A nearest-neighbor imputation approach to mapping tree species over large areas using forest inventory plots and moderate resolution raster data

Abstract

The paper describes an efficient approach for mapping multiple individual tree species over large spatial domains. The method integrates vegetation phenology derived from MODIS imagery and raster data describing relevant environmental parameters with extensive field plot data of tree species basal area to create maps of tree species abundance and distribution at a 250-m pixel size for the entire eastern contiguous United States. The approach uses the modeling techniques of k-nearest neighbors and canonical correspondence analysis, where model predictions are calculated using a weighting of nearest neighbors based on proximity in a feature space derived from the model. The approach also utilizes a stratification derived from the 2001 National Land-Cover Database tree canopy cover layer. Data pre-processing is also described, which includes the use of Fourier series transformation for data reduction and characterizing seasonal vegetation phenology patterns that are apparent in the MODIS imagery.A suite of assessment procedures is applied to each of the modeled dataset presented. These indicate high accuracies, at the scales of assessments used, for total live-tree basal area per hectare and for many of the most common tree species found in the study area. The end result is an approach that enables the mapping of individual tree species distributions, while retaining much of the species covariance found on the forest inventory plots, at a level of spatial detail approaching that required for many regional management and planning applications. The proposed approach has the potential for operational application for simultaneously mapping the distribution and abundance of numerous common tree species across large spatial domains.

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A nearest-neighbor imputation approach to mapping tree species over large
areas using forest inventory plots and moderate resolution raster data
B. Tyler Wilson
⇑
, Andrew J. Lister, Rachel I. Riemann
Forest Inventory and Analysis, Northern Research Station, USDA Forest Service, 1992 Folwell Avenue, Saint Paul, MN 55108, USA
article info
Article history:
Received 7 December 2011
Received in revised form 2 February 2012
Accepted 5 February 2012
Keywords:
Nearest-neighbor imputation
Canonical correspondence analysis
MODIS
Vegetation phenology
Forest inventory
Species distribution
abstract
The paper describes an efficient approach for mapping multiple individual tree species over large spatial
domains. The method integrates vegetation phenology derived from MODIS imagery and raster data
describing relevant environmental parameters with extensive field plot data of tree species basal area
to create maps of tree species abundance and distribution at a 250-m pixel size for the entire eastern con-
tiguous United States. The approach uses the modeling techniques of k-nearest neighbors and canonical
correspondence analysis, where model predictions are calculated using a weighting of nearest neighbors
based on proximity in a feature space derived from the model. The approach also utilizes a stratification
derived from the 2001 National Land-Cover Database tree canopy cover layer. Data pre-processing is also
described, which includes the use of Fourier series transformation for data reduction and characterizing
seasonal vegetation phenology patterns that are apparent in the MODIS imagery.
A suite of assessment procedures is applied to each of the modeled dataset presented. These indicate
high accuracies, at the scales of assessments used, for total live-tree basal area per hectare and for many
of the most common tree species found in the study area. The end result is an approach that enables the
mapping of individual tree species distributions, while retaining much of the species covariance found on
the forest inventory plots, at a level of spatial detail approaching that required for many regional man-
agement and planning applications. The proposed approach has the potential for operational application
for simultaneously mapping the distribution and abundance of numerous common tree species across
large spatial domains.
Published by Elsevier B.V.
1. Introduction
1.1. Background
National and regional maps of forest characteristics have long
been of interest in the United States. Types and levels of sophisti-
cation of large area forest maps have varied through time, ranging
from crude choropleth maps of timber volume produced by Sar-
gent (1884), to satellite-based, national maps of land cover (Homer
et al., 2007) and forest biomass (Blackard et al., 2008). Forest maps
have been and are being used for many things, including for assess-
ing the risks and impacts associated with pest outbreaks (Krist
et al., 2010; Pontius et al., 2010), for assessment of areas that are
impacted by large disturbances (Olthof, 2004; Wang and Xu,
2009) or by slow decline (Rogers et al., 2010) for examining the po-
tential impact of urbanization (Riemann et al., 2008) for mapping
species richness for conservation planning (McPherson and Jetz,
2007; Ohmann et al., 2007) for studying the impacts of differences
in forest management and policy in different ownership types (Oh-
mann et al., 2007; Uuttera et al., 1998) for landscape scale assess-
ment of suitable habitat for wildlife species (Riordan and Rundel,
2009; Weber and Wolf, 2000) and for state and regional resource
assessments (Falk and Mellert, 2011).
Several common themes emerged from review of these and
other mapping efforts. First, land use policy decisions are often
made at the landscape (broad) scale (McCarter et al., 1998) because
landscape processes, like risk of forest pests (Krist et al., 2010)or
fire (Rollins et al., 2006), occur over large areas. Second, distribu-
tion and abundance information is often needed for individual spe-
cies as opposed to forest types because individual species can play
significant roles in natural systems, may have high economic im-
pact, or may be indicators for ecosystem health (Iverson and Pra-
sad, 1998; Poland and McCullough, 2006; Riemann Hershey,
2000). Third, the maintenance of a realistic species covariance
structure across a set of maps of individual species is important be-
cause species assemblage information is used in coarse scale mod-
eling of ecosystem processes like response to disturbance
(McPherson and Jetz, 2007), urbanization, and climate change
(Iverson and Prasad, 1998; Woodall et al., 2009). Finally, maps
should include accuracy assessments that indicate utility for multi-
ple scales of use.
0378-1127/$ - see front matter Published by Elsevier B.V.
doi:10.1016/j.foreco.2012.02.002
⇑
Corresponding author. Tel.: +1 651 649 5189.
E-mail address: barrywilson@fs.fed.us (B.T. Wilson).
Forest Ecology and Management 271 (2012) 182–198
Contents lists available at SciVerse ScienceDirect
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1.2. Goals, objectives, and justification of methods used in the study
The main goal of the current study is to develop a systematic
and operational approach to mapping individual tree species dis-
tributions across large spatial domains, along with several example
maps and associated accuracy assessments. The broad objectives of
the study are to build upon previously documented modeling ap-
proaches by taking advantage of a combination of satellite imagery
and other raster datasets, forest inventory data, statistical meth-
ods, and automated workflows. Specific objectives include the
following:
1. Use extensive, standardized, and well-established training data
sources that adequately represent conditions in the analysis area for
model building and validation. Field plot data from the United States
Department of Agriculture Forest Service Forest Inventory and
Analysis (FIA) program represent a comprehensive, unbiased, and
consistent sample dataset of known accuracy that has long been
used for mapping (Blackard et al., 2008; Riemann Hershey, 2000;
Zhu and Evans, 1994). Similar use of forest inventory plot data
has occurred in Canada (Gillis and Leckie, 1993), Europe (Casalegno
et al., 2011), parts of the Asia–Pacific region (Bystriakova et al.,
2003) and elsewhere.
Using FIA data allows for the incorporation of detailed informa-
tion on individual trees and site factors, use of well-defined vari-
ables, development of consistent mapping workflows, and
utilization of the forest inventory system infrastructure such as
field guides and reporting tools. FIA data are updated regularly,
making possible future map updates using consistent methods.
2. Incorporate information that reflects landscape composition and
configuration in a cost-effective way. Several mapping studies have
used univariate, interpolative approaches like inverse distance
weighting, geostatistical approaches like kriging or stochastic sim-
ulation (e.g. Hershey and Reese, 1999), or approaches based on
highly-detailed, resource-intensive satellite imagery (Homer
et al., 2007; Ohmann and Gregory, 2002; Rollins et al., 2006). Uni-
variate approaches often do not show underlying land cover pat-
terns in the final maps, and maps made using highly detailed,
resource-intensive satellite imagery for very large areas can be
expensive and time-consuming to produce and update, as indi-
cated, for example, by the multi-year time lag between the Land-
sat-based NLCD project’s scheduled updates.
To avoid such difficulties, data from the Moderate Resolution
Imaging Spectroradiometer (MODIS) satellite-borne sensor (Justice
et al., 1998), coupled with other moderate resolution raster data-
sets, were used in the current study, following Blackard et al.
