# gism2

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### Mapping Basics:

Noriel Christopher C. Tiglao, Dr. Eng 24 January – 4 February 2005 Statistical Research and Training Center (SRTC) Quezon City, Metro Manila Mapping Basics Module 2

### Presentation Outline:

Presentation Outline Introduction Basic Coordinate Systems Geodetic Datum and Reference Systems Map Projections

### Basic Coordinate Systems:

Basic Coordinate Systems

### Geodetic Datum and Reference Systems:

Geodetic Datum and Reference Systems

### Introduction:

Introduction Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth Hundreds of different datums have been used to frame position descriptions since the first estimates of the earth's size were made by Aristotle

### Introduction (contd.):

Introduction (contd.) Datums have evolved from those describing a spherical earth to ellipsoidal models derived from years of satellite measurements Modern geodetic datums range from flat-earth models used for plane surveying to complex models used for international applications

### Introduction (contd.):

Introduction (contd.) While cartography, surveying, navigation, and astronomy all make use of geodetic datums, the science of geodesy is the central discipline Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters

### Introduction (contd.):

Introduction (contd.) Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in GIS, precise positioning systems, and navigation systems Technological advancements that have madeT possible global positioning measurements with sub-meter accuracies requires careful datum selection and careful conversion between coordinates in different datums

### Reference Ellipsoids:

Reference Ellipsoids Reference ellipsoids are usually defined by semi-major (equatorial radius) and flattening (the relationship between equatorial and polar radii) Other reference ellipsoid parameters such as semi-minor axis (polar radius) and eccentricity can computed from these terms

### Reference Ellipsoids (contd.):

Reference Ellipsoids (contd.) Ellipsoidal earth models are required for accurate range and bearing calculations over long distances Ellipsoidal models define an ellipsoid with an equatorial radius and a polar radius. The best of these models can represent the shape of the earth over the smoothed, averaged sea-surface to within about one-hundred meters

### Reference Ellipsoids Parameters:

Reference Ellipsoids Parameters a : semi-major axis (equatorial radius) b : semi-minor axis (polar radius) flattening :

### Reference Ellipsoids Definitions:

Reference Ellipsoids Definitions

### Earth Surfaces:

Earth Surfaces The earth has a highly irregular and constantly changing surface Models of the surface of the earth are used in navigation, surveying, and mapping Topographic and sea-level models attempt to model the physical variations of the surface Gravity models and geoids are used to represent local variations in gravity that change the local definition of a level surface

### Earth Surfaces (contd.):

Earth Surfaces (contd.) The topographical surface of the earth is the actual surface of the land and sea at some moment in time. Aircraft navigators have a special interest in maintaining a positive height vector above this surface. Sea level is the average (methods and temporal spans vary) surface of the oceans. Tidal forces and gravity differences from location to location cause even this smoothed surface to vary over the globe by hundreds of meters.

### Earth Surfaces (contd.):

Earth Surfaces (contd.) Gravity models attempt to describe in detail the variations in the gravity field. The importance of this effort is related to the idea of leveling. Plane and geodetic surveying uses the idea of a plane perpendicular to the gravity surface of the earth, the direction perpendicular to a plumb bob pointing toward the center of mass of the earth. Local variations in gravity, caused by variations in the earth's core and surface materials, cause this gravity surface to be irregular

### Earth Surfaces (contd.):

Earth Surfaces (contd.) Geoid models attempt to represent the surface of the entire earth over both land and ocean as though the surface resulted from gravity alone. Bomford (1980) described this surface as the surface that would exist if the sea was admitted under the land portion of the earth by small frictionless channels. The WGS-84 Geoid defines geoid heights for the entire earth

### The Datum:

The Datum An ellipsoid gives the base elevation for mapping, called a datum. Examples are NAD27 and NAD83 in the US, Luzon Datum and PRS92 in the Philippines. The geoid is a figure that adjusts the best ellipsoid and the variation of gravity locally. It is the most accurate, and is used more in geodesy than GIS and cartography.

The Geiod

### Earth Surfaces (contd.):

Earth Surfaces (contd.)

