How do we quantify a forest?
In order to track changes in a forest community over time or space, or to compare forest communities in different regions, it is essential to be able to quantify the forest in some meaningful, consistent way.  At Hubbard Brook we do this in two ways.  First of all, we quantify forest composition in terms of total basal area and density for each tree species.  Basal area is the cross-sectional area of a tree trunk at breast height (1.37 m above ground level), therefore incorporating the size of the trees, while density is strictly the number of stems over a given area.  Secondly, we measure biomass of the forest.  Biomass is simply the mass (or weight) of the trees, and can be broken down into different plant parts.

1. Forest composition overview

Forest censuses are conducted every five years on W6 (as well as on W1 and W5, and every 2 years in the "Bird Area"--click here to access data and documentation for individual inventories).  To accomplish this, each watershed has been divided into a number of grid units (or "plots"), each a 25 x 25 m square1 (208 units on W6; click here for a map of the W6 grid). Each grid corner is marked by a numbered rebar or PVC stake. The stake at the NE corner of each grid unit has the number for that plot (so if you are standing at a stake, the number is referring to the grid unit to your south and east).  Sampling design has changed slightly over the years,2 but basically for each plot, the diameter of every tree >10.0 cm dbh is measured and recorded, species and health (or "vigor") are noted,3 and trees from 2.0 to 9.9 cm dbh are measured in a 3 m strip at the bottom of each plot (click here for a layout of the plot).

From this diameter data we can quickly calculate basal area for one tree  (BA=pi*(dbh/2)2, where dbh is generally converted to meters), then sum all the trees of the same species in a plot and divide by the areal size of one plot (0.0625 ha for the watershed plots4) to get basal area for the plot.5  Or we can add up the individual tree basal areas for a subset of plots or for the whole watershed, and divide by the appropriate area to get basal area over a larger scale.  Generally we break this down by species and diameter size class, for instance considering all beeches >10 cm dbh (in reality this is >9.5 cm) or all sugar maples from 2 to 9 cm dbh (in reality, 1.5 to 9.4 cm).6 Density is calculated by adding up the number of trees in a plot or group of plots and dividing by the area (in hectares) under consideration.  Frequency is calculated as the percentage of total plots under consideration in which a given species is found. These measures, collectively called "phytosociology", allow us to compare abundance and relative size among the tree species present in the forest.

Try our phytosociology calculation program!

2. Biomass overview

Calculating biomass involves a little more forethought.  If the only information we collect from a tree in our census is species and dbh, we need to first come up with some equations that relate diameter to the mass of a tree of each species.  To do this we have to cut some trees down.  This was done at Hubbard Brook in the 1960s by Robert Whittaker and others.  They cut down 7 trees from each of three different elevation zones on W6 (upper, middle, lower--click here for a map) for each of the three major hardwood species (sugar maple, beech, and yellow birch), as well as 15 red spruce trees and 15 mountain maples7 from the upper elevation zone.  For each tree they measured dbh and height, cut the tree into pieces, and weighed all the parts (including bole wood, bole bark, live branches, dead branches, leaves+twigs, and roots) (see Details of our allometric equations for more information).  For example:

 Sugar maple, low elevation: Tree DBH  Height  Wood   Bark     Branches   Leaves   Roots #  (cm)  (cm)     (g)    (g)    Live  Dead    (g)     (g)                     (g)   (g) 1   13.9   1873   63770   9570    4440   504   1169   17300 2   23.1   2007  201170  27740   48220   965   5401   56010 11   6.4    840    6430    960     560    59    310    2030 12   1.9    413     460    104      90   3.3     78     263 13  29.7   2456  411160  43350   89270   394   8064   97210 14  47.0   2608  937800 166000  374700   630  19045  239900 17  66.0   2830 1961400 206400 1200000 19560  40002  505000

Whittaker then chose to use bole volume as the best indicator (the independent variable) of the mass of the parts.  The best mathematical approximation to a tree bole turned out to be a rotated parabola.  So, using dbh and height, he calculated a parabolic volume for each tree bole using the following equation:

