Geographers Perspectives on the World

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1 What is Geography? Geography is not just about city and country names Geography is not just about population and growth Geography is not just about rivers and mountains Geography is a broad field that studies all sorts of phenomena on the Earth s surface, including natural and human components, and these are termed human and physical geography. Geography is present in your everyday life: The air you breathe, the water you drink, the place where you live, the people you meet

2 Geographers Perspectives on the World Location matters Real-world relationships Horizontal connections between places Importance of scale (both in time and space)

3 Definition: Introduction to Maps A graphic depiction on a flat medium of all or part of a geographic realm in which real world features have been replaced with symbols in their correct spatial location at a reduced scale. To map is to transform information from one form to another --- Mathematics Earth surface map Paper --- Geography

4 Neat line Map Elements Title Border Map/Spatial Data Ground Legend Scale Inset Place name North Arrow Credits

5 Data Symbolization There are a number of characteristics of symbols that we can use of to make visual distinctions in thematic information (Jacques Bertin s Visual Variables): Size Shape Color Hue (color) Color Value (intensity) Texture Orientation Arrangement

6 The Effect of Classification Four common ways to display continuous data in ArcView (i.e. these are options in the Legend Editor): Equal Interval Quantiles Natural Breaks Standard Deviation

7 Natural Breaks Quantiles Equal Interval Standard Deviation

8 Representing the Real World In a GIS, the representation of real world phenomena makes use of digital data formats Earth surface Digital data representation

9 Binary Notation Everything is represented as 0s and 1s in a computer. These two-state forms correspond to yes/no, on/off, open/closed Binary Decimal 1 digit 0, 1 1 bit 0,1,2, 9 2 digits 00, 01 2 bits 00, 01, 10, 11 97, 99 3 digits 000, bits 000, 001, 010, , 003, 100, , , 999 One to one correspondence Decimal Binary ?

10 Two Fundamental Sorts of Representations Regardless of what phenomena of interest we chose to include in our geographic representation, we first must choose between a model that either represents geography as discrete objects OR represents geography as fields Most GIS approaches focus on the discrete object view, and we ll look at it in greater detail, although we will look at field representations as well

11 Entities Data Objects In the discrete object view, we associate each and every entity we wish to represent with its own data object a digital building block used in a data structure to represent an entity (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) point line polygon (area) (x,y) (x,y)

12 The Field View In contrast to the discrete object view, which models the world in terms of entities, the field view approaches the world as consisting of continuous phenomena: The field view represents the real world as a finite number of variables, each one defined at every possible position (p.69 of the text) This view is inherently problematic for digital representation, which necessarily has to discretize the world into some set of minimum units

13 Spatial Data Models Raster uses individual cells in a matrix, or grid, format to represent real world entities Vector uses coordinates to store the shape of spatial data objects

14 Vector Data Model - Objects Features in the real world are represented by objects that are chosen to approximate their shape Geographic Primitives Points 0 dimensional Lines 1 dimensional Polygons 2 dimensional

15 Vector Data Model - Topology Topology defines spatial relationships. The arcnode data structure supports the following topological concepts: Area definition: Arcs connect to surround an area, defining a polygon Containment: Nodes (or arcs) can be found within a polygon Connectivity: Arcs connect to each other at shared nodes Contiguity: Arcs have a defined direction, and left and right sides

16 Raster Data Model The raster data model represents the Earth s surface as an array of two-dimensional grid cells, with each cell having an associated value: Cell (x,y) Cell value rows columns Cell size = resolution

17 Cell Size & Resolution The size of the cells in the raster data model determines the resolution at which features can be represented The selected resolution can have an effect on how features are represented: 10 m Resolution 5 m Resolution 1 m Resolution

18 Rules for Assigning Cell Values Cell values are assigned to cells accorded to some set of rules, and selecting those rules differently can also effect the representation of features:

19 Vectorization and Rasterization Often, an application will require the combination of data from many sources, represented using more than one spatial data model, e.g. political boundaries (vector model) being used in conjunction with satellite remote sensing derived raster data In different instances it is desirable to convert the data in either direction: Vectorization: The conversion of raster data to the vector data model Rasterization: The conversion of vector data to the raster data model

20 Vectorization - Lines Through this procedure, there is some information loss at various stages of the process: Lost information

21 Rasterization - Issues The key issues to are: cell size, and its effect on the spatial representation of entities AND how we choose cell values to represent attributes This is simpler compared to vectorization.