(2008) and Ruefenacht et al. (2008). The large swath width, mod-
erate pixel size, and high temporal frequency of MODIS data allow
users to efficiently produce maps, overcome issues of cloud con-
tamination, and incorporate intra-annual vegetation phenology
by using temporal composites (Bradley et al., 2007; DeFries et al.,
1997; Moody and Johnson, 2001; Wolter et al., 1995) and time ser-
ies analysis (Spruce et al., 2011). While some spatial detail is lost
by using MODIS compared to Landsat data (250-m vs. 30-m pixel
resolution), logistical efficiencies, fewer issues with cloud contam-
ination, and potential benefits of using phenological time series
data outweighed the loss of spatial resolution (Nelson et al.,
2009). Finally, using coarser spatial resolution raster data mitigates
concerns about uncertainty in the location of field data when inte-
grated with these data during modeling. Based on Forest Service
field tests, typical Global Positioning System instrumentation used
to determine the coordinates of forested sites have an average
measurement error ranging from roughly 1–5 m under open can-
opy to roughly 5–20 m under closed canopy. Again using the ear-
lier comparison to a Landsat pixel, a MODIS pixel has an area
that is approximately 70 times larger, but an edge that is only
about eight times larger. Therefore, given the uncertainty associ-
ated with field plot coordinates, co-registration errors between
plots and pixels (i.e. where a field plot is incorrectly associated
with a neighboring pixel) are more likely to occur with finer reso-
lution raster datasets.
3. Base methods on functional relationships seen in ecological sys-
tems. ‘‘Black box’’ empirical approaches like neural networks can
often outperform more traditional mapping methods, but Tu
(1996) reports several disadvantages of these methods, including
the inability to interpret the models, proneness to overfitting,
and the empirical nature of model development, which does not
necessarily maintain process–level relationships. Ohmann and
Gregory (2002) developed mapping methods using canonical cor-
respondence analysis (CCA) (ter Braak, 1986), a constrained ordi-
nation technique, to exploit multivariate relationships among
species and between species and environmental data to incorpo-
rate process–level relationships into predictive modeling. CCA is
one of several multivariate ordination methods used by ecologists
to order the data found in a contingency table, typically one con-
sisting of multiple species and environmental observations for a
list of sites. For such a contingency table, ordination methods ar-
range species along a set of environmental gradients. CCA is used
to create linear combinations of predictors that represent the envi-
ronmental gradients that explain the greatest amount of variability
(inertia) in the multivariate species data (McGarigal et al., 2000).
By ‘‘tuning’’ the set of predictor data to the species composition
data, the set of maps of predictions of individual species should
be more likely to retain their original covariance structure and
maintain logical consistency.
Another way to raise the likelihood of maintaining natural rela-
tionships in a set of species-level maps is to use a k-nearest neigh-
bor (kNN) approach. The kNN approach to estimation uses
similarity (proximity) in a set of predictor variables, the values of
which are known for all data points, in order to impute a set of re-
sponse variables, the values of which are known only for a set of
reference data points, to the set of target data points for which
the values of the response variables are not known. The response
variables from the set of kreference data points that are most sim-
ilar (nearest) to a given target data point are then summarized
(typically, averaged) in order to generate a predicted value. In
some cases, the values of the response variables associated with
each reference data point are weighted based on their similarity
(proximity) to the target data point. The kNN approach is nonpara-
metric, intuitive, and has been broadly applied in forestry and
other mapping applications (McRoberts et al., 2002, 2007; Eskelson
et al., 2009). For the example where the reference data points con-
sist of FIA plots and the target data points consist of pixels, the kNN
approach would utilize the same small pool of kreference plots for
each estimate for each species for a given target pixel, thus raising
the likelihood of maintaining logical consistency in the species
covariance structure of the set of response variables. In theory at
least, using kNN together with a set of predictor variables gener-
ated from the output of a CCA model (similar to Ohmann and Greg-
ory, 2002) would be expected to do even better at maintaining
these complex, natural relationships in the species data.
2. Materials and methods
2.1. Study area
The study area for this investigation is roughly the eastern half
of the contiguous United States, which corresponds with the area
surveyed by the Northern and Southern FIA programs (Fig. 1). This
area was selected for several reasons, including data availability, as
well as the challenges the region poses. It includes the states that
were the first in the national FIA program in which annualized
B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198 183

Author's personal copy
inventories were implemented and for which there is an extensive
set of current field plot data. The area spans several ecological re-
gions and represents a variety of landscapes and climatic zones.
The states included in the study have sampling intensities that
range from one to three times the FIA standard of approximately
one plot per 2400 hectares.
2.2. Data sets
2.2.1. Response variables
Field plot data used for model calibration and accuracy assess-
ment were provided by the FIA program. FIA collects data annually
from a series of field plots that are located in cells created by a uni-
form hexagonal tessellation of the country. The FIA inventory is
conducted in three phases (Bechtold and Patterson, 2005). In Phase
1, all plots are characterized with respect to land use and owner-
ship class and assigned a stratum that will later be used for post-
stratification for variance reduction, using some combination of
aerial photography, satellite imagery, and ancillary data. In Phase
2, field crews visit permanent plots that contain a forested land
use and collect information on individual trees and site variables.
In Phase 3, field crews collect additional information on forest
health variables on a 1/16th subset of the Phase 2 plots. The FIA
data used in this study included 190,888 Phase 2 plots in the study
area collected during the period of 2001–2006, with the exception
of Louisiana (2001–2005), and Florida and Texas (2001–2007).
Per-species basal area per hectare of live trees (referred to as
live-tree basal area throughout the manuscript), with a diameter
measured at breast height (DBH) greater than or equal to 1’’, was
selected as the response variable for two reasons. First, when com-
pared to other measurements such as height, which is difficult to
collect precisely, or volume, which is modeled from various tree
measurements, basal area is calculated from one of the most reli-
able field measurements made on a tree, namely DBH. Second,
since basal area is generally correlated with crown area (e.g. Lister
et al., 2000), it is assumed that it is also correlated with the spectral
characteristics of forests that are measurable by satellite-based
sensors.
2.2.2. Predictor variables
The study used several raster datasets assumed to be correlated
with tree species distribution and vegetation composition. Sea-
sonal vegetation phenology data were derived from the Enhanced
Vegetation Index (EVI) of the 250-m MOD13Q1, Version 4, MODIS
Terra data product. EVI (Liu and Huete, 1995) is an adjustment to
the Normalized Difference Vegetation Index (NDVI) that compen-
sates for soil and atmospheric effects and has been shown to be
more sensitive to canopy type and structure than NDVI (Gao
et al., 2000). The MODIS data included a subset of 100 typically
snow-free, growing season images (i.e. late March through Novem-
ber) from 134 16-day maximum value composite (MVC) images
that were collected between January of 2001 and October of
2006, a period that roughly coincides with the field plot data col-
lection period. Climate data were extracted from the Daymet 18-
year dataset of mean monthly growing-degree days and total pre-
cipitation (Thornton et al., 1997).
Topographic data were derived from the US Geological Survey
Elevation Derivatives for National Applications (EDNA) dataset
and included elevation, compound topographic index (CTI), and
slope-aspect index (SAI). CTI (Moore et al., 1991) is a measure of
site wetness based on landscape position and is correlated with
several soil characteristics (Gessler et al., 1995). SAI (Frank, 1988)
is a measure of site orientation and is correlated with solar insola-
tion and exposure to prevailing winds. Geospatial location data in
the form of coordinate eastings and northings were also used. Fi-
nally, the study utilized the US Environmental Protection Agency’s
Level III Ecoregions that were derived from Omernik (1987). Ecore-
gions were represented by a set of associated dummy variables,
whereby each pixel was assigned a value of 1 or 0 based on its loca-
tion relative to each ecoregion. These were included to account for
the effects of any residual spatial trends in the attribute of interest
that were not explained by the other predictor variables, i.e. non-
stationarity in the underlying model. All rasters were projected
to Albers Equal Area projection and resampled, if necessary, to
250-m (6.25 ha) pixels.
