1. GIScience 2000 Raster Data Pixels as Modifiable Areal Units E. Lynn Usery U.S. Geological Survey University of Georgia

2. GIScience 2000 Outline MAUP Concepts from Socioeconomic Data Raster Resolution as MAUP Experimental Approach Results Conclusions

3. GIScience 2000 Objectives Relate raster resolution effects to MAUP Analyze effects of resolution on computation of parameters for water models Develop empirical base for deciding appropriate resolution for particular modeling result Examine pixels as modifiable units in database projection

4. GIScience 2000 MAUP Concepts Individuals in spatial analysis are often zones Scientific study - definition of objects precedes measurement. Not true for spatial data - areas are aggregated after data collected for one set of entities Farm fields aggregated to counties for statistical analysis

5. GIScience 2000 MAUP Concepts No rules for aggregation; no standards; no international convention Areal units for geographic study are arbitrary, modifiable, and subjective Possible m zones from n individuals is combinatorial 1000 objects (individuals) in 20 groups (zones) = 101260 Does it matter?

6. GIScience 2000 MAUP Scale Problem

7. GIScience 2000 MAUP Scale Problem Male juvenile delinquency vs income based on 252 Census tracts (Gehlke and Biehl, 1934). Number of Units Correlation Coefficient 252 -0.5020 175 -0.5800 125 -0.6620 50 -0.6850 25 -0.7650

8. GIScience 2000 MAUP Aggregation Problem

9. GIScience 2000 MAUP Aggregation Problem A.H. Robinson - grouping scheme correlations

10. GIScience 2000 MAUP Solutions? An insoluble problem; if so, ignore it Problem that can be assumed away; work at individual level Powerful analytical device; manipulate aggregations to get optimal zoning Ruzycki (1994) - Used GIS to create 1000's of aggregations of census block groups in Milwaukee and calculated 3 indices of racial segregation for each aggregation; statistically analyzed results.

11. GIScience 2000 Application of MAUP Concepts to Raster Data Pixel is zone. Various resolutions (pixel sizes) corresponds to scale problem of MAUP Grouping of pixels in different ways to form larger units corresponds to the aggregation problem of MAUP

12. GIScience 2000 Land Cover Example Classify land cover from different image sources for same area using same classification system –Landsat TM (30 m) –SPOT MX (20 m) –Ikonos (4 m) Do you get same percentages of land cover in each category?

13. GIScience 2000 Water Modeling Example Data collected at 30 m resolution –DEM –Land cover from TM Aggregate data to get 10 acre (210 m) cells for parameter determination for AGNPS How to aggregate?

14. GIScience 2000 Experimental Approach Analysis requires DEM, slope, and land cover at 30, 60, 120, 210, 240, 480, 960, 1920 m cells Starting point is 30 m DEM and land cover Calculate slope at 30 m cell size from DEM Resample land cover How to generate slope at 60 m and larger cell sizes? How to aggregate land cover?

15. GIScience 2000 Method of Calculation Slope calculated from DEM –30, 60, 120, 210, 240, 480, 960, 1920 m cells Compute slope from 30 DEM Aggregate DEM from 30 m to each lower resolution Compute slope from aggregated elevation data

16. GIScience 2000 30 m DEM120 m DEM120 m slope 60 m slope 30 m DEM30 m slope60 m slope 30 m DEM60 m DEM 30 m DEM30 m slope120 m slope Sample of Slope Generation Approaches compute aggregate compute

17. GIScience 2000 Results - DEM

18. GIScience 2000 Results - DEM

19. GIScience 2000 Image Results -- DEM 30-480 m Pixels210-480 m Pixels

20. GIScience 2000 Results -- Slope Slope % 30 to 480m Pixels 7.8816 7.8232 7.5870 7.8251 8.1604 8.5415 8.2065 7.9530 7.7434 7.7092 Slope % 210 to 480m Pixels 7.9514 7.8969 7.6244 7.7855 8.1263 8.5087 8.2157 7.8606 7.6390 7.6081 Regression Output: Constant0.2762 Std Err of Y Est1.1626 R Squared0.7690 No. of Observations500 Degrees of Freedom498 X Coefficient(s)0.8860 Std Err of Coef.0.0218

21. GIScience 2000 Results -- Slope Slope –Method of calculation affects results –Higher resolution aggregation directly to large pixel sizes yields better results than multistage aggregation (e.g., 30 m to 960 m is better than 30 m to 60 m to 120 m to 240 m to 480 m to 960 m) –Even multiples of pixels hold results while odd pixel sizes introduce error

22. GIScience 2000 Slope Image Comparison 30 m to 480 m pixels210 m to 480 m pixels

23. GIScience 2000 Sample of Land Cover Aggregation Approaches 30 m LC210 m LC480 m LC 210m LC 30 m LC60 m LC120 m LC 30 m LC120 m LC 30 m LC960 m LC1920 m LC aggregate

24. GIScience 2000 Results - Land Cover -- 120 M Pixels

25. GIScience 2000 Results - Land Cover -- 210 m Pixels

26. GIScience 2000 Results - Land Cover -- 480 m Pixels

27. GIScience 2000 Results-Land Cover -- 960 m Pixels

28. GIScience 2000 Image Results - Land Cover 30-480 m Pixels240-480 m Pixels

29. GIScience 2000 Image Results - Land Cover 30-210 m Pixels120-210 m Pixels

30. GIScience 2000 Resampling Asia Land Cover Land cover data (21 categories) at 1 km pixel size for Asia Resample to 2,4,8,16,25, and 50 km pixels Tabulate land cover percentages at each resolution to assess scale effects Aggregate in various ways and retabulate to assess aggregation effects

31. GIScience 2000 Asia Land Cover Lambert Azimuthal Equal Area Projection, 8 km pixels

32. GIScience 2000 Scale Effect Results Asia Land Cover

33. GIScience 2000 Aggregation Effect Results Asia Land Cover

34. GIScience 2000 Conclusions MAUP affects remotely sensed data Resolution of images corresponds to MAUP scale problem Resampling corresponds to MAUP aggregation problem Higher resolution data are more accurate (scale effect)

35. GIScience 2000 Conclusions Areas of land cover vary significantly (up to 30 %) based on aggregation method –Nearest neighbor resampling leads to inaccurate aggregations based on modal category concepts Continuous data (DEM and slope) retain values better through aggregation because of averaging (bilinear) during resampling. Continental land cover datasets shows significant effects on land cover areas resulting from categorical (nearest neighbor) resampling.