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ANALYZING TIME SERIES OF SATELLITE IMAGERY USINGTEMPORAL MAP ALGEBRA

Jeremy Mennis1 and Roland Viger1,2

1 Dept. of Geography, University of Colorado2 U.S. Geological Survey

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Objective

To develop a prototype implementation of a library of temporal map algebra functions for spatio-temporal image analysis.

Map algebra: an approach to raster data handling which treats spatial data layers as variables which may be combined using mathematical operators.

(Tomlin, 1990)

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Approach

Spatio-temporal data raster sets are treated as 3-D ‘data cubes.’

Map algebra functions are extended from 2 to 3 dimensions.

Temporal map algebra functions are referred to as ‘cube functions.’

0 1 2

5 6 7

10 11 12

0 1 2

5 6 7

10 11 12

0 1 2

3 4 5

6 7 8

0 1 2

3 4 5

6 7 8

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Local Functions

0 1 2

5 6 7

10 11 12

0 1 2

5 6 7

10 11 12

0 1 2

3 4 5

6 7 8

0 1 2

3 4 5

6 7 8

9 10 11

12 13 14

15 16 17

+

0 1 2

5 6 7

10 11 12

0 1 2

5 6 7

10 11 12

27 28 29

30 31 32

33 34 35

0 1 2

5 6 7

10 11 12

0 1 2

5 6 7

10 11 12

27 29 31

33 35 37

39 41 43

9 11 13

15 17 19

21 23 25

+

Conventional Map Algebra Local Function

Three-Dimensional Map Algebra Local Function

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Focal Functions

0 1 2 3 4

5 6 7 8 9

10 11 12 13 14

15 16 17 18 19

21 22 23 24 25

0 1 2 3 4

5 6 7 8 9

10 11 12 13 14

15 16 17 18 19

21 22 23 24 25

0 1 2 3 4

5 6 7 8 9

10 11 12 13 14

15 16 17 18 19

21 22 23 24 25

0 1 2 3 4

5 6 7 8 9

10 11 12 13 14

15 16 17 18 19

21 22 23 24 25

Timestep

Column

Row

1 2 3 4 5 12345

1

2

3

4

5

Row

1

2

3

4

5

Column

1 2 3 4 5

Conventional Map Algebra 3x3 Focal Neighborhood

Three-Dimensional Map Algebra 3x3x3

Focal Neighborhood

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Zonal Functions

0 1 2

3 4 5

6 7 8

+

+

Conventional Map Algebra

Three-Dimensional Map Algebra

Zone Sum

Zone Sum

Value Layer Zone Layer

0 1 2

5 6 7

10 11 12

0 1 2

5 6 7

10 11 12

0 1 2

3 4 5

6 7 8

Value Cube

0 1 2

5 6 7

10 11 12

0 1 2

5 6 7

10 11 12

Zone Cube

Output Table

Output Table

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Interactive Data Language (IDL)

• Language and Environment used for implementation

• is an interpreted language developed by Research Systems, Inc. (now owned by Kodak)

• has a library of image processing, math, statistics, visualization, and user interface components.

• was developed for remote sensing image processing (ENVI)

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Spatio-Temporal Data Structure

Timestep

Column

Row

3 Dimensional Array of the form:

[row, column, timestep]

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Example Implementation: cubeFocalSum

1 function cubeFocalSum, arr_in…..7 for row=0,x[1]-1 do begin8 for col=0,x[2]-1 do begin9 for time=0,x[3]-1 do begin10 arr_out[row,col,time] = FocalSum ( arr_in,row,col,time )11 end12 end13 end

…iterates over each [row, column, timestep] to sum a set of values within a spatial, temporal, or spatio-temporal neighborhood.

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Case Study: ENSO-Vegetation Dynamics

Objective:

To determine the effect of ENSO on southern African vegetation, over different land covers

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Case Study: ENSO-Vegetation Dynamics

NINO 3.4 Sea Surface Temperature Anomaly

Southern Oscillation Index 5 Month Running Mean

ENSO Phase Data:

Monthly, 1982-1993

(http://iri.columbia.edu/climate)

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Case Study: ENSO-Vegetation Dynamics

Land Cover Data:

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Case Study: ENSO-Vegetation Dynamics

Zone Cube

–ENSO anomolies•3 categories (warm, neutral, cold)

•Varying over time

–Land Cover•6 categories (woodland, etc…)

•Constant through time

Merged with cubeLocalSum operation, assigning a unique identifier to each combination of land cover and ENSO phase.

