Estimating Variation in Landscape Analysis

Introduction

• General Approach– Create spatial database (GIS)– Populate polygons with sample data– Simulate change for variable of interest– Generate maps

• Common Uses– Managerial– Scientific– Public policy

Spatial Landscape Analyses: how & why?

Introduction

Hessburg, P.F., Smith, B.G., and R.B. Salter. 1999. Detecting Change in Forest Spatial Patterns from Reference Conditions. Ecological Applications, 9 (4) 1232-1252.

Wales, B.C. and L.H. Suring. 2004. Assessment Techniques for Terrestrial Vertebrates of Conservation Concern. In: Hayes, J.L., Ager, A.A., and R.J. Barbour (Tech. Eds. Methods for Integrated Modeling of Landscape Change. USDA Forest Service GTR-610. pp 64-72.

Spatial Landscape Analysis: what?

Problem• The results of landscape simulation are

often reported without an estimate of uncertainty

2045

2095

1995

http://www.fsl.orst.edu/clams/prj_lamps_simulation.html

Research Goals

•To examine the potential effects of variation in sample data on the results of landscape simulation

•To begin to develop ways to communicate these effects

Study Objectives1. Estimate the area of late seral forest

(LSF) structure in a 6070 ha reserve over 30 years (FVS) Hummel)

2. Calculate the effect of sampling uncertainty on the estimates in each decade (Monte Carlo/SAS) (Cunningham)

Methods: 1. LSF Area

Fslscape.shp10ofms10secc10seoc10si10ur10yfms11secc11ur11yfms13secc13seoc13si13ur13yfms18secc

1:12,000

Ø Ø

1 polygon1=ABGR/ABCO

7ac (0.05%) Ø Ø

Ø

1 polygon

1= PSME

10 ac (0.07%)

1 polygon1=ABLA2/PIEN349 ac (2.3%)

5 polygons

1=ABLA2/PIEN2

7 ac (1.83%)

18 polygons

2=ABGR/ABCO

11=ABGR/PIEN

5=PSME

3139 ac (21%)

3 polygons1=ABGR/ABCO

1=ABLA2/PIEN

1=PSME

38 ac (0.25%)

Ø

Ø Ø

1 polygon1=PSME

49 ac (2.3%)

6 polygons1=PICO

5=PSME

652 ac (4.3%)

2 polygons2=PSME

41 ac (0.3%) Ø

44 polygons6=PICO

22=PIPO

17=PSME

1115 ac (7.4%)

7 polygons5=PIPO

2=PSME

343 ac (2.3%)

10 polygons3=PICO

7=PSME

694 ac (4.6 %)

36 polygons3=PICO

8=PIPO

25=PSME

7582 ac (50%)

15 polygons2=PICO

6=PIPO

7=PSME

354 ac (2.3%)

4 polygons4=PIPO

515 ac (3.4%)

SI SEOC SECC UR YFMS OFMS

10

11

13

18

Landscape Summary Matrix

Area of LSF Structure

Basal area (BA) at least 55.2 m2/haBA of trees greater than 61.0 cm dbh ≥ 8.3 m2/ha BA of trees greater than 35.6 cm dbh ≥ 33.1 m2/ha

BA of trees less than 35.6 cm dbh ≥ 8.3 m2/ha

If LSF=1

If not LSF=0

0

1000

2000

3000

4000

5000

6000

7000

8000

2001 2011 2021

year

tota

l acr

es

Results 1: LSF area estimate

Methods: 2. Sampling Error

nx

n

iix

1

Bootstrap Re-sampling• Developed in the 1980s (Efron),

based on classical statistical theory from the 1930s.

• Computer-intensive method that creates an empirical distribution function of a statistic to estimate its true distribution function.

• The SD of a sample of bootstrap means is the bootstrap estimate of the true SD of the mean.

X i=5 x*1 x*2 …… x*B

1 (15) 5 (12) 3 ( 7 ) …… 2 ( 4 )

2 ( 4 ) 4 ( 9 ) 1 (15) …… 1 (15)

3 ( 7 ) 5 (12) 2 ( 4) …… 4 ( 9 )

4 ( 9 ) 3 ( 7 ) 2 ( 4 ) …… 5 (12)

5 (12) 1 (15) 3 ( 7 ) …… 2 ( 4 )

= 9.4 = 11.0 = 7.4 …… = 8.8x x

*1 2*x B*x

What is a Bootstrap Sample?

Bootstrapped Samples (200)

SC

0 (4.8)

PVT

LSF Probabilities each Decade

Results 2 : LSF mean & SE

0

100

200

300

400

500

600

700

800

900

1000

1,174 2,550

hectares

LSF

0

100

200

300

400

500

600

700

800

900

1000

2,226 2,954 3,683

hectares

LSF

Decade 1

Decade 2

0

100

200

300

400

500

600

700

800

900

1000

hectares

LSF

Decade 3

1690 ha (se 233 ha)

2060 ha (se 251 ha)

3674 ha (se 109 ha)

Comparison of Results 1 & 2

projected area in late successional forest (LSF) structure

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

1 2 3

decade

are

a (

ha

)

LSF structure projectedby FVS

minimum area of LSFstructure predicted usingSAS

maximum area of LSFstructure predicted usingSAS

Acknowledgements• Pat Cunningham

• Tom Gregg

• Tim Max

Further information

Gregg, T.F.; Hummel, S. 2002. Assessing sampling uncertainty in FVS projections using a bootstrap resampling method. In: Crookston, N.L.; Havis, R.N., comps. Second Forest Vegetation Simulator Conference; 2002 February 12-14; Fort Collins, CO. Proc. RMRS-P-25. Ogden, UT: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station: 164-167.

shummel@fs.fed.us