Using FVS to Estimate QMD of the N Largest Trees

1. Using FVS to Estimate QMD of the N Largest Trees H. Bryan Lu Washington Department of Natural Resources Olympia, WA

2. Motivation • DNR has used FVS to develop yield tables for various projects. • QMD of the N largest trees was used in these projects to make decisions. • Neither a keyword nor a function exists in FVS to compute QMD of the N largest trees. • FVS has a limit on the number of keywords and statements used.

3. Methods • Method 1 – IF-ENDIF Approach • Find the total TPA for trees with DBH >= 0 • If the total TPA > N, find the total TPA for trees with DBH >= DBHDist(3,i) where i = 1, 2, …, 6 • Repeat Step 2 until either the total TPA <= N or i = 6 • Determine both the minimum upper and the maximum lower bounds of DBH • Estimate QMD of the N largest trees

4. Methods (Continued) • Method 2 – Smith-Mateja Approach • Find the total TPA for trees with DBH >= 0 • Find the total TPA for trees with DBH >= DBHDist(3,i) where i = 1, 2, …, 6 • Use the FVS function “LinInt” to estimate QMD of the N largest trees

5. Methods (Continued) • Method 3 – Percentile Approach • Compute (1 – 1/N)x100% to get the starting DBH • Use the starting DBH to determine the minimum upper bound of DBH and to compute the total TPA for trees with DBH >= the minimum upper bound of DBH • Use the minimum upper bound of DBH to find the maximum lower bound of DBH and to compute the total TPA for trees with DBH >= the maximum lower bound of DBH • Estimate QMD of the N largest trees

6. Scenarios • Case 1 – QMD40 within both bounds Tup DBHup 40 QMD40 = ? Tlow DBHlow

7. Scenarios (Continued) • Case 2 – QMD40 outside the upper bound 40 QMD40 = ? Tup DBHup

8. Scenarios (Continued) • Case 3 – QMD40 outside the lower bound Tlow DBHlow 40 QMD40 = ?

9. Results

10. Conclusions • To be consistent, all methods used the FVS function DBHDist(3,i) where i = 1, 2, …6. • The differences among the three methods are the way to find the bounds around the QMD of the N largest trees. • Three possible cases existed. Case 2 would occur more if N is larger. Case 3 would occur more if N is smaller. • Method 2 is simple and flexible. It does not need to find the bounds around QMD of the N largest trees.

11. Conclusions (Continued) • Method 1 and Method 3 produced a smaller deviation from “true” values than Method 2 does. It can be improved by adding the capability of finding the bounds around QMD of the N largest trees. • The deviation from “true” values might be larger if a stand has very few large trees and lots of small trees.