Parabolic volume = ½ pi*(dbh/2)2 * height

 Sugar maple, low elevation: Tree DBH  Height Parabolic #   (cm)   (cm)   Volume                   (cm3) 1   13.9   1873   142111 2   23.1   2007   420563 11   6.4    840    13511 12   1.9    413      585 13  29.7   2456   850748 14  47.0   2608  2262368 17  66.0   2830  4840990

Then for each tree part, he plotted the log10 of the actual mass vs. the log10 of the calculated parabolic volume of the bole, and did regression analysis to get an allometric equation relating the volume to the mass of the part.  This was done separately for each of the three hardwood species across three different elevation zones (only one set for spruce and one set for mountain maple).  For example:

Now we can use those regression equations to estimate the mass of each tree part for the trees from any of our censuses.  To do so, we need to know the parabolic volume of the tree bole.  This can be calculated with dbh, which we have, and tree height--Oops!--which we don't have.  We didn't record tree height because it is too time consuming to do this for every tree.

To estimate tree height we have another set of equations.  In the spring, when the trees have not yet leafed out, it is possible to measure the heights of the trees with a clinometer.  We have done so, several times,8 on a sample of trees at different elevations.  By plotting height vs. the dbh of the tree, we can again do regression analysis to come up with an equation by which we can estimate height from dbh.  This was done separately for each of the three major hardwood tree species across the three elevation zones.9  For example:

So, finally!!.....with the dbh measurements from our survey, we first use the appropriate equation for species and elevation to estimate height for each tree.   Then we calculate parabolic volume of the bole from the estimated height and the dbh.  Then, using the appropriate equations for each species in each separate elevation zone, we can estimate the mass of all the parts from the estimated parabolic volume.  This is done for each tree separately in a computer program.10

To summarize this information, generally we add up all the individual masses for a given tree part for each species in a plot, then sum them over multiple plots and divide by the collective area of the plots to express a total biomass in megagrams per hectare (Mg/ha) for each part for each species.  We are also interested in knowing the total tree biomass (in Mg/ha) for a plot or group of plots.  Our landscape biomass program yields a table that has both biomass by part and species, and a grand total for the plots selected.

Biomass, when divided into size classes(see 6) and followed over time, gives us an idea of the maturity and productivity of a forest stand.  Mature forests have most of their biomass in larger trees while younger forests, have more of their biomass in saplings or even shrubs and herbs.  With the exception of Watershed 5, which became a "young" forest when it was clearcut in 1984, none of our biomass estimates for watersheds include herbs or shrubs.  This is because most of the forest stands at Hubbard Brook are at a stage where the herb and shrub layers have very little biomass compared to the trees.  It should also be noted that although the biomass calculation program includes roots, and root biomass is included in the "total" column, most of the official reported biomass estimates from Hubbard Brook only include aboveground biomass, and therefore exclude roots.

(Note:  this is actually a very simplified explanation of the workings of our biomass programs. We hope to eventually treat the very complicated, and very important topic of the history and legacies of biomass calculation at Hubbard Brook in much greater detail.  We have started to do this below in Details of our allometric equations and in the Footnotes.)

3. A note on vegetation zones

All of these measures are typically calculated for the whole study area as well as for different "sub-areas" OR for different vegetation zones within the study area (click here for a map of both for W6).  "Sub-areas" generally include upper, middle, and lower, which are simply three arbitrary elevation zones of relatively equal area in the watershed (also sometimes referred to as "thirds").  Vegetation zones, although correlated with elevation, are defined by the different plant communities in relation to topographic position. Each plot is assigned to a vegetation zone based on the dominant plant community found within.

While our single tree biomass calculation program more or less uses the elevation-defined "sub-areas" (since these are what the original allometric equations were based on), our phytosociology and landscape biomass calculation programs include options for the vegetation zones as well as options to select various groups of plots.  The landscape biomass calculation program calculates biomass using the allometric equations for the "sub-area" that each selected plot falls into.  Then the biomass is summed and averaged for all plots selected.

