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\begin{document}

\title{Carbon sequestration potential of process-based river restoration}



\author[1]{Sarah Hinshaw}%
\author[1]{Ellen Wohl}%
\affil[1]{Colorado State University}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
Floodplain restoration can enhance capacity for carbon sequestration by
facilitating higher water tables, deposition of fine sediment, and
increased input and residence time of organic matter. We measured
floodplain soil organic carbon stocks in nine stream restoration
projects across the western United States and compared them to nearby
degraded and reference condition floodplains. Degraded floodplains had
the lowest soil mean carbon stocks in the majority of floodplains
measured (range 161-894 Mg C/ha), and reference stocks had the highest
stocks (range 391-904 Mg C/ha) of those with statistically significant
differences between the three categories. Across all sites measured,
stream restoration sites, referred to as treatment sites, had stocks
(range 203-1028 Mg C/ha) similar to degraded condition floodplains but
the largest range. When modeled under degraded conditions, four out of
nine of the treatment sites had significantly higher OC stocks than
predicted. Climate and geologic variables are most influential in
predicting carbon stocks, and floodplains in the interior western USA
have the highest carbon stocks. As the demand for carbon sequestration
increases due to climate change, ecologically responsible floodplain
restoration provides a significant opportunity for carbon storage.
However, despite the statistically significant relationships we observed
in this dataset, the variations within the data in relation to
degraded/treatment/reference categories illustrate the uncertainties in
quantifying the effects of restoration on floodplain carbon stocks.%
\end{abstract}%



\sloppy


\textbf{1. Introduction}

Stream restoration can potentially increase floodplain carbon stocks by
enhancing deposition of organic matter and sequestration of soil organic
carbon. Within the global carbon cycle, however, potential magnitudes of
organic carbon stocks in the freshwater hydrosphere are not yet well
constrained and the uncertainty is particularly substantial for carbon
stocks in river corridors (i.e., active channels and floodplains; Battin
et al., 2009; Aufdenkampe et al., 2011; Hilton and West, 2020). This
uncertainty partly reflects the limited number of field-based
quantifications of river corridor carbon stocks (Sutfin et al., 2016;
Hinshaw and Wohl, 2021) and partly reflects the substantial spatial
variability that can be present in these stocks, with limited portions
of a river corridor accounting disproportionately for total carbon stock
in the river network or the entire watershed (Wohl et al., 2012; Wohl
and Knox, 2022). Despite these uncertainties, there is a growing need to
quantitatively estimate and predict organic carbon stocks in river
corridors in connection with the potential for carbon sequestration as
one of the goals of stream restoration (e.g., Yan et al., 2022).

Here, we examine whether there are detectable differences in floodplain
carbon stock in categories of impacted or degraded floodplains,
treatment floodplains that have recently undergone restoration, and
reference floodplains that display relatively greater floodplain
function and connectivity. This study design conceptually models carbon
storage potential as a result of restoration at short and longer
timescales, where treated floodplains represent short timescales and
reference floodplains represent longer timescales. Before-after
restoration studies are necessary to directly attribute changes in
carbon stocks to restoration activities. We recommend this strategy in
future as more restoration projects emphasize hydrologically
reconnecting the channel and floodplain, but these studies will be most
effective when they include a timespan of a decade or more from before
to after treatment. We were not able to access the restoration sites in
this study before treatment.

We first review existing knowledge of organic carbon stocks in river
corridors and how human activities have altered these stocks. We then
discuss how stream restoration might enhance carbon stocks and describe
the design of this study, in which our objective is to determine whether
there are differences in carbon stocks in the three categories of
floodplains at diverse sites in the western United States.

\textbf{Organic carbon stocks in river corridors}

Carbon stock refers to the mass of carbon stored in a carbon pool such
as soil or living vegetation. Carbon sequestration refers to the ability
to capture and store carbon; sequestration can maintain or increase
carbon stocks. Within river corridors, floodplains typically contain
much greater carbon stock than active channels. Within floodplains,
carbon stocks occur as living biomass (i.e., vegetation and aquatic
organisms), dissolved carbon in surface and ground water, dead biomass
including large wood in the floodplain, and soil organic carbon (Sutfin
et al., 2016; Wohl et al., 2017). Floodplain soil organic carbon (SOC)
typically forms the largest stock within a river corridor unless the
river corridor lacks a floodplain (Scott and Wohl, 2018b). Published
values for floodplain SOC range from 1.4 Mg C/ha at a site in South
Carolina, USA to 7735 Mg C/ha on a floodplain in northwestern Montana,
USA (Sutfin et al., 2016). We seek to quantitatively estimate existing
and potential floodplain SOC stocks in connection with floodplain
restoration. Although riparian vegetation growth increases organic
carbon stocks within aboveground biomass (e.g., Hanberry et al., 2015),
we do not account for living biomass (plants and vegetation) in this
study. Rather, we focus on SOC as an integrative representation of
above- and below-ground carbon stocks at longer timescales.

Although typically the largest carbon stock in floodplains, SOC is
highly spatially variable (Samaritani et al., 2011; Sutfin et al., 2016;
Wohl et al., 2017). In this context, we use soil to refer to all mineral
sediment and particulate organic matter in floodplain alluvium.
Floodplain SOC stocks reflect complex interactions among climate;
geology; soil moisture, texture, and residence time; biomass; and
organic matter supply (Hinshaw and Wohl 2021). Optimal conditions for
large floodplain SOC stocks are wide, wet, relatively stable valley
bottoms with long sediment residence times, cooler climates, and high
organic matter inputs (Sutfin et al., 2016; Hinshaw and Wohl 2021;
Sutfin et al., 2021). Residence times of floodplain sediment and
associated SOC depend on fluvial erosion rates and vary from years to
decades in small floodplains or locations close to the active channel(s)
to thousands of years in larger floodplains and at locations farther
from the channel (Wohl, 2015; Sutfin and Wohl, 2019). Residence time of
floodplain SOC also reflects rates of mineralization through microbial
processing that releases CO\textsubscript{2} to the atmosphere and
dissolved organic carbon to downstream transport and to groundwater
(Bouillon et al., 2009; Handique, 2015).

Spatial and temporal variations in soil moisture, organic matter inputs,
and soil residence time can create significant lateral and longitudinal
variations in floodplain SOC in large floodplains (Lininger et al.,
2018) and longitudinal variations in smaller mountain streams (Scott and
Wohl, 2018a; Sutfin and Wohl, 2019). Consequently, quantitative
estimates of floodplain SOC stock may be most accurate and appropriately
applied at the reach scale, where a reach is a length of river corridor
with consistent channel and valley geometry that is at least several
times as long as average channel width. Spatial variations in floodplain
SOC also complicate attempts to use space-for-time substitutions in
which sites from different rivers or different portions of a river are
used to understand potential temporal changes following restoration, for
example. This is the approach we use in this study, but we acknowledge
the limitations and uncertainties inherent in this approach.

