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Raster GIS Fundamentals

Now we will examine another sort of information system. Recall that our problem, expressed as its most formal aspect, is to create meaning from information. And to this end, we are studying information systems. We have found that information systems can be described and differentiate information systems based on their formal cpacities to:

  • Provide structures for representing entities or phenomena (referencing systems.)
  • Provide procedures for associating representations with eachother.
  • Provide procedures for transforming representations
  • Provide facilities for combining the structures and procedures and visualizing information.


We have seen that relational database management systems and vector GIS are closely related -- vector GIS is basically built from the principles of relational databases, extending their storage, associative and query capabilities into two dimensions. Raster GIS is very much different from relational and vector GIS systems in each of these capacities. Relational tools are useful when dealing with rasters and their value tables, but the basic representations associations and transformations that we do with rasters are fundamentally different. Raster GIS provides us with new structures for representing conditions and events, and they lend themselves to a vastly different vocabulary of operations for transforming and associating these references. For an overview of Raster GIS in the context of the ArcGIS Spatial Analyst, see

Readings:

  • Using ArcGIS Spatial Analyst Especially Chapters 3-7
  • To be overwhelmed by the diversity and utility of map algebra functions, look in the AcrMap Online Help Table of Contents under Extensions->Spatial Analyst, GeoProcessing Functional Reference and Map Algebra Functional Reference.
The same material is presented in the ArcGIS on-line help table of contents. In this first discussion of raster GIS, we will be covering the first six headings under the Spatial Analyst section. You will probably want to read these.

A Bit of History

The earliest GIS architectures, implemented by Roger Tomlinson in the Canadian Land Inventory in the mid '60s emulated traditional map drafting. Entities were represented by points and lines that could be drawn with an automated drafting machine (aka pen plotter.) An outline history of GIS can be found at National Center for Geographic Information and Analysis History of GIS and Mapping the Unknown: How Computer Mapping at Harvard Became GIS.

At The Harvard Lab for Computer Graphics and Spatial Analysis (at the Harvard Graduate School of Design) in the late sixties and early seventies, Carl Steinitz and many others were experimenting with ways to use digital geographic data to emulate the Cartographic Overlay techniques portrayed by Ian McHarg in his book Design with Nature. McHarg and Steinitz collaborated in the first digitally augmented landscape planning studio at the GSD in 1967.

The students and researchers at harvard were using a computer language called FORTRAN, IBM's highly customizeable information tool to represent landscapes and things that may happen on them. In Fortran one of the fundamental forms of representation is a Matrix -- an array of values. Naturally, someone began to experiment with this structure to represent the character of locations in 2-d space, and Raster GIS was born.

Consider a simple overlay operation: find areas that are covered with forest and also above a certain elevation First try to imagine how you derive this geometry if your forest cover and zoning maps were stored as lists of vertex coordinates as they are in a vector GIS system. Now consider how you could calculate this if your two maps are stored as arrays of evenly-spaced values. It turns out that this array structure is VERY efficient for represnting the attributes of places and how they may interact with eachother.

One of the reserachers at the Harvard Lab was a student named C. Dana Tomlin. Tomlin found a good thesis topic when he figured out that the many diferent things that you could do with these arrays can be chained together into systems of equations that operate like Algebra. At this point, He siezed the opportunity to lay out a taxonomy of these operations and a notation for designing and sharing models made up of Map Algebra equations.

Consider how the design of a notation for representing abbstract or physical things and their relationships affects our understanding and portrayal of our universe. Another case in point: How would the world be different if we had adopetd the calculus notation of Leibnitz vs. Isaac Newton or E.F. Codd?

Map Algebra

Consider the concept of an algebraic function: Y = f(X) stated as the quantity Y is a function of the quantity X. That function may be something like the equation for a line: Y = aX + b.

