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Chris Woodall Northern FIA St. Paul, MN

Estimating the Quadratic Mean Diameter of Fine Woody Debris for Forest Types of the United States. Chris Woodall Northern FIA St. Paul, MN. Vicente Monleon Pacific Northwest FIA Portland, OR. Outline. Background Objectives/Methods Results Forest Type Validation Future Options

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Chris Woodall Northern FIA St. Paul, MN

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  1. Estimating the Quadratic Mean Diameter of Fine Woody Debris for Forest Types of the United States Chris Woodall Northern FIA St. Paul, MN Vicente Monleon Pacific Northwest FIA Portland, OR

  2. Outline • Background • Objectives/Methods • Results • Forest Type • Validation • Future Options • Conclusions

  3. National Down Woody Inventory Estimate attributes of small, dead and down woody debris in forests across the United States

  4. What is Fine Woody Debris? Diameter less than 3 inches

  5. Intersection Diameter

  6. We Do Not Record FWD Diameters! We tally number of FWD by transect diameter class…

  7. FWD Estimators slope correction factor slope length of the transect number of FWD pieces tallied in the diameter class constant to convert to the proper units quadratic mean diameter mean proportion of stratum h observed transect lengths falling within the population domain indicator variable

  8. FWD QMD • Needed for Volume Estimates • Just use Midpoint of Diameter Class?

  9. Mid-point Squared vs. QMD2 * inches

  10. Theoretical Distribution of Diameters

  11. FWD QMD • Measured Empirically • Very Few Published Estimates Available • Available by Individual Species

  12. FWD QMD • Brown, J.K.; Roussopoulos, P.J. 1974. • Nalder, I.A; Wein, R.W.; Alexander, M.E.; de Groot, W.J. 1999. • Nalder, I.A; Wein, R.W.; Alexander, M.E.; de Groot, W.J. 1997. • Roussopoulos, P.J.; Johnson, V.J. 1973. • Ryan, K.C.; Pickford, S.G. 1978. • Sackett, S.S. 1980. • Van Wagtendonk, J.W.; Benedict, J.M.; Sydoriak, W.M. 1996.

  13. Van Wagner, C.E. 1982. Graphical estimation of quadratic mean diameters in the line intersect method. For. Sci. 28: 852-855. Estimate distribution of FWD Diameters Estimate midpoint of area under curve by size class Graphical Estimation Technique

  14. Graphical Estimation Technique

  15. Estimate QMD2 by forest type group for US using Graphical Method Validate by comparing to published QMD2 Suggestions for future work Objectives

  16. Each fully forested 150 degree FWD transect on each subplot treated as observation 9700 observations CWD class 3-9 inches and 9-27 inches treated as additional size classes Standardize counts by 10 feet on 150 degree transect Analysis

  17. Analysis Example Class Counts by Size Class for Forest Type Group 0-0.24 = 60.7 0.25-0.99 = 28.2 1.00-2.99 = 7 3.00-8.99 = 1.2 9.00-27.0 = 0.3 Average by Forest Type Group

  18. Non-linear Model: E(FWD Tally Count) = b0 + (starting QMD)b1 QMD2 Estimation: b1 is used to estimate FWD diameter distribution… thus estimate midpoint of area under curve and FWD QMD2 Validation: Mean absolute relative differences between published QMD2 and study QMD2 estimates Coefficient of Variation for published QMD2 estimates themselves Analysis

  19. Results

  20. Given strong “reverse J-Shaped” distribution…good non-linear fit by forest type group b1 estimates ranged from -1.6 to -2.5 … most around -2.2 Thus, QMD2 estimates did not vary greatly by forest type group Results

  21. Results

  22. Small FWD: 53% Medium FWD: 46% Large FWD: 34% Validation – All Forest Types * Compared to QMD’s for individual species

  23. Mean Difference (Published vs. Study Results) for all Size Classes = 12.1% Average CV between all Published Estimates = 72.0% Validation – Douglas-Fir

  24. Mean Difference (Published vs. Study Results) for all Size Classes = 28.0% Average CV between all Published Estimates = 62.7% Validation – Ponderosa Pine

  25. Mean Difference (Published vs. Study Results) for Small and Medium Classes = 39.7% Average CV between all Published Estimates = 81.2% Validation – Western Larch

  26. Disagreement among empirical studies Disagreement between empirical studies and this study’s theoretical model FIA needs estimates by Forest Type…Now Where Direction Do We Head?

  27. Empirically sample FWD QMD’s by forest type groups across US Costly Effort confounded by local variations and species mixtures What about shrubs? Option 1

  28. Assuming mixture of tree/shrub species in most forests also causes a mixing of FWD QMDs…use very general QMD’s (i.e. Graphical Estimation outputs) Assumption maybe too broad Exacerbates error in common, pure stands Improvement over squared midpoint diameter Option 2

  29. Use allometric scaling of tree branching to establish FWD QMD’s Option 3 (from Enquist, 2002)

  30. Scaling exponent of number of branches versus branch radius = -2.0 Exponent for all forest types in US as found in this study = -2.19 Allometric Scaling

  31. Conclusions • Graphical Method may be appropriate for national defaults – work to be done • Extreme local variation confounds even regional QMD summaries • Allometric scaling is intriguing direction cwoodall@fs.fed.us

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