Estimating Variation in Landscape Analysis
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Estimating Variation in Landscape Analysis
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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?
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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?
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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
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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
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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)
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Methods: 1. LSF Area
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Fslscape.shp10ofms10secc10seoc10si10ur10yfms11secc11ur11yfms13secc13seoc13si13ur13yfms18secc
1:12,000
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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
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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
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0
1000
2000
3000
4000
5000
6000
7000
8000
2001 2011 2021
year
tota
l acr
es
Results 1: LSF area estimate
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Methods: 2. Sampling Error
nx
n
iix
1
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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.
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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?
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Bootstrapped Samples (200)
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SC
0 (4.8)
PVT
LSF Probabilities each Decade
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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)
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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
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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.