ABSTRACT

This website makes available to the dedicated enthusiast of Joshua Tree National Park large displays of 1-meter resolution and 2-meter resolution aerial photographs and topographic maps. The data for these displays were acquired through the MicroSoft TerraServer (MSTS) facility from the United States Geological Survey (USGS). MSTS and USGS have collaborated to provide a huge data bank of picture elements called "tiles", whose boundaries coincide with grid lines of the Universal Transverse Mercator (UTM) Global Positioning System (GPS). GPS units (receivers) and GPS-compatible maps are very useful for situations where accurate knowledge of location is required, including driving, hiking, and climbing. UTM, MGRS, and UGPS, three standard GPS grid reference methods which employ latitude measurements incommensurably with metric measurements, are briefly discussed. Proposals are presented for purely metric normalizations of UTM (NUTM) and of MGRS, and for a spectrum of new purely Metric Global Positioning Grids (MGPG) including specifically the  Metric Grid Reference Window (MGRW) facility which is superior to MGRS  in providing unicity of truncated addresses over large areas when used with large scale customized MGPG maps. Over a background showing the  Cylindrical Mercator Projection  of the world, a display of one third of the  NUTMAP (Normalized UTM Map) provides a graphic visualization of the NUTMAP and the incommensurability of latitude measurements with metric measurements. The thick horizontal  green  lines indicate the approximate locations of those curved  latitude lines at multiples of 8-degrees which form the horizontal boundaries of the UTM/MGRS  Grid Zones (or REGIONS) while the thin horizontal  red  lines indicate the exact locations of the  metric grid lines at multiples of 1000 kilometers  which form the straight horizontal boundaries of metric DOMAINS. A list of  Global Positioning System references  is provided. Dale dePriest  provides an excellent description of  How Your GPS Works. Attention is called to certain GPS units, GPS-compatible maps, and digital cameras.  The website contains many links as well as a copious supply of GOOGLE search engine windows for general inquiries.

MGRS replaces a pair of UTM digits by a pair of letters in order to provide high-order truncated addresses which have large areas of unicity, and its use by the United States Armed Forces was directed by the  Joint Chiefs of Staff in 1949 (email - click refresh). An associated display shows clearly that  MGRW Case #2 windows can provide a separation between homonymous neighbors (repeats) of truncated addresses which is twice as great as that provided by  MGRS  without the replacement of digits by letters and at a cost of only one additional character in the truncated address.

The Customized Metric Grid Reference Window Facility provides rectangular windows of various sizes and shapes through which restricted areas of the globe can be viewed and locations within those areas can be uniquely addressed by means of truncated addresses. The boundaries of the rectangles are metric grid lines which serve as boundaries of DOMAINS (or of SQUARES). The two smallest window sizes are the single SQUARE and the single DOMAIN; all other windows comprise sets of DOMAINS, up to and including the entire globe. The proposed Window Facility is graphically illustrated by means of a  display  showing the entire 60 by 20 array of 1200 metric DOMAINS which are all 1000 kilometers tall (except for the south polar and north polar DOMAINS which are only about 985 kilometers tall). It is to be noted that latitude lines and even the very concept of latitude play no role in the Customized Metric Grid Reference Window Facility since it is my observation and considered opinion that the concept of latitude is antithetical to good metric gridding. Graphic illustration of the total non-relatedness of latitude bands and metric bands is provided by Andrew and Wesley in a display of NE USA and in the three leftmost columns of Table 1 and Table 3,  by displays for Anthony TX-NM and Joshua Tree National Park,  and by a Normalized UTM Map (NUTMAP) display. A template is provided for the contruction of Windows (download cust_wind.doc).

The Customized Metric Grid Reference Window Facility supports 5 different sizes of Reference Window through which restricted areas of the globe may be viewed, and corresponding forms of truncated addresses for locations within those restricted areas. Here, the term truncated address means high-order or left-end truncation, which clearly has the effect of limiting the area throughout which the address remains valid without having any effect on the precision or resolution of the address. All character-lengths of truncated addresses are quoted for 1-meter resolution addresses. In practice, of course, low-order or right-end truncations are regularly used when shorter addresses are desired and reduced precision is tolerable or desirable, but we do not here consider such low-order truncations.

In an email I received at UTC-7 2001.10.14.0809,  Tom Terry of the USNG  (United States National Grid)  effectively stated that the US Military (designed MGRS as a modification of UTM in 1947 and) adopted the MGRS modification of UTM in 1949 in order not only to allow control over the precision of addresses by low-order (right-end) truncations and 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 addresses. 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, it should be noted that MGRW Case #2 constitutes  a two-character truncation which can provide a considerable improvement over MGRS without replacing dual-digits by dual-letters.

