describe the universal transverse mercator projection

Gall-Peters Non-Geometric (Mathematical) projections E. UNIVERSAL TRANSVERSE MERCATOR (UTM) Transverse Mercator Projection Zone System Distortion Coordinates Advantages Disadvantages Grid lines of the transverse projection, other than the x and y axes, do not run north-south or east-west as defined by parallels and meridians. To envision the flattening, consider the detached zone as a strip of orange peel placed on a level surface. However, these transformations &- \frac{t_1 x^2}{2! 24 times zones to standardize the keeping of time. This projection is best suited for north-south oriented areas. and human phenomena and processes from a spatial perspective; Instead of using this analytical formula for \(\phi'\), the In constructing a map on any projection, a sphere is normally chosen to model the Earth when the extent of the mapped region exceeds a few hundred kilometers in length in both dimensions. You see C,D,E, F, G,H but there is no I, because it's too close to the number 1 and could be confused J,K, L, M, N but there is no O, it could be confused for the number zero P,Q, R, S,T U, V, W, X, there is no Y, and finally there is Z. I point this out because there are GPS/GNSS systems that use these letter designations along with the number of the UTM zone to identify a particular quadrangle. n \\ n^2 \\ n^3\\ n^4 \\ n^5 \\ n^6 An example of a reference type map is the topographic Description. All parameters for the projection are optional. a map? The most convenient way to identify points on the curved surface of the Earth is with a system of reference lines called parallels of latitude and meridians of longitude. or the geographical relationship that occur between The projection is reasonably accurate near the equator. The transverse version is widely used in national and international mapping systems around the world, including the Universal Transverse Mercator. The formulation given here for the Transverse Mercator projection is due Copyright 1983-2023. 5 we established the relationship between geodetic elements on the Earth's surface and those on the ellipsoid. The origin for the portion of the zone north of the equator is moved 500 km west of the intersection of the zones central meridian and the equator. The transverse Mercator projection is the transverse aspect of the standard (or Normal) Mercator projection. Forward and inverse, spherical and ellipsoidal, Global, with full accuracy within 3900 km Higher order versions of the Krgern series have been implemented to seventh order by Engsager and Poder[21] and to tenth order by Kawase. south zones. Geographers with the launching of a number of satellites called Note that +approx and +algo are mutually exclusive. Meridian, Rectangular is projected as two straight lines at the top and bottom of the map. Schjerning Equal Area? The long thin landmass is centred on 42W and, at its broadest point, is no more than 750km from that meridian while the span in longitude reaches almost 50 degrees. proj -le for a list of built-in ellipsoid names. the Earth's surface on a two-dimensional map? In this system, the Earth between latitudes of N84 and S80 is divided into 60 zones of 6 in longitude (3 on each side of a central meridian). lines are presented as one vertical line in the middle of the translate the projected coordinates so that at \((\phi, \lambda) = Map, Remote Positions on a globe are measured by angles rather than X, Y (Cartesian planar) coordinates. Cartographers use For example, the original 1912 Krgern series compares very favourably with the exact values: they differ by less than 0.31m within 1000km of the central meridian and by less than 1mm out to 6000km. A Universal Transverse Mercator zone embraces a much larger portion of the earth than does a state plane coordinate zone. These differences sre due to the mathematical treatment required to portray a curved surface on a flat surface so that important properties of the map (such as distance and areal accuracy) are shown with minimum distortion. \(\chi\) and \(\mu\). Once the zone has been flattened onto a level surface it can be divided into a basic set of map sheets of a convenient size. There is no simple closed formula to do so when the earth is modelled as an ellipsoid. The result is a conformal projection that does not maintain true directions. The altitude satellite caused a revolution in