\textbf{Human alterations and restoration of floodplain carbon stocks}

Human alterations of river corridors can reduce organic carbon stocks in
floodplain vegetation, downed wood, and soil (Hanberry et al., 2015;
Wohl et al., 2017). Alterations include floodplain drainage that reduces
primary productivity and soil moisture; deforestation that reduces
primary productivity; and removal of large, downed wood from the channel
and floodplain that reduces sediment trapping and eventual soil
development. In addition, flow regulation, artificial levee
construction, and channelization decrease channel-floodplain
connectivity, in turn reducing associated floodplain inundation and
deposition of sediment and organic matter.

Stream restoration can potentially enhance carbon stocks by restoring
processes that facilitate higher floodplain water tables and associated
reducing conditions in the soil, as well as greater floodplain primary
productivity and increased deposition of sediment and organic matter.
Access to soil moisture from raised water tables facilitates new
riparian vegetation growth that provides higher supply of organic matter
via leaf litter. The conditions optimal for promoting large floodplain
carbon stocks correspond to Stage 0 anastomosing wet woodland or
anastomosing grassed wetland in the Cluer and Thorne (2014) stream
evolution model. Reconfiguration and reconnection of river corridors to
achieve Stage 0 conditions has been increasingly applied in the United
States as part of stream restoration efforts within the past decade
(Booth et al., 2009; Powers et al., 2019; Mattern et al., 2020;
Flitcroft et al., 2022).

The process of stream restoration implementation has a non-zero carbon
footprint, estimated by Chiu et al. (2022) as 9-14 kg
CO\textsubscript{2} per meter of stream restored. However, ecological
restoration can transform the relative proportions of landscapes
considered as carbon sources versus sinks and provide significant
capacity to more efficiently sequester, rather than emit, carbon over
decadal timescales (Zhou et al., 2020).

Commonly, only a small portion of the project budget for most stream
restoration projects is allocated to monitoring, and practically no
budget is allocated to measure carbon stocks. However, incentives exist
for practitioners to start measuring carbon. Other than the
informational value of quantification of carbon sequestered from the
atmosphere, carbon credits in the units of tons of carbon can be sold on
the carbon market (Wara, 2007; Schneider et al., 2019). This practice is
widely applied within industries of agriculture and forestry (Ribaurdo
et al., 2010; Paul et al., 2013), and floodplain restoration could also
qualify for carbon offsets (e.g., Matzek et al., 2015; Sapkota and
White, 2020).

To our knowledge, only one study thus far has directly examined the
effects of restoration on carbon stock in river corridors. Samaritani et
al. (2011) compared soil carbon stocks and fluxes in channelized and
restored portions of the Thur River in Switzerland in the context of
spatial heterogeneity and temporal variability but did not explicitly
compare total carbon stock between restored and degraded areas. The
restored floodplain had a larger range and higher heterogeneity of
organic carbon stocks and fluxes. Related studies indicate the effects
of human alterations on river corridor carbon stock by comparing altered
and natural river corridors in the same region. Cabezas and Comin (2010)
found that floodplain soils with natural land cover have higher organic
carbon stocks than agricultural portions of the floodplain along Spain's
Middle Ebro River, a pattern similar to that from Lininger and Polvi
(2020), who showed decreasing floodplain SOC stocks with increasing
human alteration in Swedish river corridors.

To enhance our understanding of carbon sequestration potential in stream
restoration, we must address at least two questions: (1) Can measurable
quantities of carbon be added to floodplain soil through restoration,
and over what timescales?, and (2) What framework best facilitates
understanding and measuring carbon stocks in stream restoration?
Ideally, measurement of carbon in stream restoration would occur before
and after restoration takes place. As a surrogate for pre and post
restoration conditions, we use three alternative floodplain states to
evaluate floodplain SOC stocks: degraded, treatment, and reference.
Alternative states are self-reinforcing states of equilibrium that can
exist simultaneously under the same environmental conditions (Holling,
1973; May, 1977). We consider our categories of floodplain to
approximate alternative states of semi-equilibrium that have been
affected by different levels of human intervention. We use the
terminology of degraded, treatment, and reference to designate potential
near-endmembers and an intermediate position on a spectrum of
restoration, but recognize that 1) degraded and reference sites are not
exact endmember positions, 2) the treatment, or stream restoration
project category, is likely not in equilibrium and may fall anywhere
along the spectrum, and 3) reference conditions do not always provide
ideal comparisons because we may not be able to restore streams to a
selected reference state (Dufour and Piegay 2009), and it may not be
possible to find exact matches between reference, treatment, and
degraded sites with respect to the many environmental variables that can
influence river corridors and carbon stock.

We use the term treatment instead of restored because stream restoration
sites are not ``restored'' as soon as construction takes place. The term
degraded can encompass a range of impaired or impacted floodplain
conditions. Degraded sites represent intensive land uses that have
degraded natural floodplain processes over time, and commonly include
histories of levee construction, channel straightening, grazing,
agriculture, timber harvest, or other activities that disconnect
channels from their floodplains. We use degraded as a descriptive term
and recognize that degraded floodplains can fall within a spectrum of
conditions that may not be directly caused by one single type of
floodplain alteration. Rather, floodplains chosen for the degraded
category can represent the culmination of land or resource uses that may
have limited floodplain function over the past few centuries.

The primary objective of this study is to quantitatively compare
floodplain organic carbon stocks in degraded, treatment, and reference
stream corridors. Given the assumptions outlined above, we hypothesize
that degraded sites contain the least carbon, treatment sites contain an
intermediate amount of carbon, and reference sites contain the most
carbon. Our secondary objective is to use the data to examine factors
that influence floodplain SOC stock at sites across the regional scale
of the western United States.

\textbf{2. Study Areas}

We include data from 9 sites in the western United States (6 in Oregon,
2 in Utah, 1 in Colorado; Figure 1, Table 1). Each site includes all
three categories of degraded, treatment, and reference floodplain
sampling areas, with multiples of each category of reach where possible.
We combined data for multiple treated reaches along the same stream
where applicable, particularly in Fivemile Bell and Whychus Creek in
Oregon and East Canyon Creek in Utah. In all sites except Colorado,
floodplain categories are as physically close to each other as possible,
typically along the same streams, to reduce variability due to climate
and geology. In Colorado, the first iteration of samples was lost in
transit; thus, we provide all three categories from different locations
within the South Park region of Colorado but acknowledge the limitations
of direct comparison between categories.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Associated with each treatment site is at least one reference site and
at least one degraded site. In two cases, two sites within the same
ecoregion share a reference site. This occurs in Deep Creek and Lost
Creek in Oregon and Kimball Creek and East Canyon Creek in Utah. These
two sets of sites are within reasonable proximity to share the same
reference site of Gray's Creek (Oregon) and McLeod Creek (Utah),
respectively. Some but not all degraded sites in our dataset are
candidate sites for future restoration projects and can thus benefit
from baseline data before restoration takes place. We chose each
floodplain and assigned it to a category based on personal
communications with local stakeholders and project designers,
particularly scientists at the USDA Forest Service, Utah State
University Swaner Preserve and EcoCenter, and the stream restoration
company EcoMetrics in Colorado. Individual site characteristics are
listed in Table 1.

