1 analyzing time series of satellite imagery using temporal map algebra jeremy mennis 1 and roland...
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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: [email protected]
Roland Viger: [email protected]
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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.