### Map Scale:

Map Scale Map scale is based on the representative fraction, the ratio of a distance on the map to the same distance on the ground. Most maps in GIS fall between 1:1 million and 1:1000. A GIS is scaleless because maps can be enlarged and reduced and plotted at many scales other than that of the original data.

### Map Scale (contd.):

Map Scale (contd.) To compare or edge-match maps in a GIS, both maps MUST be at the same scale and have the same extent. The metric system is far easier to use for GIS work.

### Scale of a Baseball Earth:

Scale of a Baseball Earth Baseball circumference = 226 mm Earth circumference approx 40 million meters RF is : 1:177 million

### Length of the Equator at Scale:

Length of the Equator at Scale

### Geographic Coordinates:

Geographic Coordinates

### The Prime Meridian:

The Prime Meridian

### The International Meridian Conference (1884: Washington DC):

The International Meridian Conference (1884: Washington DC) “That it is the opinion of this Congress that it is desirable to adopt a single prime meridian for all nations, in place of the multiplicity of initial meridians which now exist.” “That the Conference proposes to the Governments here represented the adoption of the meridian passing through the center of the transit instrument at the Observatory of Greenwich as the initial meridian for longitude.” “That from this meridian longitude shall be counted in two directions up to 180 degrees, east longitude being plus and west longitude minus.”

### Geographic Coordinates:

Geographic Coordinates Geographic coordinates are the earth's latitude and longitude system, ranging from 90 degrees south to 90 degrees north in latitude and 180 degrees west to 180 degrees east in longitude. A line with a constant latitude running east to west is called a parallel. A line with constant longitude running from the north pole to the south pole is called a meridian. The zero-longitude meridian is called the prime meridian and passes through Greenwich, England. A grid of parallels and meridians shown as lines on a map is called a graticule.

### Geographic Coordinates as Data:

Geographic Coordinates as Data

### Coordinates Systems:

Coordinates Systems A coordinate system is a standardized method for assigning codes to locations so that locations can be found using the codes alone. Standardized coordinate systems use absolute locations. A map captured in the units of the paper sheet on which it is printed is based on relative locations or map millimeters. In a coordinate system, the x-direction value is the easting and the y-direction value is the northing. Most systems make both values positive.

### Geographic Coordinate Systems:

Geographic Coordinate Systems Longitude, Latitude and Height The most commonly used coordinate system today. The Prime Meridian and the Equator are the reference planes used to define latitude and longitude The geodetic latitude of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid.

### Geographic Coordinate Systems (contd.):

Geographic Coordinate Systems (contd.) Longitude, Latitude and Height The geodetic longitude of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane.

### Geographic Coordinate Systems (contd.):

Geographic Coordinate Systems (contd.)

### Geographic Coordinate Systems (contd.):

Geographic Coordinate Systems (contd.) Earth Centered, Earth Fixed X, Y and Z ECEF Cartesian Coordinates (XYZ) define three dimensional positions with respect to the center of mass of the reference ellipsoid. The Z-axis points toward the North Pole. The X-axis is defined by the intersection of the plane define by the prime meridian and the equatorial plane. The Y-axis completes a right handed orthogonal system by a plane 90 degrees east of the X-axis and its intersection with the equator.

### Geographic Coordinate Systems (contd.):

Geographic Coordinate Systems (contd.)

### Datums in Use:

Datums in Use Hundreds of geodetic datums are in use around the world. The Global Positioning system is based on the World Geodetic System 1984 (WGS-84). Parameters for simple XYZ conversion between many datums and WGS-84 are published by the Defense mapping Agency.

### Datum Shifts:

Datum Shifts Coordinate values resulting from interpreting latitude, longitude, and height values based on one datum as though they were based in another datum can cause position errors in three dimensions of up to one kilometer.

### Datum Conversions:

Datum Conversions Datum conversions are accomplished by various methods. Complete datum conversion is based on seven parameter transformations that include three translation parameters, three rotation parameters and a scale parameter. Simple three parameter conversion between latitude, longitude, and height in different datums can be accomplished by conversion through Earth-Centered, Earth Fixed XYZ Cartesian coordinates in one reference datum and three origin offsets that approximate differences in rotation, translation and scale.