Timestep

Column

Row

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Case Study: ENSO-Vegetation Dynamics

Vegetation Dynamics

NDVI - Monthly

1982-1993

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Case Study: ENSO-Vegetation Dynamics

Mean NDVI by Land Cover and ENSO Phase

Land Cover Warm Phase Neutral Phase Cold Phase

Woodland 0.40 0.45 0.32

Wooded Grassland 0.31 0.35 0.27

Closed Shrubland 0.21 0.24 0.22

Open Shrubland 0.17 0.18 0.17

Grassland 0.33 0.38 0.32

Cropland 0.33 0.38 0.34

Functions: cubeZonalMean of NDVI data cube and (cubeLocalSum of ENSO phase and Land Cover data cubes)

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Case Study: ENSO-Vegetation Dynamics

Mean NDVI by Land Cover and ENSO Phase

Land Cover Warm Phase Neutral Phase Cold Phase

Woodland 0.40 0.45 0.32

Wooded Grassland 0.31 0.35 0.27

Closed Shrubland 0.21 0.24 0.22

Open Shrubland 0.17 0.18 0.17

Grassland 0.33 0.38 0.32

Cropland 0.33 0.38 0.34

Functions: cubeZonalMean of NDVI data cube and (cubeLocalSum of ENSO phase and Land Cover data cubes)

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Case Study: ENSO-Vegetation Dynamics

Mean Spatial and Temporal NDVI Variance by Land Cover and ENSO Phase

Neighborhood Land Cover Warm Phase Neutral Phase Cold Phase

3x3x1 Woodland 0.0022 0.0022 0.0032

Spatial Wooded Grassland 0.0014 0.0015 0.0019

Variance Closed Shrubland 0.0010 0.0010 0.0010

Open Shrubland 0.0007 0.0008 0.0006

Grassland 0.0018 0.0019 0.0024

Cropland 0.0016 0.0016 0.0024

1x1x3 Woodland 0.0059 0.0072 0.0077

Temporal Wooded Grassland 0.0040 0.0051 0.0054

Variance Closed Shrubland 0.0024 0.0028 0.0028

Open Shrubland 0.0012 0.0016 0.0011

Grassland 0.0041 0.0050 0.0063

Cropland 0.0057 0.0063 0.0091

Functions: cubeZonalMean of (cubeFocalVariance of NDVI data cube) and (cubeLocalSum of ENSO phase and Land Cover data cubes)

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Case Study: ENSO-Vegetation Dynamics

Mean Spatial and Temporal NDVI Variance by Land Cover and ENSO Phase

Neighborhood Land Cover Warm Phase Neutral Phase Cold Phase

3x3x1 Woodland 0.0022 0.0022 0.0032

Spatial Wooded Grassland 0.0014 0.0015 0.0019

Variance Closed Shrubland 0.0010 0.0010 0.0010

Open Shrubland 0.0007 0.0008 0.0006

Grassland 0.0018 0.0019 0.0024

Cropland 0.0016 0.0016 0.0024

1x1x3 Woodland 0.0059 0.0072 0.0077

Temporal Wooded Grassland 0.0040 0.0051 0.0054

Variance Closed Shrubland 0.0024 0.0028 0.0028

Open Shrubland 0.0012 0.0016 0.0011

Grassland 0.0041 0.0050 0.0063

Cropland 0.0057 0.0063 0.0091

Functions: cubeZonalMean of (cubeFocalVariance of NDVI data cube) and (cubeLocalSum of ENSO phase and Land Cover data cubes)

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Case Study: ENSO-Vegetation Dynamics

• Vegetation response lags behind the occurrence of an ENSO event.

• Alternate NDVI used– focused on the growing season after an

ENSO phse

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Case Study: ENSO-Vegetation Dynamics

Mean NDVI by Land Cover and the January-April Period Following each ENSO Phase

Land Cover Warm Phase Neutral Phase Cold Phase

Woodland 0.54 0.56 0.54

Wooded Grassland 0.43 0.42 0.45

Closed Shrubland 0.29 0.28 0.36

Open Shrubland 0.21 0.20 0.27

Grassland 0.44 0.46 0.46

Cropland 0.46 0.50 0.51

Functions: cubeZonalMean of NDVI data cube and (cubeLocalSum of Growing Season ENSO phase and Land Cover data cubes)

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Case Study: ENSO-Vegetation Dynamics

Mean NDVI by Land Cover and the January-April Period Following each ENSO Phase

Land Cover Warm Phase Neutral Phase Cold Phase

Woodland 0.54 0.56 0.54

Wooded Grassland 0.43 0.42 0.45

Closed Shrubland 0.29 0.28 0.36

Open Shrubland 0.21 0.20 0.27

Grassland 0.44 0.46 0.46

Cropland 0.46 0.50 0.51

Functions: cubeZonalMean of NDVI data cube and (cubeLocalSum of Growing Season ENSO phase and Land Cover data cubes)

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Conclusion

• Temporal map algebra provides a useful approach for manipulation and analysis of time series of imagery

• The cube function approach provides an extensible framework for the implementation of temporal map algebra

• Future research: a rich, non-proprietary library of temporal map algebra functions

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Acknowledgements

Thanks to Jun Wei Liu for data preprocessing. Data were provided by NASA Goddard Distributed Active Archive Center, the University of Maryland Global Land Cover Facility, and the National Oceanic and Atmospheric Administration Climate Diagnostics Center. This research was supported by NASA grant NAG5-12598.

Jeremy Mennis: jeremy@colorado.edu

Roland Viger: rviger@usgs.gov

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Interactive Data Language (IDL)

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Data Input1. A text file that encodes a unique ID for each location.

\

2. A text file where the first column encodes the locational ID and subsequent columns encode time series of observations.