaries which are projected longitude lines concave toward the central meridians and horizontal boundaries which are projected latitude lines convex toward the equator, detectable on the  GPS-Compatible Highway Maps by Alexis Publishing.   If we were to project DOMAINS back to the GLOBE, we would find that on the GLOBE, DOMAINS have horizontal boundaries which are curves concave toward the equator. In fact, if we were to project metric grid lines back to the GLOBE, we would find that on the GLOBE: projected horizontal metric grid lines are curves concave toward the equator within each ZONE and projected vertical metric grid lines are curves convex toward central meridians of ZONES.

It is of particular import to note that the horizontal boundaries of REGIONS projected onto the UTMAP are curves which are convex toward the equator and which are totally unrelated to the horizontal boundaries of DOMAINS or to any other metric grid lines.

The REGIONS which have been projected from the GLOBE to the UTMAP are totally incommensurable and incompatible with the UTM metric grid. The major flaw mentioned in Section 0, which was present in the original design of UTM and perpetuated in its derivative MGRS, is the forced use of REGIONS in the formation of addresses of locations, that is, in all the standard metric grid reference methods. The normalization which overcomes this major flaw is simplicity itself.

The complete normalization which we hereafter apply to both UTM and MGRS consists of normalizing ZONE numbers to the range 00 to 59 and using DOMAINS rather than REGIONS in the formation of addresses of locations. We give the normalization of the important UTM grid the name Normalized Universal Transverse Mercator or NUTM. But since we hold that MGRS should simply be discarded due to its obfuscatory replacement of numeric digits by letters within GPS addresses, we do not give its normalization a separate name. In my opinion, it is unfortunate that the  Public XY Mapping Project  has elected to base its proposed Standard for a United States National Grid for Spatial Addressing on the unnormalized MGRS grid. Part of the reason appears to be what the Project personnel claim to be the  Power of Truncated USNG Values  to yield unicity of truncated MGRS addresses over large areas. But it is made clear in Section 9 below, and by the displays to which Section 9 links, that there are many normalized grids which offer much greater areas of truncation unicity without any necessity to replace numeric digits by letters within GPS addresses.

The address of a location on the UTMAP expressed in a metric grid reference method must specify first the SIGNATURE of the method (which depends on the DATUM) and then must effectively specify the ZONE and HEMIsphere, and the easting and northing of the location within the HEMIsphere of the ZONE. Specification of the ZONE requires 2 alphanumeric characters, digits or otherwise. An easting with 1-meter precision requires 6 digits (or alphanumeric characters). A northing with 1-meter precision requires 7 digits (or alphanumeric characters). Already without specification of the hemisphere the number of alphanumeric characters required for an address totals 15, and that is the conventionally established maximum for GPS addresses of locations to 1-meter precision. To specify the hemisphere requires only a single bit of information which can either be combined with the high-order northing digit or be combined with the ZONE designation in a variety of ways, as we shall see below.

Thus the information needed for a complete metric grid reference method address takes the following general form

and in detail contains the following information

where the letters have the following meanings:

Clicking on the Civilian UTM Grid Reference System link within the Maps 101 webpage shows that the Natural Resources Canada organization presents its addresses in very nearly the above format, although the HEMIsphere information is missing since the addresses are restricted to the Northern Hemisphere. (See also the Military Grid Reference System link in Maps 101.)

It should now be noted that the ZONE-HEMI and the high-order northing digit  M  together constitute the designation of a DOMAIN.

In standard GPS Unit displays, the high-order northing digit is frequently retained even though it has already been incorporated into the ZONE-HEMI information to form the DOMAIN name and hence has become redundant unless the GPS Unit is to be used in conjunction with a metric grid map which lacks DOMAIN boundaries and names. Any map which purports to be a metric grid map must, of course, contain suitably spaced metric grid lines which are annotated with the high-order digits of their coordinates down to at least the kilometer level, which means at least 3 high-order easting digits and 4 high-order northing digits (inspect carefully the GPS-Compatible Highway Maps designed by Noel J. Hotchkiss and published by Alexis Publishing).

