Estimating aboveground live understory vegetation carbon in the United States

We use data from the Digital Photo Series database to develop a suite of allometric models to estimate UVEGC for dominant forest types (Ottmar et al 2004, Wright et al 2010). The Digital Photo Series Database is a collection of UVEG data from field sites located in major forest types throughout the US (Wright et al 2010). Although the data are principally used for fire fuel modeling and monitoring, the current study takes advantage of plots that were clipped and weighed to measure UVEG biomass, including shrubs, nonwoody material (e.g. forbs and graminoids), and seedlings. Additionally, percent cover, height measurements, and seedling densities were collected at most plots allowing for the development of allometric models for predicting UVEG biomass. The biomass value was multiplied by 0.5 to estimate carbon in each respective UVEG pool. The Digital Photo Series Database is maintained by the USDA Forest Service Fire and Environmental Research Applications Team in Seattle, Washington (http://depts.washington.edu/nwfire/dps/).

The FIA program employs a multi-phase inventory, with each phase contributing to the subsequent phase. First, current aerial photography (e.g. National Agriculture Imagery Program, USDA Farm Services Agency (2008)) is used in a prefield process to determine the land use (e.g. forest or cropland) at all sampling points (i.e. plot locations). Next, each sample point is assigned to a stratum using imagery or thematic products (e.g. National Land Cover Database, Homer et al 2012). A stratum is a defined geographic area (e.g. state or estimation unit) that includes plots with similar attributes; in many regions, strata are defined by predicted percent canopy cover. Permanent ground plots are distributed approximately every 2428 ha across the 48 conterminous states. Each permanent ground plot comprises a series of smaller fixed-radius (7.32 m) plots (i.e. subplots) spaced 36.6 m apart in a triangular arrangement with one subplot in the center. Tree- and site-level attributes—such as diameter at breast height (dbh) and tree height—are measured at regular temporal intervals on plots that have at least one forested condition defined in the prefield process (USDA Forest Service 2016). On a subset of the base intensity plots distributed approximately every 38 848 ha additional forest ecosystem attributes are measured including UVEG characteristics. The UVEG, or 'Vegplot' measurements include species type and percent cover of shrub and nonwoody species for height layers of 0–0.61 m, 0.62–1.83 m, 1.84–4.88 m, and >4.88 m (Schulz et al 2009). However, no actual heights were collected in the Vegplots. Only a subset of intensive plots had Vegplot measurements (24 392 subplots, or 5% of the total), and those that did were mainly concentrated in the South Central US and West Coast. The years sampled of the Vegplot data spans from 2001 to 2011, with the majority sampled between 2007 and 2010.

To fill the spatial gaps in Vegplot data we combined them with similar 'Microplot' data from the FIA program collected throughout the US This dataset not only contains percent cover of shrub and herbaceous species, but also their heights (Woodall and Monleon 2008). Similar to Vegplot data, the measurements were not collected for all intensive plots, rather a subset (45 700 subplots, or 15% of the total). Importantly, the area of Microplots is much smaller (13.5 m⁻²) than the Vegplots, which cover the whole subplot (168 m⁻²). The Microplots were sampled from 2002 to 2013 with the majority sampled between 2005 and 2010.

Microplot and Vegplot data that were collected in the same location and in the same year were used to develop models for harmonizing the two datasets. Scatterplots of percent cover observed on the Microplots and Vegplots indicated a consistent bias in the Microplot measurements. Microplot percent cover tended to be lower than Vegplot percent cover for small values, but higher for larger values. This may be due to the differences in perceptions of field crews in determining shrub and nonwoody covers over the smaller Microplots versus the larger Vegplots. In any case, a polynomial model was used to adjust the Microplot percent cover to be more similar to the Vegplot. Additionally, due to the fact that there are no height measurements recorded on the Vegplots (only height classes), height was predicted from percent cover from models developed from the Microplot data (figure 1). The new allometric models developed from the Digital Photo Series database were then used to estimate UVEGC on each FIA subplots where measurements of UVEG existed.