2.2.3. Differences in spatial resolution
Comparing values for a 6.25 ha pixel using reference data from a
0.067 ha FIA field plot (see Bechtold and Patterson (2005) for a
Fig. 1. Map of the study area (shaded in gray).
184 B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198

Author's personal copy
complete description of the cluster–plot design) involves relating
two datasets describing very different spatial units of land. This
difference will be most noticeable when local environmental het-
erogeneity causes fine-scale spatial variability within the larger
6.25 ha area. In such a case, the 0.067 ha plot may sample a condi-
tion that is quite different from the predominant condition associ-
ated with the larger area sampled by the pixel. A mixture of forest
and non-forest land cover can also occur together, introducing an-
other type of heterogeneity within a 6.25 ha pixel. Both situations
will result in an increase in the variability observed between pixel
values and field plot values in some areas, whether due to environ-
mental heterogeneity, land use history, or current forest
fragmentation.
2.3. Description of the methodology
2.3.1. Pre-processing the predictor variables
In an effort to reduce the dimensionality of the EVI dataset, as
well as correct for residual atmospheric effects in the imagery, a
slightly modified version of the Fourier-based adjustment step of
the FASIR methodology described by Sellers et al. (1994) was con-
ducted. A Fourier series was fit individually for each pixel to the
full set of 100 EVI MVC images for the region using a reweighted
least squares algorithm. A Fourier series can be expressed as a
2
p
-periodic polynomial of the form
y¼a
0
þX
h
n¼1
ða
n
cosðntÞþb
n
sinðntÞÞ;ð1Þ
where tis the time period expressed in radians, his the number of
harmonics in the series, and a
0
,a
n
, and b
n
are coefficients. For the
purposes of the current study, a Fourier series with two harmonics
was found to be adequate to represent the general form of the time
series data.
Because EVI is negatively biased by clouds and snow, the same
Fourier series was fit again using weighted regression, giving spu-
rious low values less weight in the regression than high values. A
simplified weighting function
W
t
¼1:5
r
t
=maxðrÞ
ð2Þ
where r
t
is the residual from the initial model for compositing per-
iod t, was used rather than the step-wise weighting function de-
scribed by Sellers et al. (1994). The weighted regression resulted
in the estimation of five Fourier coefficients for each pixel, in effect
reducing by twentyfold the number of variables required to de-
scribe the general shape of the corrected EVI time series data.
A similar Fourier procedure transformation was used for the
monthly climate data. In this case all 12 months of data were used
in a simple regression with equal weighting. Since the Daymet data
were originally generated at 1-km pixel resolution, the resultant
Fourier coefficient data were resampled to 250-m pixels using a
bilinear interpolation algorithm. The EDNA data were originally
generated at 30-m pixel resolution. Prior to resampling, a focal
median function was applied using a 9 by 9-pixel moving window.
These focal median values of elevation, CTI, and SAI were then
resampled to 250-m pixels using a nearest-neighbor algorithm
(Nelson et al., 2009). Finally, a layer stack was produced of the
21 predictor datasets: five phenology coefficients, five temperature
coefficients, five precipitation coefficients, five topographic metrics
(including geospatial coordinates), and ecoregion (see Table 1).
2.3.2. Gradient nearest neighbor
Generally following the gradient nearest neighbor (GNN) meth-
odology described by Ohmann and Gregory (2002), the FIA field
plot data and the predictor datasets were used together in a canon-
ical correspondence analysis (CCA) model. The original formulation
of GNN is a two-step process, and those steps were followed in the
current study. First, a CCA model was fit to the data that related the
multivariate response variable (i.e. live-tree basal area per hectare
of each individual tree species) from the field plots to the set of
predictor variables in the raster layer stack. Second, the results
from the CCA model were used to impute field plot values of
live-tree basal area to pixels based on measures of nearness in
the weighted canonical variate space.
The ade4 package for the R statistical language (Dray and Du-
four, 2007) was used to conduct the CCA modeling via eigenanaly-
sis. Due to computational constraints, a model was constructed
using a random sample of 25,000 from the total set of field plots.
Each of the 56 Level III ecoregion codes was included in the model
as a factor. The resultant estimated loadings from the model were
applied to the raster layer stack to construct a set of canonical vari-
ates. Each canonical variate was then weighted by its respective
eigenvalue (i.e. a measure of its relative explanatory power) in or-
der to create a stack of weighted canonical variates that would be
used during imputation. Only the first eight canonical variates
were used, since the smaller number captured most of the inertia
explained by the model and also reduced processing time during
the imputation step. Both the CCA and the imputation steps were
conducted globally across all states rather than individually by
smaller mapping units.
2.3.3. Grouping pixels to reduce processing time
A minimum-distance classification was performed to group to-
gether and label similar pixels. The plot identification number of
the single nearest-neighboring plot (here called the seed plot)
was assigned to each pixel based on proximity in the feature space
defined by the eight weighted canonical variates. In this way, pix-
els are assigned a group label, based on similarity of predictor char-
acteristics. There are as many groups as there are plots, and each
pixel in the map is assigned a single group label. It is these groups
that are used in the imputation step below.
2.3.4. Sub-pixel stratification during imputation
As discussed earlier in Section 2.2.3, a 6.25 ha MODIS pixel may
include both forested and non-forested conditions, while a
0.067 ha field plot would more frequently fall within one condition
or the other simply by virtue of its smaller size. Rather than assum-
ing that the entire 6.25 ha pixel can be represented by a single plot
Table 1
Overview of predictor variables.
B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198 185

Author's personal copy
and imputing the plot’s attributes to each pixel directly, sub-pixel
information was derived from the 30-m NLCD 2001 tree canopy
cover dataset. This dataset has been used by some FIA regions dur-
ing Phase 1 post-stratification for variance reduction, as described
by Gormanson et al. (2009). A multi-step procedure was imple-
mented to incorporate this sub-pixel information.
1. Field plots were assigned to forest or non-forest strata. The NLCD
tree canopy product, which is a 30-m model-based map of esti-
mated tree canopy cover percentage, was classified into two strata:
one with less than 25% canopy cover (called the ‘‘non-forest’’ stra-
tum and assigned a value of 0) and the other with 25% or greater
canopy cover (called the ‘‘forest’’ stratum and assigned a value of
1). It was then determined to which stratum each field plot be-
longed by spatial intersection of the plots with this stratification
layer. This threshold value was chosen based on a survey of na-
tional and international definitions of forest based on canopy cover
that generally range from 10–40% (Lund, 2002).
2. kNN imputation was performed using plots within each stratum
to attach basal area estimates to each group. For plots in each stra-
tum, the kplots that were nearest to each group (i.e. the seed plot
for each group) in the feature space defined by the weighted
canonical variates from the CCA model, excluding the seed plot it-
self, were identified using the yaImpute package for R (Crookston
and Finley, 2008). The basal area values associated with these near-
est neighboring plots were used to compute the weighted mean to-
tal live-tree and per-species live-tree basal areas. The weight for
each neighboring plot within a stratum assigned to a given plot
was calculated using an inverse distance weighting function, and
was based on Euclidean distance in feature space, according to
W
p
¼d
x
p
X
k
p¼1
d
x
p
,;ð3Þ
where d
p
is the distance between the given plot and the neighboring
plot pand xis the weighting exponent. Euclidean distance was an
appropriate distance metric because the axes of the canonical vari-
ate-based feature space are constrained to be orthogonal to one an-
other. This step produced two estimates for each group, i.e. one
derived from the knearest-neighboring plots in each of the two
strata (see Section 2.3.6 for a description of the methodology for
determining the values for kand x).
3. A forest stratum proportion layer was developed. A focal mean
function was performed on the 30-m stratification layer from step
1, using a kernel size of 9 by 9 pixels. The focal mean layer was
then resampled to 250-m pixel resolution using a nearest-neighbor
algorithm in order to determine the approximate proportion of
each 250-m pixel that belonged to the ‘‘forest’’ stratum.
4. The forest stratum proportion layer was used for sub-pixel strat-
ification to compute the basal area estimate assigned to each pixel,
within each group, to produce the final map. The results from step
2 (i.e. the imputation results computed for each group by stratum)
were joined with each pixel using the group label as the key in or-
der to calculate a weighted mean estimate of live-tree basal area.
