Representation of Geographic Data · building appropriate representations of the world di erent measures of the world co-vary, and understanding the ... objects and their attributes

Representation of Geographic Data

GIS 5210

Jake K. Carr

Week 2

Representation of Geographic Data Jake K. Carr

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 tobuilding appropriate representations of the world

different measures of the world co-vary, and understanding thenature 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 errorprone!

small things (i.e. human lives) are very intricate in detail

viewed in aggregate human activity exhibits structure acrossgeographic spaces


Digital Representation of Life


The Fundamental Problem

Deciding what data/information can be discarded as the inessentialwhile retaining the salient characteristics of the observable world

Distinguishes between controlled variation, which oscillates arounda 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 ofthe time lag between them1

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 consequencesanywhere in two-dimensional or even three-dimensional space

How and why does spatial and temporal context affect what wedo?

1Thanks to the TA!Representation of Geographic Data Jake K. Carr

Tobler’s First Law of Geography

Everything is related to everythingelse, but near things are morerelated than distant things

Tobler, 1970


Spatial Autocorrelation

Autocorrelation is the similarity between observations as a functionof the time

Spatial autocorrelation is similarity in the location of spatialobjects and their attributes

manifestation of Tobler’s Law!

Is a measure of the degree to which a set of spatial features andtheir associated data values tend to be clustered (positive spatialautocorrelation) or dispersed (negative autocorrelation)


Spatial Autocorrelation

Understanding spatial variation, the scale of spatial variation, andthe 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 inposition, 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 aboutthe geographic world

At its most primitive, an atom of geographic data (strictly, adatum) links a place, often a time, and some descriptive property

The fundamental problem: “the world is infinitely complex, butcomputer systems are finite”


What is a Data Model?

Levels of abstractions that convertreality to data in the computer

Conceptual models ⇒ discreteobjects 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 isoccupied by objects with well-defined boundaries that are instancesof 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 onedefined 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 theboundary of objects, or X = f (A)


Rasters vs Vectors

There are two methods that are used to reduce geographicphenomena 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 arrayof cells, each of which is usually square, but sometimes rectangular:

all geographic variation is then expressed by assigningproperties or attributes to these cells

cells are called pixels (short for picture elements)

In the raster data model, individual grid cells have one value thatrepresent a single phenomenon

IMPORTANT: Raster accuracy is limited by the resolution of thecell


Raster Representation

Each color represents a different value of a nominal-scale variabledenoting 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 ofpoints 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 differentattributes representing numerous phenomena


Vector Representation

Effect of a vector representation:

solid purple line ⇒ represents an areadashed blue line ⇒ approximation by a polygon


A Complete Representation of Geography?

Conceptual and logical levels ofrepresenting geographic reality

A hierarchy of abstraction

A big question to think about

GIS provides the mean to do this,by organizing data by theirspatial distribution


Generalization

Simplifying the view of the world:

describe entire areas, attributing uniform characteristics tothem, even when areas are not strictly uniform

identify features on the ground and describe theircharacteristics, again assuming them to be uniform

some degree of generalization is almost inevitable in allgeographic data

A geographic database cannot contain a perfect description;instead, its contents must be carefully selected to fit within thelimited capacity of computer storage devices!


Simplification Examples


Simplification of Coastlines

(A) the actual coastline

(B) approximation using 100-kmsteps

(C) 50-km step approximation

(D) 25-km step approximation


Data 6= Information

In the context of computing, both data and information refer tofacts and statistics collected

But data is the quantities, characters, or symbols on whichoperations are performed by a computer, and information is thecontext or meaning of data

GIS can deal with data easily

GIS can handle information too

But GIS often has trouble to effectively process knowledge andwisdom


Data Types

Data is organized in a GIS database based on whether it is acollection 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 ofrecords, it is useful to try and limit the memory allocated toeach 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 21056 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 andrequire 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 arguethat (A) is misleading and thatspatially extensive variables shouldalways be converted to spatiallyintensive form before being displayedas choropleth maps.


For Next Time!

Read Chapter 4 from Longley et al.2

Finish Lab 1

Bring Lab book with you on Tuesday!

2Lecture slides adapted from Longley et al.Representation of Geographic Data Jake K. Carr

Documents

Representation of Geographic Data · building appropriate representations of the world di erent measures of the world co-vary, and understanding the ... objects and their attributes