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GIScience 2000
Raster Data Pixels as Modifiable Areal Units
E. Lynn Usery
U.S. Geological Survey
University of Georgia
GIScience 2000
Outline
• MAUP Concepts from Socioeconomic Data
• Raster Resolution as MAUP
• Experimental Approach
• Results
• Conclusions
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
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
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?
GIScience 2000
MAUP Scale Problem
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
GIScience 2000
MAUP Aggregation Problem
GIScience 2000
MAUP Aggregation Problem
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4
A=2x=2y=4 A=4
x=2y=4
A=8x=2y=4
R = 0.7150 R = 0.5000R = 0.8750
A.H. Robinson - grouping scheme correlations
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.
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
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?
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?
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?
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
GIScience 2000
30 m DEM 120 m DEM 120 m slope
60 m slope
30 m DEM 30 m slope 60 m slope
30 m DEM 60 m DEM
30 m DEM 30 m slope 120 m slope
Sample of Slope Generation Approaches
compute aggregate
aggregate
aggregate
aggregate
compute
compute
compute
GIScience 2000
Results - DEM
Regression Output:0.980539Constant3.105509Std Err of Y Est0.959085R Squared
34No. of Observations32Degrees of Freedom
0.983164X Coefficient(s)0.035898Std Err of Coef.
120-210m30-210m76766153464978767578464569707167575660636465606038385152
GIScience 2000
Results - DEM
Regression Output:-1.38617Constant2.274152Std Err of Y Est0.97968R Squared
10No. of Observations8Degrees of Freedom
1.010755X Coefficient(s)0.051466Std Err of Coef.
210-480m30-480m65636365404061614849787756623334616132335356
GIScience 2000
Image Results -- DEM
30-480 m Pixels 210-480 m Pixels
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:
Constant 0.2762 Std Err of Y Est 1.1626 R Squared 0.7690 No. of Observations 500 Degrees of Freedom 498
X Coefficient(s) 0.8860
Std Err of Coef. 0.0218
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
GIScience 2000
Slope Image Comparison
30 m to 480 m pixels 210 m to 480 m pixels
GIScience 2000
Sample of Land Cover Aggregation Approaches
30 m LC 210 m LC 480 m LC
210m LC
30 m LC 60 m LC 120 m LC
30 m LC 120 m LC
30 m LC 960 m LC 1920 m LC
aggregate aggregate
aggregate aggregate
aggregate aggregate
aggregate aggregate
GIScience 2000
Results - Land Cover -- 120 M Pixels
30_original
2360.07
14026.41
8667.72
8607.87
17203.86
4669.65
14773.41
25133.67
5554.08
583.83
22166.55
120_30res
2466.72
14224.32
8786.88
8627.04
17343.36
4743.36
14860.8
25509.6
5705.28
593.28
22432.32
30-120 %
-4.52
-1.41
-1.37
-0.22
-0.81
-1.58
-0.59
-1.50
-2.72
-1.62
-1.20
Land Cover Category
Pecan Groves
Recently Disturbed Land / Harvested Cropland
Pastures
Cypress Dominant Weltands
Mature Deciduous
Young Planted Pine
Mature Planted Pine
Mixed Dominant Deciduous / Pine
Roads / Urban Complex
Open Water
Crops (Cotton, Peanuts)
GIScience 2000
Results - Land Cover -- 210 m Pixels
210_30res
2424.048
14632.4352
8492.98272
8625.20352
17536.88544
4689.43104
15527.12928
25465.72608
5641.4208
612.62304
22213.0944
210_120res
2500.71948
14413.31792
8679.74592
8812.05912
17169.84292
4600.08892
14894.05588
25624.6564
5680.64672
648.33468
22171.28188
210 % diff
-3.16
1.50
-2.20
-2.17
2.09
1.91
4.08
-0.62
-0.70
-5.83
0.19
Land Cover Category
Pecan Groves
Recently Disturbed Land / Harvested Cropland
Pastures
Cypress Dominant Weltands
Mature Deciduous
Young Planted Pine
Mature Planted Pine
Mixed Dominant Deciduous / Pine
Roads / Urban Complex
Open Water
Crops (Cotton, Peanuts)
GIScience 2000
Results - Land Cover -- 480 m Pixels
210-240d30-240d30-210d480_240res480_210res480_30res
-36.45-10.4419.062764.80002026.30562503.3376