The weight was based on the resampled forest stratum proportion
layer. For example, if the forest stratum proportion layer indicated
that a pixel with a given group label was 75% forest, then the ‘‘for-
est’’ stratum basal area estimate from step 2 for the group label as-
signed to that pixel received a weight of 0.75 and the ‘‘non-forest’’
stratum basal area estimate received a weight of 0.25.
2.3.5. Assessment of the results
Each output dataset produced in this study was assessed using a
variety of methods designed to identify the location, magnitude
and type of error, across a range of scales at which the dataset
might be used. The methods used in the assessment protocol are
described in full detail in Riemann et al. (2010). Rather than relying
on a single metric, the protocol employs a suite of assessments,
including multi-scale comparisons of data distributions and spatial
agreement of estimates, as well as an examination of spatial and
distribution patterns of local differences. All assessments were
conducted for maps of total live-tree basal area, and a selection
of three species that represent different ecological and distribution
patterns. A smaller set of summary metrics was calculated for all
273 tree species found in the study area.
In this study, modeled results were compared to data collected
on FIA plots. Although all FIA plots were used in model develop-
ment, only the 2nd through 8th nearest-neighboring plots were
used to estimate basal area for each associated pixel. This assures
that each plot contributes only minimally, via the CCA model but
not the imputation, to the estimate for the corresponding pixel.
Thus, for comparisons between the field plot values and the mod-
eled pixel values with which they are associated, it is assumed that
the two datasets are independent.
Assessments for total live-tree and per-species live-tree basal
area estimates were performed at three scales defined by tessella-
tion of the area by a hexagonal mesh with various spacing of hexa-
gon centers (area): 50 km (216,500 ha), 100 km (866,000 ha), and
200 km (3.5 million ha). Additionally, assessments for total live-
tree basal area were also conducted using a finer hexagonal mesh
with hexagon centers spaced at 30 km (78,100 ha). For each scale,
model-based and field plot-based estimates were calculated for
each hexagon and compared. Field plot-based estimates were cal-
culated from the plots occurring within a hexagon, and model-
based estimates were calculated from the value of those pixels that
intersected with the FIA plots. Assessing agreement across a range
of scales allows a map user to better understand the changes in ob-
served accuracy, i.e. the difference between field plot and modeled
estimates, at different scales of observation and use. Fig. 3c indi-
cates the number and distribution of plots within hexagons at each
scale. All hexagons used in the assessment were completely within
the boundaries of the region.
Each assessment was conducted using several metrics. First,
model-based and field plot-based data distributions were com-
pared using empirical cumulative distribution curves. The Kol-
mogorov–Smirnov statistic (KS) was calculated to quantify the
agreement between the distributions of the two datasets, in terms
of the maximum distance between their empirical distribution
functions. KS is a robust statistic that makes no assumptions about
the distribution of data and is independent of scale changes (e.g.
Feller, 1948).
Second, model-based and field plot-based local area estimates
(i.e. per hexagon) of basal area were compared. Scatterplots were
generated for each scale of analysis, and several indices of agree-
ment were calculated to summarize the relationship between the
field plot-based and model-based estimates at each scale: agree-
ment coefficient (AC), systematic agreement (AC
sys
), unsystematic
agreement (AC
uns
), and root mean square error (RMSE) (Ji and Gal-
lo, 2006; Riemann et al., 2010). The agreement coefficient metrics
devised by Ji and Gallo (2006) are particularly helpful because they
are symmetric (assume error in both datasets), standardized (value
range does not change with size of data values), and with the terms
AC
sys
and AC
uns
, they describe independently both the systematic
agreement (proximity to the y=xline) and unsystematic agree-
ment (level of scatter about the reduced major axis (RMA) regres-
sion line) present in the scatterplot. The RMA regression line,
sometimes referred to as the geometric mean functional relation-
ship, is calculated in a similar way to the ordinary least squares
regression line, but with the assumption that there is error in both
the xand yaxes and is therefore symmetrical regardless of the
ordering of the axes. The AC is a combination of AC
sys
and AC
uns
.
RMSE was also included to provide information on the magnitude
of difference in data units (m
2
/ha).
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Third, confidence intervals were calculated for the estimates
based on the field plots found in each hexagon at the 216,500 ha
scale (the finest scale used), and the distribution of the frequency
at which the model-based estimates fall within these confidence
intervals was both mapped and plotted relative to increasing plot
mean. These metrics provide information that map consumers
can use to gauge the appropriateness of the overall map products
for various uses at different scales.
2.3.6. Determining the values of k and x
Because of the innumerable potential combinations of values for
kand the inverse distance weighting exponent (xin Eq. (3)), both
with and without stratification during the imputation step, the
authors adopted an objective and systematic approach to optimize
these parameters and determine their relative impact on the final
results (e.g. Eskelson et al., 2009). First, ignoring the stratification
layer, for each value of kfrom 1 to 10 a baseline root mean squared
error (RMSE) in the predicted mean live-tree basal area for each of
the fine-scale hexagonal estimation units (216,500 ha) was com-
puted by using a weighting exponent of 0, resulting in equal
weighting of each of the kneighbors. Second, this process was re-
peated using the stratification layer. Finally, a range of weighting
exponents was tested, in increments of .5 in order to find evidence
of a local minimum in the associated RMSE. For the set of three
points nearest to the local minimum associated with each value
of k, a 2nd degree polynomial was fit and the local minimum was
estimated to determine the ‘‘optimal’’ weighting exponent. The
estimated optimal RMSE and weighting exponent were then calcu-
lated for each value of k. These results were used to determine the
appropriate weighting factor, value for k, and whether or not to uti-
lize the stratification layer for the mapping procedure.
3. Results and discussion
3.1. Canonical correspondence analysis model
The total inertia in the multivariate response variable, live-tree
basal area by tree species, was computed by correspondence anal-
ysis, with the CCA model explaining approximately 11% of that to-
tal. Given the fact that the predictor variables associated with each
pixel were summarized over a 6.25 ha area while the response
variables associated with each plot were measured over a .067 ha
area somewhere within a pixel, one would expect substantial noise
in the relationship between the two, particularly in heterogeneous
landscapes. Given these facts, the inertia explained by the CCA
model was considered meaningful, since ter Braak and Verdons-
chot (1995) suggest that for ecological data, the percentage of iner-
tia explained by a CCA model is typically less than 10%, particularly
for those data exhibiting a strong gradient or with a strong pres-
ence/absence aspect, as is the current case when modeling tree
species over large areas. In order to facilitate a better understand-
ing of the relative explanatory power of the predictor variables, an
inertia partitioning methodology similar to the one described in
Borcard and Legendre (1994) was followed. Because a complete
analysis of all combinations of the predictor variables was imprac-
tical, they were grouped into the five categories listed in Table 1:
phenology, temperature, precipitation, topography, and ecoregion.
The inertia partitioning was conducted using these five categories,
with the results depicted in Table 2.
Overall, the results suggest that for the current study area, the
ecoregion category provides by far the greatest explanatory power
of the set of predictor variable categories, with 61% of the explain-
able inertia, either alone or in combination with other predictor cat-
egories. Fully 42% of the explainable inertia due to the model can be
attributed to this category alone. This should not be surprising, given
that ecoregions are intended to depict spatial patterns in the compo-
sition of the biotic and abiotic factors used to define ecosystems.
However, it should also be noted that the ecoregion category con-
tains the largest number of predictor variables, with 56 individual
ecoregions spanning the study area. Taking this into account, the
average total contribution of each predictor variable in the ecoregion
category is roughly 1% of the explainable inertia, with an average of
0.75% attributed to each of these variables alone. The average total
contribution of predictor variables from the other categories, which
each contain only five variables, is 2.04% (0.10% alone) for tempera-
ture, 1.95% (0.56%) for phenology, 1.95% (0.21%) for topography, and
1.80% (0.12%) for precipitation. Given that climate, topography, and
vegetation are some of the central attributes used to delineate eco-
regions, the average explanatory power attributed to the vegetation
phenology variables alone is noteworthy in that it is substantially
higher the others. These results suggest that the ecoregion and phe-
nology variables, on average, contribute relatively greater explana-
tory power that cannot be attributed either wholly or in part to
other predictor variables in the model.