4. Details of our allometric equations

In a 1974 Ecological Monographs paper, Whittaker et al. published a subset of all the allometric equations they developed as described above.  They had collected 7 trees from each of three elevation zones for sugar maple, beech and yellow birch. However, species-specific equation coefficients are included in the publication only for a combined low and mid elevation--that is, Whittaker pooled 14 trees of each species to produce equations more realistically applicable to the Northern Hardwood forest.  In the same paper they calculated biomass for W6 based on a 1965 tree survey, presumably using the published equations.  However, in trying to reconstruct the published 1965 biomass estimates for W6 using the original tree census data and Whittaker's entire set of equations (mostly unpublished), we have determined that in making the published biomass calculation, Whittaker used the elevation-specific (upper, middle and lower) equations for each major hardwood species, rather than the pooled mid and low equations published in the paper.  Therefore, we continue to use these species-specific, elevation-specific equations (each based on 7 trees) for the calculation of biomass for sugar maple, beech and yellow birch.  This makes little difference except that if you go to the 1974 paper and try to find the equation coefficients used in our biomass programs, you will not find them.  With our single tree biomass calculator you can actually estimate the same tree using the low and then the mid equations to see how much they differ--and they do differ.

Red spruce, balsam fir and white birch allometric equations are really only appropriate for the upper elevation zone ("Spruce-fir / High elevation hardwoods"), although the single tree biomass calculator allows calculation of these at middle and low elevations as well.  There is virtually no spruce, fir or white birch in the forest on Watershed 6 below the upper zone.  Thus, both Whittaker's allometric equations and the height equation for spruce were developed from trees in the upper zone.(see 9)  Since there is only one set of allometric equations and only one height equation for spruce, the single tree calculator reports the same biomass (that for the upper elevation) for a spruce of any given diameter for each of the elevation choices.  The same is true for balsam fir.  Whittaker did not do any dimension analysis of fir, but we did a later allometry study of fir boles, using 20 mature trees from the upper zone on Watershed 5.  For estimating fir biomass in our programs, we use our equations for bole wood and bark, and Whittaker's spruce equations for all other fir plant parts. As with spruce, the single fir height equation was developed from upper elevation trees.  There have been no allometric equations developed for white birch, so we use Whittaker's equations for yellow birch.  We do, however, have a height equation for white birch developed from upper elevation trees.  For white birch, the single tree biomass calculator uses the elevation-specific allometric equations for yellow birch and the single height equation for white birch, so the reported biomass does change with elevation choice although the reported height does not.

Leaf area and number of leaves is calculated for sugar maple, beech, yellow birch and white birch in the single tree biomass calculator.  These values are derived by taking the leaf+twig biomass calculated from Whittaker's allometric equations, and multiplying by the percentage of the biomass that is leaf blades.   Then we can calculate total leaf blade area using the estimated mass of leaf tissue per cm2 of blade area; and total leaf number using the average blade area per leaf.  These percentages and parameters are published in Table 1 of the 1974 Whittaker et al. paper for each of the three species at a combined low and mid elevation. For white birch, we use the coefficients for yellow birch.

The chemistry calculations use the most up-to-date data that we have available.  Chemical analysis of plant tissues was first conducted in 1965, but recent analyses of recent tissue samples have generally produced results very similar to those from the original 1965 samples.  We have also been able to reproduce the 1965 analytical results by reanalysis of the original tissue samples. Therefore, much of the chemistry data dates back to 1965. However, since that time we have done considerable work on Ca, Mg, and Zn, especially in the wood, and have used these newer data for those elements.

Whittaker, R. H., F. H. Bormann, G. E. Likens and T. G. Siccama. 1974. The Hubbard Brook Ecosystem Study: forest biomass and production. Ecol. Monogr. 44(2):233-254.

Footnotes

1  On Watershed 6, the grid was started at the weir and was laid out with surveying equipment moving upslope. The grid is slope-corrected, meaning that grid unit lengths are equal in 2-D (for example, as viewed in an aerial photo). Therefore, grid unit lengths vary in 3-D (e.g. if measured on the ground) depending on the steepness of the slope (the steeper the slope, the longer the grid length). On the edges, where the actual watershed boundary ran through a 25 x 25 m block, the block was considered "in" (and therefore established) if more than 50% of the block was within the watershed and "out" (and therefore dropped) if less than 50% was within the watershed. Thus there are some portions of the edge of the watershed not included in a grid unit and some grid units contain area outside the watershed. Tree censuses include all trees in all grid units regardless of whether the tree was in or out of the watershed. Some trees in the watershed are not counted because they are not within an established grid unit. We figure the two cancel each other out to give us a reasonable representation for the watershed. The 25 x 25 m grids for W1 (200 units) and W5 (360 units) were established in a similar manner, relative to their respective weirs. There was no attempt to line up watershed grids relative to one another. Treatments (e.g. the calcium addition on W1) for the most part were conducted along the actual watershed boundaries, not along grid lines.
Layout of the Bird Area plots is in four belt transects 2200 to 2900 m long and 10 m wide. Each transect line is divided into between 88 and 116 plots, each roughly 25 m long x 10 m wide, for a total of 397 plots. The actual length of each plot varies, but is included in the data so that an exact area can be calculated. The Valley plots are arranged in a grid covering the entire Hubbard Brook valley. Each plot is circular with a radius of 12.62 m for an area of 500 square meters. There are 431 plots in the vegetation dataset.