Now think of two dimensional patterns being substituted for the one-dimensional scalar values X and Y. In Map Algebra you may have a function stated as:
SCHOOL_ACCESS = distance(SCHOOLS) < 2000m
SLED_SLOPE = slope(ELEVATION) > 20
SCHOOL_SLED = SCHOOL_ACCESS * SLED_SLOPE

Think about how these functions allow us to abstractlym symbolically, formally relate relationships between patterns, to make new pattterns from interesting functions of existing patterns!

Structures for Representation

It may be useful to think of the representational and functional vocabulary of raster GIS in the context of what we know about Relational Database Management Systems and Vector GIS. Whereas the latter are primarily oriented toward representing Distinct Entities Raster GIS is oriented toward representing Locations, Neighborhoods, and Regions.

In lecture we will demonstrate these basic representational procedural capabilities using ArcGIS. If you want to study them in your own time, look at: Using ArcGIS Spatial Analyst Especially Chapters 3-7"> The PDF document, Using ArcGIS Spatial Analyst. We may also refer to illustrations provided Illustrations of Raster Representation Vocabulary.

Cells

To begin with, the fundamental unit of analysis in raster systems is the Cell. A cell represents a location in teselated space. The condition of a given cell is recorded as a numeric value for each cell. A raster or layer, sometimes referred to as a GRID, is a regular arrangement of cells. The process of choosing a size for these cells and assigning values to them is called sampling.

There are basically two types of grids. There are integer grids, in which the attribute for each cell is an integer, and there are fewer than a few thousand possible values for cells. In this case, we talk about the association of cells having the same value as a zone. Each zone in an integer grid is represented by a row in the grid's value table.

We also have grids in which the values represent small incremental changes, represented as floating (decima0) point numbers like elevation, or distance. These grids have so many potential values that the concept of zones is typically not applied, and these grids do not have value tables.

Cells may have values of Integers and Floating Point numbers, but in developint the logic of raster GIS it is necessaqry to allow cells to have a value of NoData or null, as well. Nodata cells affect map algebra functions in various interesting and useful ways as we will see.

Layers (aka Rasters or Grids)

Another fundamental unit of analysis in raster GIS is a Layer. Layers are containers for handling regualr arrays of cells. Cells are usually square, but some people have argued thhat they should be hexagons. Why?

Layers are geographically referenced and can be stacked up, creating relationships among cells that share the same location (see local functions below.)

Zones

In an interger-bbased grid, each unique cell value is associated with a row in a Value Attribute Table Each cell sharing the same value (e.g. 24: Forest) is associated with every other cell having the same value on that layer. These related areas of cells (which need not be continuous is known as a Zone. If we wanted to figure out some summary such as Average of values on a layer such as Elevation, for each zone, such as Forest or Residential, we could use an associative procedure known as a Zonal Function to find the average elevation that coocurs over all forested and residential cells.

We can use the value attribute table with various relational procedures.

Basic Raster Transformations and Associations

The following is a discussion of the basic raster functions expected in any Raster GIS software implementation. For a guide to where these functions may be found in your ESRI Toolbox, See Quick Reference to the Basic Raster Toolkit in ArcGIS

  • Local Functions are the most basic of the associtive operations in raster GIS. These functions produce a new grid where the value of each cell is determined as some arithmetic operation among the values of the same-location cells on any number of input layers. The simplest of these local functions are basic boolean statements which yield a true (1) or false (0) value based on the values in a single layer.
  • Reclass this means of aggregating categorical values is similar to our use of lookup tables.
  • Focal Functions This class of associative functions evaluates a new grid by summarizing statistics in the neighborhood around each cell on some other layer.
  • Zonal Functions This means of association produces a new grid of zones that summarize the values of a data grid over the areas covered by the zones in a zone grid.
  • Surface Analysis Functions are rather complex to begin with, but they are so powerful, that we will begin by looking at how the associations of cells in a raster of elevations, a digital elevation model (DEM) can be analyzed to calculate slope and aspect
  • Distance Functions Produce a new layer where each cell has the value corresponding to the Diatance to the nearest valued cell in some other layer.
  • Sampling How do we make a raster layer?

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