Using FVS to Estimate QMD of the N Largest Trees

H. Bryan LuWashington Department of Natural Resources

Olympia, WA

December 9, 2011 1

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

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

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

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

Scenarios• Case 1 – QMD40 within both bounds

December 9, 2011 6

Tup

Tlow

40

DBHup

DBHlow

QMD40 = ?

Scenarios (Continued)• Case 2 – QMD40 outside the upper bound

December 9, 2011 7

40

Tup

QMD40 = ?

DBHup

Scenarios (Continued)• Case 3 – QMD40 outside the lower bound

December 9, 2011 8

40

Tlow

QMD40 = ?

DBHlow

Results

December 9, 2011 9

Statistics of Deviations from "True" QMD40Stats M1 M2 M3

Counts 1,407 1,407 1,407Mean 1.62 11.48 1.62Std 2.30 21.08 2.30Max 13.10 135.44 13.10Min 0.00 0.00 0.00Best 1,108 307 1,107Best (%) 79% 22% 79%

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

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