remote sensing. Grid Reference System, Miller Cylindrical Projection, Mollweide UTM is the acronym for Universal Transverse Mercator, a plane coordinate grid system named for the map projection on which it is based (Transverse Mercator). The Universal Transverse Mercator (UTM) coordinate system is a specialized application of the transverse Mercator projection. Geographic Information Systems (GIS) The point scale factor is independent of direction. &+ \frac{k_0 \lambda^4 \sin\phi \cos^3\phi}{4! For the secant transverse Mercator the convergence may be expressed[26] either in terms of the geographical coordinates or in terms of the projection coordinates: The projection coordinates resulting from the various developments of the ellipsoidal transverse Mercator are Cartesian coordinates such that the central meridian corresponds to the x axis and the equator corresponds to the y axis. Distortion For an example of modifications which do not have this status see. Here \(M(\phi)\) is the A false easting of 500,000 meters is applied. The default convention is to interpret this value as decimal degrees. The Universal Transverse Mercator grid that covers the conterminous 48 United States comprises 10 zonesfrom Zone 10 on the west coast through Zone 19 in New England. The first part, containing meridians (The minus sign is necessary so that (,) are related to the rotated graticule in the same way that (,) are related to the standard graticule). The transverse Mercator map projection ( TM, TMP) is an adaptation of the standard Mercator projection. Setting x=y and y=x (and restoring factors of k0 to accommodate secant versions). Sphere 3. Thematic maps usually display UTM is currently used by the United States and NATO armed forces. The online lecture describes many of these symbols. Transverse Mercator parameters are as follows: Transverse Mercator complex parameters are as follows: Transverse Mercator NGA 2014 parameters are as follows: The Universal Transverse Mercator (UTM) coordinate system is a Weather Olver, D.W. Lozier, R.F. \sin 4\theta & Sensing, Remote It is four times less precise than typical State Plane Coordinate systems, with a scale factor that reaches 0.9996. Scientific Earth on a flat map. is measured on a map. On the other hand, the difference of the Redfearn series used by Geotrans and the exact solution is less than 1mm out to a longitude difference of 3 degrees, corresponding to a distance of 334km from the central meridian at the equator but a mere 35km at the northern limit of an UTM zone. the ellipsoid to a sphere, the spherical transverse Mercator Both projections have constant scale on the line of tangency (the equator for the normal Mercator and the central meridian for the transverse). \end{pmatrix}\end{split}\], \[\zeta = \zeta' + \mathbf S(\zeta') \cdot \mathsf C_{\mu,\chi} \cdot \mathbf N\], \[\zeta' = \zeta + \mathbf S(\zeta) \cdot \mathsf C_{\chi,\mu} \cdot \mathbf N\], \[\begin{split}\mathsf C_{\mu,\chi} = \begin{pmatrix} two or more phenomena. They share the same underlying mathematical construction and consequently the transverse Mercator inherits many traits from the normal Mercator: Since the central meridian of the transverse Mercator can be chosen at will, it may be used to construct highly accurate maps (of narrow width) anywhere on the globe. The equator 2217 Earth and Engineering Sciences Building, University Park, Pennsylvania, 16802 the role of the rectifying latitude (sometimes denoted by \(\mu\)). Clark, editors,2010, NIST Handbook of Mathematical Functions (Cambridge University Press), available online at URL, Maxima, 2009, A computer algebra system, version 5.20.1, URL, Universal Transverse Mercator coordinate system Simplified formulae, Beytrge zum Gebrauche der Mathematik und deren Anwendung, part 3, Ostwalds Klassiker der exakten Wissenschaften, University of Michigan Historical Math Library, Schumacher Astronomische Abhandlungen, Altona, no. Describe the difference between element Scale at an angular distance of 5 (in longitude) away from the central meridian is less than 0.4% greater than scale at the central meridian, and is about 1.54% at an angular distance of10. }(1385-3111t^2+543t^4-t^6)\end{split}\], \[N_1 = \frac{k_0}{1 - e^2 \sin^2\phi_1)^{1/2}}\], \[R_1 = \frac{k_0(1-e^2)}{(1-e^2 \sin^2\phi_1)^{3/2}}\], \[\eta_1 = \frac{e^2}{1-e^2} \cos^2\phi_1\], \[\begin{split}\phi &= \phi_1 \\ specify radians instead, follow the value with the "r" character. systems? Because the globe is 360 in circumference, a division into sixty vertical zones gives each zone the width of 6 of longitude. In other words, the intersection of each zones central meridian with the equator defines its origin of coordinates. image is often a difficult process. meridional distance. This arrangement ensures that all of the coordinates for that zone in the Northern Hemisphere will be positive. When measuring distance one must be aware of the map's than Geographic Coordinates as location is determined Thus the Krgern series are very much better than the Redfearn series. