# Datums, Coordinates, & Projections UNCLASSIFIED

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1 Datums, Coordinates, & Projections

2 Lesson Objectives Modeling the earth Horizontal Datums: Traditionally Derived Regional Horizontal Datums Satellite Derived: World Geodetic System 1984 Vertical Datums and the Earth Gravitational Model Coordinate Systems: Geographic (Lat\Lon) Universe Transverse Mercator (UTM) Military Grid Reference System (MGRS) NGA s Primary Map Projections Datum Transformation & Coordinate Conversion

3 Geospatial Foundation Theory The World Geodetic System, Coordinate Systems, & Projections Geographic: 38 41' 08.73" N " W Cartesian: X= 1,109,928m Y= -4,860,097m Z= 3,965,162m UTM: mE mN MGRS: 18S UH

4 Learning Objective Discuss the difference between traditionally derived and satellite derived datums Understand the components of datums Know why datum mismatch is important to you Describe the ellipsoid, geoid and topographic surface and how they affect datums Identify the difference between Geodetic, UTM and MGRS coordinate systems Understand the principles of projections Describe the process of datum transformation and coordinate conversion

5 Foundation Data Foundation Data

6 Digital Point Positioning Data Base (DPPDB) Digital Nautical Chart (DNC) Foundation Data Controlled Image Base 5 meter (CIB5) Foundation Data Foundation Feature Data (FFD) Navigation Safety Gravity Magnetics Digital Terrain Elevation Data Level 2 (DTED2)

7 What is Location? Relative: Closeness of estimated position to another position. Absolute: Closeness of estimated position to true location. Z Y { { X

8 What is Location? Consider Location only makes sense when compared to some frame of reference. Relative - Bldg 215 is to the left of the post office Absolute N, W

9 What is Location? The Relative Approach Building 215 Post Office

10 What is Location? The Absolute Approach? N Greenwich, UK Equator Prime Meridian Still Relative Positioning!!!

11 What is Location? The Absolute Approach? N, W N Greenwich, UK Equator Prime Meridian Now It s Absolute Positioning!!!

12 Modeling the Earth 4th Century 1670 A.D. B.C. - The Earth assumed to be perfectly round; hence, a sphere In 250 B.C., Eratosthenes was the first to approximate Earth s circumference at 46,250 km (he was off by only 15%) Sphere is not accurate due to flattening at the poles due to rotation r = radius of the Earth

13 Modeling the Earth Is there a perfect Earth model?

14 Modeling the Earth The Ellipsoid/Spheroid is a better approximation of the Earth s shape N Equatorial Axis (Semi-Major Axis): a Polar Axis (Semi-Minor) Semi-Minor Axis: b a b S Rotation about the polar axis result is the 3-dimensional Ellipsoid of Revolution or Oblate x2 y2 z2 Spheroid + + =1 a 2 a 2 b2

15 Modeling the Earth Oblateness (or polar flattening) specified by ratio: f ( a b) = a In 1670, Newton predicted the ratio to be 1/300 Current, satellite derived values are closer to 1/298

16 Satellite Observations The European Remote Sensing Satellite, ERS-1, captures the earth s shape without water and clouds from 780 km. This image shows the true undulating shape of the Earth and image looks more like a sloppily peeled potato, not a smoothly shaped ellipse. Satellite geodesy has enabled geodesists to determine the earth s geocentric center to w/in +/- 10 cm. A worldwide horizontal datum requires an accurate estimation of the earth s center

17 Horizontal Datum DEFINITION Horizontal Datum - A base reference for a coordinate system. It includes the position and orientation of an initial point of origin and an ellipsoid that models the surface of the earth in the region of interest. North American Datum 1927 (NAD27) US Geological Center: Meades Ranch - Kansas Clarke Ellipsoid (1866)

18 Components of Datums The Ellipsoid b a WGS-84 Ellipsoid Semi-major Axis: a = m Semi-minor Axis: b = Flattening Ratio: f=(a-b)/a = 1/ Rotate Ellipse in 3 Dimensions: f The ellipsoid is a mathematical model for the shape of the planet. It gives cartographers a smooth mathematical surface to put a coordinate system on.