\textbf{Table 1. Site characteristics of stream restoration projects
considered in the study.}\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
\textbf{Restoration Project Stream Name} & \textbf{Sample
Size\textsuperscript{a}} & \textbf{Location} & \textbf{Year of Sampling
Area Treatment} & \textbf{Average Elevation (m)} & \textbf{Ecoregion
(Level III)\textsuperscript{b}} & \textbf{Drainage Area
(km\textsuperscript{2})} & \selectlanguage{ngerman}\textbf{Mean Annual Temperature (°C)} &
\textbf{Mean Annual Precipitation (mm)}\tabularnewline
Fivemile Bell, OR & 120 & 124.0097\selectlanguage{ngerman}°W 43.8472°N & 2018 & 15 & Coast Range
& 21 & 11.3 & 2067\tabularnewline
Staley Creek, OR & 62 & 122.3828\selectlanguage{ngerman}°W 43.4839°N & 2017 & 687 & Cascades &
105 & 10.7 & 1378\tabularnewline
South Fork McKenzie River, OR & 53 & 122.2883\selectlanguage{ngerman}°W 44.1596°N & 2018 & 345 &
Cascades & 560 & 10.9 & 1973\tabularnewline
Whychus Creek, OR & 82 & 121.4274\selectlanguage{ngerman}°W 44.3623°N & 2016 & 829 & Blue
Mountains & 670 & 8.4 & 311\tabularnewline
Deep Creek, OR & 87 & 120.0585\selectlanguage{ngerman}°W 44.3258°N & 2018 & 1337 & Blue
Mountains & 224 & 6.6 & 536\tabularnewline
Lost Creek, OR & 50 & 120.3348\selectlanguage{ngerman}°W 44.1906362°N & 2012 & 1227 & Blue
Mountains & 21 & 7.4 & 424\tabularnewline
East Canyon Creek, UT & 89 & 111.5487\selectlanguage{ngerman}°W 40.7314°N & 2015-19 & 1932 &
Wasatch and Uinta Mountains & 130 & 6.3 & 541\tabularnewline
Kimball Creek, UT & 43 & 111.5181\selectlanguage{ngerman}°W 40.7193°N & 2019 & 1944 & Wasatch
and Uinta Mountains & 77 & 6.3 & 535\tabularnewline
Salt Creek, CO & 87 & 106.0103\selectlanguage{ngerman}°W 38.9571°N & 2022 & 2833 & Southern
Rockies & 43 & 3.2 & 353\tabularnewline
\textsuperscript{a}Sample sizes refer to number of floodplain soil
samples collected and include shared reference samples for sites where
references were shared, and do not include sites without a complete set
of categories. The total sample size is 598. \textsuperscript{b}From
Esri US Federal Datasets & \textsuperscript{a}Sample sizes refer to
number of floodplain soil samples collected and include shared reference
samples for sites where references were shared, and do not include sites
without a complete set of categories. The total sample size is 598.
\textsuperscript{b}From Esri US Federal Datasets &
\textsuperscript{a}Sample sizes refer to number of floodplain soil
samples collected and include shared reference samples for sites where
references were shared, and do not include sites without a complete set
of categories. The total sample size is 598. \textsuperscript{b}From
Esri US Federal Datasets & \textsuperscript{a}Sample sizes refer to
number of floodplain soil samples collected and include shared reference
samples for sites where references were shared, and do not include sites
without a complete set of categories. The total sample size is 598.
\textsuperscript{b}From Esri US Federal Datasets &
\textsuperscript{a}Sample sizes refer to number of floodplain soil
samples collected and include shared reference samples for sites where
references were shared, and do not include sites without a complete set
of categories. The total sample size is 598. \textsuperscript{b}From
Esri US Federal Datasets & \textsuperscript{a}Sample sizes refer to
number of floodplain soil samples collected and include shared reference
samples for sites where references were shared, and do not include sites
without a complete set of categories. The total sample size is 598.
\textsuperscript{b}From Esri US Federal Datasets &
\textsuperscript{a}Sample sizes refer to number of floodplain soil
samples collected and include shared reference samples for sites where
references were shared, and do not include sites without a complete set
of categories. The total sample size is 598. \textsuperscript{b}From
Esri US Federal Datasets & \textsuperscript{a}Sample sizes refer to
number of floodplain soil samples collected and include shared reference
samples for sites where references were shared, and do not include sites
without a complete set of categories. The total sample size is 598.
\textsuperscript{b}From Esri US Federal Datasets &
\textsuperscript{a}Sample sizes refer to number of floodplain soil
samples collected and include shared reference samples for sites where
references were shared, and do not include sites without a complete set
of categories. The total sample size is 598. \textsuperscript{b}From
Esri US Federal Datasets\tabularnewline
\bottomrule
\end{longtable}

Restoration techniques used at each treatment site varied, but the basic
objective was to hydrologically reconnect the channel and floodplain.
The primary techniques involved (i) introducing large wood or beaver dam
analogues to the channel to create obstructions that would enhance
in-channel sedimentation and overbank flow and/or (ii) re-grading the
valley floor by removing or adding floodplain sediment and decreasing
the flow stage needed to create overbank flow (Powers et al., 2019).
Most of the river restoration projects employing these techniques have
been undertaken only within the past decade, limiting the ability to
evaluate longer-term patterns of river response, including carbon
sequestration.

\textbf{3. Methods}

\emph{3.1 Field Methods}

We followed the field methods described in Hinshaw and Wohl (2021) and
collected 11 soil samples per moisture class (wet or dry), where
possible, in each category (degraded, treatment, reference) of
floodplain using a 3-cm-diameter 30-cm-length spoon sampling soil corer.
The sample size of 11 per category is drawn from supplemental
information in Sutfin and Wohl (2017), where bias and variance are shown
to stabilize after 11 samples per geomorphic unit. Moisture categories
were determined based on vegetation (riparian vs upland species),
microtopography, and soil moisture conditions at the time of sampling.
Moist soil with wetland vegetation (e.g., sedges, rushes) was
categorized as wet; all other sites were categorized as dry. All
sampling was conducted during relatively dry summer conditions. Dividing
samples into separate moisture categories is intended to account for
differences in carbon content of saturated vs dry soil found in previous
literature (e.g., Moyano et al., 2012; Manning et al., 2015) and we used
simple t-tests to test for differences between wet and dry samples. At
each sampling location, we noted vegetation present and sample depth.

