Longley Chapter 3. Representations

Transcription

1 Longley Chapter 3 Digital Geographic Data Representation Geographic Data Type Data Models Representing Spatial and Temporal Data Attributes The Nature of Geographic Data Representations Are needed to convey information Fit information into a standard form or model In the diagram the colored trajectories consist only of a few straight lines connecting points Almost always simplify the truth that is being represented There is no information in the representation about daily journeys to work and shop, or vacation trips out of town 1

2 Representations Occur: In the human mind, when information is acquired through the senses and stored in memory In photographs, which are two dimensional models of light received by the camera In written text, when information is expressed in words Digital Representation Uses only two symbols, 0 and 1, to represent information The basis of almost all modern human communication Many standards allow various types of information to be expressed in digital form MP3 for music JPEG for images ASCII for text GIS relies on standards for geographic data 2

3 Why Digital? Economies of scale One type of information technology for all types of information Simplicity Reliability Systems can be designed to correct errors Easily copied and transmitted At close to the speed of light Accuracy of Representations Representations can rarely be perfect Details can be irrelevant, or too expensive and voluminous to record It s important to know what is missing in a representation Representations can leave us uncertain about the real world 3

4 The Fundamental Problem Geographic information links a place, and often a time, with some property of that place (and time) The temperature at 34 N, 120 W at noon local time on 12/2/99 was 18 Celsius Schematic representation of the lives of three US citizens in space (two horizontal axes) and time (vertical axis) The potential number of properties is vast In GIS we term them attributes Attributes can be physical, social, economic, demographic, environmental, etc. Types of Attributes Nominal, e.g. land cover class Ordinal, e.g. a ranking Interval, e.g. Celsius temperature Differences make sense Ratio, e.g. Kelvin temperature Ratios make sense Cyclic, e.g. wind direction 4

5 Cyclic Attributes Do not behave as other attributes What is the average of two compass bearings, e.g. 350 and 10? Occur commonly in GIS Wind direction Slope aspect Flow direction Special methods are needed to handle and analyze The Fundamental Problem (cont.) The number of places and times is also vast Potentially infinite The more closely we look at the world, the more detail it reveals Potentially ad infinitum The geographic world is infinitely complex Humans have found ingenious ways of dealing with this problem Many methods are used in GIS to create representations or data models Spatial Data Types are represented with Data Models 5

6 Spatial Data Types continuous: elevation, rainfall, soil type areas (polygons): unbounded: landuse, market areas, soils, rock type bounded: city/county/state boundaries, ownership parcels, zoning moving: air masses, animal herds, schools of fish networks (lines): roads, transmission lines, streams points: fixed: wells, fire hydrants, trees, addresses moving: cars, wolves, birds Discrete Objects and Continuous Fields These are the two ways of conceptualizing geographic variation The most fundamental distinction in geographic representation Discrete objects, or data that represents phenomenon with welldefined boundaries Continuous fields, or data that represents variation of value of a theme consistently and continuously over space 6

7 Discrete Objects Characteristics of Discrete Objects: Points, lines, and areas Countable Persistent through time, perhaps mobile Biological organisms Animals, trees Human made objects Vehicles, houses, fire hydrants Continuous Fields Characteristics of continuous fields: Properties that vary continuously over space Value is a function of location Property can be of any attribute type, including direction Elevation as the archetypical example: A single value at every point on the Earth s surface The source of metaphor and language Any field can have slope, gradient, peaks, pits 7

8 Examples of Fields Soil properties, e.g. ph, soil moisture Population density But at fine enough scale the concept breaks down Identity of land owner A single value of a nominal property at any point Name of county or state or nation Atmospheric temperature, pressure Difficult Cases Lakes and other natural phenomena Often conceived as objects, but difficult to define or count precisely Weather forecasting Forecasts originate in models of fields, but are presented in terms of discrete objects Highs, lows, fronts 8

9 How Do We Represent These Data Types in a GIS? The Raster and Vector data models Rasters and Vectors How to represent phenomena conceived as fields or discrete objects? Raster Divide the world into square cells Register the corners to the Earth Represent discrete objects as collections of one or more cells Represent fields by assigning attribute values to cells More commonly used to represent fields than discrete objects 9

10 Concept of Vector and Raster Real World Raster Representation R T 1 R T 2 H R 3 R 4 R R 5 R 6 R T T H 7 R T T 8 R 9 R Vector Representation point line polygon Characteristics of Rasters Pixel size The size of the cell or picture element, defining the level of spatial detail All variation within pixels is lost Assignment scheme The value of a cell may be an average over the cell, or a total within the cell, or the commonest value in the cell It may also be the value found at the cell s central point 10

11 Raster representation Each color represents a different value of a nominal-scale field denoting land cover class Legend Mixed conifer Douglas fir Oak savannah Grassland Representing Data using Raster Model Area is covered by grid (usually) with equal sized cells Location of each cell calculated from origin of grid: two down, three over (usually from upper left, but lower left in ARCVIEW) commercial industrial Res. Res. public Called raster cells or pixels (picture elements) raster data often called image data Attributes are recorded by assigning each cell a single value based on the majority feature (attribute) in the cell, such as land use type