19 Traditional Horizontal Datums Limitations to the Traditional Approach NAD 27 ED 50 (Clarke Ellipsoid ) (International Ellipsoid) Many nations established their own datum - Standards and procedures vary widely Coordinates from different datums are completely incompatible - Relative to Initial Point of Datum - Will vary as a function of Ellipsoid parameters

20 Horizontal Datums Regional vs. Global Approach Global replaces regional datums with a common, accurate standard One system for maps of the entire planet

21 Horizontal Datums World Geodetic System 1984 (WGS-84) Formal DoD Earth reference frame An Earth Centered Earth Fixed (ECEF) Cartesian coordinate system w/the origin fixed to +/- 10 cm. Defined by ellipsoid parameters, angular velocity, and gravitational constant Includes gravity model: Earth Gravity Model 96 Prime Meridian Semi-major axis (a): 6,378,137.0m Flattening ( f ): 1/ Rotational velocity (ω): x rad/sec Gravitational Constant (GM): x 108m3/s2

22 What is the Problem for DoD? World Geodetic System The DoD Standard WGS 84 is used on almost all new NGA-produced GI&S products (all digital) There are still hundreds of legacy local datums in use throughout the world on existing products > 30 Datums with > 5 Ellipsoids used by NGA > 150 Datums with > 25 Ellipsoids used by others It would take NGA years and lots of DoD money to update the entire existing product line NGA can transform Datums and convert coordinates between WGS 84 and over 200 local datums

23 Where is the Datum Problem? Most widely used local Datum/Ellipsoid pairs North American Datum Clarke 1866 European Datum International WGS Datum Tokyo Datum Bessel South American Datum International Arc Datum Clarke 1880

24 Impact of Datum Mismatch Map dated WGS-84 Map dated NAD-27 15S WC S WN

25 WGS-84 vs. Traditional Datums Coordinate Shifts From Local Datums to WGS 84 Location Datum (US) 18Q VT NAD27 (Japan) 52S BS TOKYO (Europe) N ED E (Africa) S ARC E Shift 201meters 754 meters 176 meters 296 meters

26 Datum Shifts 97:44:25.19 West Longitude (WGS-84) Horizontal Benchmark Texas Capital Dome Arc European Datum WGS :16:28.82 North Latitude (WGS-84) NAD 27 + Australian Geodetic System meters + Ordnance Survey meters Modeled from Peter H. Dana 9/1/94 Tokyo

27 Lessons Learned Collateral Damage? Local Datum Target WGS 84 Strike aircraft missed targets by 300m w/ins set to local datum & targets derived from WGS-84 Navigational systems set on a different datum than the chart can quickly ground naval vessels

28 Datums Matter Actual Position Datum shift applied GPS Position No datum shift applied GPS IS VITAL TO, BUT ALSO LIMITED IN SUPPORT OF, MILITARY TACTICAL NAVIGATION. ITS RELIABILITY DEPENDS ON THE USERS' UNDERSTANDING OF CHARTS, NAVIGATION, AND THE OPERATION AND LIMITATIONS OF THE GPS EQUIPMENT USED. LACKING THIS BASIC UNDERSTANDING CAN CONTRIBUTE TO SEVERE MISHAPS. - NAVSAFECEN ZCollege OCT 00 National Geospatial Intelligence

29 Vertical Datum Traditional surveys are referenced to Mean Sea Level (MSL), which is commonly referred to as the Geoid. The geoid is a closed surface of constant gravity potential approximated by MSL & the theoretical extension of MSL through land areas. GPS surveys are referenced to the Ellipsoid.

30 Vertical Datum Earth Modeling Terminology Topographic Surface Geoid Physical Model Land Ocean Ellipsoid Geometric Model

31 Vertical Datum The relationship between the reference ellipsoid, the geoid, & the physical surface of the Earth. Earth s Physical Surface Geoid h Geoid Separation (- N) H Geoid Ellipsoid Geoid Separation (+ N) Geodetic height (h), geoid separation (N), and elevation (H) are depicted above and related by: h ~ H + N H (orthometric height) is measured traditionally N is modeled using Earth Geoid Model 96 or 180

32 Vertical Datum Modern Methods Use of GPS to help determine geometric relationships between given points Use of satellite radar to measure sea level directly; helps determine geoid shape