3.2. Sub-pixel stratification and the values of k and x
The proposed methodology was implemented to produce mod-
eled results using several combinations of values for kand the in-
verse distance weighting exponent x, as well as with and without
stratification, in order to optimize parameter selection for the
imputation step. The results are shown in Fig. 2. As expected, the
three graphs of RMSE each show evidence of reaching a minimum
for some small value of krelative to the large number of plots used
in the imputation. When using equal weighting, a minimum of
1.07 (square meters per hectare) occurred when kequals 4,
amounting to a 13.9% reduction in RMSE from kequals 1. The
graph of RMSE using equal weights with stratification shows an
overall improvement with a minimum of 0.99 at kequals 6, repre-
senting an overall reduction in RMSE of 20.5%. With optimal
weighting and stratification, an estimated minimum of 0.97 was
achieved at kequals 8 and a weighting exponent of 1.88, giving a
22.1% reduction in RMSE. These results indicate that both the value
of kand the use of the stratification layer had substantial impacts
on the overall RMSE, while the weighting of neighboring plots did
not. The modeled results that are assessed in the next section were
produced using parameters near the estimated minimum achieved
above, with kequals 7, a weighting exponent of 1.75, and stratifi-
cation, resulting in an RMSE of roughly 0.97.
3.3. Comparative assessment of estimates
Assessment metrics at the 216,500, 816,500, and 3.5 million
hectare scales were calculated for all 273 species and results for
Table 2
Partitioning of inertia.
Inertia Total (%) Variables Relative (%)
Overall inertia 69.108 100.00 – –
Inertia explained by model 7.311 10.58 – –
Explainable inertia attributed to category:
Phenology 0.712 9.74 5 1.95
Temperature 0.745 10.19 5 2.04
Precipitation 0.657 8.99 5 1.80
Topography 0.714 9.76 5 1.95
Ecoregion 4.483 61.32 56 1.09
Explainable inertia attributed exclusively to category:
Phenology 0.204 2.78 5 0.56
Temperature 0.036 0.49 5 0.10
Precipitation 0.044 0.60 5 0.12
Topography 0.077 1.05 5 0.21
Ecoregion 3.057 41.82 56 0.75
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the 100 most common species, based on estimated total live-tree
basal area in the study area, are presented in Table 3. In order to
facilitate interpretation of the metrics found in the table, detailed
results for total live-tree basal area and for three of the individual
species are discussed here. The three species selected for detailed
reporting (sugar maple, flowering dogwood, and river birch) were
chosen to represent a range of distribution patterns, overall preva-
lence, and ecological niches, all of which can affect different as-
pects of map production and interpretation. For example, sugar
maple represents a relatively common canopy species, although
it occurred on only 7.5% of the plots, and can represent a substan-
tial proportion of the basal area in stands where it occurs. In con-
trast, river birch is a rare species, found on only 0.3% of the plots,
and typically constitutes a minor proportion of the stands in which
it occurs. Flowering dogwood tends to have very low basal area per
hectare values on the plots where it is found, and represents a spe-
cies that occurs as an understory, rather than a canopy, tree. There-
fore, each of the tree species illustrated in the assessment figures
and graphs that follow represents a particular condition that could
impact modeling results, as well as assessment of those results
using FIA plot data.
A map of modeled total live-tree basal area for all 273 species is
presented in Fig. 4a and maps for sugar maple, flowering dogwood,
and river birch are presented in Figs. 5a, 6a, and 7a, respectively.
Little’s (1971) species range boundaries were overlaid on the maps
of individual species (shown in red on the figures) and generally
show good agreement in terms of the spatial distribution of these
species.
3.3.1. Total live-tree basal area per hectare
Fig. 3a shows scatterplots, along with associated assessment
metrics, of model-based vs. plot-based per-hexagon estimates of
total live-tree basal area at four scales: 78,100, 216,500, 866,000,
and 3,500,000 ha. Each point on the scatterplot corresponds with
the total live-tree basal area estimate for one of the hexagons at
the given scale. In each scatterplot, the black line is the y=x line
and the green line is the RMA regression line. Similarity measures
between plot-based and model-based estimates increase with
coarser scales of assessment, as indicated by the scatterplots,
cumulative distribution functions (CDFs), and their associated
summary metrics (AC, AC
sys
and AC
uns
, and RMSE).
The results for the KS metric (Fig. 3b) are more ambiguous,
showing improvement with coarser scales (0.13 at 78,100 ha down
to 0.036 at 866,000 ha), but slightly poorer results at the coarsest
scale (0.064 at 3,500,000 ha). This is likely due to the fact that, be-
cause of the irregular shape of the study area boundary, the total
area assessed by the mesh of hexagons changes slightly from one
scale to the next. This effect is most noticeable near the Florida
peninsula, but also to a lesser degree around the Great Lakes and
New England (Fig. 3c). Also, at the coarsest scale there are many
fewer hexagons used to compute the metric and it is therefore esti-
mated with greater uncertainty than at the finer scales. Because of
the strong similarity between the two distributions at all scales, it
should be noted that KS values were found always to correspond
with the difference between the two distributions at the y-
intercept.
Fig. 4b and c present differences in model-based and plot-based
estimates strictly at the 216,500 ha scale. This is the finest scale of
assessment at which there is reasonable confidence in the FIA-de-
rived estimate for each hexagon, with sampling errors averaging
34% of the plot estimate for all hexagons in the study area. Each
hexagon at this scale contains an average of 89 plots, and ranges
from 0% to 100% forested, based on the NLCD stratification layer.
The model-based estimates fall within the plot-based 90% confi-
dence interval over 74 percent of the time at this scale, for hexa-
gons with both high and low basal area values. Hexagons with
modeled estimates that are below the confidence interval (under-
estimation) are much less common than those with modeled esti-
mates that are above (overestimation), at 3% and 23%, respectively.
Seven percent of the hexagons had plot-based estimates of zero
and modeled estimates that were greater than zero. This is most
likely due to the fact that the stratification layer used to determine
the forest stratum proportion did not account for all aspects of
FIA’s definition of forest (Woudenberg et al., 2010). In particular,
it did not account for minimum area or width, nor did it account
for non-forest land uses where trees occur such as orchards, shel-
terbelts, and developed areas (Riemann, 2003).
3.3.2. Individual species basal area per hectare
While forest trees occur on 41% of the FIA plots in the study
area, individual tree species occurrence on FIA plots ranges from
0% to 17%. Figs. 5–7 present detailed assessment results for sugar
maple, flowering dogwood, and river birch. Overall agreement
(part b in the Figs. 5–7), as measured by AC values for these three
species, ranges from 0.06 to 0.93 at the 216,500 ha scale, 0.68–
0.97 at the 866,025 ha scale, and 0.85–0.99 at the 3.5 million ha
scale. In general terms, AC values less than 0.5 represent poor
agreement, while 1.0 represents perfect agreement. Values for sys-
tematic agreement (AC
sys
) tend to be better, with sugar maple and
flowering dogwood having values approaching 1.0 at all scales re-
ported, and river birch having values ranging from 0.79 to 0.99,
from finer to coarser scales of assessment. This represents substan-
tial systematic agreement, particularly considering that even sugar
maple, a relatively common species in the study area, occurs on
only 7.5% of the plots. High systematic agreement indicates that
the modeled estimates are not showing any strong bias, from lower
to higher basal area, when considering the dataset as a whole.
Unsystematic agreement, reflecting the level of scatter about the
RMA regression line (Ji and Gallo, 2006), was almost always lower
than the other two AC metrics. This indicates that, despite the lack
of bias, there is still considerable variability in the basal area esti-
mates not explained by the model, particularly at finer scales. Gi-
ven the low overall inertia explained by the model at the scale of
individual plots, this result was not surprising.