8.773.29-6.0013570.560014874.925214032.4704
-5.332.507.438755.20008312.45828979.8624
6.511.98-4.858847.36009463.76829025.7952
-7.010.346.8717372.160016233.471017431.4976
-8.06-11.70-3.364976.64004605.24004455.4816
3.11-4.35-7.7015505.920016003.209014859.2608
0.65-0.23-0.8925735.680025904.475025676.4352
6.98-8.04-16.145483.52005894.70725075.5744
-30.51-20.387.76691.2000529.6026574.1600
-0.992.973.9222440.960022220.283023127.1648
Land Cover Category
Pecan Groves
Recently Disturbed Land / Harvested Cropland
Pastures
Cypress Dominant Weltands
Mature Deciduous
Young Planted Pine
Mature Planted Pine
Mixed Dominant Deciduous / Pine
Roads / Urban Complex
Open Water
Crops (Cotton, Peanuts)
GIScience 2000
Results-Land Cover -- 960 m Pixels
Land Cover Category
Pecan Groves
Recently Disturbed Land / Harvested Cropland
Pastures
Cypress Dominant Weltands
Mature Deciduous
Young Planted Pine
Mature Planted Pine
Mixed Dominant Deciduous / Pine
Roads / Urban Complex
Open Water
Crops (Cotton, Peanuts)
210-480d30-480d30-210d960_480res960-210res960_30res
-19.69-3.1213.842755.974 2302.61752672.64
11.542.93-9.7413688.0042 15473.589614100.48
-18.79-12.415.389737.7748 8197.31838663.04
0.26-12.68-12.989554.0432 9578.88888478.72
-9.94-0.208.8617821.9652 16210.427217786.88
17.7611.60-7.484317.6926 5249.96794884.48
9.015.76-3.5714331.0648 15749.903715206.4
0.942.651.7326916.6794 27170.886527648
21.4223.773.004777.0216 6078.91026266.88
40.1640.190.06275.597460.5235460.8
-8.52-6.741.6324987.523026.17523408.64
GIScience 2000
Image Results - Land Cover
30-480 m Pixels 240-480 m Pixels
GIScience 2000
Image Results - Land Cover
30-210 m Pixels 120-210 m Pixels
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
GIScience 2000
Asia Land Cover Lambert Azimuthal Equal Area Projection, 8 km pixels
GIScience 2000
Scale Effect ResultsAsia Land Cover
50 km25 km16 km8 km4 km2 kmLand Cover Category
-6.09-13.91-16.18-13.85-15.1816.20Urban & Built-Up Land
1.870.480.990.800.71-0.56Dryland Cropland & Pasture
-2.93-3.93-3.76-4.21-4.314.22Irrigated Cropland & Pasture
-1.78-2.52-2.50-2.46-2.232.22Cropland/Grassland Mosaic
-2.74-6.63-5.48-5.47-5.765.69Cropland/Woodland Mosaic
-1.37-0.58-1.25-1.12-1.041.00Grassland
2.871.421.752.031.69-1.61Shrubland
-1.08-4.35-5.21-4.70-4.194.17Mixed Shrubland/Grassland
16.0315.6513.2312.5513.43-13.02Savanna
0.05-1.33-0.23-1.95-1.641.86Deciduous Broadleaf Forest
10.653.930.540.17-0.250.62Deciduous Needleleaf Forest
3.603.041.493.152.24-2.19Evergreen Broadleaf Forest
4.3512.509.8211.1610.65-10.40Evergreen Needleleaf Forest
2.003.872.732.171.83-2.10Mixed Forest
14.78-12.128.965.055.33-4.78Herbaceous Wetland
62.6114.7825.1212.4010.32-9.00Wooded Wetland
3.656.126.786.316.32-6.25Barren or Sparsely Vegetated
21.9629.139.5919.7423.42-18.84Herbaceous Tundra
-8.362.065.243.842.67-2.70Wooded Tundra
-4.3519.5715.896.273.700.03Mixed Tundra
-4.35-18.69-15.18-19.03-17.4817.91Snow or Ice
GIScience 2000
Aggregation Effect ResultsAsia Land Cover
25f825f4225f225f1Land Cover Category
5.56-6.94-6.94-8.33Urban & Built-Up Land
-0.48-1.14-1.95-1.36Dryland Cropland & Pasture
0.20-0.370.31-1.03Irrigated Cropland & Pasture
-3.59-2.051.38-0.75Cropland/Grassland Mosaic
-3.32-2.59-2.76-4.00Cropland/Woodland Mosaic
1.290.180.430.81Grassland
-1.99-0.65-1.06-1.41Shrubland
-4.13-1.89-3.77-3.30Mixed Shrubland/Grassland
-4.980.70-2.46-0.32Savanna
-1.99-1.99-2.84-1.38Deciduous Broadleaf Forest
-4.21-7.36-5.84-6.07Deciduous Needleleaf Forest
1.800.09-1.98-0.54Evergreen Broadleaf Forest
10.639.388.757.81Evergreen Needleleaf Forest
0.520.121.421.83Mixed Forest
-31.25-29.69-20.31-23.44Herbaceous Wetland
-41.18-19.12-16.18-29.41Wooded Wetland
3.962.082.332.38Barren or Sparsely Vegetated
14.7120.5914.715.88Herbaceous Tundra
8.5910.358.3311.36Wooded Tundra
10.005.005.0025.00Mixed Tundra
-7.50-3.33-14.17-15.00Snow or Ice
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)
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.