22 Georeferencing GOAL: To assign a location to all the features represented in our geographic information data In order to do so, we need to make use of the following elements: ellipsoid/geoid To determine a position datum on the Earth, you ll need to understand how projection these elements relate to coordinate system each other in order to scale specify a position The next few lectures will introduce you to these elements

23 Geodesy Review Sphere The simplest 3D model of the earth Ellipsoid A more accurate model that takes into account some of the Earth s irregularity Geoid The most accurate, most complex model of the Earth, taking into account the Earth s minor variations from an ellipsoid Geodetic datum The information that ties an ellipsoid model to the geoid model

24 Ellipticity of the Earth How far is the Earth from being a perfect sphere? Semi-major axis a The two axes of an ellipsoid b Semi-minor axis Using these two axes lengths we can calculate the ellipticity (flattening) of an ellipsoid, with f = 0 being a perfect sphere and f = 1 being a straight line

25 The Earth as Geoid Geoid The surface on which gravity is the same as its strength at mean sea level If the Earth were completely uniform in its geological composition, landforms and density, then the geoid would match the ellipsoid exactly

26 Geodetic Datum In order to manage the complexities of the shape of a geoid model of the Earth, we use something called a geodetic datum Datum -- n. (dat - m) \ any numerical or geometric quantity which serves as a reference or base for other quantities e A geodetic datum is used as a reference base for mapping It can be horizontal or vertical It is always tied to a reference ellipsoid

27 What is a Projection? Map projection - The systematic transformation of points on the Earth s surface to corresponding points on a planar surface The easiest way to imagine this is to think of a light bulb inside of a semi-transparent globe, shining features from the Earth s surface onto the planar surface

28 Projections Distort Because we are going from the 3D Earth 2D planar surface, projections always introduce some type of distortion When we select a map projection, we choose a particular projection to minimize the distortions that are important to a particular application

29 Three Families of Projections There are three major families of projections, each tends to introduce certain kinds of distortions, or conversely each has certain properties that it used to preserve (i.e. spatial characteristics that it does not distort): Three families: 1. Cylindrical projections 2. Conical projections 3. Planar projections 3 2 1

30 Preservation of Properties Every map projection introduces some sort of distortion because there is always distortion when reducing our 3- dimensional reality to a 2-dimensional representation Q: How should we choose which projections to use? A: We should choose a map projection that preserves the properties appropriate for the application, choosing from the following properties: 1. Shape 2. Area 3. Distance 4. Direction Note: It may be more useful to classify map projections by the properties they preserve, rather than by the shape of their developable surfaces

31 Tissot s Indicatrix Tissot s Indicatrix is a graphical tool which we can use to assess the properties preserved by a projection Tissot s Indicatrix allows us to take a feature that is a perfect circle before projection, and then see how it looks once projected (usually the distortion causes it to be elliptical in shape) We can calculate s = "area scale" = the product of semimajor and semi-minor axes of the ellipse

32 Coordinate Systems We are going to discuss two kinds of coordinate systems: The geographic coordinate system expresses positions in terms of latitude and longitude, and like all spherical coordinate systems, the definitions of these quantities are in terms of angles Planar coordinate systems place a Cartesian grid on a 2-dimensional surface (like our projected maps and geodatabases) and express a position in terms of (x,y) coordinate pairs

33 The Geographic Coordinate System Every coordinate system needs to have an origin where the coordinate values are zero, and the geographic coordinate system s origin is specified using: The Equator is the origin for latitude positive in N. hemisphere negative in S. hemisphere The Prime Meridian is the origin for longitude positive in E. hemisphere negative in W. hemisphere

34 Planar Coordinate Systems Once we start working with projected spatial information, using latitude and longitude becomes less convenient We can instead use a planar coordinate system that has x and y axes, an arbitrary origin (a Cartesian plane), and some convenient units (e.g. ft. or m.) When applied in a geographic context: Eastings are x values Northings are y values

