Representing the world
from infinitely complex reality to models and representations
Outline - what is representations, digital representations, Discrete objects and fields, Rasters and vectors and Projections.
Representations
Representations are needed to convey information. They are need to fit information into a standard form or model. In burglar diagram the coloured trajectories consist only of a few straight lines connecting points. If we looked closer we would reveal more information. They almost always simplify the truth.
Accuracy of Representations
Representations can rarely be perfect. Details can be irrelevant, or too expensive and voluminous to record. Its important to know what is missing in a representation. Representation can leave us uncertain about the real world.
Digital Representation
At its root 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 too be expressed in digital form. MP3 for music, JPEG for images, ASCII for text, GIS relies on standards for geographic data.
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 speed of light.
Digital data standards
Extensible Markup Language (XML). Help information systems share data particularly on the internet. In geographic information systems, a variety of standards. eg GML and KML, GeoRSS, GeoJSON. In GIS the open geospatial consortium (OGC) sets the standards for geo-spatial data.
Storing Digital geographic data
Geographic information links a place, and often a time, with some property of that place(and time). The temperature at 35N,120W at noon local time on 28/9/05 was 18 celsius. The potential number of properties is vast. In GIS we term them attributes. Attributes can be physical, social, economic, demographic, environmental etc. Attributes(data) can be classified by their type.
Nominal Attributes
Most basic data type. Otherwise known as categorical attributes, simply names or categories.
Ordinal Attributes
Ordinal attributes have an ordered or ranked relationship. The contain more information then nominal/categorical attributes as each attributes related to others in the rank.
Interval Attributes
With interval data, such as temperature, the differences between each value make sense. 40 degree Celsius is twice as hot as 20 degree Celsius. Interval values are not absolute - 0 degree Fahrenheit is clearly not 'no temperature' or absolute 0!
Ratio Attributes
Ratio attributes have a meaningful 0 point. Height above sea level is a classic ratio attribute.
Cyclic Attributes
Classic example is wind direction. Not a data type we will encounter too often.
The problem of reducing infinite complexity
The number of places and times is also vast. Potentially infinite data. The more closely we look at the world, the more detail it reveals. Potentially ad infinitum - Fractals! The geographic world is infinitely complex. Many methods are used in GIS to create representations or data models.
Geographic representation : 2 types
1. Discrete Objects : The most fundamental distinction in geography.Discrete objects examples are world as a tble-top. Objects with well-defined boundaries.
Points, lines and polygons. Countable state minnesota - 10000 lakes. Persistent through time, perhaps mobile. Biological organisms fit this model well eg animals and trees. As do human-made objects- vehicles, houses, fire hydrants.
2. Fields: Properties that vary continuously over space. Value is a function of location. Property can be of any attribute type, including directions. Elevation as the archetype. 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.
Rasters
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.
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.
Assigning reality into pixels. 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.
Vector data
Used to represent points, lines and polygons. All are represented using coordinates. One per point, lines as polylines. Straight lines between points. Areas as polygons. Straight lines between points, connecting back to the start. Point locations recorded as coordinates.
Raster vs Vector
Volume of data : Raster becomes more voluminous as cell size decreases.
Source of data : Remote sensing, elevation data come in rater form. Vector facvoured for a administrative data.
Analysis : Some Analyses are better suited to raster [map calculation, suitabitlity indices etc.], some to vector [route finding, network analysis etc.]
"Raster is vaster, and vector is correct" [only works with a Northern accent!]
But:
apperent precision of vector assumes high locational accuracy gerneralisation
Representing the globe
the earth is a 3d sphere [well, almost] in order to locate a point on the surface of a sphere , we a set of coordinates. Coordinates will tell us how near to the top or bottom of the sphere we are ,or how far around but where do we start?
Word geodectic system (wgs 84)
standard (3d) method of represting our geoid [last revesion established in 1984] used by gps coordinates are latitude and longitude greenwich is at prime meridian [zero line of longitude]. All places to east have +ve longitude, all to the west are -ve latitudes emanate from the poles.
3D into 2D- Projecting
But what if we want to view a 3D object in 2 D. 2D planes are easier to deal with (ever tried navigating with a globe.) Projections enable us to represent 3D coordinates on a 2D surface. But losing a dimension means we lose some information - different projects lose different information.
Mercator Projection
Invented for navigation purposes by Gerardus mercator in 1569. Bearings (angles) are preserved (particularly useful when navigating a ship with a compass). Area and distance are not preserved.
Defining Spatial/Coordinate reference systems.
Knowing which coordinate reference system (CRS) your coordinates are in is absolutely vital for being able to specify your point on the earth correctly. Frequently in GIS you will work with data which refer to points on the earth using different CRSs. Therefore in order to compare them, you will need to know which data are in which CRS and how to convert between them - getting the wrong CRS is one of the most common sources of error in GIS. All of the projections described in the slides above (and many more besides) can be identified with a unique spatial reference system identifier (SRID)
SRID, EPSG and Proj.4
One of the more commonly used sets of SRID values are maintained by the European Petroleum Survey Group - EPSG. For example EPSG: 4326 refers to the WGS 84 world geodetic system. EPSG:27700 refers to british national grid. Proj.4 is a library for converting between spatial reference systems. Most EPSG identifiers will also have a Proj.4 string. For example, the Proj4 string for EPSG:4326 is
+proj=longlat + ellps = WGS84 + datum = WGS84 + no_defs
If you want to find an SRID code for a particular spatial reference system or its related Proj4 String, visit http://spatialreference.org
Summary
- Reducing the infinite complexity of the read world results in incomplete representations of it.
- Spatial data present a unique and interesting set of challenges.
-There is yet to be a definitive solution to many of them-we will only ever have abstractions from reality.
We need to decide what is (un)acceptable in our analysis.
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