The modeled estimates for the three species examined in detail
indicated low levels of species presence at the edges of their
respective ranges, while the plot data reported no species presence
(part c in the Figs. 5–7). The lack of agreement in these areas could
be due in part to poor model performance at the boundaries of
Fig. 2. Graph of root mean squared error (RMSE) in mean total live-tree basal area
(m
2
/ha) for the 216,500 ha hexagons as a function of the number of neighbors (i.e.
value of k), weighting exponent, and stratification.
188 B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198

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species occurrence, likely a result of the way the forest stratum
layer was created, as discussed in the previous section on the total
live-tree basal area results. Another contributing factor could be
the relatively poor accuracy assessment dataset available in these
areas, i.e. where the plot-based estimate is based on only a few
plots that contain the species. With the individual species datasets,
Fig. 3. Scatterplots (a) and cumulative distribution functions (b) of map vs. plot-based estimates of total live-tree basal area (m
2
/ha), with maps of plot counts (c) by hexagon
for each of four scales. Agreement/error metric values associated with each scale appear on the figures.
B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198 189

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Table 3
Assessment results.
Tree species Scale/metric
Plot-level 216,500 ha 866,000 ha 3.5 million ha
Plots (%)
a
ba
b
AC
c
AC
sysd
KS
e
AC AC
sys
KS AC AC
sys
KS
American basswood 2.6 3.35 0.76 0.97 0.25 0.92 0.99 0.18 0.98 0.99 0.06
American beech 4.1 3.10 0.89 0.99 0.15 0.95 1.00 0.14 0.99 1.00 0.19
American elm 5.6 1.48 0.68 0.97 0.19 0.88 0.99 0.09 0.97 1.00 0.06
American holly 1.3 1.12 0.76 0.95 0.10 0.93 1.00 0.09 0.98 1.00 0.12
American hornbeam 2.2 1.11 0.71 0.99 0.19 0.93 1.00 0.15 0.98 1.00 0.14
American sycamore 1.0 2.81 0.34 0.89 0.23 0.81 0.98 0.15 0.96 0.99 0.14
Ashe juniper 0.3 8.77 0.92 0.98 0.04 0.95 0.96 0.05 0.94 0.95 0.05
baldcypress 0.5 7.57 0.77 0.97 0.10 0.82 1.00 0.10 0.91 0.99 0.13
balsam fir 4.7 3.77 0.96 1.00 0.04 0.97 1.00 0.04 0.99 1.00 0.08
balsam poplar 0.8 2.65 0.88 0.97 0.06 0.97 1.00 0.07 0.88 0.99 0.09
bigtooth aspen 1.9 3.65 0.82 0.99 0.13 0.92 1.00 0.13 0.96 0.99 0.12
bitternut hickory 1.6 1.69 0.39 0.93 0.21 0.81 0.99 0.11 0.95 1.00 0.06
black ash 2.0 3.22 0.83 0.99 0.14 0.95 0.98 0.17 0.98 0.98 0.23
black cherry 7.8 1.69 0.81 0.98 0.10 0.93 0.99 0.08 0.98 1.00 0.09
black hickory 1.2 1.68 0.95 1.00 0.11 0.99 1.00 0.13 1.00 1.00 0.12
black locust 1.3 2.06 0.72 0.98 0.26 0.91 0.99 0.23 0.98 1.00 0.14
black oak 4.6 3.21 0.89 1.00 0.19 0.96 1.00 0.13 0.99 1.00 0.09
black spruce 1.6 4.48 0.92 1.00 0.04 0.97 1.00 0.04 0.98 0.99 0.05
black walnut 1.9 1.96 0.55 0.96 0.24 0.90 1.00 0.21 0.96 1.00 0.13
black willow 0.6 3.14 -0.24 0.71 0.40 0.24 0.72 0.24 0.82 0.92 0.15
blackgum 5.7 1.33 0.85 0.99 0.14 0.96 1.00 0.14 0.99 1.00 0.18
blackjack oak 0.7 1.60 0.65 0.98 0.18 0.91 1.00 0.17 0.96 1.00 0.15
boxelder 1.5 2.15 0.36 0.89 0.33 0.75 0.97 0.17 0.90 0.98 0.08
bur oak 1.3 3.85 0.65 0.96 0.25 0.89 0.99 0.23 0.97 0.99 0.14
cabbage palmetto 0.2 8.35 0.88 0.97 0.01 0.20 0.22 0.01 0.95 0.95 0.01
cedar elm 0.2 2.72 0.55 0.98 0.09 0.86 0.99 0.09 0.98 1.00 0.12
cherrybark oak 1.0 2.46 0.80 0.99 0.13 0.94 1.00 0.12 0.98 1.00 0.12
chestnut oak 2.4 5.74 0.90 0.99 0.09 0.98 1.00 0.11 0.99 1.00 0.10
Chinese tallowtree 0.3 2.41 0.90 0.98 0.08 0.91 1.00 0.09 0.62 0.72 0.09
chinkapin oak 0.8 2.09 0.74 0.97 0.23 0.94 1.00 0.22 0.98 1.00 0.19
common persimmon 1.4 0.70 0.59 0.98 0.12 0.88 1.00 0.12 0.98 1.00 0.18
eastern cottonwood 0.4 6.36 -1.05 0.53 0.39 0.18 0.91 0.31 0.80 0.98 0.15
eastern hemlock 2.5 5.60 0.86 0.99 0.09 0.95 0.99 0.10 0.98 0.99 0.12
eastern hophornbeam 3.3 1.12 0.50 0.93 0.20 0.84 0.98 0.09 0.97 1.00 0.08
eastern red cedar 3.2 2.30 0.81 0.99 0.33 0.93 1.00 0.22 0.99 1.00 0.12
eastern redbud 1.0 0.78 0.57 0.97 0.20 0.88 1.00 0.14 0.98 1.00 0.14
eastern white pine 3.4 5.13 0.87 0.98 0.16 0.94 0.99 0.19 0.97 0.99 0.21
flowering dogwood 3.8 0.84 0.87 1.00 0.13 0.96 1.00 0.11 0.99 1.00 0.13
green ash 4.0 2.45 0.59 0.94 0.23 0.81 0.99 0.11 0.90 1.00 0.09
hackberry 1.5 1.93 0.47 0.94 0.31 0.82 0.99 0.19 0.97 1.00 0.08
hawthorn spp. 0.8 1.00 0.19 0.91 0.36 0.76 0.97 0.26 0.84 0.99 0.13
honey mesquite 0.9 3.62 0.90 1.00 0.02 0.96 1.00 0.01 1.00 1.00 0.01
honeylocust 0.7 1.92 0.32 0.95 0.28 0.85 1.00 0.23 0.98 1.00 0.12
jack pine 0.8 4.87 0.78 0.97 0.11 0.91 1.00 0.18 0.84 0.97 0.24
laurel oak 1.5 3.16 0.85 0.99 0.08 0.98 1.00 0.09 0.98 0.99 0.06
live oak 0.7 4.34 0.84 1.00 0.07 0.96 1.00 0.09 0.98 0.99 0.09
loblolly bay 0.2 3.88 0.28 0.89 0.03 0.84 0.88 0.03 0.97 0.97 0.04
loblolly pine 8.0 9.77 0.97 1.00 0.09 0.99 1.00 0.08 1.00 1.00 0.05
longleaf pine 0.9 4.55 0.86 0.99 0.06 0.95 1.00 0.07 0.99 1.00 0.08
mockernut hickory 4.0 1.47 0.85 1.00 0.15 0.96 1.00 0.13 0.99 1.00 0.13
northern pin oak 0.6 3.81 0.61 0.92 0.14 0.86 0.98 0.19 0.85 1.00 0.17
northern red oak 6.5 3.75 0.87 0.99 0.13 0.95 1.00 0.12 0.99 1.00 0.06
northern white-cedar 2.0 9.09 0.86 0.99 0.08 0.95 1.00 0.09 0.98 1.00 0.10
Osage-orange 0.5 2.56 0.40 0.97 0.25 0.82 1.00 0.26 0.96 0.99 0.23
overcup oak 0.4 3.98 0.55 1.00 0.15 0.82 0.99 0.19 0.94 0.99 0.28
paper birch 4.4 2.30 0.91 0.99 0.09 0.94 0.99 0.11 0.97 0.99 0.19
pecan 0.3 2.62 0.23 0.87 0.21 0.82 0.99 0.15 0.93 1.00 0.12
pignut hickory 3.7 1.77 0.86 0.99 0.16 0.96 1.00 0.11 0.99 1.00 0.13
pin oak 0.2 3.62 0.09 0.83 0.25 0.74 0.96 0.28 0.87 0.97 0.24
Pinchot juniper 0.1 3.69 0.74 0.93 0.03 0.92 0.95 0.02 0.97 0.99 0.01
pitch pine 0.4 3.43 0.92 1.00 0.09 0.78 0.96 0.08 0.94 0.99 0.05
pond pine 0.2 4.76 0.48 0.96 0.04 0.73 0.98 0.04 0.98 0.99 0.06
pondcypress 0.4 7.30 0.87 0.94 0.04 0.97 1.00 0.03 0.99 0.99 0.03
ponderosa pine 0.2 14.05 0.99 1.00 0.08 0.96 0.96 0.13 0.99 0.99 0.19
post oak 3.6 2.80 0.89 1.00 0.14 0.97 1.00 0.13 0.99 0.99 0.17
quaking aspen 5.0 4.65 0.95 1.00 0.11 0.99 1.00 0.13 1.00 1.00 0.21
red maple 16.8 3.51 0.93 1.00 0.12 0.98 1.00 0.13 1.00 1.00 0.13
red mulberry 0.8 1.13 -0.12 0.92 0.28 0.70 0.99 0.17 0.96 1.00 0.12
red pine 1.2 8.55 0.76 0.98 0.17 0.93 0.99 0.20 0.97 0.99 0.22
red spruce 1.4 4.21 0.90 0.99 0.03 0.97 0.99 0.04 0.99 1.00 0.04
redberry juniper 0.1 4.80 0.81 1.00 0.02 0.87 0.97 0.02 0.95 0.95 0.03
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plot-based sampling errors at the 216,500 ha scale were much
higher relative to those of the total live-tree basal area estimates.
