The most reliable methods of forest biomass and carbon storage calculations are based on using forest inventory data (e.g., [
1]). For our analysis, we used the 1989 and 1997 forest inventory data from the largest forest inventory database that is available—USDA Forest Service FIA (Forest Inventory and Analysis)—as the basis for biomass and carbon estimation in Georgia. We used the functions of tree diameters and heights for calculating the total below- and aboveground tree foliage and dry biomass for each measured tree on the FIA plots. When separate equations for foliage biomass were not available, the foliage biomass was calculated by subtracting the total tree biomass estimate without foliage from the total tree biomass estimate with the foliage following the example of [
13]. Per-tree values were expanded to per-acre and per-area total tree aboveground biomass using the FIA expansion factors [
14,
15]. Belowground biomass was estimated consistently with [
16], using a model relating the quantities of belowground biomass to the aboveground biomass. The biomass densities per unit area were calculated using appropriate sums of the expansion factors.
2.1. Study Site, Biomass, Forest Types, and Species Groups
The study site is the state of Georgia, located in the southeastern United States, which is the part of the country with the fastest changes in forest growth [
4]. This research is a part of a larger project on biomass assessment (e.g., [
17]) and its production sustainability at different levels of utilization. Below, we describe the underlying assumptions for the biomass estimation in different forest types and species groups.
There are many definitions of biomass used by different authors. The USDA Forest Service uses the notion of “total tree”. This is the aboveground portion of tree, without foliage, stump, and roots (e.g., [
18]). In practical application of the US forest inventory, the term “total biomass” denotes the total aboveground biomass of a sample tree 2.54 cm (1 inch) diameter at breast height (DBH) or larger. Per tree values must be multiplied by appropriate expansion factors to obtain per area information [
14]. This kind of biomass is also called woody biomass (e.g., [
8]), and it is an estimate of the amount of economically important goods, which are usually expressed in green pounds. [
19] defines “total tree” as bole, top, branches, stump, and roots. Some authors also use the term “complete tree” (e.g., [
18]), which is not clearly defined, but it seems to have the same meaning as “total tree”. Some publications do not explain the meaning of “biomass”, which makes the use of the information in these publications more difficult and subject to erroneous interpretation. In this report, we use the terms “total tree biomass” and “total aboveground biomass without foliage” consistently with the use of this term in the USDA Forest Service publications. These quantities are expressed in dry tons.
Estimation of biomass for roots, foliage, and woody part of tree is desirable, because it reflects differences in properties of tree parts and in their role in the carbon cycle. Thus, for example, tree biomass can be harvested as wood products (e.g., timber, pulp, chips, etc.), while the foliage and root biomass usually remain on site. Further, foliage biomass is decomposed relatively quickly, while stumps and roots are decomposed at a much slower rate. Accordingly, we computed dry biomass of foliage and the stump–root system. Foliage biomass was calculated using a series of regression equations and by subtraction of estimates of biomass without foliage from the estimates of biomass with foliage. Since the root system of the tree comprises approximately 20% of merchantable bole biomass [
19], we calculated belowground biomass from aboveground biomass using [
16] regression equation. As discussed above, total biomass is defined as the sum of total tree wood, foliage, and root biomass. The amount of carbon was estimated from dry biomass using a factor of 0.5 [
1,
2] and expressed in Tg (10
12 g).
The basic unit in the inventory database is a condition on the sample plot, which can be identified as a sampled part of the forest stand. Each condition/plot consists of individual tree measurements, which are subsequently generalized to all trees in the given stand. Any stand is an aggregation of trees, and the stand biomass is defined as the sum of the biomass of the individual trees that comprise the stand [
20]. Accordingly, we calculated tree, foliage, and root biomass per acre as a sum of the biomass, calculated with regression equations for each sampled tree, subsequently multiplied by its appropriate tree expansion factor, to obtain the value it represented per unit area. Finally, these values per unit were multiplied by the appropriate plot expansion factors to obtain the values for the summing up into whole state, cover types, and species groups.
For the most important tree species in Georgia (shortleaf and loblolly pine, longleaf and slash pine, red oak, sweetgum, yellow poplar, tupelo-blackgum, and white oaks), we used species-specific biomass equations for the calculation of the dry tree and foliage biomass. The sum of the tree biomass for these species in Georgia accounts for approximately 80% of all woody biomass in the forests [
9]. For other species, we used general equations developed for “all” or “other” trees. Equations used for computing the tree dry biomass from tree DBH and tree total height are listed in
Table 1.
