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\begin{document}

\title{Logjam Characteristics as Drivers of Transient Storage in Headwater
Streams}



\author[1]{Anna Marshall}%
\author[2]{Xiaolang Zhang}%
\author[2]{Audrey Hucks Sawyer}%
\author[1]{Ellen Wohl}%
\author[3]{Kamini Singha}%
\affil[1]{Colorado State University}%
\affil[2]{Ohio State University}%
\affil[3]{Colorado School of Mines}%


\vspace{-1em}



  
  \date{June 08, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
Logjams in a stream create backwater conditions and locally force water
to flow through the streambed, creating zones of transient storage
within the surface and subsurface of a stream. We investigate the
relative importance of logjam distribution density, logjam permeability,
and discharge on transient storage in a simplified experimental channel.
We use physical flume experiments in which we inject a salt tracer,
monitor fluid conductivity breakthrough curves in surface water, and use
breakthrough-curve skew to characterize transient storage. We then
develop numerical models in HydroGeoSphere to reveal flow paths through
the subsurface (or hyporheic zone) that contribute to some of the
longest transient-storage timescales. In both the flume and numerical
model, we observe an increase in backwater and hyporheic exchange at
logjams. Observed complexities in transient storage behavior may depend
largely on surface water flow in the backwater zone. As expected,
multiple successive logjams provide more pervasive hyporheic exchange by
distributing the head drop at each jam, leading to distributed but
shallow flow paths. Decreasing the permeability of a logjam or
increasing the discharge both facilitate more surface water storage and
elevate the surface water level upstream of a logjam, thus increasing
hyporheic exchange. Multiple logjams with low permeability result in the
greatest magnitude of transient storage, suggesting that this
configuration maximizes solute retention in backwater zones, while
hyporheic exchange rates also increase. Understanding how logjam
characteristics affect solute transport through both the channel and
hyporheic zone has important management implications for rivers in
forested, or historically forested, environments.%
\end{abstract}%



\sloppy


\textbf{Logjam Characteristics as Drivers of Transient Storage in
Headwater Streams}

A. Marshall\textsuperscript{1}, X. Zhang\textsuperscript{2}, A.H.
Sawyer\textsuperscript{2}, E. Wohl\textsuperscript{1}, and K.
Singha\textsuperscript{3}

\textsuperscript{1}Department of Geosciences, Colorado State University,
Fort Collins, CO, USA

\textsuperscript{2}School of Earth Sciences, The Ohio State University,
Columbus, OH, USA

\textsuperscript{3}Colorado School of Mines, Hydrologic Science and
Engineering Program, Golden, CO, USA

Corresponding author: Anna Marshall (amarsh01@colostate.edu)

Key Points:

\begin{itemize}
\tightlist
\item
  Transient storage is maximal when there are many jams (large
  longitudinal distribution density) with low permeability (tightly
  packed jam).
\item
  Solute breakthrough in the flume is more sensitive to surface flow
  paths than subsurface flow paths, suggesting much of the observed
  transient storage occurs in backwater zones behind jams.
\item
  Configurations with greater transient storage also have the greatest
  rates of hyporheic exchange and longest residence times in the
  subsurface.
\end{itemize}

Abstract

Logjams in a stream create backwater conditions and locally force water
to flow through the streambed, creating zones of transient storage
within the surface and subsurface of a stream. We investigate the
relative importance of logjam distribution density, logjam permeability,
and discharge on transient storage in a simplified experimental channel.
We use physical flume experiments in which we inject a salt tracer,
monitor fluid conductivity breakthrough curves in surface water, and use
breakthrough-curve skew to characterize transient storage. We then
develop numerical models in HydroGeoSphere to reveal flow paths through
the subsurface (or hyporheic zone) that contribute to some of the
longest transient-storage timescales. In both the flume and numerical
model, we observe an increase in backwater and hyporheic exchange at
logjams. Observed complexities in transient storage behavior may depend
largely on surface water flow in the backwater zone. As expected,
multiple successive logjams provide more pervasive hyporheic exchange by
distributing the head drop at each jam, leading to distributed but
shallow flow paths. Decreasing the permeability of a logjam or
increasing the discharge both facilitate more surface water storage and
elevate the surface water level upstream of a logjam, thus increasing
hyporheic exchange. Multiple logjams with low permeability result in the
greatest magnitude of transient storage, suggesting that this
configuration maximizes solute retention in backwater zones, while
hyporheic exchange rates also increase. Understanding how logjam
characteristics affect solute transport through both the channel and
hyporheic zone has important management implications for rivers in
forested, or historically forested, environments.

1 Introduction

Spatial heterogeneity in flow paths within a river corridor drives
stream solute exchange between mobile areas of the channel and
relatively immobile transient storage zones. Transient storage can be
generally segregated into surface transient storage---where water flows
slowly through recirculation zones and stagnant areas of low
velocity---and subsurface transient storage (controlled in part by
hyporheic exchange---where stream water flows through the subsurface and
returns to the channel). Transient storage has numerous benefits to
river corridor ecosystem services and processes including i) increased
biogeochemical cycling (Fischer et al., 2005; Battin et al., 2008;
Tonina \& Buffington, 2009; Harvey \& Gooseff, 2015; Marttila et al.,
2018); ii) nutrient and pollutant processing (Harvey \& Wagnert, 2000;
Hall et al., 2002; Ensign \& Doyle, 2005; Stewart et al., 2011); iii)
increased habitat diversity and thermal refugia (Mulholland et al.,
2004; Hester \& Gooseff, 2010); and iv) flow attenuation (Herzog et al.,
2018). Transient storage can be increased by morphologic and geologic
features that create spatial heterogeneity in water velocity and drive
alternate patterns of downwelling and upwelling along the bed. Examples
of such features include bedforms and other variations in channel
cross-sectional geometry (Bencala, 1983; Harvey \& Bencala, 1993;
Kasahara \& Wondzell, 2003; Ensign \& Doyle, 2005; Gooseff et al.,
2007), logjams (Hester \& Doyle, 2008; Sawyer et al., 2011; Marttila et
al., 2018; Ader et al., 2021), and variations in alluvial thickness and
grain-size distribution (Harvey et al., 1996). Here, we focus on the
effects of logjams as an important morphologic element that creates both
surface transient storage in the channel (for example, backwater zones)
and subsurface transient storage in porous media (for example, hyporheic
exchange).