These ranged from a mean sampling error of 62% for sugar maple
to 112% for river birch, as compared to 34% for total live-tree basal
area. This suggested that much of the disagreement between mod-
el-based and plot-based estimates could be due to uncertainty
with the FIA plot-derived estimates as much as due to inaccuracies
in the modeled dataset.
The covariance of a purposive sample of eight of the species,
representing a range of spatial distribution patterns, was assessed
by a series of joint distribution scatterplots generated at the
216,500 ha scale (Fig. 8). These scatterplots indicate that the
covariance structure amongst these species that is apparent in
the plot-based estimates was generally retained by the model-
based estimates at this scale of assessment. Species that are often
observed on the same plot in the field, such as sugar maple and
beech, are more likely to be predicted to co-occur within a pixel
by the model. Similarly, species that are seldom observed together
in the field, such as black cherry and river birch, are less likely to
co-occur within a pixel.
Each of the 273 tree species present in the field plot data used in
the study has different spatial and ecological characteristics that
can affect the certainty with which it can be modeled at a given
scale from the set of input data used in the study. Species which
occur primarily as understory species, or occur as a minor propor-
tion of the stands in which they occur, will have a less distinct
spectral signature than species that occur as dominant in the can-
opy. Rare species occurred on fewer plots and thus probably did
not provide adequate training data to build a robust model because
existing training data did not necessarily represent the full range of
conditions in which the species occurs. Similarly, species that do
not have strong relationships with either biotic or abiotic factors
are also difficult to model. As the results from this study seem to
indicate, modeling many species at once as covariate response
variables (i.e. species assemblages) may have the added benefit
of improving the accuracy of some species by taking advantage
of relationships between species in their distributions.
Given these per-species uncertainties, caution should be shown
in interpreting and utilizing the results for each species. As a con-
servative starting point, the results in Table 3 are limited to the 100
most abundant species in the study area, and these generally show
encouraging results, particularly at the coarsest scales of assess-
ment. In general, the trend for almost all of these species is for
AC metrics to increase with coarser scales of assessment, with
median values of 0.82 for AC and 0.99 for AC
sys
at the finest scale
rising to 0.98 and 1.0, respectively at the coarsest scale. There are
just a few species on the list that do not follow this pattern, e.g.
cabbage palmetto and sand pine. However, in all such cases, the
species in question have ranges located near the boundary of the
study area and their results are therefore affected by differences
in the area assessed by the hexagons at different scales.
The species results for the KS metric suggest that it is relatively
insensitive to the scale of assessment, with median values ranging
from 0.13 at the finest scale to 0.12 at the coarsest scale. There are
individual species on the list that indicate either a positive or neg-
ative trend across scale; however, these again appear to be due to
where the species range falls relative to the study area boundary.
Species that have ranges located near the study area boundary,
even abundant ones such as yellow-poplar, will generally show a
trend of increasing KS values with coarser scales, while those with
Table 3 (continued)
Tree species Scale/metric
Plot-level 216,500 ha 866,000 ha 3.5 million ha
Plots (%)
a
ba
b
AC
c
AC
sysd
KS
e
AC AC
sys
KS AC AC
sys
KS
river birch 0.4 2.37 -0.06 0.79 0.29 0.68 0.94 0.25 0.85 0.99 0.13
sand pine 0.1 9.26 0.92 1.00 0.03 0.54 0.90 0.03 0.56 0.76 0.03
sassafras 2.4 1.22 0.69 0.99 0.18 0.90 1.00 0.18 0.96 1.00 0.19
scarlet oak 2.3 2.90 0.89 1.00 0.15 0.97 1.00 0.16 0.99 1.00 0.19
shagbark hickory 2.4 1.94 0.64 0.99 0.16 0.87 1.00 0.13 0.97 1.00 0.10
shortleaf pine 2.6 3.77 0.95 1.00 0.12 0.97 1.00 0.10 0.97 1.00 0.12
silver maple 0.6 7.10 -0.14 0.74 0.31 0.59 0.93 0.24 0.79 0.96 0.13
slash pine 1.7 8.23 0.96 1.00 0.06 0.99 1.00 0.05 1.00 1.00 0.04
slippery elm 2.1 1.23 0.60 0.97 0.25 0.88 1.00 0.16 0.97 1.00 0.13
sourwood 2.4 1.40 0.90 0.99 0.11 0.95 1.00 0.12 0.98 1.00 0.13
southern red oak 3.3 2.12 0.85 1.00 0.09 0.96 1.00 0.11 0.99 1.00 0.17
striped maple 0.9 0.99 0.86 0.99 0.09 0.96 1.00 0.11 0.99 1.00 0.12
sugar maple 7.5 5.09 0.93 1.00 0.16 0.97 1.00 0.16 0.99 1.00 0.13
sugarberry 0.9 2.47 0.79 0.97 0.19 0.95 1.00 0.12 0.97 1.00 0.08
swamp tupelo 1.3 5.15 0.78 0.99 0.10 0.95 1.00 0.11 0.99 1.00 0.08
sweet birch 1.5 2.60 0.83 0.98 0.06 0.91 0.98 0.04 0.98 0.99 0.03
sweetbay 1.1 2.51 0.76 0.97 0.07 0.95 1.00 0.11 1.00 1.00 0.13
sweetgum 8.1 3.06 0.94 1.00 0.10 0.98 1.00 0.13 0.99 1.00 0.17
tamarack 1.1 3.65 0.89 1.00 0.08 0.96 1.00 0.08 0.88 0.95 0.10
Virginia pine 1.5 3.53 0.81 1.00 0.14 0.95 1.00 0.12 0.99 1.00 0.12
water oak 4.8 2.41 0.92 1.00 0.07 0.98 1.00 0.07 1.00 1.00 0.06
water tupelo 0.3 11.52 0.71 0.97 0.11 0.81 0.99 0.09 0.85 0.96 0.12
white ash 4.9 2.22 0.82 0.99 0.18 0.94 1.00 0.14 0.98 1.00 0.10
white oak 8.4 3.75 0.92 1.00 0.13 0.97 1.00 0.09 0.98 1.00 0.09
white spruce 1.7 2.27 0.79 1.00 0.10 0.92 1.00 0.11 0.99 0.99 0.18
willow oak 1.0 2.81 0.64 0.98 0.11 0.91 1.00 0.09 0.96 1.00 0.17
winged elm 3.2 1.07 0.85 1.00 0.13 0.95 1.00 0.14 0.98 1.00 0.22
yellow birch 3.0 2.77 0.89 0.98 0.10 0.94 0.98 0.12 0.96 1.00 0.17
yellow-poplar 5.3 3.95 0.88 0.99 0.14 0.97 1.00 0.16 0.99 1.00 0.21
Median of 100 species 1.5 2.98 0.82 0.99 0.13 0.94 1.00 0.12 0.98 1.00 0.12
a
Percentage of plots on which the species occurs.