Samples were obtained at 30-cm vertical intervals at multiple depths to
90 cm from the same sampling hole where the floodplain sediment was
sufficiently deep. Soil texture by hydrometer and total and organic
carbon analyses were done by a commercial laboratory. Bulk density
estimates were assigned based on soil type using the median estimate
from a collection of approximations using pedotransfer functions from
Leonaviciute (2000) and Ruehlmann and Korschens (2009); regression
analyses of data from Chaudhari et al. (2013); and a table of common
bulk density values from StructX (Structx 2023). In total, 653 samples
collected over the summers of 2020-2022 were used in the analyses for
this study. The bulk density values were used in the following equation
to convert from organic carbon content to organic carbon stock (Eq. 1):

\(\text{Organic\ Carbon\ Stock\ }\left(\frac{\text{Mg}}{\text{ha}}\right)=Organic\ Carbon\ \%\ *1\ m\ depth*\text{bulk\ density\ }\left(\frac{\text{Mg}}{m^{3}}\right)*10,\ 000\frac{m^{2}}{\text{ha}}\){[}1{]}

\emph{3.2 Data Analysis}

\emph{3.2.1 Within-site comparisons}

Without considering stream restoration intervention, the long-term
carbon sequestration potential at a particular degraded site could be
conceptually considered as the difference in carbon stocks between
reference and degraded categories. Accordingly, the short-term carbon
storage since restoration, if any, could be represented conceptually by
the difference between degraded and treatment categories. We examined
relationships of carbon stock via within-site comparisons, where we
compared carbon stocks between degraded, treatment, and reference
categories within one site using ANOVA tests and pairwise comparisons
between treatments using the emmeans package in R version 4.2.2 (Lenth
2023, R Core Team 2022).

\emph{3.2.2 Predicting treatment stocks under degraded conditions}

With the intent to conceptually estimate carbon sequestered since
restoration treatment, we predicted treatment floodplain carbon stocks
with models created for degraded floodplains. Hypothetically,
model-predicted treatment stocks represent pre-treatment conditions at
the treatment category floodplain, i.e., if it were still degraded. We
utilize this method as a thought exercise and recognize the large
assumption that pre-restoration conditions are similar to the degraded
floodplains associated with each restoration project. We acknowledge the
centrality of the assumption and suggest that direct, repeat pre and
post measurements would better represent the estimate of carbon
sequestered since restoration. After predicting treatment stocks using
the degraded-derived models, we calculated the differences between
measured and predicted treatment stocks as a first-order approximation
of how much carbon could be sequestered if environmental conditions are
sufficiently similar between degraded, treatment, and reference sites.

3.2.3 \emph{Across-site comparisons}

We tested for differences between degraded, treatment, and reference
carbon stocks (Mg/ha) for sites combined by Level III ecoregion (Omernik
and Griffith, 2014). We categorized Type III ecoregions by where the
treatment floodplain was located for a set of degraded, treatment, and
reference floodplains within a site.

Along with testing categories and regions for all data, we also explored
models that best explain carbon stock for the entire dataset. We used
ANOVA tests for both the ecoregion comparisons and the entire dataset
categorical comparisons and compared estimated marginal means with the
emmeans package in R (Lenth 2023). Then, using the complete dataset, we
investigated correlations between carbon stock and potential numeric
predictor variables related to soil texture and climate. Using variables
with significant correlations and additional categorical predictor
variables of research interest, we used three types of models to
estimate carbon content (\%). We used carbon content rather than stocks
to avoid uncertainty introduced by the assigned bulk density values that
were used to calculate stocks, i.e., we used direct laboratory results
with no modification. We split the dataset using 80\% of sample points
for model building and the remaining 20\% for model evaluation.

We compared three modeling approaches to carbon estimation using a
variety of predictors including treatment category within a site. In all
models discussed, we excluded data from Colorado due to the
non-associated nature of the degraded-treatment-reference datasets in
this region. In the Colorado dataset, degraded, treatment, and reference
sites are far (\textgreater{}10 km) apart and not along the same stream.
Using data from Oregon and Utah only, we began with a linear mixed
model. To account for the lack of independence of samples from the same
floodplains, lack of independence of samples from different depths from
the same hole, and the availability-based nature of the stream
restoration projects we chose to sample, we modeled carbon content as a
mixed model with random and fixed effects in a nested block study design
using the lmer function from the lme4 package in R version 4.1.3 (R Core
Team, 2022). Due to the large number of complexities to be considered in
the mixed generalized linear model, we also modeled carbon using a
gradient boosted regression tree model that utilizes elements of
decision trees and machine learning to account for characteristics of
the dataset without the need to account for the same linear model
sensitivities. The gradient boosting model was built with the dismo
package in R (Hijmans et al., 2021). Parameters for this model were
those suggested by Elith et al. (2008). In addition, we modeled the data
with a random forest model using regression decision trees with the
randomForest package in R (Liaw and Wiener 2002). We compared results
from the three models with the root mean square error (RMSE) and the
coefficient of determination (R\textsuperscript{2}) between 20\% of the
data reserved for model evaluation and the model predictions.

