LECTURE TWO Representations, Projections and Coordinates

Transcription

1 LECTURE TWO Representations, Projections and Coordinates

2 GEOGRAPHIC COORDINATE SYSTEMS

3 Why project?

4 What is the difference between a Geographic and Projected coordinate system?

5 PROJECTED COORDINATE SYSTEMS Mathematical procedure for transforming the round Earth into a two-dimensional surface A projection is chosen based on the purpose of the map All projections maintain some form of accuracy while sacrificing others NO PROJECTION IS PERFECT

6 PROJECTIONS Create a point of contact between 3D and 2D surface Each contact point is called a tangent The contact points determine the locations on the 2D surface of zero distortion In general, distortion increases away from tangent

7 PROJECTION TYPES Conic Cylindrical Azimuthal

8 CYLINDICAL PROJECTIONS Projected onto a cylinder Equator is most common tangent line Reasonably true shapes and distances within approximately 15 of tangent

9 AZIMUTH PROJECTIONS Globe is transferred onto a circular plane Tangent to a point on the plane True directions are shown from one central point to all other points Good for showing continents and poles

10 CONIC PROJECTIONS Globe is transferred onto a cone-shaped plane Tangent along one or more standard line Used for mid-latitude zones with east-west orientation

11 DISTORTIONS FROM PROJECTIONS 1. Distance 2. Direction 3. Area 4. Shapes

12 PROJECTION SUB-TYPES 1. Conformal Used to preserve local shapes by ensuring angles are maintained Accomplished by establishing 90 angles between parallels and meridians Disadvantage is that area is distorted

13 PROJECTION SUB-TYPES 2. Equal Area Projections Preserve area of spatial features Paralells and meridians are not at 90 angles Shape and angle are distorted

14 PROJECTION SUB-TYPES 3. Equidistant Projections Preserve the distance between points Scale is maintained along lines (i.e. true lines) Shapes and area are distorted

15 PROJECTION SUB-TYPES 4. True Direction Projections Preserve the direction (angles) from center of map to all other locations Some true-direction projections are also equalarea, equidistant and conformal projections

16 SPECIFIC PROJECTIONS Each type of projection has many specific projections that aim to maintain certain features at the expense of others

17 SPECIFIC PROJECTIONS Albers conical equal-area commonly used to project the United States

18 SPECIFIC PROJECTIONS Mercator Cylindrical is most well-known for portraying the whole world Reasonably true shapes and distances within 15 of tangent Much distortion occurring near the poles

19 UTM Universe Tranverse Mercator (UTM) is good for maintaining area, shape and direction for relatively small areas.

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21 DATUM Defines a position on an ellipsoid relative to the centre of the earth These sets of points are used to determine the shape of the earth and to define geographic coordinate systems In North America, the 1927 Datum (NAD27) was replaced by the 1983 Datum (NAD83), resulting in different coordinates for all places

22 Decimal Degrees lat: long: Degrees, minutes, seconds lat: N long: W

23 DMS to DECIMAL DEGREES 45 43'41 W 1. Calculate the total number of seconds: 43'41" = (43* ) = 2621 seconds 2. The fractional part is total number of seconds divided by 3600: 2621 / 3600 = ~ Add fractional degrees to whole degrees to produce the final result: = Since it is a West longitude coordinate, negate the result The final result is

24 DECIMAL DEGREES TO DMS Subtract the whole number portion of the coordinate, leaving the fractional part. The whole number is the number of degrees = 45 degrees 2. Multiply the remaining fractional part by 60. This will produce a number of minutes in the whole number portion x 60 = = 43 minutes 3. Multiply the fractional part of the number of minutes by 60, producing a number of seconds x 60 = = 41 seconds Since the value has a negative sign, the coordinate is West The final result is 45 43'41W

25 DATA CLASSIFICATION

26 CHOROPLETH MAPS Constructed form values describing the properties of areas that are non-overlapping, such as census tracts or provinces Each area contains a colour, shade or texture to symbolize the value of a specific variable Distribution of colours is dependant on how the data is classified

27 CLASSIFICATION METHODS Natural Breaks: Classes are created based on natural groupings in the data distribution Class boundaries or break points are defined by picking the break that best group similar values and maximize the differences between classes As a result, the features are divided into classes whose numeric boundaries are set where there are relatively big jumps in the data values

28 CLASSIFICATION METHODS Equal Interval: The range of values in the data distribution is divided into equal-sized intervals There are usually fewer values at the extremes, thus the numbers of values are less in the extreme classes This option is useful to highlight changes in the extremes

29 CLASSIFICATION METHODS Quantile: The data distribution is divided so that the number of values is the same in each class As a result, the interval sizes are not equal

30 CLASSIFICATION METHODS Standard Deviation: The range of possible values is divided into intervals based on how far away values are from the mean

31 CLASSIFICATION METHODS Manual: The range of possible values is divided into intervals based on user-defined classes