b
Mean basal area (m
2
/ha) for the species on plots where the species occurs.
c
Agreement coefficient (larger values indicate better agreement, max=1).
d
Systematic agreement (larger values indicate better agreement, max=1).
e
Kolmogorov–Smirnov statistic (smaller values indicate better agreement, min=0).
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ranges that fall more centrally in the study area will show the
opposite trend, such as northern red oak. The KS metric, which
measures the maximum deviation between the plot-based and
model-based CDFs, was always found, regardless of species, to cor-
respond with proportion of hexagons where the plot-based esti-
mate was zero and the model-based estimate was non-zero.
Fig. 4. Map of total live-tree basal area, ranging from low (light yellow) to high (dark green) (a), with map of differences in estimates (b) and graph of 90% confidence intervals
and model estimates (c) at 216,500 ha scale.
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This last result, coupled with the finding that KS is generally
insensitive to scale, suggests a systematic issue with the method-
ology. There are a number of potential explanations for this. One
is the difference in spatial resolution between the plots and pixels,
Fig. 5. Map of sugar maple live-tree basal area, ranging from low (light yellow) to high (dark green), and range boundary (red outline) (a), with scatterplots of estimates at
three scales (b) and map of differences at 216,500 ha scale (c).
B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198 193

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as discussed in Section 2.2.3, where fine-scale spatial variability
within an individual pixel results in poorer agreement between
the plot-based and model-based estimate for that pixel. Another
is the choice of the value of k. Using kNN for estimation represents
Fig. 6. Map of flowering dogwood live-tree basal area, ranging from low (light yellow) to high (dark green), and range boundary (red outline) (a), with scatterplots of
estimates at three scales (b) and map of differences at 216,500 ha scale (c).
194 B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198

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a necessary trade-off between bias and variance. While the optimi-
zation procedure suggested in this study is designed to minimize
RMSE (i.e. the square root of the sum of the squared bias plus
the variance), bias alone will be minimized when kequals one. This
Fig. 7. Map of river birch live-tree basal area, ranging from low (light yellow) to high (dark green), and range boundary (red outline) (a), with scatterplots of estimates at three
scales (b) and map of differences at 216,500 ha scale (c).
B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198 195

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bias will be most apparent near the boundaries of the data range, in
particular near the lower limit of zero. A final explanation,
mentioned earlier in the discussion of the detailed assessment of
total live-tree basal area and the three highlighted species, may
be the fact that there is a definitional mismatch between the forest
stratum proportion layer and the FIA forest definition, which de-
fined the areas over which tree measurements were taken. The
maps produced are thus of a slightly different population than
the one sampled by the FIA plots, i.e. they depict basal area of all
trees, not just those found on forest land as defined by FIA. This
could be tested only if the FIA sampling frame were expanded to
include non-forest areas with trees such as urban parks and rural
windbreaks. Accounting for definitional differences between the
forest stratum proportion layer and the FIA sampling frame is
therefore a possible area of improvement in the proposed mapping
methodology that remains in alignment with the stated objectives
established for the study.
There are many univariate and multivariate mapping
approaches from which to choose, and an almost infinite combina-
tion of these methods and associated parameters. Clearly, no single
method is ideal for all situations and data types, nor meets all
possible efficiency criteria. Methods that are optimized to meet
one goal (e.g. high spatial resolution) can be suboptimal for
another (e.g. computing time and storage requirements, temporal
frequency). The proposed approach was thus designed using a
series of tradeoffs to take into account desirable output attributes,
statistical considerations, and a desire to leverage efficiencies that
would permit the efficient production of large area maps that could
meet user needs. Preliminary results from this study have already
been used by some state agency analysts to assist in the identifica-
tion of priority forest landscape areas, such as those likely to be
impacted by certain forest pests and diseases, as required by the
2008 Farm Bill.
The methodology presented in the current study could easily be
adapted to produce maps of any field plot attribute that can be
summarized to the plot level, because the approach in effect uses
a relational database concept. The fundamental structures upon
which all of the per-species maps are based are the imputed map
of plot identification numbers (i.e. group labels), the associated ta-
ble of stratified neighboring plots and weights, and the forest stra-
tum proportion layer. All other post-processing steps are
essentially database operations that join summarized field plot
attributes to the imputed plot identification number map on a
per-pixel basis. It seems reasonable to assume that the proposed
methodology could be used for the production of maps of other
attributes, especially those expected to be highly correlated with
Fig. 8. Scatterplots of basal area covariance amongst eight species. Each point depicts mean live-tree basal area (m
2
/ha) values for two species for a single 216,500 ha
hexagon. Each scatterplot contains two sets of points, one derived from the plots and the other from the model. The inset map indicates the number of plots or pixels that
contributed to the plot-based and model-based means for each hexagon.
196 B.T. Wilson et al. / Forest Ecology and Management 271 (2012) 182–198

Author's personal copy
total live-tree and per-species live-tree basal area. These include
tree-level attributes such as volume, biomass, and standing dead-
tree attributes, as well as site-level attributes like proportion for-
est, forest type, or possibly stand age and height. The exceptions
are non-ecological field plot attributes, such as ownership, because
these bear little correlation either to the plot’s forest or tree char-
acteristics or the ecological predictor layers used in the modeling.
Rigorous accuracy assessment is required, including the types of
multi-scale assessments presented in the current study. Though
such an examination is beyond the scope of the current study, re-
lated studies are underway to determine the utility of such data-
sets for regional ecosystem services valuation and forest carbon
modeling efforts.
4. Conclusions
The methodology presented here provides a cost-effective
means for conducting regional to continental-scale mapping of tree
species abundance and distribution. Its production efficiency arises
from integrating the FIA database of field plots with readily-avail-
able moderate resolution raster datasets in a straightforward eco-
logically-based modeling framework. The explanatory power of the
CCA model used in the study was bolstered by the inclusion of both
ecological zone and vegetation phenology data. For the 100 most
abundant tree species in the study area and at the scale of estima-
tion units assessed, the nearest-neighbor imputation methodology
produced results that compared favorably with estimates gener-
ated from FIA field plot data. Accuracy of the results improved
slightly with the use of a weighting function based on distance in
the canonical variate space, but substantially more so by using a
stratification layer based on the 2001 NLCD tree canopy cover
dataset and by selecting an optimal value for k. The issue of model
overestimation at the edges of species ranges seen in some individ-
ual tree species may stem from an insufficient sample of field plots
being used to produce the field plot-based estimates or from a
stratification layer that includes trees on all lands while the FIA
sampling frame does not.
Acknowledgements
The authors would like to thank Janet Ohmann and Matthew
Gregory of the collaborative USFS/OSU LEMMA project for their
work on GNN that planted the germ of this project; Mark Hansen,
Mark Nelson, and Ron McRoberts of the FIA program for their
thoughtful comments that helped flesh out many of the concepts
presented; Mark Finco and Vicky Johnson of the USFS Remote
Sensing Applications Center and Doug Griffith of FIA for their assis-
tance in pulling together the raster datasets used in the project; as
well as the anonymous reviewers whose comments greatly im-
proved the clarity and focus of the manuscript.
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