### ECEF XYZ to Latitude,Longitude and Height:

ECEF XYZ to Latitude,Longitude and Height

### Latitude,Longitude and Height to ECEF XYZ:

Latitude,Longitude and Height to ECEF XYZ

### XYZ Three Parameter Datum Conversion:

XYZ Three Parameter Datum Conversion

### Molodensky Datum Transformation (contd.):

Molodensky Datum Transformation (contd.) The Standard Molodensky formulas can be used to convert latitude, longitude, and ellipsoid height in one datum to another datum if the Delta XYZ constants for that conversion are available and ECEF XYZ coordinates are not required.

### Molodensky Datum Transformation (contd.):

Molodensky Datum Transformation (contd.)

Map Projections

### Introduction:

Introduction A transformation of the spherical or ellipsoidal earth onto a flat map is called a map projection. The map projection can be onto a flat surface or a surface that can be made flat by cutting, such as a cylinder or a cone. If the globe, after scaling, cuts the surface, the projection is called secant. Lines where the cuts take place or where the surface touches the globe have no projection distortion.

Map Projections

### Distortions in Map Projections:

Distortions in Map Projections Map projections are attempts to portray the surface of the earth or a portion of the earth on a flat surface. Some distortions of conformality, distance, direction, scale, and area always result from this process. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projection are attempts to only moderately distort all of these properties. Conformality When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps.

### Distortions in Map Projections (contd.):

Distortions in Map Projections (contd.) Distance A map is equidistant when it portrays distances from the center of the projection to any other place on the map. Direction A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions. Scale Scale is the relationship between a distance portrayed on a map and the same distance on the Earth. Area When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area (or equivalent) map.

### Slide57:

No flat map can be both equivalent and conformal.

### Map Projections:

Map Projections Projections can be based on axes parallel to the earth's rotation axis (equatorial), at 90 degrees to it (transverse), or at any other angle (oblique). A projection that preserves the shape of features across the map is called conformal. A projection that preserves the area of a feature across the map is called equal area or equivalent. No flat map can be both equivalent and conformal. Most fall between the two as compromises. To compare or edge-match maps in a GIS, both maps MUST be in the same projection.

### Different Map Projections:

Different Map Projections Different map projections result in different spatial relationships between regions.

### Cylindrical Projections:

Cylindrical Projections Cylindrical projections result from projecting a spherical surface onto a cylinder. When the cylinder is tangent to the sphere contact is along a great circle (the circle formed on the surface of the Earth by a plane passing through the center of the Earth). In the secant case, the cylinder touches the sphere along two lines, both small circles (a circle formed on the surface of the Earth by a plane not passing through the center of the Earth). When the cylinder upon which the sphere is projected is at right angles to the poles, the cylinder and resulting projection are transverse. When the cylinder is at some other, non-orthogonal, angle with respect to the poles, the cylinder and resulting projection is oblique.

### Cylindrical Projections (contd.):

Cylindrical Projections (contd.)

### Conic Projections:

Conic Projections Conic projections result from projecting a spherical surface onto a cone. When the cone is tangent to the sphere contact is along a small circle. In the secant case, the cone touches the sphere along two lines, one a great circle, the other a small circle.

### Conic Projections (contd.):

Conic Projections (contd.)

### Azimuthal Projections:

Azimuthal Projections Azimuthal projections result from projecting a spherical surface onto a plane. When the plane is tangent to the sphere contact is at a single point on the surface of the Earth. In the secant case, the plane touches the sphere along a small circle if the plane does not pass through the center of the earth, when it will touch along a great circle.

### Azimuthal Projections (contd.):

Azimuthal Projections (contd.)

### Standard Parallels:

Standard Parallels

### Secant Map Projections:

Secant Map Projections

### Cylindrical:

Cylindrical Cylindrical Equal Area Cylindrical Equal-Area projections have straight meridians and parallels, the meridians are equally spaced, the parallels unequally spaced. There are normal, transverse, and oblique cylindrical equal-area projections. Scale is true along the central line (the equator for normal, the central meridian for transverse, and a selected line for oblique) and along two lines equidistant from the central line. Shape and scale distortions increase near points 90 degrees from the central line.

### Cylindrical (contd):

Cylindrical (contd) Behrmann Cylindrical Equal-Area Behrmann's cylindrical equal-area projection uses 30:00 North as the parallel of no distortion.