2  The first W6 survey in 1965 was conducted at the advent of computing and the sampling design was made assuming hand calculation of the resulting data. To keep the amount of data down, trees >1.5 cm dbh were measured only on a 10 x 10 m plot within each grid unit rather than on the entire 25 x 25 m grid unit. As it turns out, that first survey was analyzed with a computer anyway. When it was decided to resurvey in 1977, all trees >10.0 cm dbh were measured in each 25 x 25 m grid unit. The total number of data points was no longer an issue, and measuring all the trees was just as easy as having to lay out the 10 x 10 m plots to measure a subset. Small trees <10.0 cm dbh were excluded in this survey. Subsequent surveys on W6 have occurred at five year intervals and, as in 1977, have included all trees >10.0 cm dbh in each of the 208 25 x 25 m grid units.
Small trees from 2.0 to 9.9 cm dbh have been included in each survey on W6 after 1977, but different sampling schemes have been employed. In 1982 and 1987, roughly 35 of the grid units were selected at random to have trees of this size class measured over the entire 25 x 25 m area. As beech saplings flourished, this method became impractical because of the difficulty in keeping track of so many small trees over such a large area. In 1992, trees 2.0 to 9.9 were measured in a 3 m strip across the bottom (south edge) of each grid unit (an area of 3 x 25 m) for all 208 units.
This sampling scheme has continued to the present time on both W6 and W1. The W5 pre-harvest survey similarly included all trees >10 cm dbh in each of the 360 grid units, and all small trees 2.0 to 9.9 cm dbh on only 42 of the units. The W5 post-harvest surveys utilize various plot systems (see data documentation for details), but each sampling included all trees >1.5 cm dbh. Bird Area and Valley plot surveys include all trees >10 cm dbh in each plot; smaller trees were not included in these surveys.

3  Only live trees were measured in 1965, and "sick" trees were not singled out and noted as such. In all subsequent years, all standing trees, live and dead were measured, and "sick" trees were noted. In 1977, the beech bark disease (BBD) infestation was evident throughout the forest as a profusion of scale insects covering many of the tree boles. It was deemed worthwhile to document the situation while surveying the W6 trees, and beech trees were given a special vigor code if they were infested with the insect ("1" if the tree was otherwise healthy, "2" if the canopy was in decline (i.e. "sick")). Although the insect population had tapered off, beech trees were still evaluated for presence of the disease through the1987 survey. Surveys in other areas during this time also included the BBD vigor codes.

4  On Watershed 1, there are two rain gauge clearings within the watershed.  For the plots that are partially cleared, an adjustment is made in the calculation of area so that only the forested portion of the plot is included. The is one plot (number 144) which is entirely cleared and thus has no trees in the data files.

5  It must be noted that plot by plot comparisons to track changes in basal area, density or biomass from year to year are not completely valid. This is due, first of all, to the changing sampling scheme mentioned above.(see 2) Secondly, although care was taken to avoid the problem, it is possible and probable that individual trees very close to the edges of the grid units "drift" back and forth between plots from year to year depending on the decision of the individual observer in assigning each tree to a plot. The position of the stakes marking some grid corners may also shift slightly from year to year due to instability (i.e. falling over in shallow soil and being replaced at not quite the same point), effectively allowing trees to "drift" from one plot to another. This inability to directly compare trees, at least in W6, has been alleviated with the numbering (with an aluminum tag) of every tree on W6 in 2002. From 2002 forward, each tree can be tracked through time and plot by plot comparisons can be made. The Bird Area trees were tagged in 1991 and the Valley trees are tagged, so subsequent surveys here also allow direct plot comparisons.

