Lab #3 Map Projections.

Transcription

1 Lab #3 Map Projections

2 Map Projections Projection: a systematic arrangement of parallels and meridians on a plane surface representing a geographic coordinate system (Chang, 2015). Map projections are geometrical or mathematical calculations which convert features from a spherical surface to a flat surface. A coordinate system for that projection is then added. Projection refers to the notion of shining light through the earth surface and projecting latitudes, longitudes and geographic features onto a developable surface.

3 Map Projection Families Common projections can be grouped into one of four families, three of which are based on developable geometric forms the cylinder, the cone, and the plane. A fourth family, often referred to as simply mathematical, include projections which do not fit a geometric form, but are simply mathematically-derived graticules (ex., pseudocylindrical)

4 Map Projection Parameters Projections have a variable list of important parameters, including standard points, standard lines/parallels, central meridians, and lines of origin.

5 Map Projection Cases Tangent Case: a) azimuthal/planar b) cylindrical c) Conic From: Dent, B.D.; Torguson, J.S. & Hodler, T.W Cartography: Thematic Map Design, 6 th Edition. New York, New York : McGraw-Hill. p. 38 Secant Case: a) azimuthal/planar b) cylindrical c) conic From: Dent, B.D.; Torguson, J.S. & Hodler, T.W Cartography: Thematic Map Design, 6 th Edition. New York, New York : McGraw-Hill. p. 39

6 Map Projections Due to the nature of transferring features from a spherical to a flat surface, every projection has inherent distortions. All map projections share a key set of geometric properties, including: i. Area ii. Shape iii. Distance iv. Direction Type of Projection Properties Maintained Properties Distorted Equivalent (Equal-area) area direction, shape, distance Equidistant distance direction, area Azimuthal Conformal direction and distance from a central point angles at any point, shapes for small areas shape, area the size of large areas

7 Map Projection Distortions Conical tangent and secant projection and associated patterns of distortion Distortion is minimized and scale is most accurate closest to the standard parallels Cylindrical tangent and secant projection and associated patterns of distortion

8 Projection Datum Datum: mathematical model of the the Earth s surface, which serves as the reference or base for calculating the geographic coordinates of a location. (Chang, 2015) The older, North American Datum of 1927 ( NAD27 ) was based on the Clarke Spheroid of 1866 which had reference points (in the form of surveying monuments) on the ground. The newer, NAD83 datum is based on the Geodetic Reference System of 1980 (GRS 1980), which has the centre of the earth as a reference. The size and shape of the earth was calculated from satellites. When projecting datasets includes use of a different datum, a mathematical transformation is required. These transformations (where available) are generally included within GIS software.

9 Projection Datum (cont d) Differences in a feature s position between NAD83 and NAD27 can be from ~ 10 m to ~ 200 m, depending on where in North America they are measured. The original Ontario Base Map (OBM) series was in NAD27 (often with a - 4,000,000m y-shift) and so other OBM-related GIS datasets created in that period inherited those spatial properties. Systematic shifts can easily be dealt with inside most GIS packages, provided the nature of the shift is known. If the projection (including that information) is not already defined, it can be. With a defined projection and shift, that layer can then be reprojected (into an alternative projection).

10 Lambert Conformal Conic Projection Conformal, secant projection, based on two standard parallels Small shapes and local angles are relatively accurate Area is minimally distorted and east-west distances are accurate near the standard parallels Area is increasingly distorted further from the standard parallels Required parameters: Units 1 st standard parallel 2 nd standard parallel Central meridian Latitude of projection s origin Suitable for areas or countries extending east-west (Canada, USA), at large and medium scales.

11 UTM (Universal Transverse Mercator) Projection Cylindrical, secant, conformal projection UTM projection is derived by positioning the cylinder east-west, perpendicular or Transverse to the standard Mercator projection where the cylinder is oriented north-south

12 UTM (Universal Transverse Mercator) Projection Universal points to the fact that the projection is applicable world-wide UTM consists of 60 zones, 6 degrees of longitude wide (360 /6 = 60), around the world, positioned north-south. From: Dent, B.D.; Torguson, J.S. & Hodler, T.W Cartography: Thematic Map Design, 6 th Edition. New York, New York : McGraw-Hill. p. 58

13 The central meridian for each UTM zone, corresponds to a line of longitude, six degrees from the central meridian of neighbouring zones. UTM in Canada Canada is covered with 16 zones, 7-22 Ontario is covered with 4 zones, Thunder Bay is in UTM zone 16, with a central meridian at 87 ; the central meridian for UTM zone 15 is at 93 (six degrees west), and so on.