Let us consider then just those address formats in which the high-order northing digit has been incorporated into the ZONE-HEMI information in some way so as to form a designation of a DOMAIN. Such addresses take the form

Now our task is primarily one of deciding how to structure the DOMAIN information so that it not only uniquely determines each of the 1200 DOMAINS of the UTMAP but also has other desirable properties. The main desirable property of the DOMAIN is that it yield an address format which is highly comprehensible to humans. Since the standard UTM grid has been in use for many years, this property almost requires that any proposed new format be very similar in both form and function to that of standard UTM. A property which apparently the United States Military considers of importance is that of providing for truncated addresses which are unique over large areas. The address modifications applied in MGRS to attain unicity of truncated addresses over large areas make interpretation of those addresses essentially impossible when used with maps which lack the special MGRS notations, as we shall see below. This is the main reason I stated in Section 0 that use of truncated addresses by military personnel is likely to be risky, but beyond this reason there is always the possibility that a computed complete target address will lie outside the area of unicity of its truncated version. Hence although the exposition below shows several address formats which cater to the provision of truncated addresses having large areas of unicity, I place little importance in the ability of a grid to support truncated addresses. However, in the interest of completeness and to show what is possible, the exposition below presents several address formats which support truncation. Some have areas of unicity considerably larger than those of MGRS, one is an improved version of Normalized MGRS, and one provides the same area of unicity as MGRS without making addresses uninterpretable when used with maps lacking the special MGRS notations. We next define several specific address formats after introducing the concept of SQUARES.

Before moving to the definitions of specific address formats, we need to define the concept of the 100km SQUARES, both within NUTM and within MGRS.

Many GPS Units display location addresses essentially in the 2-level hierarchical form shown above and repeated here

SIGNATURE DOMAIN  H D K h d m  H D K h d m

Finding a location within a set of maps from an address in this form can be tedious since a DOMAIN is 1000km tall and may be more than 600km wide. Location searches are made easier if the search can be narrowed in stages. To that purpose, this website follows the lead of MGRS and transforms the above address form to the following 3-level hierarchical format

SIGNATURE DOMAIN  H H  D K h d m  D K h d m

The dual-numeral  H H  is composed of the high-order easting digit  H  and the (remaining) high-order northing digit  H  and hence designates a 100km-by-100km square area within the DOMAIN. The vertical and horizontal boundaries of the 100km square area are UTM grid lines whose coordinates are integer multiples of 100km. We give the name SQUARE to all such 100km square areas in the UTMAP. The remainder of the address, namely

D K h d m  D K h d m

designates a 1-meter square within the SQUARE. Each DOMAIN is 10 SQUARES tall, which implies that the northing index H  runs the full range from 0 through 9 in each DOMAIN. But the eastings within each DOMAIN span at most the range from about 166km to about 834km (see Section 4), which implies that the easting index  H  runs at most the range from 1 through 8. Thus the maximum array of SQUARES which can occur in a DOMAIN is the 8 by 10 array shown below.

1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0

If a UTMAP were to be clearly marked with no more than DOMAIN boundaries, DOMAIN designations, and SQUARE boundaries (the 100km metric grid lines), then a simple address having the form

SIGNATURE DOMAIN  H H  D K h d m  D K h d m

would be readily interpretable in that simple counting would lead to the specified SQUARE. If designations of the SQUARES were also shown, then address interpretation would be immediate. In either case, of course, some form of interpolation is required to locate within the SQUARE the position indicated by the remaining digits

D K h d m  D K h d m  of easting and northing.

Again, compare MGPG COLUMN 1 of the UTMAP [4 megabyte download] with the Cylindrical Mercator Projection and note that the Continental United States is covered by UTM ZONES 10-19 (NUTM/MGPG ZONES 09-18).