6  A size class is centered on an even centimeter, so generally when we say "trees >10 cm dbh" we really mean >9.5 cm (with 10.0 in the center of the 10 cm size class which includes trees 9.5 to 10.4 cm) and "trees 2 to 9 cm dbh" are actually 1.5 to 9.4 cm. In the W6 1965 survey, diameters were recorded to the closest centimeter so that a tree measuring 9.5 cm was recorded as 10 cm. For this survey year, no adjustment is required for size class summaries. However, in subsequent surveys in all of our study areas, diameters were recorded to the closest 0.1 cm and sampling schemes made a cutoff at 10.0 cm (except W5 post-harvest for which the following does not apply).(see 2)  Thus only half of the 10 cm diameter class (10.0 to 10.4) was measured and recorded. In some years the other half of the class (9.5 to 9.9) was measured along with the smaller trees, but the sampling scheme was different for the smaller trees and thus we cannot simply add together these two halves of the 10 cm diameter class. Instead we have assumed that there are roughly the same number of trees 9.5 to 9.9 as there are 10.0 to 10.4 for a given species in a given plot, and have doubled the number of 10.0 to 10.4 cm trees for density summaries. We have used this technique also for basal area and biomass--doubling the calculated basal area or biomass for any tree 10.0 to 10.4 cm dbh. This of course inflates the estimate in the 10 cm class--it would have been more appropriate to "create" the correct number of 9.5 to 9.9 trees and then calculate biomass based on those diameters, but this would have involved much more complicated programming. Since there are typically only a few trees in this size class (about 1% of the stems on W6 in 2002), we decided not to worry about it.
For the smaller trees, the 2 cm diameter class has the same problem (again, except for W5 post-harvest surveys). Again we assume there are the same number of trees 1.5 to 1.9 cm as there are 2.0 to 2.4 cm, and we double the 2.0 to 2.4 trees as described above. Since there are generally many saplings in this range, the inflated basal area and biomass estimated may be more problematic. On the other hand, there may very well be more trees 1.5 to 1.9 than there are 2.0 to 2.4 so this perhaps balances out.
It should be noted that while we measure and record trees 9.5 to 9.9 cm dbh when we are doing small tree plots, these trees are excluded from our calculations since we have already accounted for them in the doubling process for the 10 cm size class as described above. This solution works fine in most cases, however, the user of our interactive calculators may run into problems using the "select a diameter range" option if the chosen range starts or ends between 9.5 and 10.4. For example, if 9.5 is the lower diameter and 9.9 is the upper, the results will show no trees. If 2 is the lower and 10 is the upper, no trees 9.5 to 9.9 will be included, and only the 10.0 trees will be doubled--an underestimate. If 2 is the lower and 10.4 is the upper, the results should be correct--no trees 9.5 to 9.9 will be included, but trees 10.0 to 10.4 will be doubled to make up for the 9.5 to 9.9 trees that were left out. If 9.7 is the lower diameter and 20.7 is the upper diameter, trees 9.7 to 9.9 are excluded and all trees 10.0 to 10.4 are doubled--an overestimate. To alleviate this problem we would recommend to always include or exclude this entire range in the selection--starting either <9.5 or >10.4 and ending either <9.5 or >10.4. A similar problem results if the selected range starts between 2.0 and 2.4, so it is best to start either at 2 (which will include doubling to make up for the 1.5 to 1.9 trees that were not measured) or above 2.4. The easiest solution in using the "select a diameter" option is to always enter whole diameter classes, i.e. start with an X.5 and end with an X.4. This works all the way down to 1.5 cm--there are no trees in the data below 2.0 cm, so entering 1.5 cm instead of 2.0 makes no difference in the output.
For W5 post-harvest surveys, the inclusion of all trees >1.5 cm alleviates the need for doubling and thus these issues are not relevant.

