By James D. Arney, PhD and Dan Opalach, PhD.
Forest Biometrics Research Institute (FBRI)
There are an increasing number of operational field cruises being designed where the precision of measurements has been specified at levels either not necessary or not efficient. A recent example is the measurement of individual tree Dbh (diameter at breast height) to the nearest 0.1-inch precision rather than the more traditional 1-inch precision.
An actual field inventory of approximately 60,000 acres with 1,500 stands was used to evaluate alternative field methods for measuring Dbh. This inventory was sampled over a three-year period using variable plot cruising designs to accommodate the full range of tree sizes found in the various stands. This analysis was completed in July 2017, but the question continues.
The plots were systematically spread through each stand at a rate of approximately one plot for every 2.5 acres. This resulted in a total of 23,342 plots over 1,500 stands.
Only a single basal area factor (Baf) was used in each stand where the cruiser attempted to use a factor which would result in 3 – 9 trees per plot. The actual result was an average of 5.8 trees per plot over all plots in all three years.
This forest was predominately Douglas-fir (62%) and Western Hemlock (20%) with 19 other associated species.
Total heights were measured on approximately every third tree with care to obtain some heights for every species in each stand. This resulted in measured heights for 36 percent of the 135,585 trees sampled by species and Dbh across all plots.
All sample trees were recorded to the nearest 0.1-inch Dbh. Since the use of diameter tapes will always have a tendency to be biased high due to moss, branches and loose debris, the diameter measurements were not rounded to the nearest 0.1-inch. Instead, the diameter measurements were truncated to the 0.1-inch Dbh. This means that a diameter tape showing 12.47 inches (to the nearest 1/100th inch) is truncated to 12.4 rather than rounded up to 12.5 inches.
Four copies of the inventory database were built:
1) Dbh = 0.1 Inch. All plots were compiled by stand using a nominal log length of 32-feet to a minimum top diameter inside bark of 5.0 inches. The FBRI Forest Projection and Planning System (FPS Version 7.51) forest management software suite was used to compile and report all volume and value statistics. The compiled results are displayed by site class (Table 1).
Table 1. Compiled using Dbh observations to the 0.1-inch precision.
2) Dbh = 1.0 Inch. A copy of the full inventory database was then made. In this copy of the database, all trees in the sample plots were rounded to the nearest 1-inch class (from the 0.1-inch precision Dbh measurements). For example, all trees between 11.6 and 12.5 inches were adjusted to 12.0 inches. Everything else remained intact from the original database (Table 2).
Table 2. Compiled using Dbh observations to the 1-inch precision.
3) Dbh = Highest. A third copy of the inventory database was made. In this copy, all trees had their observed Dbh increased by 0.4 inches. The trees in the previous database which were 12 inches became 12.4 inches. The objective is to observe the impact of a cruise which still results in the same diameters to a precision of 1-inch being compiled at the upper limits of the diameter classes (Table 3).
Table 3. Compiled using Dbh observations to the 1-inch precision at upper class limits.
4) Dbh = Lowest. A forth copy of the inventory database was made. In this copy, all trees had their observed Dbh decreased by 0.4 inches. The trees in the second database which were 12 inches became 11.6 inches. The objective is to observe the impact of a cruise which still results in the same diameters to a precision of 1-inch being compiled at the lower limits of the diameter classes (Table 4).
Table 4. Compiled using Dbh observations to the 1-inch precision at lower class limits.
The results from these four compilations of the same inventory were then compared to one another to observe if the difference in precision of Dbh measurements has an impact on the total standing inventory report (Table 5).
As may be observed in the lower portion of Table 5, the percentage differences of the various ways of handling Dbh precision have essentially a one percent or less impact on any of the inventory statistics. This comparison is the same magnitude for both the “per acre” and “Total” inventory statistics.
Table 5. Comparison of the four variations of compiling the same cruise.
As may be observed in Table 5, the small shift in recorded Dbh may cause the Baf expansion of numbers of trees by size to shift accordingly. However, the height statistics are un-affected by this variation in diameter measurement precision. Significantly more variation would be anticipated by sending a second team of cruisers out to re-sample this inventory. Subsequent samples are observed to vary the total inventory by five percent or more. Due to this expectation and experience, differences of one percent are not considered significant enough to report.
Cost of Precision
These results demonstrate an important factor when designing a field inventory. That factor is field precision of equipment and staff. From the office it would appear that greater precision of inventory statistics would be available if the cruisers measured trees to a higher resolution. While individual trees being sampled may be recorded to a higher precision, it may be a false expectation to assume that forest-wide statistics have a higher precision.
This cruise established plots at a density of one plot per 2.5 acres. Other independent field samples would most likely result in plot centers occurring at other points in each stand. The resulting variance has been commonly observed to be much greater than 1 percent. Therefore, the added precision of Dbh measurements has not improved the resulting standing inventory statistics.
Let us assume that a knowledgeable and experienced team of cruisers could provide a production rate of about 20 plots per day per cruiser on this inventory. They would sample about one-third of tree heights and record Dbh to the nearest 1-inch diameter class.
These 23,342 plots would require 1,167 cruiser days to complete the project. Now, experience shows that measuring each tree to 0.1-inch will add approximately 45 seconds to the time spent measuring and recording each tree. Since there were 135,585 sample trees in this field inventory, this additional time accumulates to 212 cruiser days. This is an 18 percent addition to the time required to complete the project for no additional information or precision.
If we assume an average cost of field inventory to be $7.00 per acre, the expected cost of the inventory would be approximately $420,000. An additional 18 percent in field time due to tree measurements to 0.1-inch would result in an added expense of about $75,000.
This additional cost would be much better spent on cruising more stands in a given year than spending more time on each plot for no additional gain in knowledge. Therefore it is recommended that operational timber cruises be designed so that Dbh is measured to the nearest 1-inch.
Please contact either Jim Arney or Dan Opalach (by using the contact forms below) at the Forest Biometrics Research Institute for further discussion on this or any other topic regarding forest inventory, management and planning.