7. The MGRS 100km SQUARES within DOMAINS.

For reasons probably related to a desire to attain a large Area of Truncation Unicity (ATU), the United States Military decided to convert the NUTM dual-digit SQUARE designator  H H  to a systematically-patterned dual-letter SQUARE designator and to call the result its  Military Grid Reference System (MGRS) . The original unnormalized MGRS SQUARE-designator pattern is illustrated in a display of the northern hemispheric portions of the unnormalized ZONES numbered 07 through 12. The horizontal green lines indicate the approximate locations of curved REGION boundaries (projected latitude lines). The horizontal grey lines are straight DOMAIN boundaries (metric grid lines). The first letter of each dual-letter SQUARE designator is clearly a column designator, namely an easting element. The second letter of each dual-letter SQUARE designator is clearly a row designator, namely a northing element. The 3-ZONE cycle of 8 easting elements per cycle is evident, cleverly using 24 letters of the 26 letter alphabet. But the interesting aspect of the pattern is the 20-SQUARE (2-DOMAIN or 2000km) cycle length for the northing element, which is evident in both odd-numbered and even-numbered ZONES even though the concept of the DOMAIN is not present in the literature. Furthermore, there is no evident or conceivable relationship between the REGION boundaries and the 20-SQUARE cycle of the northing elements, which should have alerted any alert observer of MGRS that something was amiss. At the same time, the 20-SQUARE cycle of the northing elements should have been the only clue needed by an alert observer to redefine MGRS sensibly. The failure of professionals in the cartography field to recognize and correct either the minor flaw detailed in Section 2 or the major flaw detailed in Section 4 is surprising, but the failure of the United States Military to recognize and correct the major flaw even after it had introduced a 2000km vertical cycle into its own MGRS is truly astonishing. Many of my thoughts on these matters are chronicled in a sequence of emails sent during a brief period in SEP 2000, with the first indication of problem recognition occurring on 00.09.11 and the first step toward problem solution taken on 00.09.13.

To illustrate the incommensurability between UTM/MGRS REGIONS and the metric grid lines, I offer the following photograph of a portion of the New Mexico Road Map from Alexis Publishing which shows clearly the green (slightly) curved 32-degree latitude line passing through the town of Anthony TX/NM which lies almost in the middle of the UTM/MGRS SQUARE whose (NAD27MGRS) name CF and boundary lines are marked in purple. The reader is invited to  click here for the original full-size photograph  and to  click here for a display comparing NAD83MGRS with NAD83NUTM for this SQUARE.

Observe by clicking on this display that there is a 5-letter shift northward in the northing elements of odd-numbered ZONES ( TM8358.1 Section 3-3.3.2), but that there seems to be no stated or obvious reason why the shift should be northward rather than southward. The 10-letter shift mentioned in TM8358.1 Section 3-3.2 seems to be related to a change which was made in replacing an older MGRS-1 based on NAD27 with a newer MGRS-2 based on NAD83 (or WGS84) rather than to a vertical shift within either MGRS-1 or MGRS-2. (Incidentally, this 10-letter shift seems to have caused serious problems for certain professionals.) The 5-letter shift present in MGRS causes an asymmetry in the ATU, as can be seen in the following display. When one uses a 10-letter shift with a normalized MGRS one gets an improved symmetric ATU, as is shown both in terms of SQUARES and in terms of DOMAINS. MGRS yields an ATU of 2000km vertically and 3 ZONES horizontally. The normalized UTM, NUTM, yields an ATU of only 1000km vertically but 10 ZONES horizontally, and, for the ATU-obsessed, the Metric Global Positioning Grid (MGPG) defined below in Section 9  yields an ATU of 2000km vertically and 10 ZONES horizontally. All three of these grid reference methods are shown in a comparative display of DOMAIN names and nearest homonymous neighbors.

The forms that address truncations must take in order to attain the ATU values just quoted are shown for each grid.

8. Partitioning the UTMAP to Specify DOMAINS and Metric Grids.

From Section 1 and Section 6 we see that the sole remaining ingredient in the specification of metric grid reference methods and location addresses is the specification of DOMAIN names. In Section 4 we saw that the UTMAP comprises exactly 1200 DOMAINS which are arranged in a 60-by-20 array. Since specification of DOMAIN names in an orderly fashion depends on partitioning the 60-by-20 array in an orderly fashion, we now focus on ways to partition the array into COLUMNS of ZONES and ROWS of metric bands.