\textbf{4. Results}

\emph{4.1 Within-site comparisons}

In all sites except those in Colorado, either treatment or reference
stocks are highest, and either treatment or degraded are the lowest of
the three categories (Figure 2, Tables 2 \& 3). Reference stocks are
generally estimated to be higher than degraded stocks (seven of nine
sites) although the result is only significant at the 95\% confidence
level for three sites. Colorado sites excluded, the only sites with
statistically highest stocks are reference sites (Fivemile Bell, Whychus
Creek, and East Canyon Creek). Colorado sites have the highest stocks in
degraded floodplains, lowest in treatment floodplains, and intermediate
stocks in reference floodplains. Although we expected carbon stocks to
vary with moisture, only three floodplains of the 38 measured (East
Canyon Creek Degraded Reach 1, Staley Creek Degraded Reach 2, and South
Fork McKenzie Reference Reach) have significant differences between
carbon stocks for wet versus dry samples. Therefore, for simplicity, we
did not account for moisture when conducting tests for significant
differences between categories.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Table 2.} Carbon stocks at each site. Every site consists of
three sampling categories: degraded, treatment, and reference. In
several sites, multiple reaches were measured within a category at each
site.\selectlanguage{english}
\begin{longtable}[]{@{}llllllllll@{}}
\toprule
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Site}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Value\textsuperscript{a}}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Degraded Stocks (Mg/ha)}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Degraded Stocks (Mg/ha)}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Degraded Stocks (Mg/ha)}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Treatment Stocks (Mg/ha)}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Treatment Stocks (Mg/ha)}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Treatment Stocks (Mg/ha)}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Reference Stocks (Mg/ha)}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Reference Stocks (Mg/ha)}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Reach 1\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Reach 2\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Reach 3\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Reach 1\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Reach 2\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Reach 3\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Reach 1\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Reach 2\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Fivemile Bell}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
397 \selectlanguage{ngerman}± 115\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
293 \selectlanguage{ngerman}± 127\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
247 \selectlanguage{ngerman}± 47\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
283 \selectlanguage{ngerman}± 48\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
228 \selectlanguage{ngerman}± 63\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
593 \selectlanguage{ngerman}± 166\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\emph{Oregon Coast Range}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
12\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
11\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
31\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
17\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
24\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
25\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{347 ± 81}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{347 ± 81}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{347 ± 81}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{249 ± 30}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{249 ± 30}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{249 ± 30}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{593 ± 166*}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{593 ± 166*}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{South Fork McKenzie River} \emph{Willamette National Forest,
Oregon}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
177 \selectlanguage{ngerman}± 71\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
364 \selectlanguage{ngerman}± 73\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
348 \selectlanguage{ngerman}± 130\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
11\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{177 ± 71}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{177 ± 71}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{177 ± 71}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{364 ± 73}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{364 ± 73}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{364 ± 73}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{348 ± 130}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{348 ± 130}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{Staley Creek} \emph{Willamette National Forest, Oregon}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
279 \selectlanguage{ngerman}± 132\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
338 \selectlanguage{ngerman}± 119\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
659 \selectlanguage{ngerman}± 273\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
396 \selectlanguage{ngerman}± 146\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
11\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
15\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
15\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{313 ± 83}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{313 ± 83}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{313 ± 83}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{659 ± 273}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{659 ± 273}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{659 ± 273}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{396 ± 146}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{396 ± 146}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{Whychus Creek} \emph{near Sisters, Oregon}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
154 \selectlanguage{ngerman}± 41\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
170 \selectlanguage{ngerman}± 81\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
176 \selectlanguage{ngerman}± 43\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
249 \selectlanguage{ngerman}± 99\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
811 \selectlanguage{ngerman}± 191\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
12\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
24\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
14\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{161 ± 39}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{161 ± 39}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{161 ± 39}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{203 ± 44}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{203 ± 44}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{203 ± 44}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{811 ± 191*}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{811 ± 191*}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{Lost Creek\textsuperscript{b}} \emph{near Ochoco National
Forest, Oregon}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
355 \selectlanguage{ngerman}± 116\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
380 \selectlanguage{ngerman}± 51\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
391 \selectlanguage{ngerman}± 96\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
19\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{355 ± 116}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{355 ± 116}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{355 ± 116}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{380 ± 51}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{380 ± 51}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{380 ± 51}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{391 ± 96}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{391 ± 96}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{Deep Creek\textsuperscript{b}} \emph{Ochoco National Forest,
Oregon}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
421 \selectlanguage{ngerman}± 143\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
452 \selectlanguage{ngerman}± 58\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
515 \selectlanguage{ngerman}± 141\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
391 \selectlanguage{ngerman}± 96\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
16\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
28\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{439 ± 65}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{439 ± 65}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{439 ± 65}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{515 ± 141}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{515 ± 141}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{515 ± 141}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{391 ± 96}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{391 ± 96}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\textbf{East Canyon Creek\textsuperscript{c}} \emph{near Park City,
Utah}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
538 \selectlanguage{ngerman}± 103\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
564 \selectlanguage{ngerman}± 66\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
551 \selectlanguage{ngerman}± 89\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
430 \selectlanguage{ngerman}± 75\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
488 \selectlanguage{ngerman}± 72\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
904 \selectlanguage{ngerman}± 127\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
16\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
11\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{552 ± 46}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{552 ± 46}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{552 ± 46}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{458 ± 51}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{458 ± 51}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{458 ± 51}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{904 ± 127*}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{904 ± 127*}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Kimball Creek\textsuperscript{c}}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
894 \selectlanguage{ngerman}± 135\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1028 \selectlanguage{ngerman}± 102\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
904 \selectlanguage{ngerman}± 127\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\emph{near Park City, Utah}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
11\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{894 ± 135}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{894 ± 135}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{894 ± 135}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{1028 ± 102}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{1028 ± 102}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{1028 ± 102}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{904 ± 127}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{904 ± 127}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{Colorado Sites}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Mean C stocks\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
768 \selectlanguage{ngerman}± 116\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
763 \selectlanguage{ngerman}± 303\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
419 \selectlanguage{ngerman}± 58\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
313 \selectlanguage{ngerman}± 67\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
403 \selectlanguage{ngerman}± 92\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
645 \selectlanguage{ngerman}± 263\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\emph{South Park, Colorado}\textsuperscript{d}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
No. samples\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
15\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
11\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
11\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{647 ± 91*}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{647 ± 91*}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{647 ± 91*}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{313 ± 67}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{313 ± 67}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{313 ± 67}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{484 ± 106}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{484 ± 106}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textbf{All sites combined}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Combined mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{447 ± 34}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{447 ± 34}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{447 ± 34}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{413 ± 38}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{413 ± 38}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{413 ± 38}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{538 ± 59}\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{538 ± 59}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\textsuperscript{a} Error values are margin of error for a 95\%
confidence interval \textsuperscript{\\
b} Lost Creek and Deep Creek use the same reference reach data from
Gray's Creek. \textsuperscript{\\
c} East Canyon Creek and Kimball Creek use the same reference reach data
from McLeod Creek. \textsuperscript{d} Sites in Colorado were collected
on different streams farther away from each other than typical datasets.
Degraded Reach 1 is on the Middle Fork South Platte River, Degraded
Reach 2 is on Sheep Creek, and Degraded Reach 3 is on South Fork South
Platte River. Treatment Reach 1 is on Salt Creek, and Reference Reach 1
is on Rough and Tumbling Creek. *Three reference and one degraded
floodplain are higher than the other two categories at the 95\%
confidence level.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\textbf{Table 3.} Ranked categories of floodplains & \textbf{Table 3.}
Ranked categories of floodplains & &\tabularnewline
\midrule
\endhead
Site & Degraded Stocks & Treatment Stocks & Reference
Stocks\tabularnewline
Fivemile Bell & intermediate & lowest & highest*\tabularnewline
Staley Creek & lowest & highest & intermediate\tabularnewline
South Fork McKenzie River & lowest & highest &
intermediate\tabularnewline
Whychus Creek & lowest & intermediate & highest*\tabularnewline
Lost Creek & lowest & intermediate & highest\tabularnewline
Deep Creek & intermediate & highest & lowest\tabularnewline
East Canyon Creek & intermediate & lowest & highest*\tabularnewline
Kimball Creek & lowest & highest & intermediate\tabularnewline
Colorado Sites & highest* & lowest & intermediate\tabularnewline
indicates significance at the 95\% confidence level & * indicates
significance at the 95\% confidence level & * indicates significance at
the 95\% confidence level & * indicates significance at the 95\%
confidence level\tabularnewline
\bottomrule
\end{longtable}

