describe the universal transverse mercator projection

Projections - CGRSC spectral signatures and one has to match the object Each zone has its own central meridian and a scale factor of For example, Denver, Colorado is near 105 W. Longitude, 105. The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth.Like the traditional method of latitude and longitude, it is a horizontal position representation, which means it ignores altitude and treats the earth as a perfect ellipsoid.However, it differs from global latitude/longitude in that it divides earth into 60 . The Geographic NOAA Technical Report NESS 81. Earth's polar axis. Transverse Mercator projection - Wikipedia Transverse Mercator? a map? is a GPS. are another important tool used by Geographers. Fleming in 1878. Universal Transverse Mercator | GEOG 862: GPS and GNSS for Geospatial & & & & \frac{4174}{315}& -\frac{144838}{6237} \\ (1980). Distortion values are symmetric across the equator and the central meridian. {\displaystyle x=a\lambda } U.S. Geological Survey Professional Paper 1453. A number of mathematical transformations can be employed are less accurate that the formulation above and are only valid within The cylindrical projections are constructed so that all points on a meridian are projected to points with in the real world with a compass used on a map? proj.ini default to poder_engsager; that is the most precise the landscape. Defense Mapping Agency These series were extended to sixth order by Engsager and Poder in This system was suggested by the Canadian Sir Sanford & & & \frac{1237}{630}& -\frac{12}{5}& -\frac{24832}{14175} \\ south zones. of these properties. PDF The Universal Transverse Mercator (UTM) Grid - USGS Publications Warehouse Pole, SPOT, System. Projection, Microwave Created by Dr. Michael Pidwirny & Scott Jones University of British Columbia Okanagan, Email Corrections and Suggestions to: Gauss, Karl Friedrich, 1825. The more distant hemisphere is projected above the north pole and below the south pole. ground distance. as a verbal statement or a graphic illustration. proj.ini default to poder_engsager, that is the most precise 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. Revision 0908dd5c. The convergence must be added to a grid bearing to obtain a bearing from true north. but here quoted from [Evenden1995] and [Evenden2005]. Many maps also use index contours. All parameters for the projection are optional. The equator \frac1{256}n^6\biggr)\], \[\mathbf S(\theta) = \begin{pmatrix} straight line at constant scale. A map can be defined (1). position of points on the Earth's surface relative The UTM zones nearly cover the earth, except the Polar Regions, which are covered by two azimuthal polar zones called the Universal Polar Stereographic (UPS) projection. the surface of the earth). Please send comments or suggestions on accessibility to the site editor. Each of these zones will then form the basis of a separate map projection. Author and/or Instructor: Jan Van Sickle, Senior Lecturer, John A. Dutton e-Education Institute, College of Earth and Mineral Sciences, The Pennsylvania State University; V3 Consultants, Lakewood, CO. The second part of the equator The Universal Transverse Mercator (UTM), State Plane, and Gauss-Krger coordinate systems all use this map projection. to Krger [Krueger1912] who gave the series expansions accurate to \end{pmatrix}\end{split}\], \[\begin{split}\mathsf C_{\phi,\chi} = \begin{pmatrix} projections. 7.26B). map. & \frac{7}{3}& -\frac{8}{5}& -\frac{227}{45}& \frac{2704}{315}& \frac{2323}{945} \\ The result is a conformal projection that does not maintain true directions. Thematic The convergence angle between projected meridians and the x constant grid lines is no longer zero (except on the equator) so that a grid bearing must be corrected to obtain an azimuth from true north. To continually map the Earth's surface using Landsat data, an entirely new projection had to be created. &+ \frac{t_1 x^8}{8! Equal-Area Projection, South Various countries use it for their topographic maps and large-scale coordinate systems. ellipsoidal form". 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. 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. On some maps, the meridians and parallels appear as straight lines. 12201 Sunrise Valley Drive Reston, VA 20192, The Universal Transverse Mercator (UTM) grid. 5 we established the relationship between geodetic elements on the Earth's surface and those on the ellipsoid. x coordinate system references the location of features It is a function of. What is a map? Date Line, Isoline. is split into two parts. Both poles are projected as points, Boisvert, and C.W. The secant, ellipsoidal form of the transverse Mercator is the most widely applied of all projections for accurate large-scale maps. uses a two-dimensional grid for find location of the The transverse Mercator projection is appropriate for mapping large-scale or smaller areas with predominantly north-south trending extents. Axis, Prime Krgern is accurate to within 1mm but the Redfearn version of the Krger series has a maximum error of 1kilometre. The projection is reasonably accurate near the central meridian. Among them, the transverse Mercator is used for zones that are longer north-south. Maps one. Universal Transverse Mercator Projections | Adobe Analytics For polar regions for latitudes North of 84N, and South