Using one of the many factorizations of the number 60, we can partition the array into several equi-sized COLUMNS by vertical cuts between ZONES. In a few cases it is convenient to consider separately the two HEMICOLUMNS into which each COLUMN can be cut at the equator. Each COLUMN (or HEMICOLUMN) is now named with a single character, either a digit or a letter, symbolized for this discussion by  C . Distinct COLUMNS must have distinct names.

Using one of the many factorizations of the number 20, we can partition the array into several equi-sized ROWS by horizontal cuts between metric bands. In a few cases, the ROWS at the two poles may be narrower than the rest. Each ROW is now named with a single character, either a digit or a letter, symbolized for this discussion by  R . Normally, distinct ROWS must have distinct names, but when used with HEMICOLUMNS, ROW names need be unique only within each hemisphere.

The following UTMAP display shows latitude bands and their names rather than metric bands and their names, and shows unnormalized ZONE numbers rather than normalized ZONE numbers, but even so it serves well for purposes of visualizing the concepts of COLUMNS, ROWS, and DOMAINS (the smallest rectangles on the UTMAP, called UTM Grid Zones).

The intersection of a COLUMN named  C  and a ROW named  R  is called a TRACT and the TRACT is named  C R . A TRACT thus has a horizontal width measured in ZONES and vertical height which is an integer multiple of 1000km. A TRACT must contain no more DOMAINS than can be named by a single character. The DOMAINS in a TRACT either must all have single digit names or must all have single letter names. This restriction limits the size of TRACTS to at most 24 (or possibly 25) DOMAINS. The single character name for a DOMAIN within a TRACT is symbolized for this discussion by  Z . This single character name is the TRACT-relative name for the DOMAIN. Depending on the grid being defined, the complete name of the DOMAIN is either  C R Z  or  C Z R . The ATU of a metric grid reference method other than the Military Grid Reference System is the distance from a given SQUARE to its nearest homonymous neighbors, both horizontally and vertically, namely the TRACT size. The ATU for the Military Grid Reference System is 3 ZONES horizontally by 2000km vertically.

The above specification of names to be used for DOMAINS will satisfy the primary requirement stated in Section 5 for address formats that they be highly comprehensible to humans. The secondary requirement stated in Section 5 for address formats is that they provide good ATU support for truncation. This requirement must be met in the definitions of specific metric grid reference methods other than the Military Grid Reference System by maximizing TRACT size, especially in the horizontal dimension since ZONES are narrow at the equator and become increasingly narrow toward the two poles.

Depending on the specific metric grid reference method being defined, a simple address having the general form

SIGNATURE DOMAIN  H H  D K h d m  D K h d m

either will be given the normal specific form

SIGNATURE  C R Z H H  D K h d m  D K h d m

or will be given the abnormal specific form

SIGNATURE  C Z R H H  D K h d m  D K h d m

In most metric grid reference methods, the SQUARE designator  H H  is a dual-digit designator.  In order to maximize TRACT size in this case, truncation of either of the two specific address forms above is defined to yield the following 13-character form

Z H H  D K h d m  D K h d m

in which the  Z H H  is referred to as a titled SQUARE designator.

The above truncated address can be used easily only in conjunction with normalized metric grid maps whose SQUARES are annotated with the three character  Z H H  titled-SQUARE designators.

In the Military Grid Reference System, however, the SQUARE designator  H H  of the normal specific form has already been converted to a dual-letter SQUARE designator and MGRS truncation is defined to yield the following 12-character form

H H  D K h d m  D K h d m

An MGRS address, whether truncated or not, can be used only in conjunction with metric grid maps whose SQUARES are annotated with the dual-letter  H H  titled-SQUARE designators.