7  We have never been convinced that Whittaker actually studied mountain maple--it seems more likely that it was striped maple.  Striped maple is very common today in the watersheds in the 1 to 10 cm dbh range (Whittaker's stated size range under study for "mountain maple"), whereas mountain maple is somewhat hard to find and very rare as large as 10 cm dbh.  On the other hand, the W6 1965 survey does show an abundance of mountain maples in the 2-9 cm dbh class at the upper elevation, although this is not born out in subsequent surveys on W6.  We considered that perhaps there was a mix-up in naming the species under study, but mountain maple and striped maple were both commonly recorded in the 1965 survey, as was red maple, so the researchers were obviously aware of the names and presence of all the maple species. Furthermore, cursory study of the published sample dimensions for leaf blade area and leaf number per twig for "mountain maple" were indeed more like mountain maple than striped maple. We may never know for sure whether those really were mountain maples or misidentified as such, but for the time being we will assume that they were indeed mountain maple.

Tree height equations used in these calculation programs were developed for the most part from tree height data taken from W5 in 1984 and 1998 and from W1 and W6 in 1996.  There was no noticeable difference in tree diameter-height relationships among these samplings; that is, a tree of a given diameter in 1984 would be the same height as a tree of the same diameter in 1996. The available data are pooled in some cases, or in other cases, data from individual sampling locations are used in creating the asymptotic height functions for each species at each elevation in that location.

Exceptions to this are 1965 biomass estimates for W6, for which we use height data gathered by Eaton and others in 1965. Tree heights were estimated on W6 in 1965 with an Abney level, and not thought about again at Hubbard Brook until 1984, when trees were felled on W5 in the whole-tree harvest. With all these trees lying on the ground, we decided to take the opportunity to actually measure (rather than estimate) the tree heights. We discovered that these trees were about 30% taller than the estimates from 1965. Thus the trees' allometry changed over this period with trees becoming taller for a given diameter. We think this is due to the rapid upgrowth and "filling in" of the forest after the 1938 hurricane and possible salvage logging around 1940. For 1977 biomass estimates we use interpolated height curves, halfway between the 1965 and 1984/96/98 curves.
As mentioned above, the subsequent estimates in 1996 and 1998 agree very closely with the 1984 measurements. Another valley-wide study, conducted by Paul Schwarz between 1995 and 1998, yielded tree height estimates that were very similar to all the others (except 1965). This data has not been used in developing the height equations used here, but since it was taken independently by a different set of observers, serves as a nice cross-check to further verify the accuracy of our 1984-1998 estimates.

9  For sugar maple, beech and yellow birch, height equations were calculated separately for W1 and W6 and the appropriate set of equations used depending on which watershed is under consideration (in the landscape biomass calculation program).  For the single tree biomass calculator, the W6 height equations are used for these three species.  For white ash and red maple, the sugar maple height equations are substituted for each elevation; for pin cherry and chokecherry, the yellow birch equations are substituted for each elevation.
For all other species, a single equation is used for all elevations.  The spruce and white birch height equations both use pooled data gathered from the upper elevations of W1, W5 and W6.  The fir equation uses data from  the upper elevation zone of W6 (the only data we have available at this time), and is only appropriate for trees up to 40 cm dbh.  Fir is the only linear height equation we use, and we hope to someday collect data from some larger trees (there are very few large fir in the watersheds at this time) to develop an asymptotic equation. The "striped maple" height equation uses Whittaker's data for mountain maple at upper elevations(see 7), plus 6 striped maple trees (up to 16 cm dbh) measured by Eaton in 1966 at various elevations on W6.  This height equation is also used for mountain maple and mountain ash.

10  For the several species for which no allometric equations were developed, we substitute the equations for similar species to estimate the masses of the plant parts.  White ash biomass is calculated using allometric equations for beech (and height equations for sugar maple(see 9)).  For white birch, pin cherry, and chokecherry, the yellow birch equations are used; for red maple, the sugar maple equations are used.  For everything besides fir wood and bark (for which we have developed special fir equations), the spruce allometric equations are used to estimate fir biomass.  Striped maple, mountain maple, and mountain ash biomass are all calculated using Whittaker's equations for mountain maple.(see 7)   Hemlock biomass is calculated using the spruce equations. For all trees with a species number greater than 14, the calculators use sugar maple equations for height and biomass. There are generally very few individuals of these other species and making them all sugar maples was an easy programming solution.

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Web page created October 2001
by Ellen Denny and Thomas Siccama