The modified transverse Mercator (MTM) coordinate system is a metric grid-based method of specifying geographic locations, similar to the Universal Transverse Mercator coordinate system (UTM). However, MTM uses a transverse Mercator projection with zones spaced 3° of longitude apart, one half of the spacing of UTM zones, to further reduce distortion.
Properties Like any Mercator projection, MTM is a conformal map projection, so angles at any point, and the shape of small areas, are true. However, scale varies slightly by longitude. Due to its narrower zones, the scale factor for MTM varies less than for UTM. This allows the MTM scale factor to be set to 0.9999 (distortion of 1:10,000) in the midpoint of a zone, versus 0.9996 (1:2,500) for UTM. Like UTM, the direction of true north is not perfect grid north away from each zone's central meridian, i.e. non-central meridians are slightly curved. The deviation between grid and true north is called the angle of convergence, and is roughly proportional to the east-west (longitudinal) distance away from the central meridian, and the sine of the latitude. This deviation can be on the order of 1° in temperate latitudes and so needs to be taken into account.
Usage The MTM coordinate system is used by various government institutions in Canada in particular, especially from Ontario through to the Maritimes. Canada is covered by 32 zones, generally following the canonical 3° longitude spacing, with an adjustment in the urban area around Toronto and slight zone expansion at the east and west edges of Nova Scotia.
The province of Alberta refers to MTM as 3TM (3 degree transverse Mercator) and uses 4 zones to cover the province. MTM is more suitable than UTM for parametrizing and displaying cadastral surveys, since grid distances (calculated from MTM coordinates) differ less from ground measurements. Just like UTM, MTM eastings (X coordinates) do not align across zone boundaries, so a given map needs to be displayed wholly in one MTM zone. However, the distortion from using a given MTM zone's projection slightly outside its intended 3°-wide area is minimal, so slight mapping excursions outside the zone area are tolerated. Nevertheless, for large-scale maps, such as of a whole Province or all of Canada, or for far north areas, MTM is not suitable and different map projections need to be used. MTM is conceptually similar to the Gauss-Kruger coordinate system historically used in parts of continental Europe, even though the parameters (and scale factor) are different.
Mathematical formulae Coming from the same family of projections, conversion between latitude and longitude and MTM coordinates uses the same mathematical formulae as those for UTM. However, the parameters (in the same notation) are adapted as below for the different zone configuration.
The central meridians λ 0 {\displaystyle \lambda _{0}} reflect the 3° spacing. The central meridian scale factor k 0 = 0.9999 {\displaystyle k_{0}=0.9999} . The false easting E 0 = 304800 {\displaystyle E_{0}=304800} m by convention, rather than E 0 = 500000 {\displaystyle E_{0}=500000} m for UTM. Note, however, that Alberta uses 0 for 3TM. The false northing N 0 {\displaystyle N_{0}} remains 0 as for UTM. However, a given geographical point's northing (Y coordinate) is in general slightly different in UTM and MTM since λ 0 {\displaystyle \lambda _{0}} and k 0 {\displaystyle k_{0}} are not the same.
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