Logjams directly enhance transient storage in a number of ways. Logjams
obstruct flow and increase hydraulic resistance within the channel, thus
creating hydraulic head gradients that drive hyporheic exchange. Logjams
directly influence surface transient storage by creating low-velocity
zones within the channel (Gippel, 1995); enhancing the formation of
backwater pools (Richmond \& Fausch, 1995; Kaufmann \& Faustini, 2012;
Beckman \& Wohl, 2014; Livers \& Wohl, 2016); creating scour pools that
enhance residual pool volume (Fausch \& Northcote, 1992; Ensign \&
Doyle, 2005; Mao et al., 2008); and creating marginal eddies (Zhang et
al., 2019).

Logjams also indirectly affect surface and subsurface transient storage
by increasing the erosion and deposition of sediment (Wohl \& Scott,
2017). Logjams locally enhance entrainment of bed material and erosion
of the channel bed and banks (Buffington et al., 2002). Studies of the
effects of logjams on floodplain-sediment dynamics emphasize how the
obstructions created by logjams can result in changes in bedforms via
overbank flows and vertical accretion or bank erosion, channel avulsion,
and formation of secondary channels (e.g., Sear et al., 2010; Wohl \&
Scott, 2017).~Logjams commonly create high spatial variability in
average bed grain size and alluvial thickness upstream and downstream of
a jam (Massong \& Montgomery, 2000). Advective pumping, induced by
streamflow over a spatially heterogeneous and permeable bed, leads to a
distribution of pore-water flow paths in the streambed (W\selectlanguage{ngerman}örman et al.,
2002), which in turn enhances the magnitude of subsurface transient
storage via hyporheic exchange (Lautz et al., 2006; Hester \& Doyle,
2008; Fanelli \& Lautz, 2008; Sawyer et al., 2011; Sawyer \& Cardenas,
2012).

As might be expected, previous work indicates that greater roughness
(e.g., Harvey et al., 2003) and spatial heterogeneity within a channel
(e.g., Gooseff et al., 2007) equate to greater potential for transient
storage. A growing body of research describes wood as a driver of
channel spatial heterogeneity (e.g., Buffington \& Montgomery, 1999;
Collins et al., 2012; Faustini \& Jones, 2003) and as a driver of
transient storage (e.g., Mutz et al., 2007; Sawyer et al., 2011; Sawyer
\& Cardenas, 2012; Kaufmann \& Faustini, 2012; Doughty et al. 2020; Ader
et al., 2021; Wilhelmsen et al., 2021). Recent work used bulk electrical
conductivity (Doughty et al., 2020) and fluid electrical conductivity
(Ader et al., 2021) to examine surface and subsurface transient storage
in a small stream with and without the presence of logjams and found
that the direct presence of wood increases transient storage and does so
at a greater magnitude than other geomorphic variables, such as bedform
dimensions. Wilhelmsen et al. (2021) combined flume experiments with a
numerical model to analyze the effects of jam complexity, in combination
with channel planform complexity, on the hyporheic flow regime of small
streams. Their numerical simulations suggest that logjams decrease the
turnover length that stream water travels before interacting with the
hyporheic zone by an order of magnitude and that the broadest range of
hyporheic residence times arise where logjams and multiple channel
threads co-occur. While these field and modeling studies have shaped our
understanding of transient storage around logjams and channel
morphologies of varying complexities, an opportunity exists to test the
effects of logjam characteristics on transient storage patterns. No
study, to our knowledge, has used empirical data to comparatively
examine transient storage in a stream as the number of logjams increases
(e.g., distribution density) nor have any addressed how the structure of
jams (e.g., permeability) influences transient storage.

These characteristics of logjams are important to understand because in
natural settings, jams vary in size, shape, and permeability depending
on the abundance and composition of large wood and coarse particulate
organic matter (see terminology in Table 1). Quantifying logjam
characteristics in the field has proved challenging (Manners et al.
2007, Livers et al., 2020) and physical and numerical modeling
approaches are commonly used to further constrain field variables.
Recent work explores the influence of jam sorting and organizational
structure on logjam permeability (Spreitzer et al., 2019) and resulting
hydraulic impacts (Schalko et al., 2018; Ismail et al, 2020; Follett et
al., 2021). A small number of physical modeling studies have relied on
natural wood to study hydraulics and geomorphology (e.g., Beebe 2000;
Mutz et al., 2007; Schalko 2020; Schalko \& Weitbrecht, 2021; Spreitzer
et al., 2021), but none have used natural wood to examine logjam
accumulation characteristics (Friedrich et al., 2022). Knowledge of how
logjam characteristics influence hydrologic function is pertinent to
river management as wood is increasingly used to restore a more natural
hydrologic function to rivers (Roni et al., 2014; Grabowski et al.,
2019). Limited understanding of how logjam characteristics relate to
specific hydrologic effects constrains our ability to maximize functions
of constructed logjams to promote ecosystem services provided by
transient storage.