12 Y X Representing Data using Raster Model Easy to do overlays/analyses, just by combining corresponding cell values: crime index = juvenile + adult crime rate (I think it s potentially improper ) why raster is faster, at least for some things Simple data structure: directly store each layer as a single table analogous to a spreadsheet ) commercial industrial Res. Res. public no computer database management system (DBMS) required although GIS systems incorporate them 12

13 Y X 13

14 Raster representation Each color represents a different value of a nominal-scale field denoting land cover class Legend Mixed conifer Douglas fir Oak savannah Grassland 14

15 Raster Data Sets: Data Landsat TM(1992) & ETM+ (2002) 17/32 17/32 10/02/ /06/2002 Classified Data: 15

16 Vector Data Used to represent points, lines, and areas All are represented using coordinates One per point Areas as polygons Straight lines between points, connecting back to the start Point locations recorded as coordinates Lines as polylines Straight lines between points Representing Data using the Vector Model: General concept The fundamental concept of vector GIS is that all geographic features on the earth s surface (or on a map) can be represented either as: points (no area): trees, sample locations, crime locations, rocks, manhole covers lines (arcs): streets, sidewalks, transmission lines, streams areas (polygons): cities, counties, buildings, states, ponds and lakes, land uses, land covers Which is used in a particular instance depends on scale, among other things: for example Leonard Hall may be a point or polygon Because representation depends on shape, ArcView refers to files containing spatial data as shapefiles. 16

17 Representing Data using the Vector Model: Point (node): 0 dimension one x,y coordinate pair zero area tree, oil well, label location Line (arc): 1 dimension two (or more) connected x,y coordinates road, stream Polygon : 2 dimensions four or more ordered and connected x,y coordinates first and last x,y pairs are the same encloses an area census tracts, county, lake y=2 2 x= Point: 7,2 Line: 7,2 / 8,1 Polygon: 7,2 / 8,1 / 7,1 / 7,2 Attribute data on the right are linked to spatial data by the label ID of map features 17

18 Representing Data using the Vector Model: Data implementation Features in the theme (coverage) have unique identifiers--point ID, polygon ID, arc ID, etc Usually referred to as the Feature ID (FID) Y Common identifiers provide link to: coordinates table (for where) attributes table (for what or when) 2 3 X Coordinates Table Point ID x y Point ID Crime time 1 robbery 9:30 2 assault 11:30 3 drug 5:00 4 robbery 2:30 5 b & e 3:00 Concepts are those of a relational data base, which is really a prerequisite for the vector model (or need object-oriented computing environment) (Vector) Topology: What is it? Programmed rules in GISs like ArcGIS that establish spatial relationships between features (points, lines, polygons) Spatial Relationships each arc has a beginning and ending node Spatial Properties length, directionality of arc arcs connect to other arcs at nodes connectivity connected arcs form polygon boundaries area, perimeter of polygons arcs have polygons on their left and right adjacency or contiguity containment point or line in polygon 18

19 The Vector Data Model: Topological vs. Non topological Spatial Data Topological Vector Data contains data regarding the (spatial) relationships between features Ex. ArcGIS coverages, geodatabases Non topological no data regarding spatial relationships is recorded or stored Ex. ArcGIS shapefiles Point (node): 0-dimension single x,y coordinate pair zero area (Example: tree, oil well, label location) The data structure of a point data model 1 (2,9) Point List ID X,Y Y 2 (4,4) 1 2,9 2 4,4 3 2,2 3 (2,2) 4 (6,2) 4 6,2 (0,0) X 19

20 Line (arc): 2-dimension From Nodes (points) T Nodes (points) x,y coordinate pair(s) depend # of Nodes and vertices zero area (Example: tree, oil well, label location) The data structure of a line data model The data structure of an area (polygon) data model 20

21 GIS Data Models: Raster vs. Vector Raster data model location is referenced by a grid cell in a rectangular array attribute is represented as a single value for that cell many data comes in this form images from remote sensing (LANDSAT, SPOT, QuickBird) scanned maps elevation data from USGS best for continuous features: elevation temperature soil type land use Vector data model location referenced by x,y,z coordinates, which can be linked to form lines and polygons attributes referenced through unique ID number to tables many data comes in this form DIME and TIGER files from US Census DLG from USGS for streams, roads, etc census data (tabular) best for features with discrete boundaries property lines political boundaries transportation Raster vs Vector Volume of data Raster becomes more voluminous as cell size decreases Source of data Remote sensing, elevation data come in raster form Vector favored for administrative data Software Some GIS used to be better suited to raster, some to vector, now all handle both 21

22 The GIS Model: example Here we have multiple layers: --vegetation --soil --hydrology They can be related because precise geographic coordinates are recorded for each layer. longitude Layers may be represented in two ways: in vector format as lines in raster(image) format as pixels 22