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

and in detail contains the following information

where the SIGNATURE is the concatenation of the DATUM and the GRID and the letters have the following meanings:

blue : letters constitute easting
red  : letters constitute northing
m    : means meter
d    : means decameter
h    : means hectometer
K    : means Kilometer
D    : means Decakilometer
H    : means Hectokilometer     (100 km) - this is the 100km SQUARE digit
M    : means Megameter         (1000 km) - this is the high-order northing digit

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

Before moving on to the definitions of various size windows and the corresponding forms of DOMAIN names and truncated addresses, we need to define the concept of the 100km SQUARES in NUTM.

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

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

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

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.

The   5 7  SQUARE above which is marked in this color is the location of South Astro Dome in Joshua Tree National Park, whose full 15_character Normalized NUTM address is

NAD83NUTM  1 0 R 5 7  7 8 7 1 3  6 6 7 4 8

Now we list the 5 different sizes of Reference Window provided by the Customized Metric Grid Reference Window Facility in order from the largest window size #4 (longest address) to the smallest window size #0 (shortest address), using the address of South Astro Dome as an example.

In case  2  above, the  ?  denotes a DOMAIN designation letter which depends on the particular Case #2 window used.

In what follows,  D  denotes a  DOMAIN  while  SQ  denotes a  SQUARE. Except for Case #0 windows, the name given just below for a window is a DOMAIN name pair consisting of the names of the DOMAINS at the SW and NE corners of the window so that the window can be thought of as extending from the first named DOMAIN to the second named DOMAIN. The reader can easily compare the stated window names (made into links) with the actual windows shown below in the display.

In case  0  , the single-SQUARE window 57 which contains South Astro Dome is named  D10R  SQ57.

In case  1  , the single-DOMAIN window 10R which contains South Astro Dome is named  D10R  D10R.

In case  2  , the 24-DOMAIN window colored blue-green which covers Chile, Peru, and Equador is named  D16F  D18N.

In case  2  , the 24-DOMAIN window colored blue-green which covers the Mediterranean Area is named  D29R  D36T.

In case  2  , the 24-DOMAIN window colored blue-green which covers Afghanistan and Neighbors is named  D37P  D42S.

An associated display shows clearly that MGRW Case #2 windows can provide a separation between homonymous neighbors (repeats) of truncated addresses which is twice as great as that provided by MGRS. The yellow RECTANGLES on the left denote the DOMAINS containing repeats of the MGRS truncated address for South Astro, while the yellow RECTANGLES on the right denote the DOMAINS containing repeats of the MGRW Case #2 truncated address for the city of Kabul in Afghanistan.

In case  3  , the 40-DOMAIN window colored yellow which covers the United States is named  D09Q  D18T.

In case  3  , the 06-DOMAIN window colored yellow which covers Madagascar is named  D37J  D38L.

It should be evident from the yellow windows in the display below that Case #3 windows can be as small as desired, and can be as large as desired subject only to the condition that they not exceed 24 ZONES in width (due to the limit posed by the availability of only 24 useable capital letters). We note also that in Case #3 windows the DOMAINS are designated by dual-letter two dimensional coordinates in which the second (vertical) coordinate is purposely made to be the normalized NUTM Metric Band Designator (much like the unnormalized UTM/MGRS Grid Zone Designator ). The first (horizontal) coordinate is in effect the sole parameter of the window - the ZONE in which the letter  A  occurs is the westernmost boundary of the window. A given Case #3 window can be extended as far south or north as desired, and can be extended toward the east until the set of 24 allowable capital letters is exhausted.

In case  3  , the 48-DOMAIN window colored yellow which covers the Bering Sea Area is named  D55T  D06W.

Note that this particular window shows the desirability of numbering the ZONES from 00 to 59 rather than from 01 to 60 as is currently done in UTM and its derivative MGRS. The Europeans and the United States Military have been smart enough to use a 24_hour time system which rolls over from 2359 hours to 0000 hours (rather than to 2460), and the Babylonians were well aware that in their sexagesimal number system numbers should roll over from 59 to 00 (although they lacked a symbol for 0). Even in the ridiculous 12_hour time system used in the civilian world of the United States, the hours are correctly named except for the anomolous 12 (noon or midnight) which should have been 00. Under these circumstances it is a mystery to me why the cartographic community has retained the current numbering of ZONES from 01 to 60 for some 65 years. Rolling over from ZONE 60 to ZONE 01 in an eastward crossing of the International Date Line does not seem particularly rational whereas rolling over from ZONE 59 to ZONE 00 certainly would.

