SENSITIVITY ANALYSIS of the FOREST VEGETATION SIMULATOR Southern Variant (FVS-Sn)

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

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

3. Introduction • 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 • Wide range of sites, species composition, and canopy structure • Wide geographic/physiographic range • Array of management prescriptions

4. Introduction • 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 • Southern Research Station and Virginia Tech Forestry • 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 • 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) • 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) • Sample from coefficient distributions • Different values of each parameter drawn for each model run • 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 • 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) ln(dds) = b0 + b1(lndbh) + b2(dbh2) + … Coefficient or Parameter Predictor or Variable

10. Methods • 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) Y = f (750 parameters)

11. SI’s grouped by FVS-Sn parameter • ln(dds) equation, 30 parameters • Summed across all 28 species in tree list • Many parameters have little influence on the response • Intercept sensitivity ≈1/3rd

12. SI’s grouped by Species • Only 7 of the 28 species have SI > 1.00 • 3 species account for ≈3/4th of total sensitivity • Other species: A. rubrum, L. tulipifera, P. serotina, and O. arbereum

13. Species Sensitivity and Dominance

14. Species Sensitivity Index FVS-Sn species sensitivities vs. basal area per acre

15. Parameter SI by species

16. Parameter SI by species

17. Influential Parameters by Species

18. Findings • Initial test – large tree sub-model, one tree list • Error budget • Model sensitivity • Only a few parameters/species significantly influence model • Proportionally greater influence of softwoods • 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 • Information of distributions difficult to obtain • Background  Logistic regression from FIA data • Density-dep.  BAmax and SDImax from literature • Additional tests – increase n, new datasets • SA results will guide: • Model validation against independent data (FIA) • Calibration and recommendations • Testing of additional forest types and species compositions

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