WEST, Inc.WEST, Inc.

GRTS for the Average Joe: A GRTS Sampler for Windows

Trent McDonald

Monitoring Science Symposium Denver, CO

21-24 Sep 2004

WEST, Inc.WEST, Inc.Outline

• Motivation for the GRTS sampler

• Description of the sampler, S-Draw

• Examples

• Performance

• Planned modifications

WEST, Inc.WEST, Inc.Motivation

• Basic hypotheses: – Average Joe understands the utility of GRTS

samples– Average Joe does not totally understand the

inner workings of GRTS sampling– Average Joe could not draw a GRTS sample if

his life depended on it.

WEST, Inc.WEST, Inc.Motivation

• A GRTS sampler was needed because:– Average Joe should be able to draw GRTS

samples– I should be able to draw GRTS samples

WEST, Inc.WEST, Inc.S-Draw

• Windows application• Written in Fortran 95

– Amazing speed

– Cross-platform portability ok

– Cross-language calls easy (S-Plus, R, C++)

• Used Lahey compiler• Also S-DrawB

WEST, Inc.WEST, Inc.S-Draw

• Draws samples of – Discrete units (finite populations)– Located in either 1-D or 2-D

• Examples:– 1-D: River segments located by river mile– 2-D: Grid cells located in an area– 2-D: River segments located by coordinates of

their midpoints

WEST, Inc.WEST, Inc.S-Draw

• Coordinates of units are specified in a text file – i.e., the sampling frame is a ASCII file

• Sampling frame can optionally contain weights and ID’s

WEST, Inc.WEST, Inc.S-Draw• Frame Formats:

Sample Structure Data Included in Frame

Pre-defined 1-D 2-D

Sample weights

Coordin-ates ID's

Order of fields in frame file

Yes Yes Yes Yes x wgt id

Yes Yes Yes No x wgt

Yes Yes No Yes x id

Yes Yes No No x

Yes No Yes Yes wgt id

Yes No Yes No wgt

Yes No No Yes id

Yes No No No [# lines counted]

Yes Yes Yes Yes x y wgt id

Yes Yes Yes No x y wgt

Yes No Yes Yes x y id

Yes No Yes No x y

Yes* Yes - Yes k1 … kK wgt id

Yes* Yes - No k1 … kK wgt

Yes* No - Yes k1 … kK id

Yes*       No - No     k1 … kK  

*K specified on the first line of the frame file

WEST, Inc.WEST, Inc.S-Draw

• Example frame: Eagle studySTARTPNT_X STARTPNT_Y LINE_ID ID ENDPNT_X ENDPNT_Y

-421014 4572670 1 439 -420245 4572670

-421295 4574670 2 440 -419802 4574670

-421245 4576670 3 441 -419802 4576670

-421196 4578670 4 442 -419802 4578670

-421292 4580670 5 443 -419802 4580670

-421687 4582670 6 444 -419802 4582670

-422806 4584670 7 445 -419802 4584670

-423122 4586670 8 446 -419802 4586670

-422972 4588670 9 447 -419802 4588670

-422836 4590670 10 448 -419802 4590670

-422352 4592670 11 449 -419802 4592670

-421284 4594670 12 450 -419802 4594670

Columns following frame data ignored

WEST, Inc.WEST, Inc.S-Draw

• Does the quadrant-recursive mapping of Stevens and Olsen (2004):

0 n

1 4 2 3

4 3 1 2

1

2

3

4

2

1 3

4

WEST, Inc.WEST, Inc.S-Draw

• Pixelsize = size of smallest quadrant in recursive map

• S-Draw allows user to specify pixelsize

WEST, Inc.WEST, Inc.S-Draw

• Line segment (0,n] sampled using a systematic sample– Random start between (0,1]– Step size = 1.0

0 n1 2 3

u1 u2 u3 u4

Random start = 0.19

WEST, Inc.WEST, Inc.S-Draw

• Reverse-hierarchical ordering of sample optionally applied– Convert sample order to base-4: 10010=012004

– Reverse base-4 digits: 012004=002104

– Convert back to base-10: 002104=3610

– Sort sample on base-10 numbers

WEST, Inc.WEST, Inc.S-Draw

• Users can pre-define the hierarchical sort keys

• Digits within each level of the hierarchy are randomly permuted, and sample is drawn as usual

• Allows use of a general recursive map– Triangular-recursive– ID’s like: state.county.watershed.segment

WEST, Inc.WEST, Inc.S-Draw

• Triangular-recursive mapping:

1 2

3

4

WEST, Inc.WEST, Inc.Examples

• C:\>s-drawb –n 20 –popsize 100– Will produce 1-D GRTS sample of size 20 assuming

units are located at coordinates 1, 2, …, 100

• C:\>s-drawb –n 20 –popsize 100 –pixelsize 100– Will produce a simple random sample of size 20

• C:\>s-drawb –n 20 –popsize 100 –nrand– Will produce a fixed-size systematic sample

WEST, Inc.WEST, Inc.Examples

• Golden eagle sample:– Dense grid of transect start points spaced 2km

north-south, 100km east-west– “No-fly” transect portions eliminated, new

transect start created– Frame:

• 27,078 starting points over western US

• 2-D coordinates and ID’s

– Desire sample of 416 transects• 208 primary, 208 alternate

WEST, Inc.WEST, Inc.Examples

2-D

Coordinates and ID in frame Sample size

Frame file

WEST, Inc.WEST, Inc.Examples

WEST, Inc.WEST, Inc.Performance

• GRTS sample of size 500 from 100,000 took 4.2 seconds on my laptop

• GRTS sample of size 500 from 1,000,000 took 44.3 seconds

• Algorithms approximately O(N)• Runs should take ~ 4.45e-5(N) seconds

– N=5,000,000: ~3.7 minutes

WEST, Inc.WEST, Inc.Enhancements

• An S-Plus and R interface

• Ability to read .e00 file, and ArcGIS binary files

• Ability to take a true point sample