Announcements

1. Introduction to Geographic Information Systems (GIS)September 5, 2006SGO1910 & SGO4030 Fall 2006Karen O’BrienHarriet Holters Hus, Room 215karen.obrien@sgeo.uio.no

2. Announcements • Home pages – review • Review lecture: Thursday, September 21, 12.15-14.00, Room 323, HHH • Mid-term quiz: September 26 (chapters 1, 3, 4, 5)

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

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

5. Fields • 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 • A single value at every point on the Earth’s surface • Any field can have slope, gradient, peaks, pits

6. A raster data model uses a grid • One grid cell is one unit or holds one attribute. • 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 has a resolution, given as the cell size in ground units.

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

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

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

10. Areas are lines are points are coordinates

11. Representations • 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 • Representations can leave us uncertain about the real world

12. Representation: A fundamental problem in GIS • 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 spatial heterogeneity of data also influences this regularity or irregularity.

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

14. Scale • 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 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!!)

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

16. 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

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

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

19. 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) Example: GDP data

20. Spatial autocorrelation: • 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.

21. 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.

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

24. 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).

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

26. Sample Designs • 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)

27. 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

29. Spatial Interpolation • 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

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

31. 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.

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

33. Spatial Autocorrelation Measures • Spatial autocorrelation measures: • Geary and Moran; nature of observations • Establishing dependence in space: regression analysis • Y = f (X1, X2 , X3 , . . . , XK) • Y = f (X1, X2 , X3 , . . . , XK) + ε • Yi = f (Xi1, Xi2 , Xi3 , . . . , XiK) + εi • Yi = b0 + b1 Xi1 + b2 Xi2 + b3 Xi3 + . . . bK XiK + εi Y is the dependent variable, X is the independent variable Y is the response variable, X is the predictor variable

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

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

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