Here, we address some of the gaps in understanding the relationship
between logjam characteristics and transient storage at varying
discharges and logjam configurations. Our study objective is to assess
the relative response of transient storage to binary changes in logjam
permeability (high versus low), logjam distribution density (single
versus multiple jams along a given length of channel), and discharge
(high versus low). We achieve this objective through a two-part
approach. We use flume experiments, specifically focusing on measuring
salt breakthrough curves in the channel, to address faster timescales of
transient storage. Because breakthrough curves measured in surface water
often fail to capture some of the longer residence times in the
hyporheic zone (Harvey et al., 1996) and do not reveal spatial
information about flow paths, we also numerically simulated coupled
surface-subsurface flow in flume experiments to resolve longer flow
paths through the subsurface. We treated the jams themselves as an
extension of the porous medium with adjustable permeability. We test
four hypotheses: H1) increasing logjam longitudinal distribution density
enhances transient storage; H2) increasing the permeability of a single
logjam enhances transient storage; H3) a single low-permeability logjam
creates a comparable increase in transient storage to multiple
high-permeability logjams; and H4) transient storage increases at higher
discharge for all scenarios.

\textbf{Table 1.} Wood terminology definitions.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Term & Definition & Reference\tabularnewline
\midrule
\endhead
Large wood & Wood \textgreater{}10 cm in diameter and 1m in length &
Wohl et al., 2010\tabularnewline
Channel-spanning logjam (logjam or jam) & Any accumulation of large wood
within the bankfull channel in which three or more wood pieces are in
contact with one another & Beckman \& Wohl, 2014\tabularnewline
Coarse particulate organic matter & Any organic material that is less
than 1 cm in diameter or is composed of non-woody organic material
(i.e., leaves) & Tank et al., 2010\tabularnewline
Engineered logjam & Constructed logjam used to achieve river restoration
and stabilization target goals. & Abbe et al., 2003\tabularnewline
Longitudinal distribution density & Number of jams per channel length,
defined here as per 50 cm. & Wohl \& Beckman, 2014\tabularnewline
Permeability & Ease with which fluid passes through the logjam,
influenced by connectedness of pore spaces within the logjam & Manners
et al., 2007\tabularnewline
\bottomrule
\end{longtable}

2 Methods

\emph{2.1 Flume configuration}

Flume experiments took place at Colorado State University's Engineering
Research Center using a 9-m long and 1.2-m wide flume with a rectangular
cross section and smooth sidewalls (Figure 1). Flow was delivered to the
flume via pipes and pumps from a reservoir of water. A cobble-filled
baffle dissipated flow energy at the upstream end of the flume and a
reinforced 250-micron mesh screen at the downstream end of the flume
trapped any mobilized sediment. We sized sediment to maintain an
immobile bed and used a gravel subsurface sediment with a pebble
topcoat. A summary of all flume attributes is included as Supplemental
Information.

We used natural wood pieces of varying size to create logjams in the
flume (Figure 1). We ensured a similar wood load per jam by quantifying
the wood volume and number of large wood pieces per each jam. Each
constructed jam was pinned by one large immobile key piece of wood to
avoid jam mobility. To change the permeability of a single jam, we added
coarse particulate organic matter, mainly in the form of leaves, pine
needles, and bark. We also added a plastic impermeable material to the
jam to further reduce its permeability (Figure 1).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1.} Flume configuration (9-m long, 1.2-m wide) for (a)
longitudinal distribution density experiments and (b) permeability
experiments. (a) shows the change in jam quantity from a single jam to
multiple jams. (b) shows the change in permeability for a single logjam
from a more permeable jam to a less permeable jam with coarse
particulate organic matter additions. Data were collected at sensors
above and below the experimental reach. However, we use the ``below
jam(s)'' sensor data for results and analyses because they best
represent the combined effects of logjam distribution density and
permeability changes.

A list of all flume runs is included as Table 2. We implemented tracer
experiments with sodium chloride (NaCl) to characterize surface
transient storage flow paths via fluid conductivity. We added 360-g of
NaCl dissolved in 3.78 L of water to the flume at the injection point
(Figure 1) via a pulse injection. The ability to resolve transient
storage depends in part on the relative travel times through the mobile
portion of the channel and transient storage zones, as well as the
exchange rates between them. Given our expectation of short transport
times (on the order of minutes) in this flume-scale system, we deemed a
pulse injection sufficient to load even some the slower flow paths with
salt. The first 3-m of the flume served as a mixing zone. The
experimental section where jams and fluid conductivity sensors were
placed spanned from 3.0 to 7.5 m (Figure 1). No jams or sensors were
placed in the last 1.5-m of the flume (from 7.5 to 9.0 m) to minimize
interference from backwater effects near the sediment screen. We
measured specific conductivity at 10-s intervals during the tracer tests
using Onset Computing HOBO U-24 fluid electrical conductivity loggers
(data loggers). Data loggers recorded fluid conductivity measurements
for 30 minutes following the pulse to allow ample time for the flume to
return to background solute concentrations. Sensor placement was uniform
across all flume trials. We deployed one data logger upstream of the
NaCl injection point to measure background fluid conductivity, and two
data loggers 0.3-m upstream and downstream of the logjam(s) in the
monitoring reach, at 3 m and 7.5 m from the top of the flume (Figure 1).
We only report data from the downstream sensor for clarity as it
represents both the above and below logjam effects. The upstream sensor
data are included in the Supplemental Information. The measured instream
conductivity signals represent the combined effects of surface transient
storage in the channel (e.g., backwaters, eddies) and subsurface
transient storage via hyporheic exchange.

