Introduction to Geographic Information Systems (GIS) September 5, 2006 SGO1910 & SGO4030 Fall 2006 Karen O’Brien Harriet Holters Hus, Room 215

Announcements Home pages – review Home pages – review Review lecture: Thursday, September 21, , Room 323, HHH Review lecture: Thursday, September 21, , Room 323, HHH Mid-term quiz: September 26 Mid-term quiz: September 26 (chapters 1, 3, 4, 5)

Review Spatial Data Models Spatial Data Models Conceptual and Digital Representations Conceptual and Digital Representations Discrete Objects and Fields Discrete Objects and Fields Vector and Raster Vector and Raster

Discrete Objects Points, lines, and areas Points, lines, and areas Countable Countable Persistent through time, perhaps mobile Persistent through time, perhaps mobile Biological organisms Biological organisms –Animals, trees Human-made objects Human-made objects –Vehicles, houses, fire hydrants

Fields Properties that vary continuously over space Properties that vary continuously over space –Value is a function of location –Property can be of any attribute type, including direction Elevation as the archetype Elevation as the archetype –A single value at every point on the Earth’s surface –Any field can have slope, gradient, peaks, pits

A raster data model uses a grid One grid cell is one unit or holds one attribute. One grid cell is one unit or holds one attribute. Every cell has a value, even if it is “missing.” Every cell has a value, even if it is “missing.” A cell can hold a number or an index value standing for an attribute. A cell can hold a number or an index value standing for an attribute. A cell has a resolution, given as the cell size in ground units. A cell has a resolution, given as the cell size in ground units.

Generic structure for a grid Figure 3.1 Generic structure for a grid. R o w s Columns Grid cell Grid extent Resolution

Legend Urban area Suburban area Forest (protected) Water Raster representation. Each color represents a different value of a nominal- scale field denoting land use.

Vector Data Used to represent points, lines, and areas Used to represent points, lines, and areas All are represented using coordinates All are represented using coordinates –One per point –Areas as polygons Straight lines between points, connecting back to the start Straight lines between points, connecting back to the start Point locations recorded as coordinates Point locations recorded as coordinates –Lines as polylines Straight lines between points Straight lines between points

Areas are lines are points are coordinates

Representations Representations can rarely be perfect 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 It’s important to know what is missing in a representation –Representations can leave us uncertain about the real world

Representation: A fundamental problem in GIS Identifying what to leave in and what to take out of digital representations. Identifying what to leave in and what to take out of digital representations. The scale or level of detail at which we seek to represent reality often determines whether spatial and temporal phenomena appear regular or irregular. The scale or level of detail at which we seek to represent reality often determines whether spatial and temporal phenomena appear regular or irregular. The spatial heterogeneity of data also influences this regularity or irregularity. The spatial heterogeneity of data also influences this regularity or irregularity.

Today’s Topic: The Nature of Geographic Data (Or how phenomena vary across space, and the general nature of geographic variation)

Scale Scale refers to the details; fine-scaled data includes lots of detail, coarse-scaled data includes less detail. Scale refers to the details; fine-scaled data includes lots of detail, coarse-scaled data includes less detail. Scale refers to the extent. Large-scale project involves a large extent (e.g. India); small-scale project covers a small area (e.g., Anantapur, India) Scale refers to the extent. Large-scale project involves a large extent (e.g. India); small-scale project covers a small area (e.g., Anantapur, India) Scale can refer to the level (national vs. local) Scale can refer to the level (national vs. local) Scale of a map can be large (lots of detail, small area covered) or small (little detail, large area covered) (Opposite of other interpretations!!) Scale of a map can be large (lots of detail, small area covered) or small (little detail, large area covered) (Opposite of other interpretations!!)

Principal objective of GIS analysis: Development of representations of how the world looks and works. Development of representations of how the world looks and works. Need to understand the nature of spatial variation: Need to understand the nature of spatial variation: –Proximity effects –Geographic scale and level of detail –Co-variance of different measures & attributes

Space and time define the geographic context of our past actions, and set geographic limits of new decisions (condition what we know, what we perceive to be our options, and how we choose among them) Space and time define the geographic context of our past actions, and set geographic limits of new decisions (condition what we know, what we perceive to be our options, and how we choose among them) Consider the role of globalization in defining new patterns of behavior Consider the role of globalization in defining new patterns of behavior

Geographic data: Smoothness versus irregularity Smoothness versus irregularity Controlled variation: oscillates around a steady state pattern Controlled variation: oscillates around a steady state pattern Uncontrolled variation: follows no pattern Uncontrolled variation: follows no pattern (violates Tobler’s Law)

Tobler’s First Law of Geography Everything is related to everything else, but near things are more related than distant things. Everything is related to everything else, but near things are more related than distant things.