\emph{4.2 Modeled treatment stocks}

When treatment stocks were estimated with a degraded model fitted to
each site, the four sites of Staley Creek, South Fork McKenzie River,
Whychus Creek, and Kimball Creek showed higher measured than predicted
treatment stocks at the 95\% confidence level (Figure 2). Three sites
had lower than predicted stocks, and two did not show significant
differences. The estimated differences between measured and predicted
treatment stocks for sites where measured stocks exceeded predicted
stocks are 354 Mg/ha, 132 Mg/ha, 56 Mg/ha, and 118 Mg/ha for Staley
Creek, South Fork McKenzie River, Whychus Creek, and Kimball Creek,
respectively (Figure 2).

\emph{4.3 Across-site comparisons}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

When analyzing all sites together, we found the largest magnitude
correlations between carbon stocks and grain size, particularly between
percent silt content (\selectlanguage{greek}ρ\selectlanguage{english}= 0.531, p = 9E-49) and sand content (\selectlanguage{greek}ρ\selectlanguage{english}= -0.524,
p = 2E-47) with positive and negative correlations, respectively (Table
4). Correlations between organic carbon stocks and location data,
climate data, and elevation are weak (\textless{}0.3) but significant
and suggest that carbon stocks are somewhat higher in the high elevation
mountain ranges in the interior of the continent that have cooler
climates.

Table 4. Correlations between organic carbon stock and numeric
variables. All correlations are significant at the 95\% confidence
level.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\textbf{Variable} & \textbf{Pearson Correlation with Carbon Stock} &
\textbf{p-value}\tabularnewline
\% Silt & 0.531 & 9.2E-49\tabularnewline
\% Sand & -0.524 & 2.4E-47\tabularnewline
\% Clay & 0.298 & 7.0E-15\tabularnewline
Depth & -0.292 & 2.6E-14\tabularnewline
x (longitude) & 0.284 & 1.4E-13\tabularnewline
elevation & 0.279 & 3.8E-13\tabularnewline
y (latitude) & -0.275 & 7.9E-13\tabularnewline
Mean annual temperature & -0.244 & 2.8E-10\tabularnewline
Drainage area & -0.217 & 2.1E-08\tabularnewline
Mean annual precipitation & -0.204 & 1.4E-07\tabularnewline
NDVI & 0.124 & 1.5E-03\tabularnewline
\bottomrule
\end{longtable}

The Wasatch and Uinta Ecoregion, represented by samples collected in
Utah, had significantly higher carbon stocks than all other ecoregions
(p [?] 0.0016 for all pairwise comparisons). Within ecoregions, reference
stocks are highest in the Coast Range, Blue Mountains and Wasatch and
Uinta regions.

Combining all samples from all sites revealed significantly higher
reference carbon stocks than degraded and treatment, and no significant
difference between degraded and treatment (Figure 4). This result was
the same for a simple comparison of the three treatment categories and a
model comparison that accounted for moisture, site, sample location, and
depth.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\emph{4.4 Regional modeling}

We modeled data from all locations combined using a linear mixed model,
a random forest model, and a gradient boosted regression model (Figure
5). Because Colorado site categories (degraded, treatment, reference)
are not along similar streams like the other site datasets, we excluded
Colorado from the model comparison. With the remaining data, we included
80\% of the dataset in all three models and reserved 20\% of the dataset
for model evaluation. We compared the models with the root mean square
error and coefficient of determination (R\textsuperscript{2}) between
the measured and predicted data. The random forest model had the lowest
root mean square error (RMSE) of the 3 models at 1.26 \% OC and the
highest R\textsuperscript{2} of 0.68. All models tended to overestimate
degraded and reference carbon content of the dataset. Model descriptions
and results are shown in Table 5.

Table 5. Model predictors, results, and errors from linear mixed, random
forest, and boosted regression models built to predict \% organic carbon
in randomly selected 20\% proportion of the total data.\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Model & Predictor Variables & \% OC Estimates & \% OC Estimates & \% OC
Estimates & RMSE & R\textsuperscript{2}, modeled vs measured
data\tabularnewline
& & Deg & Treat & Ref & &\tabularnewline
Measured Data & NA & 3.09 & 2.83 & 3.93 & NA & NA\tabularnewline
Linear Mixed Model & Site, reach sample hole, depth, mean annual
temperature, NDVI, silt+clay, soil type & 3.19 & 2.78 & 4.26 & 1.33 &
0.64\tabularnewline
Random Forest Model & treatment, depth, texture, elevation, NDVI, mean
annual temperature, drainage area, land cover class, geology, ecoregion,
silt+clay, vegetation & 3.36 & 2.93 & 4.01 & 1.26 & 0.68\tabularnewline
Boosted Regression Model & treatment, depth, texture, elevation, NDVI,
mean annual temperature, drainage area, land cover class, geology,
ecoregion, silt+clay, vegetation & 3.30 & 2.73 & 4.10 & 1.36 &
0.62\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

In summary, the results presented here provide partial support for the
original hypothesis in that reference sites generally have the highest
values of floodplain soil organic carbon stock. The strongest predictors
of floodplain soil carbon stock are percent silt content and climate,
with the greatest stock in relatively cool, wet climates.

\textbf{5. Discussion}

The sites selected for soil sampling represent a geographic range of
elevation, climate, and lithology for the western United States. The
values of floodplain SOC at these degraded, treatment, and reference
sites fall within the most common range (100-1000 Mg C/ha; Sutfin et
al., 2016) of published values for floodplain SOC in temperate-latitude
rivers. Our primary objective was to determine whether there are
detectable differences in floodplain carbon stock between the
categorized floodplain states of degraded, treatment, and reference, and
to assess the carbon sequestration potential of stream restoration
within the context of these simple categories. A secondary objective was
to examine factors that influence floodplain SOC stock at a larger,
regional scale across the western United States.