We set high and low discharge values that ranged over a factor of 10
(0.001 m\textsuperscript{3}/s and 0.01 m\textsuperscript{3}/s). Initial
test runs suggested that tracer was flushed too quickly to measure with
accuracy above 0.01 m\textsuperscript{3}/s. Discharge readings were
obtained from a flow meter with \selectlanguage{ngerman}±0.2\% accuracy. Discharge for all flume
runs was fully turbulent, allowing relaxation of Reynolds number scaling
(Peakall et al., 1996). We ran replicates for all flume trials. A
digital elevation model for the flume was constructed using structure
from motion. Images were captured at regular downstream intervals with a
camera mounted at a consistent elevation and we used ground-control
points along the flume bed for additional adjustment. Images were
processed using Agisoft Metashape Professional. The resulting digital
elevation model had a resolution of less than 1~mm.

\emph{2.2 Flume Data Analysis}

Tracer tests are commonly interpreted for transient storage residence
times using solute breakthrough curves from stream sensors (e.g.,~Wörman
et al., 2002,~Anderson et al., 2005,~Lautz et al., 2006,~Wondzell,
2006,~Tonina and Buffington, 2007). We plotted in-stream fluid
conductivity data against time as breakthrough curves for each flume
run. To examine differences in breakthrough curves across discharge and
logjam characteristics, we analyzed the following information based on
the temporal moments of breakthrough curves: mass, mean arrival time,
variance, and skew (Harvey \& Gorelick, 1995; Gupta \& Cvetkovic, 2000).
The mean arrival time of the injected tracer at the point of observation
is commonly used to describe advection patterns; variance is used to
describe dispersion and diffusion characteristics. The statistical
moment of skewness represents the asymmetry of the breakthrough curve
based on solute retention and can be used as a proxy for the amount of
transient storage (Nordin \& Troutman, 1980). We interpret skewness here
as an indicator of transient storage in both the channel and in
underlying aquifer materials (e.g., Lees et al., 2000; Doughty et al.,
2020), though it is likely most sensitive to the shortest timescales of
transient storage in the channel (Harvey et al., 1996). Higher values of
skew indicate more tailing behavior exhibited in the breakthrough curve,
and therefore, more transient storage. We calculated all temporal
moments in Matlab (MATLAB, 2020). A full calculation of the temporal
moments is included in the Supplemental Information; here, we focus our
analysis on mean arrival time and skew. The former reveals changes in
travel times through the mobile zone in the channel, and the latter
reveals changes in the interaction of mobile zones with transient
storage zones. Flume run times were truncated to include one minute of
background data prior to the pulse NaCl injection and a total time of 30
minutes to provide comparable skew values between runs. Fluid
conductivity readings in the flume return to background levels in under
10 minutes, so truncation does not affect estimates of tailing in the
breakthrough curves.

Statistical analyses were performed in R Studio (R Core Team, 2020). We
statistically assessed how dependent variables (skew and mean arrival
time) changed with independent variables describing logjam
characteristics and discharge. The independent variables were the number
of logjams (single or multiple), discharge (high or low), and
permeability (high or low). We fit multiple two-way ANOVA models based
on our hypotheses (Supplemental Table 3). Tukey adjusted pairwise
comparisons were calculated using~\emph{emmeans} ~R package
(Lenth,~2020). A significance level alpha of 0.05 was used in all
statistical analyses.

\emph{2.3 Numerical Modeling}

We numerically simulated all flume runs in HydroGeoSphere to visualize
longer duration flow paths moving through the subsurface (Aquanty Inc.
2015; Brunner \& Simmons, 2012). The model domain mirrors our flume
dimensions of 1.2 m wide, 9.0 m long, and 0.1 m deep. We defined the
base and sides of the model as no-flow boundaries to represent the
bottom and sides of the flume environment. At the upstream boundary of
the flume domain, a specified inflow flux was assigned to simulate the
stepped spillway. At the downstream outlet, a critical depth boundary
condition was given to match flume observations.

The HydroGeoSphere model solves wave approximations of the Saint Venant
equation for surface flow, the Richards equation for subsurface flow,
and the advection-dispersion-diffusion equation for groundwater age. The
surface flow equation is solved on a 2-D finite-element mesh stacked
upon the subsurface grid. The surface of the model domain was
discretized with an unstructured, triangular mesh with maximum element
length of 2.0~cm. For comparison, the grain diameter of flume sediments
ranges up to 17 mm, therefore choosing a finer mesh would have been
inconsistent with the concept of a porous continuum. The subsurface
domain of our model is discretized into ten vertical layers. The three
near-surface sediment layers represent the gravel and coarse sand top
coat layer of the flume and are assigned element heights of 0.005 m and
hydraulic conductivity of 2.5×10\textsuperscript{-3} m/s. The deeper
seven mesh layers represent the underlying coarse sand layer and are
assigned an element height of 0.028~m and hydraulic conductivity of
8.9×10\textsuperscript{-5} m/s. Sediment hydraulic properties are
consistent with Wilhelmsen et al. (2021) (Table 3). Logjams were
simulated as a porous medium with varying permeability (Table 3) to test
the effect of this parameter on hyporheic flow and subsurface transient
storage. The hydraulic conductivity of the more permeable logjam(s) is 1
m/s, while the value for less permeable logjam(s) is 0.5 m/s. It is
important to note that because we treat the jams as a porous medium, we
also chose to include flow paths through the jams as part of
``subsurface'' transient storage.