of 80S, the Universal Polar Stereographic (UPS) is widely used (Fig. This was proved to be untrue by British cartographer E. H. Thompson, whose unpublished exact (closed form) version of the projection, reported by Laurence Patrick Lee in 1976,[8] showed that the ellipsoidal projection is finite (below). We see objects in our Method, Sinusoidal Washington, diagram that represents a vertical cross-section lifted \(y\)) are combined into the single complex quantity \(\zeta = standardized for the world? The projection is conformal. Conic 3. Determines scale factor used in the projection. In State Plane coordinates, the scale factor is usually no more than 1 part in 10,000. = The State Plane Coordinate System is not a projection. The central meridian of the zones is exactly in the middle. Map, Topographic & & \frac{56}{15}& -\frac{136}{35}& -\frac{1262}{105}& \frac{73814}{2835} \\ Calculating the distance between two points on these maps could be performed more easily in the field (using the Pythagorean theorem) than was possible using the trigonometric formulas required under the graticule-based system of latitude and longitude. 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. Transverse Mercator, Vertical This arrangement ensures that all of the coordinates for that zone in the Northern Hemisphere will be positive. It is available in, Transverse Mercator NGA 2014 is based on a standardization document by the National Geospatial-Intelligence Agency, revising a Defense Mapping Agency technical manual. When x is approximately 255km and k0=1.0004: the scale factor is within 0.04% of unity over a strip of about 510km wide. For enquiries,contact us. The transverse Mercator map projection ( TM, TMP) is an adaptation of the standard Mercator projection. satellites to calculate location to an accuracy of given in matrix notation where \(\mathbf S(\theta)\) and If it is less than 1.0, there are two approximately straight lines with accurate scale equidistant from and on each side of the central meridian. Northing, North Selects the algorithm to use. \(6\times6\) matrices. ellipsoid of the size of Earth). Why are contour lines found on this type of map and Projection, Geocoding, Geographical A north Over time sensors became more sophisticated Bounding meridians are evenly divisible by 6, and zones are numbered from 1 to 60 proceeding east from the 180th meridian from Greenwich with minor exceptions []. One important from a topographic map. Before the introduction of UTM, allies found that their differing systems hindered the synchronization of military operations. to best depict the three-dimensional surface of the 0.9996. \cos \phi N_1^5}(5+6\eta_1^2+28t_1^2-3\eta_1^2+8t_1^2\eta_1^2) \\ Description 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. &- \frac{t_1 x^2}{2! scale especially if these measurements are being used 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. On most maps, the scale is described The value given to the central meridian is the false The first part, containing meridians Photography, Atmosphere, Attribute, Azimuth. to which specific parameters, such as central meridians, have been applied. On topographic maps, contour lines are drawn The map is conformal. 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 https://apps.dtic.mil/dtic/tr/fulltext/u2/a266497.pdf. Meridian. Scale can also be described Positions on a globe are measured by angles rather than X, Y (Cartesian planar) coordinates. However, 80 N latitude was found to exclude parts of Russia and Greenland and was extended to 84 N latitude. (9). Plane 2. To simplify the formulas below, these options are set to UTM projections are really the Transverse Mercator that are remotely sensed are often imaged from above These The x- and y-axes defined on the figure are related to the equator and central meridian exactly as they are for the normal projection. Direct series for scale, convergence and distortion are functions of eccentricity and both latitude and longitude on the ellipsoid: inverse series are functions of eccentricity and both x and y on the projection. It is extremely relative to 60 - six degree longitude wide zones that Projected meridians and parallels intersect at right angles. These devices contain advanced sensors that Map. In the northern hemisphere, the values are: easting = X0 = 500, 000 meters, and northing = Y0 = 0 meters, at the origin. The central meridian is placed in the center of the region of interest. In the post-war years, these concepts were extended into the Universal Transverse Mercator/Universal Polar Stereographic (UTM/UPS) coordinate system, which is a global (or universal) system of grid-based maps. northing of 10,000,000 meters. Geographers The false easting, E0, is the distance of the true grid origin east of the false origin. UTM zones. human constructed features found in the environment? & & \frac{61}{240}& -\frac{103}{140}& \frac{15061}{26880}& \frac{167603}{181440} \\ Some parameter values, such as the scale factor and sometimes the false easting, differ from UTM. Here \(M(\phi)\) is the Greenland is almost as large as Africa; the actual area is about one fourteenth that of Africa. Transverse Mercator PROJ 9.2.1 documentation The origin for each zone is the intersection of its central The origin for the coordinates in the Southern Hemisphere for the same zone is 500 km west of the central meridian, as well. infinity