### Cylindrical (contd):

Cylindrical (contd) Gall's Stereographic Cylindrical Gall's stereographic cylindrical projection results from projecting the earth's surface from the equator onto a secant cylinder intersected by the globe at 45 degrees north and 45 degrees south. This projection moderately distorts distance, shape, direction, and area.

### Cylindrical (contd):

Cylindrical (contd) Peters The Peters projection is a cylindrical equal-area projection that de-emphasizes area exaggerations in high latitudes by shifting the standard parallels to 45 or 47 degrees.

### Mercator:

Mercator The Mercator projection has straight meridians and parallels that intersect at right angles. Scale is true at the equator or at two standard parallels equidistant from the equator. The projection is often used for marine navigation because all straight lines on the map are lines of constant azimuth.

### Miller Cylindrical:

Miller Cylindrical The Miller projection has straight meridians and parallels that meet at right angles, but straight lines are not of constant azimuth. Shapes and areas are distorted. Directions are true only along the equator. The projection avoids the scale exaggerations of the Mercator map.

### Oblique Mercator:

Oblique Mercator Oblique Mercator projections are used to portray regions along great circles. Distances are true along a great circle defined by the tangent line formed by the sphere and the oblique cylinder, elsewhere distance, shape, and areas are distorted. Once used to map Landsat images (now replaced by the Space Oblique Mercator), this projection is used for areas that are long, thin zones at a diagonal with respect to north, such as Alaska State Plane Zone 5001.

### Transverse Mercator (Gauss-Kruger):

Transverse Mercator (Gauss-Kruger) Transverse Mercator projections result from projecting the sphere onto a cylinder tangent to a central meridian. Transverse Mercator maps are often used to portray areas with larger north-south than east-west extent. Distortion of scale, distance, direction and area increase away from the central meridian. Many national grid systems are based on the Transverse Mercator projection

### Universal Transverse Mercator:

Universal Transverse Mercator The Universal Transverse Mercator (UTM) projection is used to define horizontal, positions world-wide by dividing the surface of the Earth into 6 degree zones, each mapped by the Transverse Mercator projection with a central meridian in the center of the zone. UTM zone numbers designate 6 degree longitudinal strips extending from 80 degrees South latitude to 84 degrees North latitude.

UTM Zones

### UTM Coordinate Example:

UTM Coordinate Example Eastings are measured from the central meridian (with a 500km false easting to insure positive coordinates). Northings are measured from the equator (with a 10,000km false northing for positions south of the equator).

### Scale Factors in UTM Projection:

Scale Factors in UTM Projection Scale Factors: a = 1.0000 b = 0.9996 c = 1.0000 The central meridian in this secant case transverse Mercator projection has a scale factor of 0.9996. The two standard lines on either side of the central meridian have a scale factor of 1.

### Coordinates Systems for the US:

Coordinates Systems for the US Some standard coordinate systems used in the United States are geographic coordinates Universal Transverse Mercator system military grid state plane To compare or edge-match maps in a GIS, both maps MUST be in the same coordinate system.

### UTM zones for 48 States:

UTM zones for 48 States

### Military Grid Coordinates:

Military Grid Coordinates

### UTM Zone for Philippines:

UTM Zone for Philippines UTM Zone 51 120 -126 Central Meridian: 123 UTM Zone 50 (for Palawan) 114 -120 Central Meridian: 117

### Philippine Reference System 1992 (PRS92):

Philippine Reference System 1992 (PRS92) In 1987, the Philippine Bureau of Coast and Geodetic Survey was incorporated as a part of the National Mapping and Resource Information Authority (NAMRIA). A total of 467 GPS stations were observed which included 330 First Order stations, 101 Second Order stations, and 36 Third Order stations This series of new observations was adjusted and published as the Philippine Reference System of 1992 (PRS92)

### PRS92 (Contd.):

PRS92 (Contd.) The Philippines uses a Clarke 1866 spheroid model (Luzon Datum): a = 6378206.4 m 1/f = 294.9786982 m GPS model: a = 6378137.0 m 1/f = 298.257223563 E0 = 500,000 N0 = 0

End