For each simulation in HydroGeoSphere, we visualized subsurface flow
paths in Tecplot. We also visualized groundwater age throughout the
subsurface, which was computed using the groundwater age mass-transport
equation embedded in HydroGeosphere. Groundwater age is similar in
concept to a residence time and includes the effects of both advection
and dispersion (Therrien et al. 2006). We calculated this age only for
visualization purposes, as it could not be used to construct residence
time distributions because of the zero-age boundary condition at the
bottom of the water column. To compute residence time distributions in
the subsurface, we released particles at the water-sediment or water-jam
interface and analyzed the flux-weighted residence times of the
9000-18000 particles that returned to the surface water. From the
flux-weighted residence time distribution, we calculated the mean travel
time in the subsurface and the skew. It is important to note that the
model-derived mean travel time in the subsurface is not directly
comparable with the flume-derived mean travel time, as the former only
considers travel due to advection in the subsurface, while the latter
considers salt transport due to advection and dispersion in the surface
and subsurface. We report both values, as both represent different
aspects of solute travel through the interconnected stream-groundwater
system. Similarly, skew in the model-derived hyporheic residence time
distribution is not directly comparable with skew in the salt
breakthrough curve. We report both values to quantify the weighting of
longer solute residence times (in one case, for the entire flume system,
and in the other case, for the hyporheic zone specifically). We also
calculated average hyporheic fluxes for each simulation. Model
parameters are included in Table 3 and more on the governing equations
is in the Supplemental Information.

\textbf{Table 2.} Flume and numerical model runs with discharge and
logjam characteristics (number of jams and permeability). All runs were
conducted in flume and numerically simulated unless otherwise noted.
Replicates were run for all flume trials.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\textbf{Number of Jams} & \textbf{Logjam Permeability} &
\textbf{Discharge}\tabularnewline
\midrule
\endhead
1 & High & High\tabularnewline
1 & High & Low\tabularnewline
1 & Low & High\tabularnewline
1 & Low & Low\tabularnewline
5 & High & High\tabularnewline
5 & High & Low\tabularnewline
5** & Low & High\tabularnewline
5** & Low & High\tabularnewline
\bottomrule
\end{longtable}

**Numerical model only

\textbf{Table 3.} Model parameters and values\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Variable & Definition & Value & Unit\tabularnewline
\midrule
\endhead
\emph{K\textsubscript{shallow}} & Hydraulic conductivity of shallow
gravel and coarse sand stratum & 2.5\selectlanguage{ngerman}×10\textsuperscript{-2} &
m/s\tabularnewline
\emph{K\textsubscript{deep}} & Hydraulic conductivity of deep coarse
sand stratum & 8.9\selectlanguage{ngerman}×10\textsuperscript{-2} & m/s\tabularnewline
\emph{K\textsubscript{high\_jam}} & Hydraulic conductivity of high
permeability logjam & 1 & m/s\tabularnewline
\emph{K\textsubscript{low\_jam}} & Hydraulic conductivity of low
permeability logjam & 0.5 & m/s\tabularnewline
\selectlanguage{greek}\emph{θ} & Porosity of sediments & 0.3 & -\tabularnewline
& van Genuchten alpha & 3.548 & 1/m\tabularnewline
& van Genuchten gamma & 3.162 & -\tabularnewline
\selectlanguage{greek}\emph{θ \textsubscript{high\_jam}}\selectlanguage{english} & Porosity of high permeability jams
& 0.7 & -\tabularnewline
\selectlanguage{greek}\emph{θ \textsubscript{low\_jam}}\selectlanguage{english} & Porosity of low permeability jams &
0.35 & -\tabularnewline
\selectlanguage{greek}\emph{α\textsubscript{l}}\selectlanguage{english} & Longitudinal dispersivity & 0.02 &
m\tabularnewline
\selectlanguage{greek}\emph{α\textsubscript{t}}\selectlanguage{english} & Transverse dispersivity & 0.02 &
m\tabularnewline
\(n_{x}\), \(n_{y}\) & Manning's coefficient & 0.03 &
s/m\textsuperscript{1/3}\tabularnewline
\bottomrule
\end{longtable}

3 Results

\emph{H1) Increasing logjam longitudinal distribution density enhances
transient storage}

Results from the flume support our hypothesis that an increase in logjam
longitudinal distribution density enhances the magnitude of transient
storage. We observed an increase in skew and mean arrival time in the
flume results with an increase in logjam longitudinal distribution
density (Figure 2). Tukey adjusted pairwise comparisons between mean
arrival time and the number of jams indicated slower advection with more
jams (p\textless{}0.0001). In other words, not surprisingly, more
logjams in the flume result in slower movement of the tracer down the
channel. Pairwise comparisons between skew and the number of jams
indicate an increase in skew with more jams present
(p\textless{}0.0001), meaning that more jams increase retention.
Numerical modeling simulations further support this hypothesis.
Increasing the longitudinal distribution density of logjams results in a
greater extent of hyporheic zone (Figure 3). Mean subsurface arrival
time and skew both increase with the addition of multiple logjams in the
numerical model (Figure 2). We see a 14\% increase in hyporheic exchange
fluxes with multiple jams present compared to a single jam at low flow
and a 2\% increase in hyporheic exchange at high flow (Supplemental
Table 5). Multiple successive jams provide more pervasive exchange by
distributing the head drop at each jam, leading to distributed but
shallow flow paths (Figure 3). Thus, greater logjam longitudinal
distribution density facilitates more surface water storage as well as
downwelling into the subsurface (Figure 4).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2.} Mean arrival time and skew for flume runs and
numerical model simulations where the longitudinal distribution density
of logjams went from a one logjam (single) to five logjams (multiple).
Both mean arrival time and skew increase with multiple jams. Note that
flume-derived transient storage statistics are particularly sensitive to
surface water flow, while model-derived transient storage statistics
only focus on flow in the subsurface (they are not directly comparable).
There are no replicate runs for the numerical model results.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3.} HydroGeoSphere simulated surface water depth (m) and
groundwater mean age (log(hour)) for the eight flume scenarios where the
logjam permeability, number of logjams, and/or discharge change. The
surface water level and connectivity between groundwater and surface
water are increased when surface water encounters a logjam. Rising
surface water level causes more water to infiltrate into the
water-sediment interface in front of the logjam and exfiltrate out
behind the logjam. Comparing the scenarios of single logjams (left) and
multiple logjams (right), a single jam drives a deep zone of fast
exchange, while multiple jams drive shallower but connected and repeated
zones of fast exchange.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\par\null

