SENSITIVITY ANALYSIS SENSITIVITY ANALYSIS
of theof the
FOREST VEGETATION SIMULATOR FOREST VEGETATION SIMULATOR
Southern Variant (FVS-Sn)Southern Variant (FVS-Sn)
Nathan D. HerringNathan D. Herring
Dr. Philip J. RadtkeDr. Philip J. RadtkeVirginia Tech Virginia Tech
Department of ForestryDepartment of Forestry
PreviewPreview
IntroductionIntroduction ObjectivesObjectives MethodsMethods ResultsResults Future WorkFuture Work
IntroductionIntroduction
Growth and Yield prediction - a critical Growth and Yield prediction - a critical need for southern U.S., especially need for southern U.S., especially Appalachian mixed forests Appalachian mixed forests
Area contains vast forest resourcesArea contains vast forest resources
High economic and biological potentialHigh economic and biological potential
Modeling issues for southern U.S. forestsModeling issues for southern U.S. forests Wide range of sites, species composition, and canopy Wide range of sites, species composition, and canopy
structurestructure Wide geographic/physiographic rangeWide geographic/physiographic range Array of management prescriptionsArray of management prescriptions
IntroductionIntroduction
Forest Vegetation Simulator (FVS)Forest Vegetation Simulator (FVS) Comprehensive and powerful G & Y model Comprehensive and powerful G & Y model Developed, distributed, and supported by the U.S. Developed, distributed, and supported by the U.S.
Forest ServiceForest Service Age independent, individual tree modelAge independent, individual tree model
Donnelly, et al. 2001 The Southern Variant…
FVS Southern Variant (FVS-Sn) Relatively recent development Covers 90 species in 13 southern states Complex model Complex model challenge for testing and challenge for testing and
validationvalidation
Project ObjectivesProject Objectives
Comprehensive evaluation of FVS-Comprehensive evaluation of FVS-SnSn – Southern Research Station and Virginia Southern Research Station and Virginia
Tech ForestryTech Forestry Evaluation includes:Evaluation includes:
Sensitivities of model coefficients and inputsSensitivities of model coefficients and inputs Stand level comparisons to independent dataStand level comparisons to independent data Confidence intervals & calibrationConfidence intervals & calibration Recommendations and adaptationsRecommendations and adaptations
ObjectivesObjectives
Sensitivities of model coefficients and inputs Sensitivities of model coefficients and inputs to stand-level basal area per acre incrementto stand-level basal area per acre increment– Sensitivity indices Sensitivity indices
Stand level BA increment explained by each model Stand level BA increment explained by each model parameterparameter
– Error budgetError budget Ranks sensitivity indices and groupingsRanks sensitivity indices and groupings
– Response surface analysisResponse surface analysis Direction and magnitude of sensitivitiesDirection and magnitude of sensitivities
– Framework for further testingFramework for further testing Other forest types in S. AppalachiansOther forest types in S. Appalachians
MethodsMethods
Sensitivity Analysis (SA)Sensitivity Analysis (SA)– Examine relationships between model Examine relationships between model
inputs & outputsinputs & outputs– Hold all model quantities constant, but Hold all model quantities constant, but
vary one quantity (+/-) to see how it vary one quantity (+/-) to see how it affects the outputaffects the output Computationally intensiveComputationally intensive
– Efficient algorithms for sampling from Efficient algorithms for sampling from parameter space parameter space LHS, FAST, etc… LHS, FAST, etc… Computationally efficientComputationally efficient
MethodsMethods
Latin Hypercube Sampling (LHS)Latin Hypercube Sampling (LHS)– Sample from coefficient distributionsSample from coefficient distributions– Different values of each parameter drawn for Different values of each parameter drawn for
each model runeach model run SASA
– Large tree sub-modelLarge tree sub-model– Tree list Tree list typical S. App. upland mixed typical S. App. upland mixed
hardwoodshardwoods 28 species sampled from 1,300 acre VT forest28 species sampled from 1,300 acre VT forest
– Initial test: n = 5000 model runsInitial test: n = 5000 model runs– One observation for each FVS-Sn model runOne observation for each FVS-Sn model run
MethodsMethods
Batch mode FVS-SnBatch mode FVS-Sn– Model coefficients entered at runtimeModel coefficients entered at runtime– Total of 2700 parameters… “in theory” Total of 2700 parameters… “in theory”
90 species x 30 parameters for each species90 species x 30 parameters for each species
28 species x 30 = 840… (750 parameters)28 species x 30 = 840… (750 parameters)
Coefficient or Parameter
Predictor or Variable
ln(dds) = bln(dds) = b00 + b + b11(lndbh) + b(lndbh) + b22(dbh(dbh22) + ) + ……
MethodsMethods
Response SurfaceResponse Surface
Response (Y) Response (Y) 10-year stand level BA 10-year stand level BA incrementincrement
Different value for each parameter in each Different value for each parameter in each model runmodel run
