GIS 5210 Week 2
The Nature of Spatial Variation Three principles of the nature of spatial variation: proximity effects are key to understanding spatial variation issues of geographic scale and level of detail are key to building appropriate representations of the world different measures of the world co-vary, and understanding the nature of co-variation can help us to predict
The Task Representing spatial and temporal phenomena in the real world: since the real world is complex, this task is difficult and error prone! small things (i.e. human lives) are very intricate in detail viewed in aggregate human activity exhibits structure across geographic spaces
Digital Representation of Life
The Fundamental Problem Deciding what data/information can be discarded as the inessential while retaining the salient characteristics of the observable world Distinguishes between controlled variation, which oscillates around a steady state, and uncontrolled variation: controlled variation like utility management uncontrolled variation climate change
Autocorrelation Informally, it is the similarity between observations as a function of the time lag between them 1 Our behavior in space often reflects past patterns of behavior thus it is one-dimensional, need only look in the past However, spatial events can potentially have consequences anywhere in two-dimensional or even three-dimensional space How and why does spatial and temporal context affect what we do? 1 Thanks to the TA!
Tobler s First Law of Geography Everything is related to everything else, but near things are more related than distant things Tobler, 1970
Spatial Autocorrelation Autocorrelation is the similarity between observations as a function of the time Spatial autocorrelation is similarity in the location of spatial objects and their attributes manifestation of Tobler s Law! Is a measure of the degree to which a set of spatial features and their associated data values tend to be clustered (positive spatial autocorrelation) or dispersed (negative autocorrelation)
Spatial Autocorrelation Understanding spatial variation, the scale of spatial variation, and the way in which geographic phenomena co-vary tells us: how we should represent the real world in our digital GIS Spatial autocorrelation is determined both by similarities in position, and by similarities in attributes: positive, zero, or negative
Contiguous Spatial Autocorrelation
Distance-based Spatial Autocorrelation (A) linear distance decay (B) negative power distance decay (C) negative exponential distance decay
Representation All representation: are needed to convey information fit information into a standard form or model almost always simplify the truth that is being represented Digital representation: digital & binary (1s and 0s) The basis of almost all modern human communication
The Fundamental Problem (Again) Geographic data are built up from atomic elements, or facts about the geographic world At its most primitive, an atom of geographic data (strictly, a datum) links a place, often a time, and some descriptive property The fundamental problem: the world is infinitely complex, but computer systems are finite
What is a Data Model? Levels of abstractions that convert reality to data in the computer Conceptual models discrete objects vs continuous fields Logical models rasters vs vectors Physical models Too many
Discrete Objects vs Continuous Fields Discrete Objects the world is empty, except where it is occupied by objects with well-defined boundaries that are instances of generally recognized categories: objects can be counted objects have dimensionality: 0-dimension points 1-dimension lines 2-dimensions areas
Discrete Objects vs Continuous Fields Continuous Field a finite number of variables, each one defined at every possible position: omnipresent, everywhere dense can be distinguished by what varies, and how smoothly In this perspective, value (A) is a function of location (X): A = f (X ) Contrast with the discrete object view define the location of the boundary of objects, or X = f (A)
Rasters vs Vectors There are two methods that are used to reduce geographic phenomena to forms that can be coded in computer databases Each can be used to represent both fields and discrete objects: usually raster is used to represent fields and vector for discrete objects Raster is faster, but vector is correcter
Raster In a raster representation geographic space is divided into an array of cells, each of which is usually square, but sometimes rectangular: all geographic variation is then expressed by assigning properties or attributes to these cells cells are called pixels (short for picture elements) In the raster data model, individual grid cells have one value that represent a single phenomenon IMPORTANT: Raster accuracy is limited by the resolution of the cell
Raster Representation Each color represents a different value of a nominal-scale variable denoting land-cover class
Raster Representation Effect of a raster representation using: (A) the largest share rule (B) the central point rule
Vector In a vector representation, features are captured as a series of points or vertices connected by straight lines: areas are often called polygons lines are often called polylines In the vector data model, discrete features can have many different attributes representing numerous phenomena
Vector Representation Effect of a vector representation: solid purple line represents an area dashed blue line approximation by a polygon
A Complete Representation of Geography? Conceptual and logical levels of representing geographic reality A hierarchy of abstraction A big question to think about GIS provides the mean to do this, by organizing data by their spatial distribution
Generalization Simplifying the view of the world: describe entire areas, attributing uniform characteristics to them, even when areas are not strictly uniform identify features on the ground and describe their characteristics, again assuming them to be uniform some degree of generalization is almost inevitable in all geographic data A geographic database cannot contain a perfect description; instead, its contents must be carefully selected to fit within the limited capacity of computer storage devices!
Simplification Examples
Simplification of Coastlines (A) the actual coastline (B) approximation using 100-km steps (C) 50-km step approximation (D) 25-km step approximation
Data Information In the context of computing, both data and information refer to facts and statistics collected But data is the quantities, characters, or symbols on which operations are performed by a computer, and information is the context or meaning of data GIS can deal with data easily GIS can handle information too But GIS often has trouble to effectively process knowledge and wisdom
Data Types Data is organized in a GIS database based on whether it is a collection of text symbols, numbers, or dates Numbers are further classified into one of four data types:
Data Types Why does this matter? because GIS databases can include tens of thousands of records, it is useful to try and limit the memory allocated to each record With numerical values, you can designate: precision the length of the field scale the number of decimal places in the field Number Precision Scale 13.56 4 2 1056 4 0 0.4326??
GI Attribute Types Attribute Types: nominal used to categorize ordinal ordered categories interval difference between values are constant ratio ratios between values are meaningful Spatially Extensive vs. Spatially Intensive: extensive values aggregated over entire area intensive true for any sub-region of the area
Soils Ranked by FCC Limiting Factors Soils with a high number of limiting factors are problematic and require remediation for agricultural production The best soils for agriculture have no or few limiting factors
Choropleth Mapping (A) a spatially extensive variable, total population (B) a spatially intensive variable, population density Many cartographers would argue that (A) is misleading and that spatially extensive variables should always be converted to spatially intensive form before being displayed as choropleth maps.
For Next Time! Read Chapter 4 from Longley et al. 2 Finish Lab 1 Bring Lab book with you on Tuesday! 2 Lecture slides adapted from Longley et al.