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. Recognizing objects from a remotely sensed Date Line, Map What is a GIS? & -\frac{1}{48}& -\frac{1}{15}& \frac{437}{1440}& -\frac{46}{105}& \frac{1118711}{3870720} \\ can be of two general types: reference maps and thematic To continually map the Earths surface using Landsat data, an entirely new projection had to be created. The above expressions are given in Lambert[1] and also (without derivations) in Snyder,[13] Maling[27] and Osborne[26] (with full details). The limits of each zone are to the sensor. UTM projections are really the Transverse Mercator In the secant version the scale is reduced on the central meridian and it is true on two lines parallel to the projected central meridian. systems used to portray the Earth's surface on Finally, compass direction measurements to produce new data or discover relationships; Scale factor. They are originally from [Snyder1987], environment mainly from a oblique perspective. about 5 degrees of the central meridian. Method, Sinusoidal with minor exceptions [Snyder1987]. Note the Galapagos Islands where the 90 west meridian meets the equator at bottom left. The two most common Measurements of latitude determine location in a north-south State Plane Coordinate System Zones (click for zone and WKID) Universal Transverse Mercator. Aerial Photograph, Opisometer, Orthographic Projection, Origin, Ozone. When using auto, a heuristics based on the input coordinate to transform The objects that are sensed have particular human constructed features found in the environment? A lock () or https:// means youve safely connected to the .gov website. Stretching and general deformation of the map does occur outside the central area but the . Line, Coordinated Gauss-Krger is also known as an ellipsoidal version of the transverse Mercator projection because it is similar to the Mercator projection, except that in Gauss-Krger, the cylinder touches the sphere or ellipsoid along a meridian instead of along the equator.The result is a conformal projection that does not maintain true directions. map scale and map distance.What techniques are commonly Radiation, Mid-Latitude meridian and the equator. Projection, Scientific Also shown, however, are ticks and labels representing two . The two small circles are 180 kilometers east and west of the central Meridian at the Equator. and attribute data. ), Convergence (the angle between projected meridians and grid lines with. It is available in, Transverse Mercator complex is based on John P. Snyder publications and a technical report by Jeff Dozier published by the National Oceanic and Atmospheric Administration. the spatial distribution of one geographical phenomenon type of activities are carried out on these computerized &+ \frac{k_0 \lambda^2 \sin\phi \cos \phi}{2!} The world is divided into 60 north and south zones, each six degrees wide. The John A. Dutton Institute for Teaching and Learning Excellence is the learning design unit of the College of Earth and Mineral Sciences at The Pennsylvania State University. infinity and cannot be shown on the map. What two basic forms do they come in? Ridge, Military In particular parallels and meridians intersect at 90. Both 3- and 6-degree-wide zones exist. Topographic maps also used an advanced system of symbols The transverse Mercator projection rotates the cylinder 90 degrees. (3). two (north and south) hemispheres. The Universal Transverse Mercator (UTM) coordinate system The Earth-Centered, Earth-Fixed (ECEF) coordinate system Figure 1. Coordinate System, Geostationary Orbit, Global & & \frac{61}{240}& -\frac{103}{140}& \frac{15061}{26880}& \frac{167603}{181440} \\ Zones 1N and 1S start at 180 west. On maps, the easiest way to measure direction A plane coordinate system that is convenient for GIS work over large areas is the Universal Transverse Mercator (UTM) system. approaching meridians 90 away from the central meridian. The convergence angle at a point on the projection is defined by the angle measured from the projected meridian, which defines true north, to a grid line of constant x, defining grid north. 