Multiple linear regressionMultiple linear regression
Sensitivity Index (SI)Sensitivity Index (SI)
tot
regreg
SS Corrected
SS Model Reduced - SS Model Full SI
Y = Y = f f (750 parameters)(750 parameters)
SI’s grouped by FVS-Sn SI’s grouped by FVS-Sn parameterparameter
ln(dds) equation, 30 ln(dds) equation, 30 parametersparameters
Summed across all Summed across all 28 species in tree 28 species in tree listlist
Many parameters Many parameters have little influence have little influence on the responseon the response
Intercept sensitivity Intercept sensitivity ≈1/3≈1/3rdrd
FVS Parameter ParameterSensitivity
INTERCEPT 26.42
LNCRWN 21.95
LNDBHC 14.81
HREL 7.52
ISOIWN 4.36
Other 4.52
Total 79.58
SI’s grouped by SpeciesSI’s grouped by Species
Only 7 of the 28 Only 7 of the 28 species have SI > species have SI > 1.001.00
3 species account 3 species account for for ≈3/4≈3/4thth of total of total sensitivitysensitivity
Other species: Other species: A. A. rubrumrubrum, , L. L. tulipiferatulipifera, , P. P. serotinaserotina, and , and O. O. arbereumarbereum
SpeciesSpecies
Sensitivity
Q. prinus 28.29
P. rigida 21.15
Q. coccinea 10.56
P. strobus 10.22
T. canadensis 3.68
Q. velutina 1.83
Q. alba 1.07
Other 2.79
Total 79.58
Species Sensitivity and Species Sensitivity and DominanceDominance
SpeciesBasal area per
acre (ft2)SI SI Rank
Q. prinus 33.13 28.29 1
Q. coccinea 16.51 10.56 3
Q. alba 12.81 1.07 7
Q. velutina 7.10 1.83 6
P. strobus 5.23 10.22 4
P. rigida 3.28 21.15 2
T. canadensis 2.69 3.68 5
Other 23.60 2.79
Total 104.35 79.58
Species Sensitivity IndexSpecies Sensitivity Index
Q. montana
Q. coccinea
Q. velutina Q. alba
P. rigida
P. strobus
T. canadensis
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35
Initial Basal Area (ft2) per Acre
Sen
sitiv
ity In
dex
Hardwoods
Softwoods
FVS-Sn species sensitivities vs. FVS-Sn species sensitivities vs.
basal area per acre basal area per acre
Species SI/BAPA
Q. prinus 0.85
Q. coccinea 0.64
Q. alba 0.08
Q. velutina 0.26
P. strobus 1.95
P. rigida 6.44
T. canadensis 1.37
Other 0.12
FVS Parameter Total Model Parameter SI
INTERCEPT 26.42
LNCRWN 21.95
LNDBHC 14.81
HREL 7.52
ISOIWN 4.36
other parameters
4.52
Total 79.58
Species SI SI/BAPA
Response Surface
Coefficient
Coefficient/BAPA
Q. prinus 9.84 0.30 5.47 0.17
Q. coccinea 3.83 0.23 2.89 0.18
Q. alba 0.31 0.02 1.80 0.14
Q. velutina 0.63 0.09 1.42 0.20
P. strobus 3.62 0.69 1.49 0.29
P. rigida 6.03 1.84 0.89 0.27
T. canadensis 1.03 0.48 0.61 0.23
Other 0.86 0.04
Total 26.42
Parameter SI by species
FVS Parameter Total Model Parameter SI
INTERCEPT 26.42
LNCRWN 21.95
LNDBHC 14.81
HREL 7.52
ISOIWN 4.36
other parameters
4.52
Total 79.58
Species SI SI/BAPA
Response Surface
Coefficient
Coefficient/BAPA
Q. prinus 8.96 0.27 22.49 0.68
Q. coccinea 2.61 0.16 10.86 0.66
Q. alba 0.25 0.02 8.36 0.65
Q. velutina 0.36 0.05 5.76 0.81
P. strobus 2.18 0.42 5.73 1.10
P. rigida 5.81 1.77 4.07 1.24
T. canadensis 1.26 0.47 2.76 1.03
Other 0.53 0.02
Total 21.95
Parameter SI by species
Influential Parameters by Influential Parameters by SpeciesSpecies
P. rigida
P. rigida
P. strobus
P. rigidaT. canadensis
P. rigidaP. rigida
P. strobus
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
0 1 2 3 4 5 6
SI/B
A
FindingsFindings Initial test – large tree sub-model, one tree listInitial test – large tree sub-model, one tree list Error budgetError budget
– Model sensitivityModel sensitivity Only a few parameters/species significantly influence Only a few parameters/species significantly influence
modelmodel Proportionally greater influence of softwoodsProportionally greater influence of softwoods
Response surfaceResponse surface– Parameter relationship to responseParameter relationship to response
Positive response surface coefficientsPositive response surface coefficients Nature of ln(dds) equationNature of ln(dds) equation
Insightful findings so far, but nothing conclusiveInsightful findings so far, but nothing conclusive
Future WorkFuture Work
Incorporate background and density-Incorporate background and density-dependent mortality into SAdependent mortality into SA– Information of distributions difficult to obtainInformation of distributions difficult to obtain
Background Background Logistic regression from FIA data Logistic regression from FIA data Density-dep. Density-dep. BA BAmaxmax and SDI and SDImaxmax from literature from literature
Additional tests – increase n, new datasetsAdditional tests – increase n, new datasets SA results will guide:SA results will guide:
1.1.Model validation against independent data (FIA)Model validation against independent data (FIA)
2.2.Calibration and recommendationsCalibration and recommendations
3.3.Testing of additional forest types and species Testing of additional forest types and species compositionscompositions
AcknowledgementsAcknowledgements
FMSC StaffFMSC Staff Dennis DonnellyDennis Donnelly Forest Service SRSForest Service SRS**
Virginia TechVirginia Tech**
** Cooperative Agreement # Cooperative Agreement # SRS 05-CA-11330134-251SRS 05-CA-11330134-251