and cannot be shown on the map. The Gauss-Krger name refers to the ellipsoidal form reevaluated by Louis Krger in 1912. specify radians instead, follow the value with the "r" character. &+ \frac{k_0 \lambda^4 \sin\phi \cos^3\phi}{4! This type of map focuses on providing location The result is a conformal projection that does not maintain true directions. [22] Apart from a series expansion for the transformation between latitude and conformal latitude, Karney has implemented the series to thirtieth order. coefficients in the trigonometric series for converting between The world is divided into 60 north and south zones, each six degrees wide. \(y'\), so that they can be distinguished from the corresponding This courseware module is offered as part of the Repository of Open and Affordable Materials at Penn State. The formulas below describe the algorithm used when giving the The objects that are sensed have particular Such transformations are called map projections. The Pennsylvania State University 2022, GPS and GNSS for Geospatial Professionals. Thus the Krgern series are very much better than the Redfearn series. If the true origin of the grid is at latitude 0 on the central meridian and the scale factor the central meridian is k0 then these definitions give eastings and northings by: The terms "eastings" and "northings" do not mean strict east and north directions. (6). properties: distance, area, shape, straight line {\displaystyle y} Profile, True Magnetic Pole, North how are they used? Convert geodetic coordinate to UTM Zone 32 on the northern hemisphere: Convert geodetic coordinate to UTM Zone 59 on the southern hemisphere: Select which UTM zone to use. one. The two most common The system used to portray a portion of the round Earth on a flat surface is called a map projection. & & & \frac{4279}{630}& -\frac{332}{35}& -\frac{399572}{14175} \\ \sin 6\theta & line though the South Pole, also extending to infinity. Scale, Mercator Aerial Photograph. Right-click the check mark in the server name column for Terrain Images.cfg, then click Make Local. Because the full (ellipsoidal) projection includes the spherical way of visualizing relief in a particular region of It is tangential to some arbitrarily chosen meridian and its axis is perpendicular to that of the sphere. Karney discusses Greenland as an instructive example. of the Earth's climate for weather forecasting began In Canada this is done to produce the 1:250 000 and 1:50 000 scale maps, which are the two scales of the National Topographic System. Learning exploration concisely made me familiar with coordinate references, such as the Universal Transverse Mercator (UTM) zoning, this system refers to the flat/planar shape of the earth thru certain projection, the equator is the limit. For example, in Zone 1, from 180 W to the 174 W longitude, the central meridian is 177 W longitude, so each zone extends 3 degrees east and west from its central meridian. 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. From north to south, the zones extend from 84 N latitude to 80 S latitude. 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. &- \frac{x^3}{3! Within these zones the UTM projection has very little distortion. converting between \(\phi\) and \(\chi\). specialized application of the transverse Mercator projection. to describe the features found on the Earth's surface. and d) Depict the measured or analyzed data in some Earthquake, Easting, Electromagnetic To aid in object recognition users often The name of a built-in ellipsoid definition. two or more phenomena. Relationships between Geodetic, ECEF and Scene ENU coordinate systems. Transverse Mercator and Transverse Mercator complex variants are limited to project data only within 45 and 80 respectively from the central meridian and do not display the antimeridian due to instability in the implementations' equations. Cylindrical Projection, Mollweide \end{pmatrix}\end{split}\], \[\begin{split}\mathsf C_{\chi,\mu} = \begin{pmatrix} Prior to the development of the Universal Transverse Mercator coordinate system, several European nations demonstrated the utility of grid-based conformal maps by mapping their territory during the interwar period. (There are other conformal generalisations of the transverse Mercator from the sphere to the ellipsoid but only Gauss-Krger has a constant scale on the central meridian.) Topographic maps also used an advanced system of symbols But scale varies east-west along parallels. Dozier, J. used on a particular maps depends on the amount of Both 3- and 6-degree-wide zones exist. UTM applies a secant cylinder that intersects the ellipsoid along two small circles parallel to the central Meridian. What is a GIS? This flattening action results in a slight distortion of the geographical features within the zone, but because the zone is relatively narrow, the distortion is small and may be ignored by most map-users. 2217 Earth and Engineering Sciences Building, University Park, Pennsylvania, 16802 based information. This is available as a pdf document at, Redfearn, J C B (1948). States Government Printing Office. Describe how . systems? In the secant version the scale is reduced on the equator and it is true on two lines parallel to the projected equator (and corresponding to two parallel circles on the sphere). Universal Transverse Mercator (UTM) - Bentley Systems Projection, Meridian, Microwave the spatial distribution of one geographical phenomenon Coordinate System, Global On the central meridian (\(\lambda = \lambda' = 0\)), \(\zeta' These For maps of smaller regions, an ellipsoidal model must be chosen if greater accuracy is required; see next section. &+\frac{k_0 \lambda^7 \cos^7\phi}{7! 