2. Copyright, 1998-2014 © Qiming Zhou GEOG3600. Geographical Information Systems The Nature of Geographical Data

3. 2  Geographical phenomena  Spatial autocorrelation and scale  Spatial sampling  Spatial interpolation  Uncertainty of geographical data

4. The Nature of Geographical Data3 Geographical phenomena  Our behaviour in space often reflects past patterns of behaviour.  Some geographical phenomena vary smoothly across space, while others may not.  The first law of geography: everything is related to everything else, but near things are more related than distant things.  This property is known as spatial autocorrelation.

5. The Nature of Geographical Data4 Spatial autocorrelation and scale  Spatial autocorrelation:  Measurements on how near and distant things are interrelated.  Temporal autocorrelation:  The relationship between consecutive events in time.  Examining spatio-temporal processes:  explanation in time need only look to the past, but  explanation in space must look in all directions simultaneously.

6. The Nature of Geographical Data5 Spatial autocorrelation and spatial objects  Spatial autocorrelation deal simultaneously with similarities in the location of spatial objects.spatial objects  If features that are similar in location are also similar in attributes, then the pattern as a whole is said to exhibit positive spatial autocorrelation.  When features that are close together in space tend to be more dissimilar in attributes than features that are further apart, the negative spatial autocorrelation is said to exist.  Zero autocorrelation occurs when attributes are independent of location.

7. The Nature of Geographical Data6 Spatial objects  Spatial objects are classified according to their topological dimension, which provides a measure of the way they fill space.  Point – dimension 0  Line – dimension 1  Area – dimension 2  Volume – dimension 3  Time – usually considered to be the fourth dimension of spatial objects, although GIS is currently incapable of dealing with it properly.

8. The Nature of Geographical Data7 Point  A point object has neither length nor breadth nor depth.  May be used to indicate spatial occurrences or events, and their spatial pattern. Large scale structure from travel time tomography of Wenchuan Earthquake (2008). On Monday 12 May 2008, an earthquake of magnitude 7.9 struck northwestern Sichuan province of China. Black lines depict the major fault zones in the region. The focal mechanism indicates that the main shock in Wenchuan County involved thrusting due to compression in NW- SE direction. The aftershocks (green circles) occurred along the Longmen Shan thrust belt. The background events (purple dots) are from the EHB catalog (1964~2007). Courtesy http://quake.mit.edu/~changli/wenchuan.html

9. The Nature of Geographical Data8 Line  A line object has length, but not breadth or depth.  Used to represent linear entities that are frequently built together into networks.  Also used to measure distances between spatial objects.

10. The Nature of Geographical Data9 Area  An area object has two dimension, length and breadth, but not depth.  Represents enclose areas of natural or artificial objects. A Forest Plan Map The Nicola Thompson Fraser Plan area is situated in the southern interior, east of the Coast Mountains and encompassing the Thompson-Okanagan Plateau, Canada. The defined forest area are presented using area objects. Courtesy thompsonokanagansustainableforestry.ca

11. The Nature of Geographical Data10 Volume  A volume object have length, breadth and depth.  Used to present natural (e.g. mine bodies and buildings) or artificial objects.

12. The Nature of Geographical Data11 Surface  A surface is a kind of volume object but its depth is actually the spot height of the surface.  Used to present natural or statistical surface objects. 3m Digital Surface Model (DSM) of Southern Sahara, Tunisia, Africa from Stereo IKONOS Satellite Image Data Courtesy Satellite Imaging Corporation http://www.satimagingcorp.com

13. The Nature of Geographical Data12 Spatial autocorrelation (A) Extreme negative spatial autocorrelation; (B) a dispersed arrangement; (C) spatial independence; (D) spatial clustering; and (E) extreme positive spatial autocorrelation. A D C B E

14. The Nature of Geographical Data13 The meaning of scale  Level of spatial detail in data  Geographical extent or scope of a project  e.g. a large-scale project covers a large area.  A small-scale project covers a small area.  Scale of a map: representative fraction (RF)  Scale is often integral to the trade off between the level of spatial resolution and the degree of attribute detail that can be handled for a given application.

