Announcements

1. Introduction to Geographic Information Systems (GIS)SGO1910 & SGO4930 Fall 2005Karen O’BrienHarriet Holters Hus, Room 215karen.obrien@sgeo.uio.no

2. Announcements • Questions about home pages? • Mid-term quiz: September 27 (chapters 1, 3, 4, 5, 6)

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. 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). • Note: it is also important in the measurement of temporal autocorrelation

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

38. Georeferencing

39. Georeferencing • Geographic information contains either an explicit geographic reference (such as latitude and longitude coordinates), or an implicit reference such as an address, road name, or postal code. • Geographic references allow you to locate features for analysis.

40. Georeferencing • Is essential in GIS, since all information must be linked to the Earth’s surface • The method of georeferencing must be: • Unique, linking information to exactly one location • Shared, so different users understand the meaning of a georeference • Persistent through time, so today’s georeferences are still meaningful tomorrow

41. Uniqueness • A georeference may be unique only within a defined domain, not globally • There are many instances of Storgatas in Norway, but only one in any city • The meaning of a reference to Greenwich may depend on context, since there are cities and towns called Greenwich in several parts of the world

42. Georeferences as Measurements • Some georeferences are metric • They define location using measures of distance from fixed places • E.g., distance from the Equator or from the Greenwich Meridian • Others are based on ordering • E.g. street addresses in most parts of the world order houses along streets • Others are only nominal • Placenames do not involve ordering or measuring

43. Placenames • The earliest form of georeferencing • And the most commonly used in everyday activities • Many names of geographic features are universally recognized • Others may be understood only by locals • Names work at many different scales • From continents to small villages and neighborhoods • Names may pass out of use in time • Where was Camelot? Or Atlantis?

44. Postal Addresses and Postcodes • Every dwelling and office is a potential destination for mail • Dwellings and offices are arrayed along streets, and numbered accordingly • Streets have names that are unique within local areas • Local areas have names that are unique within larger regions • If these assumptions are true, then a postal address is a useful georeference

45. Where Do Postal Addresses Fail as Georeferences? • In rural areas • Urban-style addresses have been extended recently to many rural areas • For natural features • Lakes, mountains, and rivers cannot be located using postal addresses • When numbering on streets is not sequential • E.g. in Japan

46. Postcodes as Georeferences • Defined in many countries • E.g. ZIP codes in the US • Hierarchically structured • The first few characters define large areas • Subsequent characters designate smaller areas • Coarser spatial resolution than postal address • Useful for mapping

47. ZIP code boundaries are a convenient way to summarize data in the US. The dots on the left have been summarized as a density per square mile on the right

48. Linear Referencing • A system for georeferencing positions on a road, street, rail, or river network • Combines the name of the link with an offset distance along the link from a fixed point, most often an intersection

49. Users of Linear Referencing • Transportation authorities • To keep track of pavement quality, signs, traffic conditions on roads • Police • To record the locations of accidents

50. Problem Cases • Locations in rural areas may be a long way from an intersection or other suitable zero point • Pairs of streets may intersect more than once • Measurements of distance along streets may be inaccurate, depending on the measuring device, e.g. a car odometer