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

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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