1. Using FVS to Estimate QMD of the N Largest Trees H. Bryan Lu Washington Department of Natural Resources Olympia, WA December 9, 2011 1

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. December 9, 2011 2

3. Methods Method 1 – IF-ENDIF Approach 1.Find the total TPA for trees with DBH >= 0 2.If the total TPA > N, find the total TPA for trees with DBH >= DBHDist(3,i) where i = 1, 2, …, 6 3.Repeat Step 2 until either the total TPA <= N or i = 6 4.Determine both the minimum upper and the maximum lower bounds of DBH 5.Estimate QMD of the N largest trees December 9, 2011 3

4. Methods (Continued) Method 2 – Smith-Mateja Approach 1.Find the total TPA for trees with DBH >= 0 2.Find the total TPA for trees with DBH >= DBHDist(3,i) where i = 1, 2, …, 6 3.Use the FVS function “LinInt” to estimate QMD of the N largest trees December 9, 2011 4

5. Methods (Continued) Method 3 – Percentile Approach 1.Compute (1 – 1/N)x100% to get the starting DBH 2.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 3.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 4.Estimate QMD of the N largest trees December 9, 2011 5

6. Scenarios Case 1 – QMD40 within both bounds December 9, 2011 6 Tup Tlow 40 DBHup DBHlow QMD40 = ?

7. Scenarios (Continued) Case 2 – QMD40 outside the upper bound December 9, 2011 7 40 Tup QMD40 = ? DBHup

8. Scenarios (Continued) Case 3 – QMD40 outside the lower bound December 9, 2011 8 40 Tlow QMD40 = ? DBHlow

9. Results December 9, 2011 9

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. December 9, 2011 10

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. December 9, 2011 11