In all five Cases of MGRW listed in Section 3, the addresses effectively constitute a hierarchy of two dimensional coordinates of successively nested (mostly) rectangular areas, and the purpose of this Section is to illustrate that point clearly. The vertical edges of each DOMAIN are curved longitude lines, and SQUARES adjacent to those edges share those curved edges, but otherwise both DOMAINS and SQUARES are rectangular since they are bounded by metric grid lines.

The Case #4 address of South Astro Dome given in Section 3 above is repeated below followed by its more detailed clarifying rendition.

NAD83NUTM  1 0 R 5 7  7 8 7 1 3  6 6 7 4 8

NAD83NUTM   [ 1 0 , R ]   [ 5 , 7 ]   [ 7 8 7 1 3 , 6 6 7 4 8 ]

This address is actually a 3-level hierarchical address which is effectively composed of the two dimensional coordinate pair  [10,R]  designating the DOMAIN having the globally absolute designation  10R  followed by the two dimensional coordinate pair  [5,7]  designating the SQUARE  57  nested within the DOMAIN  10R  followed by the two dimensional coordinate pair  [78713,66748]  designating a 1-meter square area within the SQUARE  57 .

The Case #3 address of South Astro Dome given in Section 3 above is repeated below followed by its more detailed clarifying rendition.

NAD83NUTM    B R 5 7  7 8 7 1 3  6 6 7 4 8

NAD83NUTM   [ B , R ]   [ 5 , 7 ]   [ 7 8 7 1 3 , 6 6 7 4 8 ]

This address is actually a 3-level hierarchical address which is effectively composed of the two dimensional coordinate pair  [B,R]  designating the DOMAIN having the window relative designation  BR  followed by the two dimensional coordinate pair  [5,7]  designating the SQUARE  57  nested within the DOMAIN  BR  followed by the two dimensional coordinate pair  [78713,66748]  designating a 1-meter square area within the SQUARE  57 .

The Case #2 address of South Astro Dome given in Section 3 above is repeated below followed by its more detailed clarifying rendition.

NAD83NUTM      ? 5 7  7 8 7 1 3  6 6 7 4 8

NAD83NUTM   [ ? ]   [ 5 , 7 ]   [ 7 8 7 1 3 , 6 6 7 4 8 ]

This address is actually a 3-level hierarchical address which is effectively composed of the one (!) dimensional coordinate  [?]  designating the DOMAIN having the window relative designation  ?  followed by the two dimensional coordinate pair  [5,7]  designating the SQUARE  57  nested within the DOMAIN  ?  followed by the two dimensional coordinate pair  [78713,66748]  designating a 1-meter square area within the SQUARE  57 .

The Case #1 address of South Astro Dome given in Section 3 above is repeated below followed by its more detailed clarifying rendition.

NAD83NUTM        5 7  7 8 7 1 3  6 6 7 4 8

NAD83NUTM   [ 5 , 7 ]   [ 7 8 7 1 3 , 6 6 7 4 8 ]

This address is actually a 2-level hierarchical address relative to an unspecified DOMAIN which is effectively composed of the two dimensional coordinate pair  [5,7]  designating the SQUARE  57  nested within the unspecified DOMAIN followed by the two dimensional coordinate pair  [78713,66748]  designating a 1-meter square area within the SQUARE  57 .

The Case #0 address of South Astro Dome given in Section 3 above is repeated below followed by its more detailed clarifying rendition.

NAD83NUTM            7 8 7 1 3  6 6 7 4 8

NAD83NUTM   [ 7 8 7 1 3 , 6 6 7 4 8 ]

This address is actually a 1-level non-hierarchical address relative to an unspecified SQUARE within an unspecified DOMAIN which is effectively composed of the two dimensional coordinate pair  [78713,66748]  designating a 1-meter square area within the unspecified SQUARE.

The presumption being made for use of this windowing facility is that Window Map Sets and GPS units can be designed and produced with the following properties. For any given (legitimate) two-component window specification (for example, D10R SQ57  or  D10R D10R  or  D16F D18N  or  D37P D42S  or  D09Q D18T), a Window Map Set meeting the window specification can be generated and produced, the GPS unit can be loaded with the window specification and determine to which of the five levels the window belongs, and then the GPS unit can generate addresses in the correct format for the window specification to be interpreted relative to the Map Set. Clearly, the main customization required of Map Sets is the naming of DOMAINS with mono-letter names or with dual-letter names or with full three-character NUTM names.