2.2. Data Acquisition
The USDA Forest Service used to provide the data for all states through the North Central Research Station website, but, currently, the FIA provides the access to data through the FIA DataMart website (
https://apps.fs.usda.gov/fia/datamart/, accessed on 21 January 2021). This site contains a set of data files in various formats, including the “comma separated values” (CSV) format that can be imported directly into any spreadsheet, database management system, or statistical program. The site contains also the state reports and a detailed manual for the database ([
15], based on [
14,
25] and other manuals). The hierarchically-organized data contained nine files for each inventory: survey, county, plot, subplot, condition, boundary, tree, seedling, and site tree file. This allowed analysis on various levels of resolution (tree, plot, area, county, state, region, and national) by different users (foresters, politics, timber industry).
About 100 features were recorded for each plot, subplot, and condition, including: plot number, ownership, current forest type, stand age and stand-size class, stand origin, site productivity class, site index and site index base age, land use class, basal area per acre, slope, aspect, and, in some cases, elevation, physiographic class, or soil group, treatment opportunity class, percent of unstocked area, stocking, remeasurement period, expansion factors for area, volume, growth, mortality, and removals, location in terms of longitude and latitude, and measurement date.
Over 60 variables were recorded on the tree level. Some of them were collected directly by measurement of trees: tree number, status, species and species group, current and previous DBH, total height, quality class, crown ratio and crown class, and damage and its cause. Other values (e.g., different volumes, volume, removals and mortality expansion factors, or number of trees and number of mortality trees per acre, growth, and biomass) were calculated using formulas [
15].
FIA inventories were designed to meet specified sampling errors at the state level at the 67 percent confidence interval. The maximum allowable sampling error for an area of one million acres (404,694 hectares) of timberland is 3 percent. The maximum sampling error for volume and net annual growth on timberland with a billion cubic feet (28.3 million cubic meters) of growing stock is 10% [
9]. Using the database for estimation of values on smaller scale (e.g., county level) increases the level of error due to a decrease in the sample size. During estimation of the biomass, a slightly higher error is expected due to an additional source of error from use of regression equations to predict biomass.
2.3. Biomass Estimation
Even though a majority of authors agree that using forest inventory data is the most appropriate approach for biomass and carbon sequestration calculations, they use it in different ways. One group of practical methods, represented by Brown [
26], Schroeder et al. [
11], or Brown et al. [
10], use biomass expansion factors (BEF) for converting inventoried wood volume to estimates of above- and belowground biomass. Biomass expansion factors are usually defined as a ratio of aboveground biomass density of all living trees for some predefined merchantable volume. This method is best used for secondary to mature closed forests only. Total aboveground biomass density is calculated as a product of volume per area unit, volume-weighted average wood density, and an appropriate biomass expansion factor. For American forests, BEF values vary from 0.50 to 0.69 [
26]. Because forest inventories often report total volume defined in different ways (e.g., merchantable volume only, or volume of trees above a threshold diameter), and these inventories may be the only information available, some authors propose to express volume data in a unified way, or use some common denominator, e.g., volume of trees 10 cm and greater. For example, Brown [
26] developed volume expansion factors that related total volume to various merchantable volume estimates. However, use of such an approach can lead to large and unknown errors, especially during extrapolation. Researchers using this approach believe that it is an appropriate method for broad-scale studies, because inventory data are generally collected at large scale from the population of interest and are designed to be statistically valid.
Often, inventories of volume do not characterize total forest biomass well due to the focus on commercial species, measuring trees with diameter bigger than a given threshold, and little or no information on branches, twigs, bark, stumps, foliage, roots, and seedlings and saplings. Another approach to biomass calculation uses biomass equations based on direct tree measurements (diameter at breast height—DBH or DBH and height) that do not require conversion from volume estimates. This approach involves estimating the biomass per tree or average tree of each DBH class, then multiplying the per tree value by the number of trees in the class, and summing tree component estimates for all trees or across all diameter classes. Even though some problems may exist with this method [
26], it is a viable approach that provides estimates of the total biomass as well as the various components of it. The FIA database provides for all species detailed measurement of trees with diameters of 2.54 cm (1 inch) and greater. These data can be used to calculate biomass with a smaller number of additional, uncertain assumptions. Existing biomass equations developed for most of the forest species in the southeast made this approach possible for our study. Several papers containing equations for biomass calculations based on diameter at breast height only, and on DBH and tree height, are available in the literature (e.g., [
13,
18,
21,
22,
23,
24,
27]). There are also papers describing biomass determination based on tree height alone, but this method is valid only for very young trees, e.g., 1–4 years old [
28], and they did not apply to our study.