\textbf{Figure 4.} HydroGeoSphere simulated exchange rates across the
water-sediment interface and water-jam interface for the eight scenarios
where the logjam permeability, quantity of logjams, and/or discharge
change. The area in front of each logjam is the hotspot for surface
water infiltration, while the area behind the logjam is the hotspot for
groundwater exfiltration. The submerged area of the flume in these
scenarios are different due to changes in backwater effects. Generally,
more logjams, higher flow rates, or lower logjam permeability will
create more of a backwater effect and thus extend the area available for
exchange with the subsurface.

\emph{H2) Decreasing the permeability of a single logjam enhances
transient storage}

Results support our hypothesis that a decrease in logjam permeability
enhances the magnitude of transient storage (Figure 5). Visual
observations of backwater extent in the flume suggest a less permeable
jam has a more profound impact on increasing retention in surface water
relative to a more permeable jam (Figure 6). As more wood and coarse
particulate organic matter are added to a single logjam, greater
backwater and low-velocity flow fields form. Model simulations further
show that an increase in rising surface-water level behind a less
permeable logjam resulted in a greater magnitude of water infiltrating
into the water-sediment interface in front of the logjam and exfiltrate
out behind the logjam (Figure 4). Thus, hyporheic exchange is increased
around the logjam.

Surface mean arrival time increased as the permeability of the jam
decreased in the flume (p=0.0001). In other words, a more tightly packed
jam results in slower movement of the tracer down the channel regardless
of discharge. We observed the same trend in subsurface mean arrival time
in the model (Figure 5). Pairwise comparisons of skew and permeability
in the flume results suggest that a less permeable logjam increases
surface water retention compared to a more permeable logjam in the flume
(p=0.0087). Skew in the model increases by 300\% as the permeability
decreases at low discharge and increases by over 160\% as the
permeability decreases at high discharge.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5.} Mean arrival time and skew for permeability flume
runs and numerical model simulations where the permeability a single
logjam went from high to low. Both mean arrival time and skew increase
as jam permeability decreases (i.e., the logjam is more tightly packed).
Note that flume-derived transient storage statistics are particularly
sensitive to surface water flow, while model-derived transient storage
statistics only focus on flow in the subsurface (they are not directly
comparable). There are no replicate runs for the numerical model
results.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Figure 6.} Backwater extents of flume runs with visual of
inundation extents for a) multiple jams at high flow, b) logjam with low
permeability at high flow, c) logjam with high permeabiltiy at high
flow, and d) backwater mapping for single jam flume runs; Q indicates
flow and K indicates hydraulic conductivity (permeability). Backwater
extent is greater as permeability is decreased and as the longitudinal
distribution density is increased. When comparing the backwaters of a
single logjam, the greatest backwater corresponds with a low
permeability jam at high flow. The smallest backwater extent corresponds
with a high permeability jam at low flow.

\emph{H3) A single low-permeability logjam creates a comparable increase
in transient storage to multiple high-permeability logjams}

We compared transient storage between a single low-permeability logjam
and multiple high-permeability logjams to better understand the relative
effects of these logjam characteristics. Mean arrival times for the
flume and model show a clear increase in time the tracer takes to move
through the surface and subsurface between a single low-permeability jam
and multiple high-permeability jams (Figure 7). In the flume, the tracer
moves significantly slower when multiple jams are present
(p\textless{}0.0001). Modeling results also showed approximately a 120\%
increase in subsurface mean arrival time with the presence of multiple
high permeability jams compared to a single, low permeability jam
(Figure 7).

Skew response was different based on discharge in the flume (Figure 7).
Under low-discharge conditions, more skew is observed in a single
low-permeability jam compared to multiple high-permeability jams
(p=0.002). Under high discharge conditions, more skew is observed in
multiple high-permeability jams compared to a single low-permeability
jam (p=0.0007). In other words, permeability is playing a greater role
in enhancing transient storage in the flume at a low discharge compared
to high discharge. Skew was greatest in the multiple high-permeability
logjam numerical modeling simulations relative to a single
low-permeability logjam, regardless of the discharge (Figure 7). We
observed approximately a 24\% increase in hyporheic exchange at low flow
and 12\% increase at high flow in the multiple high-permeability logjam
simulation compared to the single low-permeability logjam simulation
(Supplemental Table 5). We simulated a scenario with both increased
logjam longitudinal distribution density and decreased permeability (not
shown in the flume), which resulted in the greatest magnitude of
hyporheic exchange and surface backwater increase of all logjam
scenarios.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Figure 7.} Comparison of skew and mean arrival time values
between a single low permeability logjam and multiple high permeability
logjams. We see greater mean arrival times in multiple high permeability
jams relative to a single low permeability jam. For skew, results
between the flume and model vary based on discharge. Note that
flume-derived transient storage statistics are particularly sensitive to
surface water flow, while model-derived transient storage statistics
only focus on flow in the subsurface (they are not directly comparable).
There are no replicate runs for the numerical model results.

