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This project focuses on the sensitivity analysis of the Forest Vegetation Simulator Southern Variant (FVS-Sn) to evaluate model coefficients and inputs for forests in the southern U.S. The study aims to assess the impact of various parameters on stand-level basal area increment. By conducting comprehensive evaluations, the project aims to provide insights for future testing and adaptations in forest modeling. The methods involve sensitivity analysis techniques such as Latin Hypercube Sampling and Response Surface Analysis.
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SENSITIVITY ANALYSIS of theFOREST VEGETATION SIMULATOR Southern Variant (FVS-Sn) Nathan D. Herring Dr. Philip J. Radtke Virginia Tech Department of Forestry
Preview • Introduction • Objectives • Methods • Results • Future Work
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
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
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
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
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
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
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
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)
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
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
Species Sensitivity Index FVS-Sn species sensitivities vs. basal area per acre
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
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
Acknowledgements • FMSC Staff • Dennis Donnelly • Forest Service SRS* • Virginia Tech* * Cooperative Agreement # SRS 05-CA-11330134-251