In principle, models available for estimation of biomass from DBH alone can be expected to have large biases depending on site productivity, stand density, and age, because a short tree with a large taper and a tall tree with small taper may have the same diameters but drastically different volumes and biomass contents. The use of both DHB and height is more desirable, when both of these parameters are available, than using DBH alone, even if the heights are estimated with appropriate functions instead of measured directly. Thus, to compute the biomass and carbon quantities using our approach, we used both tree DBH and total height for each of the measured trees on each plot. While tree heights were not recorded in the 1997 FIA inventory database available online, this database contains the stand site indices, which can be used to estimate height for the dominant trees with appropriate site index equations available for all main eastern forest tree species (e.g., [
29]). Heights for all the trees on the plot can be estimated with the models developed for lake states by Hahn [
30]. Hahn’s model [
30] estimates tree height as a function of species-specific site index, stand basal area, and tree DBH. The model has the following algebraic form:
where
H is tree height (in feet);
a,
b,
c,
d,
f, and
g are coefficients (the coefficients for all species are shown in
Table A1 in the
Appendix A. If a species does not have coefficients, we use coefficients for “other softwoods” or “other hardwoods”);
e is the base of the natural logarithm (2.71828);
DBH is tree diameter at breast height (in inches); tdob is top diameter over bark (in inches), 0.0 if total height,
SI is site index of the stand (in feet, base age 50); and
BA is basal area of the stand (in square feet per acre).
Finally, since there may be discrepancies between the height estimates from the local site index models and from model (1), the height estimates for all diameters were multiplied by a ratio of dominant height estimates from the local equations over the dominant height estimates from model (1). This adjustment addresses any potential regional biases that might otherwise underestimate or overestimate heights for any given site index or diameter class, since the shape of site index curves might be different for different regions and species. Use of heights, diameters, and stand densities (through the use of the basal areas), in principle, offers an important improvement over the use of just diameters for tree biomass estimation, because besides the abovementioned principal argument, for most southern pines at the time of doing this study, there were no equations for biomass as a function of DBH alone.
2.3.1. Biomass Per Tree
As mentioned above, we found several equations for biomass calculations. Assuming that volume, biomass, and carbon content depend not only on tree diameter, but also on its height and taper, we chose equations based on both DBH and total height. Biomass of softwood species was calculated using the following modified formula, based on [
13,
18,
22], that gives biomass expressed in kilograms based on data provided in imperial units (used by the USDA Forest Service FIA program):
where
Biomass1 is a tree biomass expressed in kilograms; a and b are adjusted species or group-specific coefficients (shown in the
Appendix A Table A2);
DBH is diameter at breast height of the tree (in inches); and
H is total height of the tree (in feet).
When necessary, foliage biomass was calculated by subtraction of biomass with and without foliage. Biomass equations for hardwood species are more complicated. Their developers found that the best form of equation depends on tree diameter. In this case, tree biomass of hardwood species trees with DBH below 28 cm (11 inches) was calculated using the following equation [
24] with recalculated coefficients:
For trees with diameter at breast height equal to or greater than 28 cm, the following equation was used:
where:
Biomass2 and
Biomass3 are tree biomasses expressed in kilograms;
a,
b, and c are species or group-specific coefficients (shown in the
Appendix A Table A3), and all other symbols are as defined earlier.
Because Equations (3) and (4) cannot be used to predict foliage biomass directly, we obtained these estimates by subtraction, as described earlier.