\emph{H4) Transient storage increases at higher discharge for all
scenarios.}

Numerical model simulations and flume runs suggest that discharge has
complex effects on transient storage, likely depending on the timescale
of storage. Both flume and models show an increase in backwater when
discharge increases (Figure 3 and 6). We observed that increasing the
discharge to the flume both can store more surface water and elevate the
surface water level in front of a logjam (Figure 6). Similarly, the
submerged area of the model increased by about 20\% at higher flows for
all configurations (Supplemental Table 5).

Mean arrival times of surface and subsurface flow paths decrease with
increasing discharge in both the flume and model. In the flume, this
indicates quicker surface water flow paths with greater discharge. In
the model, this indicates faster subsurface exchange rates when
discharge increases (Figure 2, 5, and 7). Across flume trials, skew
significantly increases at low discharge compared to high discharge
(p\textless{}0.0001 averaged over the number of jams or averaged over
permeability). Numerical model simulations suggest that lower discharge
also facilitates a greater magnitude of skew as logjam characteristics
increase in complexity (i.e., when more jams are present and when a
single jam is less permeable) (Figure 2, 5, and 7). We infer that that
there is more Gaussian flow at high discharge as solutes moves quickly
through the system and the breakthrough plots show a lack of heavy tails
(see Supplemental Plots). Consequently, at low discharge, we observe
more heavy tailing behavior. This may be a matter of how easy it is to
resolve that smallest fraction of flows that stick around the longest
and overall sensitivity in the flume/model. However, the combined
results also suggest a more complex behavior that may depend largely on
surface water flow in the backwater zone.

4 Discussion

Our primary objective was to evaluate the influences of changes in (i)
logjam longitudinal distribution density, (ii) logjam permeability, and
(iii) discharge on transient storage. Using a combination of physical
and numerical modeling allowed for better constraint of both surface and
subsurface flow paths. Results suggest that increasing the longitudinal
distribution density and decreasing the permeability both increase
transient storage, regardless of the discharge. This fits with what we
expected to see based on past work. Ader et al. (2020) found that the
effects of large wood on surface and subsurface transient storage may be
very local, implying the need for multiple wood pieces and logjams to
influence segment-scale transient storage. Our observations confirm this
inference and suggest that multiple logjams lead to more distributed
flow paths and more pervasive reach-scale exchange. Studies evaluating
hyporheic interactions around beaver dams (e.g., Lautz et al.,2006;
Briggs et al., 2013) indicate that stream reaches with beaver dams
exhibit a greater degree of hyporheic interaction. Our results showing
transient storage around low permeability logjams with permeability
similar to that of a beaver dam support this understanding that a more
tightly packed logjam can enhance transient storage.

\emph{4.1 Complexities in Transient Storage Flow Paths}

We assume, based on our results, that the flume is more sensitive to
surface flow paths and the numerical model to subsurface flow paths. For
example, a mean arrival time of only minutes in the flume is likely
consistent with a combination of slow flow in surface transient storage
zones plus some of the fastest flow through subsurface zones. However,
it is too short for the slowest flow through the subsurface (see
groundwater ages in Figure 3). We therefore use the numerical model to
quantify the behavior of the longest solute travel times in the
subsurface. Both physical experiments and numerical models represent
simplifications of real conditions, but the lack of fine sediment
accumulation in the logjam backwaters, the rigid lateral boundaries, and
the impermeable boundary underlying the sediment fill in the flume may
all have influenced subsurface flow paths. In the models, it is unclear
whether more skew (which we interpret as more transient storage) equates
to a greater hyporheic exchange flux or longer residence times
(Supplemental Table 5). As has been shown in past studies (Cardenas et
al., 2004; Cardenas et al., 2008; Sawyer and Cardenas; 2009; Pryshlak et
al., 2015), the two tend to work against each other (greater exchange
rates tend to occur with shorter residence times).

We observed complex dynamics in the relationship between logjam
distribution density, permeability, discharge, and transient storage. As
logjams accumulate in a stream channel and accumulate more fine
material, upstream pooling increases, driving surface and hyporheic flow
paths and heightened complexity of the stream system (Abbe and
Montgomery,~1996; Sear et~al.,~2010). Evolution in jam complexity (both
in terms of permeability and longitudinal distribution density) can
result in the activation of the floodplain and other portions of the
hyporheic zone that might otherwise be dormant (Gooseff et~al.,~2006;
Wondzell et~al.,~2009; Doughty et~al.,~2020). Changes in inundation area
have been shown to have a profound influence on hyporheic connectivity
at field scales on the order of tens of square kilometers (Helton
et~al.,~2014). We see this in our results where increasing both
longitudinal distribution density of logjams and the amount of coarse
particulate organic material in a jam leads to an increase in wetted
area and exchange fluxes between the surface water and groundwater
(Supplemental Table 5).