15. The Nature of Geographical Data14 Level of resolution (A) A coarse-scale representation of attributes in a pattern of negative spatial autocorrelation. (B) The pattern of spatial autocorrelation at the coarser scale is replicated at the finer scale. The overall pattern is said to exhibit the property of self-similarity. AB

16. The Nature of Geographical Data15 Spatial sampling  Self-similar structure is characteristic of natural as well as social systems.  A rock may resemble the physical form of the mountain.  A small group ‘typical’ people’s opinion may resemble that of the society.  Sampling is therefore the typical way to gain geographical data.  Geographical data are only as good as the sampling scheme used to create them.

17. The Nature of Geographical Data16 Spatial sampling schema ABCD EFG Spatial sample designs: (A) simple random sampling; (B) systematic sampling; (C) systematic sampling with local random allocation; (D) systematic sampling with random variation in grid spacing; (E) clustered sampling; (F) transect sampling; and (G) contour sampling.

18. The Nature of Geographical Data17 Spatial interpolation  In sampling, part of reality to hold within our representation.  Judgement is required to fill in the gaps between the observations.  This requires understanding of the likely attenuating effect of distance between samples.  The function that fills the gaps is known as interpolation function.

19. The Nature of Geographical Data18 The attenuating effect of distance A w d B w d C w d The attenuating effect of distance: (A) linear distance decay; (B) negative power distance decay; and (C) negative exponential distance decay.

20. The Nature of Geographical Data19 Interpolation processes  Global surface fitting  Trend surface  Local surface fitting  Distance reverse weighting functions  Spline and kriging

21. The Nature of Geographical Data20 Trend surface Linear Quadratic Cubic Generic form:

22. The Nature of Geographical Data21 Interpolation 6.15.75.35.6 7.06.56.05.2 7.67.06.05.7 7.27.06.25.5 Original sample dataRegularly spaced grid Location of nearest sample points Completed grid measured interpolated Elevation Position 6 6 5 6 7 7 8 6 5 7 C D A B E

23. The Nature of Geographical Data22 Uncertainty of geographical data  The length of coast line problem  Uncertainty in the conception of geographical phenomena  Further uncertainty in the measurement and representation of geographical phenomena  Further uncertainty in the analysis of geographical phenomena

24. The Nature of Geographical Data23 The length of coast line problem  How long is the coast line of Hong Kong Island?  Indeterminate  Scale-dependent

25. The Nature of Geographical Data24 Coast line of Hong Kong Coast line of Hong Kong: The length of the coastline increases with the increasing level of details and scale. The precise length of the coast line is indeterminate.

26. The Nature of Geographical Data25 Uncertainty Real world Conception Measurement Analysis U1 U2 U3 U2: Uncertainty in the measurement and representation of geographical phenomena U3: Uncertainty in the analysis of geographical phenomena U1: Uncertainty in the conception of geographical phenomena

27. The Nature of Geographical Data26 Uncertainly in geographical concepts  Spatial uncertainty: In many cases there are no natural unites of geographical analysis.  Vagueness: Uncertainty in the position of boundaries and attributes.  Ambiguity:  Many language terms used to convey geographical information are inherently ambiguous.  Ambiguity is introduced when imperfect indicators of phenomena are used instead of the phenomena themselves.

28. The Nature of Geographical Data27 Uncertainty in measurement  Representation and measurement: difference under field and discrete object views.  scale  Resolution  Accuracy and error  Measurement error: capture, digitisation, editing errors  Data integration and sharing

29. The Nature of Geographical Data28 Uncertainty in analysis  Spatial analysis: uncertainty in data lead to uncertainties in the results of analysis.  Aggregation and analysis: in appropriate inference from aggregate data

30. The Nature of Geographical Data29 Summary  The law of geography states the property of spatial autocorrelation.  Spatial autocorrelation is the measurements on how near and distant things are interrelated.  Spatial objects are classified according to their topological dimension, which provides a measure of the way they fill space.  Geographical data are only as good as the sampling scheme used to create them.  Interpolation is the function that fills the gaps in samples.  In all steps of geographical data processing, uncertainty exists and needs to be properly handled.