1. SENSITIVITY ANALYSIS of the FOREST VEGETATION SIMULATOR Southern Variant (FVS-Sn) Nathan D. Herring Dr. Philip J. Radtke Virginia Tech Department of Forestry

2. Preview Introduction Introduction Objectives Objectives Methods Methods Results Results Future Work Future Work

3. Introduction Growth and Yield prediction - a critical need for southern U.S., especially Appalachian mixed forests Growth and Yield prediction - a critical need for southern U.S., especially Appalachian mixed forests  Area contains vast forest resources  High economic and biological potential Modeling issues for southern U.S. forests Modeling issues for southern U.S. forests  Wide range of sites, species composition, and canopy structure  Wide geographic/physiographic range  Array of management prescriptions

4. Introduction Forest Vegetation Simulator (FVS) Forest Vegetation Simulator (FVS)  Comprehensive and powerful G & Y model  Developed, distributed, and supported by the U.S. Forest Service  Age 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  challenge for testing and validation

5. Project Objectives Comprehensive evaluation of FVS-Sn Comprehensive evaluation of FVS-Sn –Southern Research Station and Virginia Tech Forestry Evaluation includes: Evaluation includes:  Sensitivities of model coefficients and inputs  Stand level comparisons to independent data  Confidence intervals & calibration  Recommendations and adaptations

6. Objectives Sensitivities of model coefficients and inputs to stand-level basal area per acre increment Sensitivities of model coefficients and inputs to stand-level basal area per acre increment –Sensitivity indices  Stand level BA increment explained by each model parameter –Error budget  Ranks sensitivity indices and groupings –Response surface analysis  Direction and magnitude of sensitivities –Framework for further testing  Other forest types in S. Appalachians

7. Methods Sensitivity Analysis (SA) Sensitivity Analysis (SA) –Examine relationships between model inputs & outputs –Hold all model quantities constant, but vary one quantity (+/-) to see how it affects the output  Computationally intensive –Efficient algorithms for sampling from parameter space  LHS, FAST, etc…  Computationally efficient

8. Methods Latin Hypercube Sampling (LHS) Latin Hypercube Sampling (LHS) – Sample from coefficient distributions –Different values of each parameter drawn for each model run SA SA –Large tree sub-model –Tree list  typical S. App. upland mixed hardwoods  28 species sampled from 1,300 acre VT forest –Initial test: n = 5000 model runs –One observation for each FVS-Sn model run

9. Methods Batch mode FVS-Sn Batch mode FVS-Sn –Model coefficients entered at runtime –Total of 2700 parameters… “in theory”  90 species x 30 parameters for each species  28 species x 30 = 840… (750 parameters) Coefficient or Parameter Predictor or Variable ln(dds) = b 0 + b 1 (lndbh) + b 2 (dbh 2 ) + …

10. Methods Response Surface Response Surface  Response (Y)  10-year stand level BA increment  Different value for each parameter in each model run  Multiple linear regression Sensitivity Index (SI) Sensitivity Index (SI) Y = f (750 parameters)

11. SI’s grouped by FVS-Sn parameter ln(dds) equation, 30 parameters ln(dds) equation, 30 parameters Summed across all 28 species in tree list Summed across all 28 species in tree list Many parameters have little influence on the response Many parameters have little influence on the response Intercept sensitivity ≈1/3 rd Intercept sensitivity ≈1/3 rd FVS Parameter Parameter Sensitivity INTERCEPT26.42 LNCRWN21.95 LNDBHC14.81 HREL7.52 ISOIWN4.36 Other4.52 Total79.58

12. SI’s grouped by Species Only 7 of the 28 species have SI > 1.00 Only 7 of the 28 species have SI > 1.00 3 species account for ≈3/4 th of total sensitivity 3 species account for ≈3/4 th of total sensitivity Other species: A. rubrum, L. tulipifera, P. serotina, and O. arbereum Other species: A. rubrum, L. tulipifera, P. serotina, and O. arbereum Species Sensitivity Q. prinus28.29 P. rigida21.15 Q. coccinea10.56 P. strobus10.22 T. canadensis3.68 Q. velutina1.83 Q. alba1.07 Other2.79 Total79.58

13. Species Sensitivity and Dominance Species Basal area per acre (ft 2 ) SISI Rank Q. prinus33.1328.291 Q. coccinea16.5110.563 Q. alba12.811.077 Q. velutina7.101.836 P. strobus5.2310.224 P. rigida3.2821.152 T. canadensis2.693.685 Other23.602.79 Total104.3579.58

14. Species Sensitivity Index FVS-Sn species sensitivities vs. 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. canadensis1.37 Other0.12

15. FVS Parameter Total Model Parameter SI INTERCEPT26.42 LNCRWN21.95 LNDBHC14.81 HREL7.52 ISOIWN4.36 other parameters4.52 Total79.58 Species SISI/BAPA Response Surface Coefficient Coefficient/ BAPA Q. prinus9.840.305.470.17 Q. coccinea3.830.232.890.18 Q. alba0.310.021.800.14 Q. velutina0.630.091.420.20 P. strobus3.620.691.490.29 P. rigida6.031.840.890.27 T. canadensis1.030.480.610.23 Other0.860.04 Total26.42 Parameter SI by species

16. FVS Parameter Total Model Parameter SI INTERCEPT26.42 LNCRWN21.95 LNDBHC14.81 HREL7.52 ISOIWN4.36 other parameters4.52 Total79.58 Species SISI/BAPA Response Surface Coefficient Coefficient/ BAPA Q. prinus8.960.2722.490.68 Q. coccinea2.610.1610.860.66 Q. alba0.250.028.360.65 Q. velutina0.360.055.760.81 P. strobus2.180.425.731.10 P. rigida5.811.774.071.24 T. canadensis1.260.472.761.03 Other0.530.02 Total21.95 Parameter SI by species

17. Influential Parameters by Species

18. Findings Initial test – large tree sub-model, one tree list Initial test – large tree sub-model, one tree list Error budget Error budget –Model sensitivity  Only a few parameters/species significantly influence model  Proportionally greater influence of softwoods Response surface Response surface –Parameter relationship to response  Positive response surface coefficients  Nature of ln(dds) equation Insightful findings so far, but nothing conclusive

19. Future Work Incorporate background and density-dependent mortality into SA Incorporate background and density-dependent mortality into SA –Information of distributions difficult to obtain  Background  Logistic regression from FIA data  Density-dep.  BA max and SDI max from literature Additional tests – increase n, new datasets Additional tests – increase n, new datasets SA results will guide: SA results will guide: 1.Model validation against independent data (FIA) 2.Calibration and recommendations 3.Testing of additional forest types and species compositions

20. Acknowledgements FMSC Staff FMSC Staff Dennis Donnelly Dennis Donnelly Forest Service SRS * Forest Service SRS * Virginia Tech * Virginia Tech * * Cooperative Agreement # SRS 05-CA-11330134-251