Existing work provides evidence for both increased transient storage
during low discharge conditions, when the water table near the stream is
low (Harvey and Bencala, 1993; Harvey et al., 1996; Wroblicky et al.,
1998) and during high discharge conditions, when the stream experiences
greater channel wetted area and floodplain inundation (Nyssen
et~al.,~2011; Doughty et al., 2020; Wilhelmsen et al., 2021).
Comparisons of mean arrival times and skew in the surface and subsurface
show consistencies across the flume and model. Our results show less
skew and shorter mean arrival times when discharge increases (Figures 2,
5, 7). In the flume, flow paths are better imaged at low discharge when
we can load more of the flow paths with a short salt pulse. In the
models, all the mean arrival times are already limited to the subsurface
(a transient storage zone), so skew is only telling us about the longest
transient storage times in that case, and a larger skew indicates a
wider, heavier-tailed distribution of residence times. We suspect
understanding the role of discharge in these environments is dependent
on sensitivity to detecting the smallest fraction of flows that stick
around the longest, which becomes increasingly challenging to do at
higher discharge. Both the flume and model results reflect
simplification of the river corridor in which flow paths cannot access a
floodplain. We recognize that longer and deeper flow paths might be
constrained by the base of the sediment box in the flume and impermeable
walls of the model. The extent of these flows in natural streams could
depend strongly on the depth of alluvial cover (Tonina and
Buffington,~2009), which is in turn influenced by the presence of large
wood, because logjams store sediments (Massong and Montgomery,~2000;
Montgomery et~al.,~2003). The interacting effect of jams, sediment
storage, and longer, deeper hyporheic exchange flows cannot be tested in
these experiments but is an area for future research.

\emph{4.2 Management Implications}

Our simulation of multiple low-permeability logjams enhanced hyporheic
exchange by the greatest magnitude, suggesting that this configuration
maximizes hyporheic exchange potential. Thus, when thinking about
designing engineered logjams to promote surface water-groundwater
exchange or restoration targeting hyporheic exchange, we infer that
those scenarios with opportunities to recruit more wood or facilitate
the formation of multiple jams, as well as retain coarse particulate
organic matter that reduces logjam permeability, will best maximize
transient storage. Although the specific magnitudes of surface transient
storage and hyporheic exchange at the field scale cannot be determined
from flume-scale experiments, the general characterization (for example,
the substantial increase in exchange rates and surface water storage
with more logjams and more fine material in a logjam) should be
consistent across flume to field scales.

Zones of transient storage are important components of stream systems,
and, similar to other stream habitats, have suffered degradation as a
consequence of human activity. Efforts to incorporate channel elements
that promote hyporheic exchange have started to emerge as a step toward
restoring stream ecosystems and associated hydrologic functions
(Crispell and Endreny, 2009; Hester et al., 2018). Additions of complex
logjam formations in altered river reaches may increase hyporheic
interactions by slowing stream water velocity, forming backwaters,
increasing flow complexity, and diverting water to the subsurface. Some
morphologic features may also retain coarse particulate organic material
that decreases the permeability of a logjam while creating the redox
gradients necessary for certain biogeochemical functions. Nevertheless,
successful applications of stream management and restoration utilizing
logjams is dependent upon understanding the role of different large wood
distributions (ranging from more dispersed distributions to many
successional jam structures to tightly packed jams) on transient
storage. Although the hyporheic benefits of ongoing installation of
morphologic features may be considerable, to our knowledge they are not
currently included as project design goals (Hester and Gooseff, 2010)
and few studies quantify the impact of restoration features on hyporheic
function (Kasahara and Hill, 2006; Crispell and Endreny, 2009; Wade et
al., 2020). Adding hyporheic benefits of existing installations as an
explicit design goal where appropriate, modifying the design parameters
of such features to maximize benefits as possible, and considering
additional features explicitly for hyporheic benefit are all needed to
incorporate and quantify transient storage benefits in restoration
projects.

Conclusions

Results from tracer experiments in our flume and numerical modeling
simulations provide insight into how logjam characteristics influence
transient storage. The presence of multiple channel-spanning logjams and
decreased logjam permeability facilitates more opportunities for solute
retention and processing in zones of transient storage. Solute
breakthrough in the flume is more sensitive to surface flow paths than
subsurface flow paths, suggesting much of the observed transient storage
occurs in backwater zones behind jams. Configurations with greater
transient storage also have the greatest rates of hyporheic exchange and
longest residence times in the subsurface. From the observed differences
in surface transient storage between stream segments with greater and
lesser amounts of large wood and more or less permeable jams, we infer
that river management designed to foster surface transient storage can
effectively focus on retaining wood (either by continuing recruitment
and transport or fixing engineered logjams in place) and retaining
coarse particulate organic matter. We conclude that transient storage is
maximal when there are many jams (large longitudinal distribution
density) with low permeability (tight packing of wood pieces). An
increase in transient storage can, in turn, improve stream health and
makes a case for river managers to strategically implement wood in river
restoration designs.

Moving forward, additional work is needed to explore whether a change in
longitudinal distribution density or permeability has a nonlinear effect
on transient storage. Other studies have shown that logjams create
nonlinear effects on stream metabolism (Day and Hall, 2017); spatial
heterogeneity of physical channel characteristics (Livers and Wohl,
2016; Livers et al., 2018), including channel and floodplain planform
(Buffington and Montgomery, 1999; Wohl, 2011); retention of particulate
organic matter (Beckman and Wohl, 2014); and animal biomass and
biodiversity (Herdrich et al., 2018; Venarsky et al., 2018). We expect
that transient storage might follow a similar pattern of nonlinearity,
but the binary nature of this experimental set-up did not allow for such
exploration.

\textbf{Acknowledgments}

This research was supported by National Science Foundation Hydrologic
Sciences (award 1819068). We thank Ian Gambill, Emily Iskin, Sawyer
McFadden, and Karl Wilhelmsen for assistance with flume runs and
numerical modeling and Ann Hess for consulting on statistical analysis.

\textbf{Open Research}

The data analyzed for this paper are included in tables in the
Supporting Information accompanying this paper. Sample scripts for
calculating temporal moments from the flume breakthrough curves and raw
conductivity data files can be accessed via HydroShare:
http://www.hydroshare.org/resource/5535e4618ce545f5a66087ca784d7150

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