Robust sampling of natural resources Robust sampling of natural resources using a GIS implementation of GRTSusing a GIS implementation of GRTS

David TheobaldNatural Resource Ecology Lab

Dept of Recreation & Tourism

Colorado State University

Fort Collins, CO 80523 USA23 September 2004

Funding/DisclaimerFunding/Disclaimer The work reported here was developed under the

STAR Research Assistance Agreement CR-829095 awarded by the U.S. Environmental Protection Agency (EPA) to Colorado State University. This presentation has not been formally reviewed by EPA.  The views expressed here are solely those of the presenter and STARMAP, the Program (s)he represents. EPA does not endorse any products or commercial services mentioned in this presentation.

CR - 829095

Practical sampling needsPractical sampling needs Most information for least cost Sample some areas with higher probability than

others– Some features are more important than others– Higher uncertainty of knowing about particular

situations– Some locations are more difficult (time, $) to

access than others Flexibility

– In-the-field decisions (e.g., access denied, extra time)

– Changes in funding (+ or -) for current project– Subsequent projects (additional funding)

augment existing dataset (but often different study area)

GRTS algorithm (Stevens 1997; Stevens and Olsen 1999; Stevens and Olsen 2004)

Why GIS framework?Why GIS framework? Spatial data is needed to as input to describe population

(frame) Spatial data used to describe strata, to describe inclusion

probabilities, including continuous variables (e.g., terrain) Ability to sample point, line, and area-based ecological

resources Flexibility in adjusting input to alter sampling design Visualize sampling design in relation to other geographic

data: (e.g., accessibility, ownership) Large, broad user base of GIS technology

Existing GIS-based samplingExisting GIS-based sampling

Sampling in ArcView v3, ArcGIS v8, v9– Typically simple random sampling (e.g., random x,

y constrained to polygon of study area) GStat (www.gstat.org): Pebesma and Wesseling. 1998.

Gstat, a program for geostatistical modeling, prediction and simulation. Computers and Geosciences 24(1):17-31.– Traditional: stratified, simple random sampling

r.le tools for GRASS– Stratified sampling

Ecological resource types Ecological resource types Areas (e.g., lakes, land cover patches)

– Discrete – represent as point shapefile, GRID with single cell• Convert to centroid or labelpoint then to GRID• Tesselate surface: e.g., watersheds, 8-digit HUCs• Discontinuous: all lakes in Oregon

– Continuous – represent as polygon, GRID as zones• Patches of vegetation types• Variation of water clarity within selected lakes• Estuarine resources• Area bias?

Lines (e.g., streams, roads)– Discrete – represent as point shapefile, GRID with single cell

• Individual stream reaches• 100’ segments

– Continuous• All possible locations on stream network

Points (e.g., individual trees, lakes)– Discrete

• all lakes in Oregon

Population(MASK: 1/Nodata) Sample

Samples(point shapefile)

Inclusion Prob.(01)

Population(MASK: 1/Nodata) Sample

Samples(point shapefile)

Inclusion Prob.(01)

Strata(01)

Env. gradient(e.g., moisture)

Special resource(e.g., riparian areas)

Processing stepsProcessing steps 1. Input

– raster or GRID of frame, inclusion probabilities– get spatial extent, grain (resolution), study area (inside,

outside, holes) 2. compute number of quad-levels, L 3. generate random permuted 1-4 labels at each L 4. add levels together to create reverse-ordered

address 5. compute sequential list order 6. threshold against inclusion probabilities 7. convert raster to point shapefile

Level 1Level 1

111 113 131 133 311 313 331 333

112 114 132 134 312 314 332 334

121 123 141 143 321 323 341 343

122 124 142 144 322 324 342 344

211 213 231 233 411 413 431 433

212 214 232 234 412 414 432 434

221 223 241 243 421 423 441 443

222 224 242 244 422 424 442 444

1 3

2 4

Level 2Level 2

111 113 131 133 311 313 331 333

112 114 132 134 312 314 332 334

121 123 141 143 321 323 341 343

122 124 142 144 322 324 342 344

211 213 231 233 411 413 431 433

212 214 232 234 412 414 432 434

221 223 241 243 421 423 441 443

222 224 242 244 422 424 442 444

1 1

1 1

2 2

2 2

3 3

3 3

4 4

4 4

Level 3Level 3

111 113 131 133 311 313 331 333

112 114 132 134 312 314 332 334

121 123 141 143 321 323 341 343

122 124 142 144 322 324 342 344

211 213 231 233 411 413 431 433

212 214 232 234 412 414 432 434

221 223 241 243 421 423 441 443

222 224 242 244 422 424 442 444

Morton address to sequential listMorton address to sequential list

75

64

931

820

12 14 36 38 44 46

13 15 37 39 45 47

16 18 24 26 48 50 56 58

17

10

25 27 49 51 57 59

20 22 28 30 52 54 60 62

21 23 29 31 53 55 61 63

4341353311

42403432

19

Reverse-Morton address to listReverse-Morton address to list

111 311 131 331 113 313 133 333

211 411 231 431 213 413 233 433

121 321 141 341 123 323 143 343

221 421 241 441 223 423 243 443

112 312 132 332 114 314 134 334

212 412 232 432 214 414 234 434

122 322 142 342 124 324 144 344

222 422 242 442 224 424 244 444

75

391

64

280

50 26 58

36 12 44 38 14 46

20 52 28 60 22 54 30 62

33 41 35 11

32

17 49 25 57 19 51 27 59

37 13 45 39 15 47

21 53 29 61 23 55 31 63

1856244816

42103440

43

Random permutation of quad Random permutation of quad valuesvalues

2

68

04

7

13

5963 31 57 37

39 23 35 45 29 17

55 51 19 13 61 49 33

52 48 46 62

27

58

36 20 32 16 14 30 26 10

24 60 28 54 18 50

40 56 44 12 22 38 34

1143

21534125471559

42

Area frame for vegetation surveyArea frame for vegetation survey

““Continuous” listing of sequential Continuous” listing of sequential pointspoints

Laramie Foothills vegetation surveyLaramie Foothills vegetation survey

SummarySummary

Flexibility of input data: point, line, area Continuous (gradients) and discrete

(strata) inclusion probabilities Visualization of sample design Can modify inclusion probability based

on accessibility constraints Develop map of “inferred population” ArcGIS tool

Distribution plansDistribution plans

Currently alpha test phaseBeta testing January 2005Release Spring/Summer 2005

Thanks! Comments? Questions?

STARMAP: www.stat.colostate.edu/~nsu/starmap GIS-GRTS tools in ArcGIS: email davet@nrel.colostate.edu

Stream frameStream frame