\emph{5.1 Within-site comparisons}

Degraded floodplains have the lowest carbon stocks in the majority of
sites, which supports the hypothesis although the results are not
statistically significant. Among sites with complete datasets, treatment
and reference were tied for having the highest carbon stocks, but the
reference category has more statistically significantly higher stocks
than the treatment category.

Deep Creek is the only site where reference soil carbon stocks are lower
than both treatment and degraded stocks. The reference site chosen for
Deep Creek was Gray's Creek, a beaver meadow about 15 km away from Deep
Creek. Gray's Creek and Deep Creek are within the North Fork Crooked
River watershed, but the two sites are underlain by different geology.
Gray's Creek lies within Eocene- to Oligocene-aged volcaniclastic tuff
in the John Day Formation, while Deep Creek overlies the Columbia River
Basalt formation of Miocene age. Basalt weathers to clay minerals, while
tuff contains higher silica content and is more resistant to weathering
than basalt. In our dataset, floodplain soils underlain by basalt
bedrock geology contained a higher proportion of silt and clay. The
results from correlation of numerical predictor variables show that
grain size has the largest magnitude of negative correlation to carbon
stock, indicating that silt and clay content are significant
contributors to carbon stock, as demonstrated in previous work (e.g.,
Cai et al., 2016). Gray's Creek also has a smaller drainage area than
Deep Creek, with 42 km\textsuperscript{2} and 224 km\textsuperscript{2},
respectively. Deep Creek hosts large ponderosa pine (\emph{Pinus
ponderosa)} trees and is classified as evergreen forest in the National
Land Cover Dataset (Homer et al., 2012), while Gray's Creek is
classified as emergent vegetation and contains no large trees other than
willows. Gray's Creek is also the reference site chosen for Lost Creek.
Lost Creek is within the same geological formation as Gray's Creek and
trends from least to greatest mean carbon stocks in degraded, treatment,
and reference sites. In hindsight, a different reference condition
should have been chosen for Deep Creek but this oversight indicates the
importance of considering the underlying geology when associating
categories of floodplain.

High variance of soil carbon stocks from our samples reflects relatively
low sample sizes per floodplain category at each site, but also aligns
with the variable nature of soil organic carbon accumulation over time.
Floodplains are highly dynamic ecosystems that undergo frequent
disturbance and include multiple stages of vegetative succession and
soil development. Floodplain heterogeneity enhances diversity of
habitats for aquatic and terrestrial species, and in turn supports more
biodiverse and resilient floodplains (Wohl, 2016). Increased
heterogeneity and river mobility within the floodplain are desirable
goals for many restoration projects, but multiple sequences of
disturbance and succession induced by frequent lateral channel migration
can also lead to a variety of patches with different soil carbon
concentrations and stocks (Lininger et al., 2018; Sutfin et al., 2021).

\emph{5.2 Modeled treatment stocks}

Predicted treatment stocks were lower than measured treatment stocks in
four sites when models using degraded category data were used to
estimate SOC stocks in treatment floodplains. Models made separately for
each site are intended to minimize variability in climate, geology, and
soil formation processes. The input of degraded data to make these
models utilizes the assumption that treatment sites were similar to
degraded sites before restoration took place. To truly test this
concept, a before-after-control-impact study design is appropriate. In
our data, magnitudes of differences in carbon stocks in treated versus
degraded, divided by the number of years since restoration, suggest
carbon sequestration rates that seem unrealistically high. If the
difference between measured and predicted carbon stocks serves as an
estimate of carbon sequestered since treatment, under the assumption
that pre-restoration conditions are well represented by degraded sites,
the magnitude of carbon stored since restoration in Staley Creek, South
Fork McKenzie River, Whychus Creek, and Kimball Creek is 354 Mg
ha\textsuperscript{-1}, 132 Mg ha\textsuperscript{-1}, 56 Mg
ha\textsuperscript{-1}, and 118 Mg ha\textsuperscript{-1}, respectively.
These four sites also contained higher treatment stocks than degraded
stocks. Divided by the number of years since restoration, the per-year
carbon sequestration approximations for the four sites are 118 Mg
ha\textsuperscript{-1} year\textsuperscript{-1} for Staley Creek, 66 Mg
ha\textsuperscript{-1} year\textsuperscript{-1} for South Fork McKenzie,
14 Mg ha\textsuperscript{-1} year\textsuperscript{-1} for Whychus Creek,
and 59 Mg ha\textsuperscript{-1} year\textsuperscript{-1} for Kimball
Creek. Table 3 in Sutfin et al. (2016) lists accumulation rates ranging
from 0.03-8 Mg C ha\textsuperscript{-1} year \textsuperscript{-1}, which
is an order of magnitude lower than the estimated differences from this
study. We cannot accurately estimate carbon accumulation rates in the
sites for this study because there are no measurements of antecedent
conditions, but the substantial difference between our inferred rates
and the range of published rates for diverse environments around the
world suggests that our inferred rates are too high. Thus, we infer that
the sites with measured treatment stocks that were higher than degraded
stocks, or higher than modeled treatment stocks, likely contained more
carbon than degraded floodplains before treatment, facilitated by
historic conditions prior to degradation that likely factored into the
choice to select the area for stream restoration. Laurel and Wohl
(2019), for example, demonstrated that relatively high soil organic
carbon stocks can persist in beaver-modified floodplains even after
beavers abandon a site and the floodplain becomes drier.

In future studies, it would be beneficial to consider time since
degradation, specific manner of degradation, and further information
about historic conditions prior to degradation when comparing the
categories of degraded, treatment, and reference. Although floodplains
such as South Fork McKenzie River and Staley Creek underwent large scale
regrading of the floodplain as part of restoration, it is promising that
their soil carbon stocks were not destroyed by the disturbance within
the organic-rich upper layer. Instead, these sites retained their
existing carbon stocks and/or sequestered carbon since treatment. For
purposes other than research, such as carbon offset verification, we
recommend that direct comparisons to estimate magnitude of carbon stored
since restoration be made on repeat pre-post data rather than assuming
degraded conditions can directly reflect pre-treatment conditions.

\emph{5.3} \emph{Across-site comparisons}

Two Colorado floodplains and all Utah sites show significant carbon
stocks compared to other regions. This is likely explained by high
elevation and low mean annual temperature compared to other areas. It is
pertinent to consider mountain valleys of the interior western USA as
zones of high potential carbon stock. Floodplain drainage, development
for agriculture, and associated degradation of wide, wet valley bottoms
with potential for high carbon stock (i.e., beaver meadow complexes and
other wetlands) could have disproportionately high impacts on carbon
sequestration (Wohl et al., 2018). Considering that US states such as
Colorado likely have lower total budgets for stream restoration compared
to states in the Pacific Northwest that are greatly driven by funding
from fisheries conservation, carbon sequestration can serve as an
additional added benefit and enhanced return on investment in stream
restoration within the Intermountain West.