Spatial Autocorrelation The degree to which near and more distant things are interrelated. Measures of spatial autocorrelation attempt to deal simultaneously with similarities in the location of spatial objects and their attributes. (Not to be confused with temporal autocorrelation) The degree to which near and more distant things are interrelated. Measures of spatial autocorrelation attempt to deal simultaneously with similarities in the location of spatial objects and their attributes. (Not to be confused with temporal autocorrelation) Example: GDP data

Spatial autocorrelation: Can help to generalize from sample observations to build spatial representations Can help to generalize from sample observations to build spatial representations Can frustrate many conventional methods and techniques that tell us about the relatedness of events. Can frustrate many conventional methods and techniques that tell us about the relatedness of events.

The scale and spatial structure of a particular application suggest ways in which we should sample geographic reality, and the ways in which we should interpolate between sample observations in order to build our representation.

Types of spatial autocorrelation Positive (features similar in location are similar in attribute) Positive (features similar in location are similar in attribute) Negative (features similar in location are very different) Negative (features similar in location are very different) Zero (attributes are independent of location) Zero (attributes are independent of location)

The issue of sampling interval is of direct importance in the measurement of spatial autocorrelation, because spatial events and occurrences can conform to spatial structure (e.g. Central Place Theorem). The issue of sampling interval is of direct importance in the measurement of spatial autocorrelation, because spatial events and occurrences can conform to spatial structure (e.g. Central Place Theorem).

Spatial Sampling Sample frames (“the universe of eligible elements of interest”) Sample frames (“the universe of eligible elements of interest”) Probability of selection Probability of selection All geographic representations are samples All geographic representations are samples Geographic data are only as good as the sampling scheme used to create them Geographic data are only as good as the sampling scheme used to create them

Sample Designs Types of samples Types of samples –Random samples (based on probability theory) –Stratified samples (insure evenness of coverage) –Clustered samples (a microcosm of surrounding conditions) Weighting of observations (if spatial structure is known) Weighting of observations (if spatial structure is known)

Usually, the spatial structure is known, thus it is best to devise application-specific sample designs. Usually, the spatial structure is known, thus it is best to devise application-specific sample designs. –Source data available or easily collected –Resources available to collect them –Accessibility of all parts to sampling

Spatial Interpolation Judgment is required to fill in the gaps between the observations that make up a representation. Judgment is required to fill in the gaps between the observations that make up a representation. To do this requires an understanding of the effect of increasing distance between sample observations To do this requires an understanding of the effect of increasing distance between sample observations

Spatial Interpolation Specifying the likely distance decay Specifying the likely distance decay –linear: w ij = -b d ij –negative power: w ij = d ij -b –negative exponential: w ij = e -bdij Isotropic (uniform in every direction) and regular – relevance to all geographic phenomena? Isotropic (uniform in every direction) and regular – relevance to all geographic phenomena?

Key point: An understanding of the spatial structure of geographic phenomena helps us to choose a good sampling strategy, to use the best or most appropriate means of interpolating between sampled points, and to build the best spatial representation for a particular purpose. An understanding of the spatial structure of geographic phenomena helps us to choose a good sampling strategy, to use the best or most appropriate means of interpolating between sampled points, and to build the best spatial representation for a particular purpose.

Spatial Autocorrelation Induction: reasoning from the data to build an understanding. Induction: reasoning from the data to build an understanding. Deduction: begins with a theory or principle. Deduction: begins with a theory or principle. Measurement of spatial autocorrelation is an inductive approach to understanding the nature of geographic data Measurement of spatial autocorrelation is an inductive approach to understanding the nature of geographic data

Spatial Autocorrelation Measures Spatial autocorrelation measures: Spatial autocorrelation measures: –Geary and Moran; nature of observations Establishing dependence in space: regression analysis Establishing dependence in space: regression analysis –Y = f (X 1, X 2, X 3,..., X K ) –Y = f (X 1, X 2, X 3,..., X K ) + ε –Y i = f (X i1, X i2, X i3,..., X iK ) + ε i –Y i = b 0 + b 1 X i1 + b 2 X i2 + b 3 X i b K X iK + ε i Y is the dependent variable, X is the independent variable Y is the response variable, X is the predictor variable

Spatial Autocorrelation Tells us about the interrelatedness of phenomena across space, one attribute at a time. Tells us about the interrelatedness of phenomena across space, one attribute at a time. Identifies the direction and strength of the relationship Identifies the direction and strength of the relationship Examining the residuals (error terms) through Ordinary Least Squares regression Examining the residuals (error terms) through Ordinary Least Squares regression

Discontinuous Variation Fractal geometry Fractal geometry –Self-similarity –Scale dependent measurement –Each part has the same nature as the whole Dimensions of geographic features: Dimensions of geographic features: –Zero, one, two, three… fractals

Consolidation Representations build on our understanding of spatial and temporal structures Representations build on our understanding of spatial and temporal structures Spatial is special, and geographic data have a unique nature Spatial is special, and geographic data have a unique nature This unique natures means that you have to know your application and data This unique natures means that you have to know your application and data