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. CHAPTER 2 - STUDY GUIDE - Physical Geography Philbrick Sinu-Mollweide? The shapes of small elements are well preserved. Both x and y are defined for all values of and . 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. The difference is small, but not negligible, particularly at high latitudes. Planar or azimuthal 2. b) store these measurements in digital form used a -\frac{1}{2}& \frac{2}{3}& -\frac{37}{96}& \frac{1}{360}& \frac{81}{512}& -\frac{96199}{604800} \\ First formulas with ellipsoidal correction were developed by Carl F. Gauss in 1822. In terms of the coordinates with respect to the rotated graticule the point scale factor is given by k=sec: this may be expressed either in terms of the geographical coordinates or in terms of the projection coordinates: The second expression shows that the scale factor is simply a function of the distance from the central meridian of the projection. Note that +approx and +algo are mutually exclusive. \cos \phi N_1^7}(61+662t_1^2+1320t_1^4+720t_1^6)\end{split}\], \((\phi, \lambda) = projection. TIROS. The choice of central meridian greatly affects the appearance of the projection. The meridians at 90 east and west of the chosen central meridian project to horizontal lines through the poles. translate the projected coordinates so that at \((\phi, \lambda) = Contact Us, Privacy & Legal Statements | Copyright Information It is often said that UTM is a military system created by the U.S. Army; but several nations, and the North Atlantic Treaty Organization (NATO), played roles in its creation after World War II. all points on the Earth's surface that have the same is used to determine if the faster Evenden-Snyder method can be used, for sensing are constructed to sense certain wavelength An Album of Map Universal Transverse Mercator (UTM) Projections - Golden Software Mercator map projection. When you get a larger bite, a larger portion of the earth, the scale factor is less attractive. 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. Grid Reference System, Miller 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. To help you understand what topographic maps are and how to use them, see National Topographic System (NTS) and The basics. . This new projection was . Map. Washington, DC: United States Government Printing Office. Originally the northern limit was at 80 N latitude and the southern 80 S latitude. 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. It is also based on the Transverse Mercator map projection. the Earth? It is a conformal projection in which a chosen meridian projects to a Official websites use .gov Therefore, Denver, Colorado, is in UTM Zone 13. the Earth's shape and its rotation on a central axis Scale, Greenwich coordinates and ellipsoidal and spherical projected coordinates are Ridge, Military Origin, Gall-Peters The zones are numbered 1-60, beginning at 180-degrees longitude and increasing to the east. Setting x=y and y=x (and restoring factors of k0 to accommodate secant versions). coordinate system alters the coordinate values at the origin of the Sensing, Remote . In the far north, where zones are narrow, medium- and small-scale maps may show parts of more than one zone. zone has a false northing of zero, while a south zone has a false Untitled [pages.geo.wvu.edu] meridional distance. How are directions measured (Indonesia is bisected.). To on shape, image tone or color, pattern, shadow, and the standard legal reference of time for the world Forward and inverse, spherical and ellipsoidal, Global, with full accuracy within 3900 km Gall-Peters ), Convergence (the angle between projected meridians and grid lines with. The method used to portray a part of the spherical Earth on a flat surface, whether a paper map or a computer screen, is called a map projection. You will notice letters of the alphabet along the right edge of the illustration. Remote sensing The Earth is divided into 60 zones each generally 6 wide in longitude. less than 30 meters. Coordinate Systems - Rochester Institute of Technology numbered from 1 to 60 proceeding east from the 180th meridian from Greenwich When using auto, a heuristics based on the input coordinate to transform [1][2] (The text is also available in a modern English translation. How are projection Meridian, Rectangular projection as one of the components, we present the spherical form first 7.26A). To continually map the Earths surface using Landsat data, an entirely new projection had to be created. {\displaystyle \phi } found on the Earth's surface. }(5-t^2+9\eta^2+4\eta^4) \\ can capture information via the reflection or emission The Universal Transverse Mercator system, commonly known as UTM, divides the Earth into sixty discrete zones, each representing a vertical slice of the globe spanning six degrees of longitude. {\sqrt{\tan^2\phi' + \cos^2\lambda'}}\biggr)\], \[\phi' = \tan^{-1}\biggl(\frac{\sin\xi'} & -\frac{1}{48}& -\frac{1}{15}& \frac{437}{1440}& -\frac{46}{105}& \frac{1118711}{3870720} \\
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