9. Definition of Specific Metric Grid Reference Methods.

First, we list a few of the many possible normalized metric grid reference methods, giving a link to a detailed description of each method. For each method we give both a 3-numeral characterization of the UTMAP partitioning on which the method is based and a 4-character coding for the ATU of the method which can serve as an abbreviated name of the method, and we give the common name of the method if it has one. The 3-numeral characterization of the UTMAP partitioning on which the method is based shows the number of COLUMNS, the number of ROWS, and the number of DOMAINS per (full-size) TRACT. A few 3-numeral characterizations of methods contain letters rather than hyphens to indicate that the methods use the COLUMN index C , the ROW index R , and the DOMAIN index Z  to distinguish between southern and northern hemispheres, or to increase TRACT size. The 4-character coding for the ATU takes the form  zzZd , which signifies that the size of the ATU is  zz  ZONES horizontally by  d  DOMAINS vertically. The number of DOMAINS per (full-size) TRACT is thus  zz x d . A few normalized metric grid reference methods have TRACTS whose vertical dimensions cause the polar TRACTS to be less than full-size, for example,  04Z6 [15-04-24]. When MGRS is used with the normal 12-character truncation its ATU is  03  ZONES horizontally by  2  DOMAINS vertically, whereas if MGRS were to be used with the 13-character truncation its ATU would be  10  ZONES horizontally by  2  DOMAINS vertically. With the sole exception of MGRS, all normalized metric grid reference methods are assumed to be used with 13-character truncation. While NUTM is presented on this website as the preferred metric grid reference method, the three additional grids 10A1, 10B1, and 10C1 are presented as variations of NUTM in which addresses for locations in the Northern Hemisphere are purely numerical and addresses for locations in the Southern Hemisphere make only minimal use of letter sequences.

Second, we illustrate use of various grid reference methods by displaying the GPS address of South Astro in Joshua Tree National Park in several forms of each of the methods.

PARTIAL LIST OF NORMALIZED METRIC GRID REFERENCE METHODS

special methods

[06-20-10]     03Z2    MGRS (Normalized MGRS - 12-character truncation)

[06-20-10]     10Z2    MGRS (Normalized MGRS - 13-character truncation)

[06-20-10]     10Z1    NUTM (Normalized UTM)

[06-10-20]     10Z2    MGPG (Metric Global Positioning Grid)

general methods

[03-20-20]     20Z1         (constructible but probably not useful)

[04-20-15]     15Z1         (constructible but probably not useful)

[05-20-12]     12Z1         (metric grid reference method)

[05T20A24]     12A2         (metric grid reference method)

[05T20B24]     12B2         (metric grid reference method)

[05T20C24]     12C2         (metric grid reference method)

[05H10A12]     12A1         (metric grid reference method)

[05H10B12]     12B1         (metric grid reference method)

[05H10C12]     12C1         (metric grid reference method)

[05-10-24]     12Z2         (metric grid reference method - superior to MGRS)

[06-20-10]     10Z1    NUTM (Normalized UTM)

[06H10A10]     10A1         (metric grid reference method)

[06H10B10]     10B1         (metric grid reference method)

[06H10C10]     10C1         (metric grid reference method)

[06-10-20]     10Z2    MGPG (Metric Global Positioning Grid)

[10-20-06]     06Z1         (metric grid reference method)

[10-10-12]     06Z2         (metric grid reference method - superior to MGRS)

[10T06A24]     06A4         (metric grid reference method - superior to MGRS)

[10T06B24]     06B4         (metric grid reference method - superior to MGRS)

[10T06C24]     06C4         (metric grid reference method - superior to MGRS)

[10-05-24]     06Z4         (metric grid reference method - superior to MGRS)

[12-20-05]     05Z1         (metric grid reference method)

[12-10-10]     05Z2         (metric grid reference method - superior to MGRS)

[12-05-20]     05Z4         (metric grid reference method - superior to MGRS)

[12-04-25]     05Z5         (metric grid reference method - superior to MGRS)

[15-20-04]     04Z1         (metric grid reference method)

[15-10-08]     04Z2         (metric grid reference method - superior to MGRS)

[15-05-16]     04Z4         (metric grid reference method - superior to MGRS)

[15-04-20]     04Z5         (metric grid reference method - superior to MGRS)

[15-04-24]     04Z6         (metric grid reference method - superior to MGRS)