33 U.S. Geoid Heights (GEOID96)

34 WGS-2000? No, Better Geoid Models WGS-84 will not change to WGS-20XX Estimates of Geoidal Separation (deviation of the vertical) will improve Earth Gravitational Model 1996 (EGM 96) Separation accurate to +/- 50 cm-1 meter (globally) Local deviations can be up to several meters Earth Gravitational Model Separation accurate to +/- 2-3 meters (globally) Local deviations can be up to 20 meters Many NGA & DoD systems still use EGM 180 National Geospatial Intelligence College (e.g. Production Equipment, GPS receivers)

35 Coordinate Systems A datum defines the initial point and reference surface A coordinate system determines how locations are referenced from the datum

36 Which Coordinate Should Be Used? a) N, E, h = 23 m b) N, E, H = 0 m c) N, E, h = 23 m d) N, E, H = 0 m e) N, E, h = 23 m f) N, E, H = 0 m g) Zone 52, m E, m N, h = 23 m h) Zone 52, m E, m N, H = 0 m i) 52S CG , h = 23 m j) 52S CG , H = 0 m k) m, m, m l) N, E, h H = 0 m m) N, E, h H = 0 m n) N, E, h H = 0 m o) Zone 52, m E, m N, h H = 0 m p) 52S CS , h H = 0 m q) m, m, m

37 Coordinate Systems Cartesian Coordinates: X= 1,109,928m Y= - 4,860,097m Z= 3,965,162m Geographic: DD N, W DM 'N, W DMS 38 41' 08.73"N, "W UTM: ,251mE 4,284,069mN MGRS: 18S UH (New) 18S UT (Old)

38 Coordinate Systems Cartesian Coordinate System Three dimensional right hand coordinate system with an origin at the center of the earth and the X axis oriented at at the Prime Meridian and the Z at the North Pole X Axis Coordinate Distance from the Y-Z Z (X,Y,Z) plane measured parallel to the X-Axis; positive from90º W Long to 90º E Long Y Axis Coordinate Perpendicular distance from the plane of the prime meridian; Y positive in the eastern hemisphere 90 E and negative in the western. Z Axis Coordinate Perpendicular distance from the plane of the equator; X positive in the northern Hemisphere Prime negative in the southern 0º Long Meridian

39 Geographic Coordinates Rules of thumb for latitude 1º latitude 1 latitude 1 latitude.1 latitude. 01 latitude 60 nautical miles 1 nautical mile 30 meters 3 meters 30 centimeters Don t forget longitude converges Don t forget the base 60 conversion 60 minutes per degree 60 seconds per minute

40 UTM Coordinates Flat Grid extending from 84N to 80S Each zone is numbered Eastward starting at 177 W (6 wide from 180 W to 174 W) Coordinates are read east then north Many map products from foreign countries use UTMs Most often used on large scale maps and charts e.g. TLM, JOGs, TPCs

41 Universal Tranverse The UTM graticule coverage Mercator Each belt is 6O in longitude wide 84o N 0 meters 10,000,000m Equator 80o S 180o 1 0o 180o 30 60

42 UTM Grid Central Meridian o 1,700,000 1,600,000 1,500,000 1,400,000 1,300,000 1,200,000 1,100,000 1,000, , , , , , , , , ,000 0o o o 0o o Zone Zone Zone ,256mE 0,567,359mN 156o

43 Military Grid Reference System (MGRS) Subdivides the UTM into 6 X 8 zones numbered 1-60 west to east and c-x from south to north Each 6 X 8 area is divided into 100,000m squares Each square gets a two-letter designator A level of detail is achieved by moving so many meters east and north within the zone (i.e. 8 digit coordinate)

44 MGRS-Old vs. MGRS-New There are two different MGRS ID schemes: MGRSOld and MGRS-New A 10 letter shift exists in the 100,000 squares causing a 1000km (600 nm) northing shift MGRS-Old is based on 3 local Ellipsoids Bessel; Clark 1866; Clark 1880 MGRS-New is based on 8 Ellipsoids GRS80; International; WGS84; WGS72; Australian National; Everest; South American 1969 (GRS67); Clark 1866 (UTM Zones 47-50)

45 Coordinate Complexity Operational Examples Operation Deliberate Force Air Force pilot passed Degrees and Decimal Minutes Navy pilot expected Degrees Minutes Seconds Combined and Joint Exercises SEAL Team drop off at Lake Towada Training Area NATO Bombing Range Exercise

46 Important Questions (Precise Targeting) Know the source of your coordinates: Is it accurate enough for precise targeting? Are coordinates coming from paper map or chart (i.e., an improper source)? Are the shooter / weapon, target locator, and target coordinates on the same datum? Does everyone involved understand the coordinate system(s) being used? Avoid friendly fire and mission failure!!!

