Massachusetts Institute of Technology Department of Urban Studies and Planning 11 520 A Workshop on Geographic Information Systems 11 188 Urban Planning and Social Science Laboratory Lecture 3 More GIS Principles Methods Projections and Coordinate Systems September 21 2005 Joseph Ferreira Jr including contributions from Visiting Prof Zhong Ren Peng who taught the class in Fall of 2003 Administrative notes Homework set 1 posted online today due in 2 weeks Lab Exercises 1 due today Lab Exercise 2 due next Monday at the start of the Lab Today s Topics Elements of the Map o Map scale symbology o Classification and thematic shading Map projections Vector Raster data models Elements of the Map Scale Ratio Scale 1 10 000 or 1 100 000 or 1 100 000 Verbal Scale One inch represents 2 000 feet 1 24 000 One centimeter represents 20 kilometers 1 2 000 000 Printout vs onscreen 10 foot pixel 72 pixels per inch onscreen One inch represents 720 feet 1 8 600 But some screens have higher lower pixel densities not all screens have square pixels also screendump to printer will change scale since printer will have different dot density than the screen Beware Good GIS software will try to match screen and printer properties to software settings so screen and printouts will show appropriate scale and show correct scalebars For the scale to be meaningful display units and hardware choices must be properly identified Large Scale or Small Scale In general Large scale 1 24 000 good for small area representation city block Small scale 1 500 000 good for large area representation metro area But scale is relative depends on the applications Large scale maps are more detailed than small scale maps Typical Scales Used In Metric System 1 10 000 or 1 25 000 1 50 000 1 100 000 In American System 1 9 600 one inch represents 800 feet 1 24 000 one inch represents 2000 feet 1 62 500 one inch represents slightly less than one mile Six Principal Visual Variables Use contrasting symbols to portray geographic differences For qualitative differences Use shape texture and hue e g land use types For quantitative differences Use size to show variation in amount or count e g population No of crime Use graytone or hue to show differences in ratio or intensity e g proportion of household in poverty population density Southern New England Counties Thematic mapping simplest display of spatially varying phenomena Note use of ArcMap help files regarding thematic map types classification choices o Different classification schemes Equal Interval Natural Breaks Quantile Standard Deviation o Number of classes color scheme etc o Normalization Why do we care o Exclusion options no data vs zero value Layouts Features of a good map lots more to good cartography see references o Title Legend Scale Bar North Arrow Data sources o Your name or organization o Other feature labels and annotations o Projections Geographic Reference System Latitude and Longitude Axis the center of earth rotation Equator The plane through the center of mass perpendicular to the axis Longitude lines slicing the earth parallel to the axis and perpendicular to the plane of equator The line goes through Greenwich has 0 longitude Range from 0 to 360 degrees or 180 degree west to 180 degree east Latitude Latitude is defined based on ellipsoid representing the shape of the earth See Prof Peter Dana s notes on projections and coordinate systems U of Colorado http www colorado edu geography gcraft notes coordsys c oordsys f html Click the images below to enlarge WG84 the World Geodetic System of 1984 is a standard ellipsoid In North America the most recent ellipsoid data it is called the North American Datum of 1983 NAD83 the earlier version is NAD27 Latitude definition A line drawn through a point of interest perpendicular to the ellipsoid at that location the angle made by this line with the plane of Equator is the latitude of that point Ranges from 90 degree south to 90 degree north What do Latitude and Longitude mean Two points on the same longitude separated by one degree of latitude are 1 360 of the circumference of earth apart or about 111 km apart One minute latitude is 1 86 km One second latitude is 30 m For the same latitude one minute of longitude separation corresponds to different distances depending on the latitude 111 km at equator nothing at the poles Nowadays latitude longitude often expressed in decimal degrees Distance calculation using latitude and longitude Latitude 90 90 Longitude 180 180 Arc distance between two points on the earth surface spherical Rcos 1 sin 1sin 2 cos 1cos 2cos 1 2 R is the radius of the spherical earth Cartesian Coordinate System Assign two coordinates to every point on a flat surface Map Projections Map projections transform the curved 3 D surface of the planet into a flat 2 D plane Note that Map projections distort map scale in various ways Transform a position on the Earth s surface identified by latitude and longitude into a position in Cartesian coordinates x y x f Y g Map projections necessarily distort the Earth and the map scale Example using Prof Peter Dana s notes U of Colorado http www colorado edu geography gcraft notes mapproj mapproj html Example using ArcMap ESRI sample data map of 50 US states Convert to Mass state plane and compare results The following contents of today s lecture is derived from Longley Goodchild Maguire and Rhind Geographic Information Systems and Science 2001 as organized by Prof Zhong Ren Peng for 11 520 in Fall 2003 Map Projection Classifications based on preservation properties The conformal property preserves the shapes of small features on the Earth s surface directions This is useful for navigation E g Mercator projection and Gnomonic projection The equal area property preserves the areas This is useful for analysis involving areas like the size of the property e g Goode s projection Any projection can have either conformal property or equal area property but not both Map Projection classifications based on physical surface models Cylindrical projections wrapping a cylinder of paper around the Earth projecting the Earth s features onto it and then unwrapping the cylinder Azimuthal or planar projections touching the Earth with a sheet of flat paper Conic projection wrapping a sheet of paper around the Earth in a cone All three types can have either conformal property or equal area property but not both Unprojected projection Plate Carr e or Cylindrical equidistance Projection Just maps