14 UTM Zone 6 degrees of longitude wide ~ 672 km on the Equator, becoming narrower towards north and south. X and Y coordinates are expressed in meters, with a six-digit easting and seven-digit northing (ex., , ). Secant meridians The central meridian has a false easting of 500,000 m to avoid having negative easting values within a zone. Y coordinates represent the distance north or south of the Equator. Small shapes and local angles accurate. Area minimally distorted within each zone.

15 UTM Projection (cont d) Some large areas (e.g, forest management units, large parks) fall between UTM zones which can cause problems with file projections and map orientations! Data can be projected into other (neighbouring) zones, though angles become increasingly distorted as distance from the normal zone increases. MNR for some time applied a false northing (i.e., Y-shift) of ,000 m to GIS datasets. These datasets also have a NAD27 datum. Required parameters: Zone Datum

16 Geographic Projection Not a true projection, but a coordinate system of the Earth s spheroid, composed of longitudes (meridians) and latitudes (parallels), and expressed in degrees. Longitudes range from 0 degrees at the Prime Meridean to + or degrees around the International Date Line, for the eastern and western hemispheres respectively Latitudes range from 0 degrees at the equator to + or -90 degrees at the north and south poles respectively For converting to other projections, coordinates are usually expressed as decimal degrees (ex ) rather than degrees-minutes-seconds (ex ) 0 (-180 ) (-90 )

17 GIS Datasets and Map Projections GIS datasets could be in several different states (with respect to map projection): (a) Dataset s projection is properly defined. thunder_bay.shp (b) Dataset s projection is undefined. thunder_bay.shp (c) Dataset s projection is not what is desired or is improperly defined thunder_ bay.shp Y = X = OrthoEngine file present UTM, Zone 16, NAD83 Y = X = ? Y = X = OrthoEngine file present UTM, Zone 15, NAD83 Fix: N/A Define the shapefile with the proper map projection. Reproject with a new name and the desired projection/datum.

18 ArcToolbox Projection Functions The Define Projection function in ArcToolbox (Data Management Tools Projections and Transformations Define Projection) is used when a file has a coordinate system but does not have a projection. Within the Define Projection function, the Modify setting can be used to correct X and Y shifts. A dataset must have a defined projection in order to be converted to a new projection. The Project function and Project Raster function are used to reproject already projected data into a new projection for vector data or raster data, respectively. The invalid sign in the Project function window often means one of two things: a) The input dataset does not have a defined projection b) The folder with the input dataset needs to be refreshed in ArcCatalog

19 Input dataset (e.g. shapefile) ArcGIS - Define Projection Function Projection to be defined. Examples Geographic coordinate system North America Projected coordinate system UTM Projected coordinate system Continental NAD 1983 NAD 1983 North America NAD 1983 UTM Zone 16N Canada Lambert Conformal Conic

20 Modifying Projections The Modify button in the Spatial Reference Properties window can be used to modify the parameters of a given projection, such as false easting, false northing, central meridian, standard parallels, latitude of origin An example is defining the -4,000,000m Y-shift in old OBM data and other products

21 ArcGIS Data Frame s Coordinate System ArcMap is capable of recognizing the projections of input layers with defined projections and projecting the layers on-the-fly to conform with the Data Frame s projection. The projection of the first layer with a defined projection added to the project is adopted by the Data Frame as the working projection. The Data Frame s projection can be changed from one projection into another one (right click on the data frame > Properties > Coordinate System > Select a coordinate system or Import the coordinate system from an existing dataset).

22 ArcGIS - Project Function Input dataset (e.g. shapefile) The defined projection of the input dataset will load automatically Output file name (e.g. shapefile) Select new projection for output dataset A geographic transformation will be required if the new projection uses a different datum than the input dataset.

23 Dataset Projections in ArcGIS Projection information for a particular dataset can be viewed in the Source tab of the Layer Properties (right-click on the layer and select Properties ) Also, a dataset s X and Y coordinates can be viewed in the Preview tab (Geographic), in ArcCatalog (lower right corner).

24 Data Types and Data Models In GIS, data types and data models are forms of representation of observed phenomena. Data models representations of spatial features/phenomena Data types representations of values Data Types: Numeric Text (string, character) Date Boolean (binary) Representations: Integer (whole number): 1, -1, 2, 102 Text (letters like a, b, c, but also characters 1, 2, 3) Time and date True/False Floating point (real number with decimal values): ,

25 Data Types/Computer Storage Data Type should be properly specified for each field in the database (to be the attribute table) based on the type and form of the data to be held in that field.

26 Data Types/Computer Storage In the early stages of personal computer hardware development, the primary concern for setting data types was to minimize the amount of binary memory required Today, the appropriate data type is chosen by considering: - the type of data (thematic/nominal, ordinal, interval/ratio, textual), - the larger context (overall database), - expected queries/analyses/etc to be performed, especially with regard for the potential user s familiarity with the data