47 Map Projections pro jec tion n. The result of causing (light or an image) to fall upon a surface or the distortion of the truth...

48 Map & Chart Projections Projections are attempts to portray the surface of the earth on a flat surface. Some distortions of conformality (shapes & angles), distance, direction, scale, and area always result from the process # # Three map projections 2 - Albers Equal-Area (Conterminous U.S.) of the US centered 3 - Transverse Mercator on Wichita, KS 1 - Unprojected Lat/Lon

49 Round Earth, Flat Map This much Earth surface... projection plane must fit on this amount of map surface! Scale Factor Examples a b c a: c: d e a b c d e a: c: e: b: d: e:

50 Spatial Attribute Preservation Choosing the right projection is crucial for achieving the map s objective. Azimuthal - preservation of direction from one point to all other points. Conformal - preservation of shape for small areas. Angles are preserved. Equal Area - preservation of area. Area of all features on the map have the same relative proportions and size as they do on the globe. Equidistant - preservation of distance. Scale stays the same across the entire map sheet.

51 Mercator Projection Good for ocean navigation Parallels of latitude are not equidistant but longitude are Great Circle: Shortest Distance Rhumb Line: Line of Constant Bearing (also called a loxodrome)

52 Transverse Mercator Projecting the sphere onto a cylinder tangent to a central meridian. Distortion of scale, distance, direction, and area increase away from the central meridian. If you rotate the cylinder every 6º of longitude and change tangency, you create the UTM projection.

53 Equal ARC Standard Projection Problem: Problem How to make raster data square and seamless over large area? ARC Projection shrinks lower latitude pixels and stretches higher latitude pixels to square data Problems printing small scale charts (JNC/GNC) Must re-project ARC data to get around problem Original Chart to be scanned 12% Scanning Stretch Process Digital Chart in ARC projection Up to 12% Shrink

54 Lambert Conformal Conic Projection Shape is preserved Great Circles are near straight lines Rhumb Line is curved Used for small scale products with large EastWest expanses Common NGA projection for: JNC, GNC, ONC (Aerial Navigation Charts)

55 Standard DoD Projections All U.S. military maps are based on projections with conformal characteristics: Maps at scales of 1:500,000 & larger for areas between 80o south and 84o north are based on the Transverse Mercator Projection Maps at 1:1,000,000 scale between 80o south and 84o north are based on the Lambert Conformal Conic Projection Maps at 1:1,000,000 scale & larger of the polar regions are based on the Polar Stereographic Projection General maps at scales smaller than 1:1,000,000 are based on projections individually selected to conform w/the intended use of the map.

56 Coordinate Conversion & Datum Transformation References: NGA TR8350.2, TEC-SR-7, DMA TM Convert from Grid to Geographic Coordinates Convert from Geographic to Cartesian Coordinates Apply Datum Transformation 3 Parameter ( X, Y, Z, and a & f of Ellipsoid) 7 Parameter ( X ε, Y ψ, Z ω, S, a & F of Ellipsoid) * For most uses 3 parameter shifts are acceptable Compute New Geographic Coordinates Compute New UTM, MGRS etc. Coordinates Error in transformation propagates to final coordinates

57 Geographic Translator (GEOTRANS) Converts coordinates among a variety of coordinate systems, projections, and datums. wide map 11 different coordinate systems and map projections Over 200 different datums Choose between Ellipsoid and MSL height Program can receive coordinates from a text file, convert them, and output results in another file.

58 GEOTRANS Processes

59 GEOTRANS Setup

60 Datums, Projections, & Coordinates Review Know What Datums Exist in AOR Always Pass Datum w/coordinate Understand Map Projection Used for Your Products Understand Coordinate System in Use Know Resources to Transform Datums and Convert Coordinates Questions?

61 Summary Horizontal & Vertical Datums Satellite derived vs. traditional datums Coordinates Geographic, GEOREF UTM, MGRS Projections Mercator, Lambert, UTM, ARC Datum Transformation and Coordinate Conversion

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