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Information on seedlings (<2.54 cm or 1 inch diameter) is collected on all FIA plots, not only intensive plots. Actual seedling data are not used in the current calculation and reporting of UVEGC, though it is considered part of this pool (Smith et al 2013). In the current approach, we used counts of seedlings collected in the Microplots to calculate seedling density, which could then be related to seedling carbon density based on models developed from the Digital Photo Series Database (figure 1).

FIA stand metrics at the subplot level were also calculated and used as variables for subsequent random forest modeling. These included: forest type, stand age (years), slope (%), mean and maximum tree height (ft), basal area (m² ha⁻¹), tree C (Mg ha⁻¹), mean diameter (cm), trees per hectare, and latitude and longitude. Although the variables are in imperial units, all results were converted to common metric units. The majority of stand characteristics were collected from 2005 to 2010, similar to the UVEG measurements, and they most closely approximate the year 2007.

Several spatial datasets were used in the random forest modeling of UVEGC. Data from the NOAA Advanced Very High Resolution Radiometer (AVHRR) sensor provide phenological metrics that indicate plant distribution and relative greenness at 1 km resolution. The current study uses a 5 year average (2006–2010) of start of season normalized difference vegetation index (NDVI) (SOSN), end of season NDVI (EOSN), duration (DUR), maximum NDVI (MAXN), and time integrated NDVI (TOTND). The 2006–2010 period was used because it coincides with the period that most of the UVEG data was collected by the FIA program (i.e. from 2005–2010). These data are distributed by the Land Processes Distributed Active Archive Center (LP DAAC), located at USGS/EROS, Sioux Falls, South Dakota (http://lpdaac.usgs.gov). Mean annual temperature and annual precipitation averaged over the same period was obtained from DAYMET (Thornton et al 2016). Elevation was obtained from the Shuttle Radar Topography Mission (Jarvis et al 2008). All datasets were aligned and converted to the same projection.

We used the subset of FIA plots having UVEG measurements in combination with geospatial data to develop a random forest model of UVEGC in the US. Random forest modeling is a machine learning approach that predicts observations using both categorical and continuous data (Liaw and Wiener 2002), and has been applied to predict litter layer carbon on FIA plots (Domke et al 2016). In this study, random forest modeling was applied to predict total UVEGC at the national scale (shrub, nonwoody, and seedling) using: (1) field collected variables, (2) geospatial variables, and (3) both field and geospatial variables. The best model approach was determined by comparing the different groups of variables against random hold-out observations of 15% of the total dataset. The model was then applied to all Phase 3 subplots across the country (130 547 plots, or 438 089 subplots), thus preserving a spatially unbiased and expanded estimate. Variable importance was assessed by percent increase in MSE of each variable after 100 permutations (%incMSE). The R package randomForest was used for all analyses (Liaw and Wiener 2002, R Development Core Team 2014).

Of the several linear and non-linear models that were explored to fit shrub height and shrub cover to aboveground shrub biomass, the Michaelis Menten form performed the most consistently (table 2, supplementary table S1, available at stacks.iop.org/ERL/12/125010/mmedia). Semi-arid forest types (ponderosa, pinyon/juniper, and aspen/birch) increased more in shrub biomass with shrub cover and height compared to other forest types, suggesting a higher density. Other conifer types (douglas fir and white/red/jack pine) had the lowest densities. For the nonwoody component, only one Michaelis Menten model using nonwoody cover was used for all forest types. Finally, for the seedling component, a linear model using seedling density was used for six forest types (table 2, supplementary table S1). The allometric relationships developed for the shrub, nonwoody, and seedling components allowed for the estimation of total UVEGC for 15 of the 32 forest types and 76% of the intensive plot observations. For the remaining forest types not directly represented by allometric models, close substitutions were made (e.g. douglas fir was used for redwood). Each of the allometric equations are recorded both in metric (table 2) and imperial units (supplementary table S1).