[20-20-03]     03Z1         (metric grid reference method)

[20-10-06]     03Z2         (metric grid reference method)

[20-05-12]     03Z4         (metric grid reference method - superior to MGRS)

[20-04-15]     03Z5         (metric grid reference method - superior to MGRS)

[20-04-24]     03Z8         (metric grid reference method - superior to MGRS)

GPS ADDRESS OF SOUTH ASTRO IN SEVERAL OF THE METRIC GRID REFERENCE METHODS

All maps for use with unnormalized metric grid methods are assumed to display UTM REGION boundaries and names.
All maps for use with normalized metric grid methods are assumed to display grid DOMAIN boundaries and names.
All maps for use with metric grid methods are assumed to display metric grid lines with coordinates.

The Unnormalized UTM address
is
NAD83-UTM  1 1 S  5 7 8 7 1 3  3 7 6 6 7 4 8  (16 characters, high-order northing digit  3  redundant)
or
NAD83-UTM  1 1 S  5 7 8 7 1 3  7 6 6 7 4 8
or
NAD83-UTM  1 1 S 5 7  7 8 7 1 3  6 6 7 4 8


The Unnormalized MGRS address (which is uninterpretible without MGRS SQUARE designations on the map)
is
NAD83MGRS  1 1 S N T  7 8 7 1 3  6 6 7 4 8
and
NAD83MGRS      N T  7 8 7 1 3  6 6 7 4 8
is
the (rather pointless) 12-character truncated form (which also is uninterpretible without MGRS SQUARE designations on the map).


The Normalized MGRS address (which is uninterpretible without MGRS SQUARE designations on the map)
is
NAD83MGRS  1 0 R N T  7 8 7 1 3  6 6 7 4 8
and
NAD83MGRS      N T  7 8 7 1 3  6 6 7 4 8
is
the (rather pointless) 12-character truncated form (which also is uninterpretible without MGRS SQUARE designations on the map).


The Normalized NUTM address   [06-20-10]  (the map must carry NUTM DOMAIN names),
is
NAD83NUTM  1 0 R  5 7 8 7 1 3  3 7 6 6 7 4 8  (16 characters, high-order northing digit  3  redundant)
or
NAD83NUTM  1 0 R  5 7 8 7 1 3  7 6 6 7 4 8
or
NAD83NUTM  1 0 R 5 7  7 8 7 1 3  6 6 7 4 8
and
NAD83NUTM    0 5 7  7 8 7 1 3  6 6 7 4 8
is
the (rather pointless) 13-character abnormal truncated form (the map should also carry NUTM titled SQUARE designators).


The Normalized MGPG address   [06-10-20]  (the map must carry MGPG DOMAIN names),
is
NAD83MGPG  1 6 N  5 7 8 7 1 3  3 7 6 6 7 4 8  (16 characters, high-order northing digit  3  redundant)
or
NAD83MGPG  1 6 N  5 7 8 7 1 3  7 6 6 7 4 8
or
NAD83MGPG  1 6 N 5 7  7 8 7 1 3  6 6 7 4 8
and
NAD83MGPG    N 5 7  7 8 7 1 3  6 6 7 4 8
is
the (rather pointless) 13-character normal truncated form (the map should also carry MGPG titled SQUARE designators).


The Normalized 06Z4 address   [10-05-24]  (the map must carry 06Z4 DOMAIN names),
is
NAD8306Z4  1 3 S  5 7 8 7 1 3  3 7 6 6 7 4 8  (16 characters, high-order northing digit  3  redundant)
or
NAD8306Z4  1 3 S  5 7 8 7 1 3  7 6 6 7 4 8
or
NAD8306Z4  1 3 S 5 7  7 8 7 1 3  6 6 7 4 8
and
NAD8306Z4    S 5 7  7 8 7 1 3  6 6 7 4 8
is
the (rather pointless) 13-character normal truncated form (the map should also carry 06Z4 titled SQUARE designators).


The reader is invited to compare these addresses in the   NUTM versus MGRS  and  MGPG versus MGRS displays.

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