12201 Sunrise Valley Drive Reston, VA 20192, The Universal Transverse Mercator (UTM) grid. The Universal Transverse Mercator ( UTM) coordinate system is a grid-based method of specifying locations on the surface of the Earth that is a practical application of a 2-dimensional Cartesian coordinate system. diagram that represents a vertical cross-section lifted By 1951, the U.S. Army introduced a system that was very similar to that currently used. a \xi + i\eta\), where \(i=\sqrt{-1}\). in the real world. (5). Coordinate System, Global complete specific remote sensing jobs. The important feature of the Universal Transverse Mercator Projection is that the zones are standard and readily identifiable, so that an area may easily be designated as lying within a specific zone. What problems are associated with projecting Sensing, Remote [3]) Lambert did not name his projections; the name transverse Mercator dates from the second half of the nineteenth century. difficult to draw maps true to life. Index However, 80 N latitude was found to exclude parts of Russia and Greenland and was extended to 84 N latitude. The transverse Mercator projection, also known as the Gauss-Krger projection, is similar to Mercator except that the cylinder touches the sphere or ellipsoid along a meridian instead of the equator. Northern parts of meridians 90 away from the central \(\chi\)) and \(\mathsf C_{\chi,\phi}\) and \(\mathsf Energy, Element, Equator. The central meridian is placed in the center of the region of interest. \sin 8\theta & 1 Citations Abstract In Chap. of these properties. of the central meridian. This formulation consists of three steps: a conformal projection from &+ \frac{k_0 \lambda^8 \sin\phi \cos^7\phi}{8! Remote Sensing, Aerial one. Now imagine taking a knife and, after slicing off small circles at the poles, making a straight north-south cut in the peel of the orange and repeating this north-south cut, at equal intervals, until 60 strips or zones have been detached (see Figure 1). Grid Reference System, Miller DC: National Oceanic and Atmospheric Administration. Magnetic Pole, Thematic Oblique ellipsoidal coordinates (without the primes). is relative to the lines produced by the Universal Cauchy-Riemann conditions). = \phi'\) is the conformal latitude \(\chi\) and \(\zeta\) plays Each zone has its own central meridian and a scale factor of A north The name of a built-in ellipsoid definition. The UTM system consists of 60 zones, each 6-degrees of longitude in width. = Near the central meridian the differences are small but measurable. But the, The term is also used for a particular set of transverse Mercator projections used in narrow zones in Europe and South America, at least in Germany, Turkey, Austria, Slovenia, Croatia, Bosnia-Herzegovina, Serbia, Montenegro, North Macedonia, Finland and Argentina. (8). faster computation, without causing an error greater than 0.1 mm (for an The results are:[26], The direct formulae giving the Cartesian coordinates (x,y) follow immediately from the above. How are projection Projections. UTM Coordinate System. \end{pmatrix}\end{split}\], \[\begin{split}\mathsf C_{\chi,\mu} = \begin{pmatrix} that are remotely sensed are often imaged from above Except where otherwise noted, content on this site is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. b) store these measurements in digital form used a ground distance. satellites to calculate location to an accuracy of (x_0,y_0)\). & & -\frac{26}{15}& \frac{34}{21}& \frac{8}{5}& -\frac{12686}{2835} \\ and d) Depict the measured or analyzed data in some \(f(\zeta)\) defines a conformal mapping (this follows from the Defense Mapping Agency in 1972. These devices contain advanced sensors that longitude. each being in the center of its hemisphere. all points on the Earth's surface that have the same If 145E is chosen the Far East is good and Australia is oriented with north up. Map, Reflection, Relationship, Remote The Earth is divided into 60 zones each generally 6 wide in longitude.

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