Both sites within the Cascades ecoregion, Staley Creek and South Fork
McKenzie River, contained higher carbon stocks at treatment sites than
at degraded or reference sites. Because the data in this study do not
directly compare pre-and post-restoration stocks, our ability to
quantify carbon sequestered directly as a result of restoration is
limited. However, both projects in this region utilized similar methods
of stream restoration, in which the valley bottom was regraded to fill
incised channels and to lower high-elevation surfaces, and large wood
was laid across the valley bottom to maintain hydraulic roughness as
vegetation reestablishes. In both cases, surface water was spread across
the valley bottom, and field observations of declining upland species
and early succession wetland vegetation suggest water tables were
raised. Whether observed increases in soil carbon stock took place at
each site or persisted from former valley conditions, the manner of
restoration sampled in this ecoregion facilitated the development of
river corridors with processes and planforms that support carbon
sequestration. In addition, carbon stocks in the form of large wood were
greatly increased at both sites via the project designs.

The most influential factors contributing to carbon stock are climate
and geology, as outlined in the conceptual framework for floodplain
carbon stock in Hinshaw and Wohl (2021) and further illuminated by
correlations between this dataset and environmental variables.
Correlations between grain size, temperature, and elevation support
patterns of carbon stocks described in existing literature (Wang et al.,
2013; Cai et al., 2016; Qi et al., 2016). Generally, SOC stock increases
with (i) elevation and associated climate trends toward cooler
temperatures in all study areas and (ii) higher proportion of silt and
clay. Geographically, SOC stock increases toward the center of the
continent. Potential SOC stock depends primarily on intermediate to long
term processes such as soil formation from weathering of underlying
lithology and gradual organic matter input from vegetation, but local
hydrologic and geomorphic conditions, especially those influenced by
floodplain restoration, can set the stage for soil carbon emissions
versus soil carbon sequestration. Elevated concentrations of SOC can
persist for decades after degradation or drying (Laurel and Wohl, 2019),
but rather than optimizing carbon stock potential, dry, degraded
floodplains gradually decrease in SOC capacity over time (Ferre et al.,
2014; Hanberry et al., 2015; Limpert et al., 2020; Lininger and Polvi,
2020).

\emph{5.4 Regional modeling}

Given that methods to verify carbon offsets commonly rely on models and
encounter substantial uncertainty (Smith et al., 2020), the three models
that we used estimated floodplain carbon stock exhibited reasonable
performance. Of the three models, the Random Forest model performed the
best. Although the linear mixed model results aligned well with the
measured carbon and the other model results, this model relies on
information about the specific sites to account for the study design and
therefore would be more laborious to use in a predictive setting in
contrast to the estimation setting used here to evaluate the models. In
general, our goal was to create a model that uses climate and landscape
variables that are easily obtainable, such as remote sensing data, to
generate a first-order estimate of carbon stock. Remote indices exist
that can be used to estimate carbon stock (e.g., Angelopoulou et al.,
2019) but are commonly developed on barren or agricultural soils that do
not contain the same level of complexity as river corridors. Future
steps for the application of these models would be to test or
incorporate validation data from outside of our study areas.

\textbf{6 Conclusions}

Our study design was constrained by the difficulty of finding exact
environmental matches when substituting space for time in comparing
reference, treatment, and degraded reaches, and by the short time since
restoration was completed at the study sites. However, the results show
that floodplains in reference conditions tend to contain higher carbon
stocks, and therefore river restoration offers an opportunity to
sequester more carbon. An important consideration is that the continuum
of degraded, treatment, and reference alternative states is not linear,
and does not always follow the assumed temporal order of degraded,
treatment, and reference. Disturbance associated with stream restoration
construction can reset floodplain SOC stock in treatment sites to lower
values than carbon stock of degraded conditions, or the disturbance may
not affect persistent carbon stocks with the floodplain chosen for
restoration. Uncertainties regarding the potential for persistent
floodplain SOC stocks that remain from conditions prior to restoration,
along with the challenges of substituting space for time in a complex
natural system with multiple interacting variables, strongly indicate
that the effects of river restoration on floodplain SOC stocks can be
most accurately assessed by (i) measuring stocks prior to restoration
and repeating these measurements over a period of years following
restoration and (ii) conducting analogous measurements on an adjacent
portion of the river corridor not undergoing restoration or on carefully
chosen degraded and reference sites.

The current estimated fluxes of carbon into and out of
floodplain-wetland corridors show carbon release through methane
emissions from wetlands (e.g., Saarnio et al., 2009), carbon dioxide
emissions to the atmosphere (Butman and Raymond, 2011), and export of
carbon out of floodplains via dissolved carbon in water (e.g., Whitworth
et al., 2014) and transport of large wood (Benda and Sias, 2003). The
magnitude of carbon sequestration versus carbon transport within
individual river corridors or on regional to global scales remains
poorly constrained (Hilton and West, 2020), but the potential for net
carbon sequestration in river corridors is likely to be notable in the
context of climate change.

Political and economic pressure to reduce carbon emissions and develop
additional ways to measure and store carbon is likely to increase (e.g.,
Lindstad and B\selectlanguage{ngerman}ø, 2018). Carbon offsets within the carbon market
currently fall into two categories: emission reduction (e.g., Sinha and
Chaturvedi, 2019) and carbon sequestration (e.g., Lal, 2007). We suggest
that stream restoration can offer both. By revitalizing hydrologic
conditions that limit the decomposition and extend the residence time of
soil organic carbon, stream restoration involving hydrologic
reconnection prevents gradual or rapid loss of carbon that is stored in
soil and released during floodplain degradation. By enhancing organic
matter input from regenerated riparian vegetation and creating
conditions for fine sediment deposition, the potential for new carbon
sequestration increases.

Despite the variations in floodplain SOC stock relative to potential
restoration effects in the data analyzed here, restoration has the
potential to enhance organic carbon sequestration and stocks by
enhancing floodplain water tables, deposition, and wetland formation.
This study shows that reference carbon stocks in anastomosing grassed
wetlands and anastomosing wet woodlands are generally higher than
degraded and treatment stocks within the same regions, giving the
restoration community something to work toward as we strive for
resilient, functioning floodplains and creative solutions to climate
change.

\textbf{Acknowledgements}

We would like to thank our funders for this project including Patagonia,
Sageland Collaborative, and Colorado Open Lands. We also thank many who
helped with fieldwork and site access, including Mark Beardsley and
Jessica Doran of EcoMetrics Colorado, Paul Powers, Juli Scamardo, Anna
Marshall, John Kemper, Taylor Kenyon, Emily Iskin, Deschutes Land Trust,
and Kate Meyer.

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