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Random forest models based on field collected and geospatial variables each explained 34% of the variation in UVEGC of the hold-out validation dataset, and each had similar RMSEs (table 3). However, the field collected variables tended to slightly underestimate UVEGC while the remotely sensed variables tended to slightly overestimate UVEGC (table 3). When all variables were combined, 40% of UVEGC was explained and with less bias than either of the two sets of variables alone. The most important variable of the field collected variables was forest type followed by stand age and slope. The most important geospatial variables were precipitation and elevation (figure 2). When both sets of variables were combined, the most important variables were field collected variables, such as forest type, slope, and stand age, followed by temperature, and to a lesser degree precipitation, and NDVI variables.

Perhaps not surprisingly, there were similar trends across environmental and stand age gradients at the national scale to those that would be expected at the stand level. For example, UVEGC increased with increasing temperature and precipitation, and decreased with increasing elevation and stand age (p-value < 0.0001 in all cases). In contrast, variables such as trees per hectare, basal area, and tree carbon were much less important in the random forest model.

When the random forest model using all variables was applied to all intensive FIA plots, the lowest UVEGC was generally associated with high latitude and arid regions while higher UVEGC was generally associated with forests with greater precipitation and warmer temperatures (figure 3(a)). For example, the two forest types that contained the most UVEGC were loblolly/shortleaf pine (17%) and oak/hickory (16%). More specifically, of the major forest types, the highest UVEGC density estimates were found in the Pacific Northwest alder/maple (1.9 Mg ha⁻¹) and Southeast loblolly/shortleaf pine (1.9 Mg ha⁻¹) groups, while the lowest densities were found in the Northeast spruce/fir (0.52 Mg ha⁻¹) and South Central Woodland hardwoods (0.52 Mg ha⁻¹) groups (supplementary table S2). These patterns were broadly similar to patterns of the current FIA estimates (figure 3(b)). However, the random forest estimates were almost always lower—as much as 100% in some areas such as Texas (figure 3(c); supplementary table S2). For all forest types, the majority of UVEGC was stored in shrubs (64%), followed by nonwoody (35%) and seedling (1%).

The UVEGC estimates from the random forest model for the conterminous US ranged from 0.047–7.605 MgC ha⁻¹. The mean was 0.977 ± 0.0008 MgC ha⁻¹ (mean ± standard error), or 1.7% of the total aboveground live tree carbon reported by Smith et al (2013) (56.5 MgC ha⁻¹). The previous UVEGC estimate reported by Smith et al (2013) was 2.8 MgC ha⁻¹ or 4.7% of the total live aboveground carbon. Therefore, the previous estimates were nearly three times higher than the random forest estimate. When means were summarized by state and forest type and multiplied by their forest areas, the sum total UVEGC for the conterminous US was 272 ± 0.21 Tg (total stock ± standard error). The cumulative distribution plots for both estimates reveal that, in addition to being consistently higher, the current FIA estimate minimum was 0.5 Mg ha⁻¹ (figure 4). In contrast, about 10% of the observations of the new estimate were below this threshold, making the overall average even lower. Both estimates were weakly, but significantly, positively correlated (R2 = 0.12; p-value < 0.0001).

The Random Forest UVEGC estimates compared well to the independent estimates in nine of the ten forest types, but poorly for two of the three fir/spruce/mountain hemlock forest sites located in Colorado and Wyoming (figure 5). The UVEGC measurements at these sites were 2.5–4 times higher than the modeled value. However, the same forest type in Washington was comparable. Neither this study's, nor the previous study's estimate, were significantly correlated with all the validation sites (p < 0.05). However, when the fir/spruce/mountain hemlock forest types were removed, both this study's and the previous estimate were positively correlated (R2 = 0.72 and 0.56, respectively, p < 0.01). The current FIA model estimate was always biased towards higher values (figures 4 and 5).