Photo credit: SERC Staff
Calculating circumference, diameter, and growth
When you installed the band, you measured the initial diameter of the tree (DBH) in centimeters, using the diameter tape; and you measured the initial window gap in millimeters, using the calipers. As you take further gap measurements, you will be able to derive the current diameter of the tree as it grows from these measurements.
A series of measurements of the gap widths indicates the changes in the circumference of the tree. However, some calculations are needed to get the actual circumference of the tree. It's most useful for comparisons to express the tree size in terms of its diameter in centimeters. The difference in gap widths represents the change in circumference, which was measured in millimeters.
So we need to do three things:
- We need to divide the change in gap width by 10 to convert it to centimeters.
- We need to convert the change in circumference to a change in diameter.
- We can then add the change in diameter to the starting diameter.
The diameter is related to the circumference by the relation diameter = circumference / π (pi). Since the gap is a change in circumference, we divide the change in the gap by π to get the change in diameter. (If your calculator does not have a π key, a sufficiently accurate value for π is 3.14159). So from the gap width measurements in millimeters, we get the change in the diameter, in centimeters, by combining the first two steps:
Change in diameter = change in gap width / (π * 10)
To calculate the change in diameter since the beginning of a growth interval:
Change in diameter = (current gap width – beginning gap width) / (π * 10),
where the change in diameter is given in centimeters and the gap widths are measured in millimeters
To calculate the new diameter:
New diameter = initial diameter + change in diameter
For example: the initial DBH was 15.0cm, and the initial gap width was 11.38mm. The current gap width is 17.52mm. So the change in gap width is
17.52 – 11.38 = 6.14mm.
Then the new diameter of the tree is
15.0 cm + (6.14 / (10 * π)) = 15.2cm
(That's 15.195 rounded to the nearest tenth of a centimeter)
You can also estimate the total aboveground weight of the tree from the DBH. This 'oven-dry biomass' refers to the weight after drying in an oven. A general equation suitable for most temperate zone trees is
Biomass in kilograms = 0.1 * DBH2.5.
That is, the DBH in cm is raised the 2.5 power and this result is multiplied by a constant. Because this is a power equation, the biomass changes very rapidly as DBH increases. The total aboveground Carbon content of the tree can then be estimated by dividing the biomass estimate by 2, that is,
Carbon (kg) = Biomass (kg) / 2.
Estimates of the change in biomass or Carbon can be adapted from the procedure for change in DBH given above.
Patterns of growth
The pattern of annual growth will depend mainly on the type of tree (e.g., evergreen or deciduous) and the climate (ranging from highly seasonal to more or less constant in temperature and/or precipitation). Your strategy of measuring the dendrometer bands will be affected by, or dependent on, these factors. If you mainly want a reliable measure of annual growth you should measure at times when the tree is not growing – it might be necessary to make additional measurements to discover when that is. In many climates, such as in the cold temperate zone, there is a distinct pattern of rapid growth in spring and summer and no growth in fall and winter. For example, at the Smithsonian Environmental Research Center (SERC, 38.89 N and -76.56 E) the typical pattern is a distinct onset of growth in May, followed by rapid growth in June and July, slowing down progressively in August and September (Figure 1). (Note we use 'day of year' for the time axis here: day of year = 1 on January 1 and day of year = 365 on December 31). For this sort of growth pattern, measurement taken before growth begins in late April (green arrow in Figure 1) and after growth ends in late September (blue arrow) will identify the whole year's growth.
