1. 1 ANALYZING TIME SERIES OF SATELLITE IMAGERY USING TEMPORAL MAP ALGEBRA Jeremy Mennis 1 and Roland Viger 1,2 1 Dept. of Geography, University of Colorado 2 U.S. Geological Survey

2. 2 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)

3. 3 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.’ 012 567 101112 012 567 101112 012 345 678 012 345 678

4. 4 Local Functions 012 567 101112 012 567 101112 012 345 678 012 345 678 91011 121314 151617 + 012 567 101112 012 567 101112 272829 303132 333435 012 567 101112 012 567 101112 272931 333537 394143 91113 151719 212325 + Conventional Map Algebra Local Function Three- Dimensional Map Algebra Local Function

5. 5 Focal Functions Row 1 2 3 4 5 Column 12345 Conventional Map Algebra 3x3 Focal Neighborhood Three-Dimensional Map Algebra 3x3x3 Focal Neighborhood

6. 6 Zonal Functions 012 345 678 + + Conventional Map Algebra Three-Dimensional Map Algebra ZoneSum ZoneSum Value LayerZone Layer 012 567 101112 012 567 101112 012 345 678 Value Cube 012 567 101112 012 567 101112 Zone Cube Output Table

7. 7 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)

8. 8 Spatio-Temporal Data Structure Timestep Column Row 3 Dimensional Array of the form: [row, column, timestep]

9. 9 Example Implementation: cubeFocalSum 1function cubeFocalSum, arr_in ….. 7 for row=0,x[1]-1 do begin 8 for col=0,x[2]-1 do begin 9 for time=0,x[3]-1 do begin 10arr_out[row,col,time] = FocalSum ( arr_in,row,col,time ) 11 end 12 end 13 end …iterates over each [row, column, timestep] to sum a set of values within a spatial, temporal, or spatio-temporal neighborhood.

10. 10 Case Study: ENSO-Vegetation Dynamics Objective: To determine the effect of ENSO on southern African vegetation, over different land covers

11. 11 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)

12. 12 Case Study: ENSO-Vegetation Dynamics Land Cover Data:

13. 13 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

14. 14 Case Study: ENSO-Vegetation Dynamics Vegetation Dynamics NDVI - Monthly 1982-1993

15. 15 Case Study: ENSO-Vegetation Dynamics Mean NDVI by Land Cover and ENSO Phase Land CoverWarm PhaseNeutral PhaseCold Phase Woodland 0.400.450.32 Wooded Grassland 0.310.350.27 Closed Shrubland 0.210.240.22 Open Shrubland 0.170.180.17 Grassland 0.330.380.32 Cropland 0.330.380.34 Functions:cubeZonalMean of NDVI data cube and (cubeLocalSum of ENSO phase and Land Cover data cubes)

16. 16 Case Study: ENSO-Vegetation Dynamics Mean NDVI by Land Cover and ENSO Phase Land CoverWarm PhaseNeutral PhaseCold Phase Woodland 0.400.450.32 Wooded Grassland 0.310.350.27 Closed Shrubland 0.210.240.22 Open Shrubland 0.170.180.17 Grassland 0.330.380.32 Cropland 0.330.380.34 Functions:cubeZonalMean of NDVI data cube and (cubeLocalSum of ENSO phase and Land Cover data cubes)

17. 17 Case Study: ENSO-Vegetation Dynamics Mean Spatial and Temporal NDVI Variance by Land Cover and ENSO Phase NeighborhoodLand CoverWarm PhaseNeutral PhaseCold Phase 3x3x1 Woodland 0.0022 0.0032 Spatial Wooded Grassland 0.00140.00150.0019 Variance Closed Shrubland 0.0010 Open Shrubland 0.00070.00080.0006 Grassland 0.00180.00190.0024 Cropland 0.0016 0.0024 1x1x3 Woodland 0.00590.00720.0077 Temporal Wooded Grassland 0.00400.00510.0054 Variance Closed Shrubland 0.00240.0028 Open Shrubland 0.00120.00160.0011 Grassland 0.00410.00500.0063 Cropland 0.00570.00630.0091 Functions: cubeZonalMean of (cubeFocalVariance of NDVI data cube) and (cubeLocalSum of ENSO phase and Land Cover data cubes)

18. 18 Case Study: ENSO-Vegetation Dynamics Mean Spatial and Temporal NDVI Variance by Land Cover and ENSO Phase NeighborhoodLand CoverWarm PhaseNeutral PhaseCold Phase 3x3x1 Woodland 0.0022 0.0032 Spatial Wooded Grassland 0.00140.00150.0019 Variance Closed Shrubland 0.0010 Open Shrubland 0.00070.00080.0006 Grassland 0.00180.00190.0024 Cropland 0.0016 0.0024 1x1x3 Woodland 0.00590.00720.0077 Temporal Wooded Grassland 0.00400.00510.0054 Variance Closed Shrubland 0.00240.0028 Open Shrubland 0.00120.00160.0011 Grassland 0.00410.00500.0063 Cropland 0.00570.00630.0091 Functions: cubeZonalMean of (cubeFocalVariance of NDVI data cube) and (cubeLocalSum of ENSO phase and Land Cover data cubes)

19. 19 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

20. 20 Case Study: ENSO-Vegetation Dynamics Mean NDVI by Land Cover and the January-April Period Following each ENSO Phase Land CoverWarm PhaseNeutral PhaseCold Phase Woodland 0.540.560.54 Wooded Grassland 0.430.420.45 Closed Shrubland 0.290.280.36 Open Shrubland 0.210.200.27 Grassland 0.440.46 Cropland 0.460.500.51 Functions:cubeZonalMean of NDVI data cube and (cubeLocalSum of Growing Season ENSO phase and Land Cover data cubes)

21. 21 Case Study: ENSO-Vegetation Dynamics Mean NDVI by Land Cover and the January-April Period Following each ENSO Phase Land CoverWarm PhaseNeutral PhaseCold Phase Woodland 0.540.560.54 Wooded Grassland 0.430.420.45 Closed Shrubland 0.290.280.36 Open Shrubland 0.210.200.27 Grassland 0.440.46 Cropland 0.460.500.51 Functions:cubeZonalMean of NDVI data cube and (cubeLocalSum of Growing Season ENSO phase and Land Cover data cubes)

22. 22 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

23. 23 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

24. 24

25. 25 Interactive Data Language (IDL)

26. 26 Data Input 1. 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.