Spatial data can be described according to: entity distinct object attribute characteristic of entity relationship linkages amongst objects (river) (discharge) (drainage basin)

Advantages of digital maps over paper • Easier to produce • Easier to store • Easier to distribute • Dimensional stability

topology mathematics of spatial relationships among point, line and area objects.

Map a graphical representation of the spatial structure of physical and/or cultural environments

Map are abstractions since they present the real world in a simplified fashion at a reduced scale.

maps are used for: 1. the display of spatial data 2. the analysis of spatial data

Cartography is the art and science of map-making

Cartographic considerations • Map scale • Data classification • Symbolization • Generalization

Map scale the ratio between distances measured on a map and the corresponding distances measured on the ground

large scale map  displays a small area in greater detail small scale map  displays a large area in lesser detail

the proposed use of a map is critical in determining the scale at which it is produced

methods for describing map scale: Representative fraction 1 : 3,500,000 Graphical (bar) Verbal “one inch equals one mile”

classes of maps Reference maps (general purpose) Thematic maps (special purpose)

Mapping process • Planning stage – needs assessment – project specifications are established (cost/time) • Data acquisition stage – primary data/secondary data • Cartographic production stage – design – drafting – proofing – printing • Product delivery stage

Georeferencing • the representation of the location of real world features within the spatial framework of a particular coordinate system

Relationship between coordinate systems and map projections • Map projections define how positions on the Earth’s curved surface are transformed onto a flat map surface • Coordinate systems provide a referencing framework by which positions are measured and computed.

Plane coordinate systems • Plane rectangular system (Cartesian) • Plane polar coordinates

Cartesian sytem (Figure 2.4) • X-axis (easting) • Y-axis (northing) • 1 st quadrant (+x, +y) • 2 nd quadrant (+x, -y) • 3 rd quadrant (-x, -y) • 4 th quadrant (-x, +y)

Plane polar coordinate system (Vector) see Figure 2.5

• Polar axis = baseline • Radius vector, vectorial angle • Positive angles are measured in clockwise direction from polar axis

conversions • One can convert from plane rectangular coordinate to plane polar coordinates using basic trigonometric functions

Geographic Coordinate System Latitude Longitude angular distance north or south of baseline (equator) angular distance east or west of baseline (prime meridian) graticule = grid of latitude and longitude lines (parallels and meridians) on a map or globe

Map projection • Is a systematic representation of all or part of the surface of a round body, especially the earth, on a plane (Snyder, 1987) • a two-dimensional spatial rendition of a the Earth’s surface (Fesperman, 2002)

Spatial properties of a map (projection) • area • direction • distance • shape

Projection type • Equal area (equivalent) • conformal (orthomorphic) • equidistant preserves area shape distance

Map projection types a developable surface is one that can be laid flat without distortion (see Figure 2.11) Cylindrical Conical Planar

Map projection aspect • Describes the orientation of the developable surface relative to the globe • normal • transverse • oblique axis of cylinder or cone parallel to earth axis axis of cylinder or cone is perpendicular to earth axis axis oriented between normal and transverse cases

Map projection viewpoints Figure 2.13

• Gnomonic – Light source at center of globe – Great circles are straight lines (navigation) • Orthographic – Light source at infinity – Equal areas preserved • Stereographic – Light source at far side of globe – Planar are conformal, cylindrical are compromised

see Table 2.1

The Ellipsoid the earth is not a sphere, but an oblate spheroid, being slight depressed at the poles satellite-based observations have allowed for the development of global standard in mathematical model

The Geoid • reference surface for vertical coordinates (above or below the datum) • equivalent to mean sea level in the earth’s oceans • determined by equal gravimetric potential