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

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.