Using BigBAF Sampling in a New England Mixedwood Forest

by Kenneth M. Desmarais

Program Forester 
Fox Research Forest NH Division of Forests and Lands
Forest Management Bureau


New England forest stands are often highly variable and local foresters have the difficult problem of sampling these forests. Traditional sampling methods such as Horizontal Point Sampling (HPS), can be extremely time consuming if a forester intends to get a point estimate with reasonable confidence limits. It is not unusual for the confidence limits by species to be ± 300% or more for a particular estimate, especially sawtimber or pulpwood volume. The problem is compounded in the region by local foresters’ preference for the 10 Basal Area Factor (BAF) prism, which usually requires them to measure about 5 to 20 trees per point. So for each single basal area observation, 5 to 20 trees must be measured, based on the stocking of the stand.

An alternative to HPS is BigBAF sampling. This method uses 2 different BAFs; a large BAF often ranging from 80 to 110 (English) for determining which trees to measure, and a smaller BAF often 10 to 20 (English), for collecting tree counts (basal areas). The large BAF is very efficient because it dramatically reduces the number of “In-trees” to measure and most of the “In-trees” are very close to point center. The smaller BAF permits the collection of tree counts with a much lower variance than would be achieved with the larger BAF.

Methods and Materials

To test this method, I used BigBAF sampling in a marked timber sale prior to cutting. The marked trees had received total enumeration so I had excellent stand volume estimates. Next, I collected data from 80 points in this 9.1 acre stand. I used an 80 BAF homemade angle gauge to determine measure trees and a 20 BAF prism for basal area counts. To measure tree diameter I used a commercially manufactured diameter tape and ocularly estimated merchantable heights to the nearest ˝ log (8 feet). The fieldwork required 4 ˝ hours to complete. Calculations were done on a Microsoft Excel spreadsheet. Point volume estimates are calculated the same way as in HPS by multiplying the mean VBAR by the mean basal area.


From my sampling, Eastern white pine sawtimber had a mean Volume to Basal Area Ratio (VBAR) of 192.86 board feet per square foot of basal area and a mean basal area of 23.25 square feet per acre resulting in an estimate of 4,484 board feet per acre. The marked pine volume was 4,908 board feet per acre, a difference of 8.4%. Eastern hemlock had a mean VBAR of 112.84 board feet per square foot of basal area and a mean basal area of 25.0 square feet. The hemlock cruise estimate was 2,821 board feet per acre compared to the marked volume of 3,017, a difference of 6.5%. Finally, Northern red oak had a mean VBAR of 97.3 board feet per square foot of basal area and a mean basal area of 14.75 square feet. The sawtimber volume estimate was 1,435 board feet per acre compared to the marked volume of 1,327 board feet per acre, a difference of 8.1%.

I used Bruce’s equation to calculate the confidence limits of the cruise:

SE%s are calculated by multiplying each standard error of the mean expressed as a percent, by a “t” value to get a range of values with a certain degree of confidence. I used a 95% degree of confidence for this cruise and my SE%s are adjusted accordingly. Each SE% within the square root sign (radicand) must be adjusted individually because they usually have different degrees of freedom.

Inserting my white pine values into the equation resulted in a confidence limit of:

± (WP).

Hemlock had a VBAR SE% of 11.2% and a basal area SE% of 23.9% resulting in a total SE% of 26.3%. Red oak had a VBAR SE% of 8.7% and a basal area SE% of 40.5% resulting in a total SE% of 41.4%.

Inspection of the above equation shows that the higher of the two radicands dominates the equation. Reducing the lesser radicand has little effect on the outcome. For example, if I were able to reduce the VBAR SE% for white pine by half, the confidence limits would be only reduced to 28.8%. However, if I reduce the basal area SE% by half, the confidence limits would be reduced to 16%. Thus, it is suggested that the two radicands be balanced for maximum efficiency. If a confidence limit of ±15% were desired, each radicand would need to be 10.6%.

This cruise had VBAR radicands of 7.2%, 11.2% and 8.7 % respectively for white pine, hemlock and red oak. However the basal area radicands were 28.6%, 23.9% and 40.5% respectively. These statistics suggest that I would have been better off using a larger BigBAF of possibly 100 BAF and spent a larger proportion of time sampling basal area instead of measuring trees.

Traditional HPS techniques would have caused increased over-sampling of individual trees and under-sampling of basal area. I think BigBAF sampling will work well in many New England forest stands.

Thanks to Dr. Kim Iles for developing the BigBAF method and helping me get started, Dr. John Bell, Dr. Thomas Burk, Dr. Mark Ducey and Dr. Jeff Gove for their additional assistance and support. The Caroline A. Fox Fund and the New Hampshire Division of Forests and Lands – Forest Management Bureau funded this project.

Originally published April 2002

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