35 Planar Coordinate Systems Some common examples of planar coordinate systems that are in use: The Universal Transverse Mercator Coordinate System is used throughout the world In the United States, the State Plane Coordinate System is used, which provides coordinate grids for each state, using multiple zones and grids in many of the larger states in order to minimize projection distortions

36 Universal Transverse Mercator

37 Universal Transverse Mercator We can describe the location of each zone in terms of its central meridian, which falls on on a meridian with an integer value of longitude

38 Universal Transverse Mercator The central meridian, which runs down the middle of the zone, is used to define the position of the origin Distance units in UTM are defined to be in meters, and distance from the origin is measured as an Easting (in the x-direction) and a Northing (in the y-direction) The x-origin is west of the zone (a false easting), and is placed such that the central meridian has an Easting of 500,000 meters

39 State Plane Coordinate System The State Plane Coordinate System (SPCS) is only defined and used in the United States Like UTM, it is divided into zones, but here zones are fully contained within states Some larger states contain multiple zones Original units are feet, many states are now switching to meters

40 Representing Scale on Maps Definition: The scale of a map is ratio between distances on the map and the corresponding distances in the real world. Scale representation on the map: Representative fraction (RF): 1:100,000, 1 to 100,000, or 1/100,000 Verbal: 1 inch is equal to 50 miles Graphic: Scale bar 10 miles Purpose (or a kind of question that scale can answer): Scale information allows us to answer questions like: 1 inch on a 1:24000 map represents what distance on the surface of the Earth? (2000 feet)

41 Scale and Map Projections When we describe map scale in terms of a representative fraction, it is easy to forget that the RF does not tell us the scale everywhere on the map! One of the implications of projection that that we must recall is that: scale is affected by the 3D to 2D transformation projections transformations introduce distortion RF is only accurate along standard lines or points

42 Map Scale and Spatial Resolution Spatial resolution is a concept that is related to map scale: It is determined by the smallest physical mark that can drawn (or discerned) on a map accurately This limits the smallest geographic feature or distance that can be represented accurately on the map This is directly related to the scale of the map - Why? Consider the relationship between the size of the smallest mark we can make (or see/accurately measure) and the smallest feature in the real world that can be represented on the map

43 Maps and GIS - Scaling Up All the detail that is encoded in this river network data is really only visible and useful when operating at more local scales This level of detail is not necessary or useful at the national scale. GIS does not modify the level of detail in the representation of features when scaling up or down

44 Maps and GIS - Scaling Down Here we can see a national scale coastline (shown in red) superimposed over local scale data, we can clearly see the generalization and lack of detail

45 The Two Types of Data in GIS Spatial data: Describing where things are AND Attribute data: Describing what things are Example: A point specified by UTM coordinates Easting = 50,000 m Northing = 5,000,000 m Zone =17 This specifies the location of a point of the ground The nature of the real-world feature located at this point would be recorded in the attribute data Traditionally, geographic data and attributes were recorded on paper too (maps), and these had the same problems as a phone book

46 The Role of DBMS in GIS System Geographic Information System Database Management System Task Data load Editing Visualization Mapping Analysis Storage Indexing Security Query Data

47 Relational Data Model The relational model organizes data in a series of twodimensional tables, each of which contains records for one kind of entity records PID # Fields Name Major Phone # John Geog David Comm This model is a revolution in database management It replaced almost all other approaches in database management because it allows more flexible relations between kinds of entities

48 Relational Join Take two tables full of different data (e.g. registrar info & parking data), and join them: PID # Name Major Phone # John D. Geog David Q. Comm PID # Name Parking Lot License Plate John D. Friday Ctr. PNT David Q. Airport Rd. JRS4089 The tables are joined through a common key which has a unique value for each record

49 Spatial Relations In addition to relations that join tables based on an identical common key, we can evaluate relations between the spatial characteristics of features: Equals same geometries Disjoint geometries share common point Intersects geometries intersect Touches geometries intersect at common boundary Crosses geometries overlap Within geometry within Contains geometry completely contains Overlaps geometries of same dimension overlap Relate intersection between interior, boundary or exterior

50 Contains Relation

51 Touches Relation

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