Most biomass studies, including BEF and allometric equation development, are typically limited to the aboveground tree components, because methods for belowground studies are technically difficult, labor-intensive, and time-consuming. Most existing biomass studies are based on relative biomass allocation between roots and aboveground components—a root/shoot (R/S) ratio. The simplest approach assumes a static relationship for root biomass determination (e.g., [
31]), but, in fact, the relationship is most likely highly variable. In fact, we know that root biomass proportions depend on species, soil type, texture and moisture, nutrient availability, etc. Cairns et al. [
16] provide a recent review of various root biomass estimation methods. The authors showed, using linear regression analysis, that aboveground biomass, density, age, and plot location (latitude) are the most important predictors of root biomass density. These three factors together explained about 84% of the variation. Comparison of their approach and other methods using R/S ratios for forests in the United States gave about 20% higher estimates. We decided to use this approach since it is relatively simple and useful for the data we had available from the FIA inventory. Root biomass was calculated as function of dry biomass of the tree with foliage [
16]:
where all symbols are as previously defined.
2.3.2. Total Biomass Calculations
Equations (2)–(5) above allow us to calculate biomass represented by a single tree with a given
DBH and total height. These values were expanded first to a single plot area and then to total inventoried area. Total biomass represented by each plot in the entire state inventory was calculated using the formula from Forest Inventory and Analysis database manuals ([
14,
15]):
where:
Biomasstree is per tree biomass calculated from Equations (2)–(4) given above,
VOLFAC is the tree expansion factor (number of trees per area unit that given tree represents in the inventory), and
EXPVOL is the plot volume expansion factor (area that given plot represents in the inventory).
2.4. Visualization of the Estimated Biomass and Carbon Quantities
At the time of this research, the USDA Forest Service provided only approximate locations of their sample plots to within the nearest 100 s (0.028 degrees), which means precision of this item along the meridian is ±1542 m for latitude and ±1094 m for longitude at latitude 45 degrees [
15]. Unfortunately, the inexact locations do not allow for applications of such analysis as kriging, co-kriging, regression, or nearest neighbor analysis. Because of that, we were forced to explore other approaches that are less sensitive to the exactness of the plot locations.
Based on the approximate locations provided by the FIA database, we generated a hypothetical map of Georgia’s forests using an algorithm based on what we call the “growing circles” approach. We assumed that, starting from the point with an approximate location, we could build polygons with area equal to the given plot area expansion factor (“number of acres that a given plot represents in current inventory”). The “growing circles” approach is based on a systematic grid of points 200 m apart. Grid points within 100 m of a road, stream, river, or pond greater than 4 hectares, or lake were identified and not processed. The goal of this method was to “grow” (increase size) each circle until its area equaled that of the FIA expansion factor. We computed the weighted distance, using the inverse of the FIA expansion factor, from each grid point to the nearest FIA point and assigned it, and the FIA plot identifier (of the closest FIA point), to each of the grid points. The second iteration involved looping through each FIA point, starting with the point with the smallest expansion factor to select all grid points assigned to each of the FIA points. If the number of selected points was less than the FIA plot area expansion factor divided by 10, then all of those selected grid points were assigned a flag representing the current FIA point, and eliminated from further processing. The number of grid points required was recorded for each inventory plot. If the number of selected points was greater than the number needed, (FIA plot area expansion factor/10) grid points were assigned a flag, starting with the smallest weighted distance. If the latter was the case, we removed that FIA point from further processing. The final iteration utilized only the FIA points that had not been assigned (FIA plot area expansion factor/10) grid points. Starting with the FIA point with the smallest expansion factor, we selected all grid points assigned the current FIA identifier (flag). Iteratively, we selected all grid points without an FIA identifier within 200 m (660 feet) of those selected points. Grid points were assigned a flag until the assigned area was equal to the current FIA point expansion factor.
The resulting grid point dataset included (for each point) the weighted distance to the nearest FIA point, the identifier to the nearest FIA point, and the flag value representing which FIA point it had been assigned. The point dataset was converted to a GRID data type using ArcView’s AsGrid request. The GRID dataset was then converted to a polygon using ArcView’s AsPolygonFTab request. The final polygon dataset contained 31,503 polygons with each polygon containing a weighted distance, “closest FIA point”, and FIA flag attribute.
The result of this approach to spatial population of FIA data is shown in
Figure 1. Given that the expansion factors were determined for each plot based on visual inspections of aerial photography, this approach produces a simplified realistic spatial representation of the inventory.