fluvial seed dispersal of riparian trees: transport and...

Fluvial seed dispersal of riparian trees: transportand depositional processesAdrienne Cunnings,1* Edward Johnson2 and Yvonne Martin11 Department of Geography, University of Calgary, Calgary, Alberta, Canada2 Department of Biological Sciences, University of Calgary, Calgary, Alberta, Canada

Received 14 January 2015; Revised 23 September 2015; Accepted 5 October 2015

*Correspondence to: Adrienne Cunnings, Department of Geography, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, T2N 1N4, Canada. E-mail:[email protected]

ABSTRACT: Fluvial seed dispersal considers both the transport and deposition of seeds where channel geomorphic structures,hydrology and seed dispersal traits contribute to transport times and depositional locations. This study examines the influence ofstream flow patterns on fluvial seed dispersal of buoyant white alder (Alnus rhombifolia) seeds by applying a one-dimensionaltransport model. Conceptually, the model separates the stream into two components: (i) the main channel where the seeds aretransported downstream; and (ii) the transient storage zone where seeds are temporarily detained or deposited on the river bank.Transport processes are characterized by an advection–dispersion equation which is coupled to a transient storage model usingan exponential decay term. The model parameters: longitudinal dispersion (DL), exchange coefficient (α), main channel area (A)and storage zone (As) are estimated based on field experiments conducted in a confined, bedrock-gravel bed river with pool-rifflemorphology located in coastal northern California. The riparian zone is inhabited by Alnus rhombifolia that disperse buoyant seedsin mid-spring coinciding with the end of the wet, Mediterranean season. Artificial seeds, with similar traits of buoyancy and densityto alder seeds, were used to quantify transport times and depositional locations. Preferential deposition resulted in stream reaches withlarger As, high As/A ratios, and faster exchange coefficients corresponding to divergent stream flow (back-eddies, re-circulatingflow, flow expansions) caused by geomorphic structures such as the ends of bar/riffle features and bends in the stream. The resultsdemonstrate the importance of transient storage for seed transport and depositional processes. Morphological features that increase achannel’s complexity create complex flow structures that detain seeds and provide a greater opportunity for deposition to occur. Themodel provides a simplification of river hydraulics to represent dispersal dynamics and lends itself to further understanding ofhydrochory processes and associated population structure. Copyright © 2015 John Wiley & Sons, Ltd.

KEYWORDS: riparian vegetation; seed dispersal and transport; floating seed dispersal; one-dimensional model; white alder (Alnus rhombifolia)

Introduction

Seed dispersal in streams and rivers is controlled by seed traitsof buoyancy and density and the hydrogeomorphic setting.Botanists and ecologists have devoted most of their attentionto seed characteristics that keep seed afloat and increase dis-persal distance (Andersson et al., 2000; Vogt et al., 2004;Groves et al., 2009).Dispersal distances have been attributed to flow conditions,

such as velocity and discharge, with buoyant seeds travellinga farther distance in flows with high discharge rates (Anderssonand Nilsson, 2002; Nilsson et al., 2002). Likewise, dispersalcurves are shaped with a positively skewed, leptokurtic distri-bution based on downstream deposition patterns found in fieldconditions from primarily a point-release using mimic seeds(Johansson and Nilsson, 1993; Riis and Sand-Jensen, 2006).Dispersal curves have been modeled by a semi-empiricalGaussian plume equation using mean velocity and hydraulicgeometry (Groves et al., 2009). Groves et al. (2009) showedthat a majority of seeds were deposited near the release pointfollowed by a long distribution tail that highlights the possibility

of long distance dispersal by a small number of seeds. Thedistribution shape of a dispersal curve is related to the chan-nel’s retention processes but little research has focused on thisconnection. The relationship between the dispersal curve andthe depositional processes is influenced by extrinsic factorssuch as river morphology, obstructions, channel roughness,in-stream vegetation and to lesser extent intrinsic factors suchas seed traits based on size, shape, and weight (Danvind andNilsson, 1997; Chambert and James, 2009; Nilsson et al.,2010). For example, straight homogenous channels such ascement channels lead to long distances of transport but lowdeposition while heterogeneous channels are better ‘filters’ ofseeds due to complex bedform structures, trapping features(i.e. vegetation, rough surfaces) and high sinuosity resultingin shorter distances of transport and high deposition.

Deposition has most often been studied in flumes where theunderlying mechanisms of capture can be examined at severalscales and where investigators have complete control of chan-nel form and flow hydraulics. At the point scale, Peruzzo et al.(2012) attributed particle attachment to the following threemechanisms: inertial impaction, meniscus climbing via surface

EARTH SURFACE PROCESSES AND LANDFORMSEarth Surf. Process. Landforms 41, 615–625 (2016)Copyright © 2015 John Wiley & Sons, Ltd.Published online 11 November 2015 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/esp.3850

tension, and entrapment by net-like structures caused by over-lapping vegetation. At the patch scale, Merritt and Wohl (2002)found a relationship between seed stranding and both thehydrologic regime and stream hydraulics. The authors noted ahigher percentage of seeds deposited in recessional flows andalso in channel morphologies that caused re-circulating flows,such as riffles, meanders and flow expansions. Flow velocityand patterns are commonly cited as the dominant controllingvariable in deposition dynamics (Schneider and Sharitz, 1988;Andersson et al., 2000; Merritt and Wohl, 2002; Nilssonet al., 2002; Gurnell et al., 2008; Chambert and James, 2009).For instance, preferentially deposited seeds are associated withriver characteristics such as those found in eddies downstreamfrom rapids (Nilsson et al., 1991), adjacent to riffles (Levine,2001) and on gravel bars (McBride and Strahan, 1984), whilethey are often absent in tranquil pool reaches (Anderssonet al., 2000). These observations suggest that complex flowstructures dictate the transport and deposition of buoyantseeds. However, numerical modeling of fluvial dispersal forbuoyant seeds has remained limited in comparison to modelingof non-buoyant seed dispersal. The latter follows similar me-chanics to sediment transport (Gurnell, 2007; Markwith andLeigh, 2008).In this study an advection–dispersion model with coupled

transient storage gives a first approximation of the processesresponsible for dispersal of buoyant seeds. The field data usedin the model estimated the hydraulic parameters and therebyinvestigated the associated hydrogeomorphic controls. Assess-ments of the model parameters (A, As, DL, and α; for definitionsee model later) were made by comparing them to standardempirical equations and field based measurements. Duringfield experiments the deposition amounts and location wererecorded to calculate the decay term used in the model andto examine the spatial pattern with standing vegetation. Separa-tion of the flow into a transport region and retention area high-lights important parameters that influence dispersal distance,travel times and depositional patterns. By simplifying complexflow structures, this study investigates the mechanisms drivingseed dispersal and deposition, such as geomorphic and hydrau-lic structures, and in-channel vegetation and debris. Whilevarying discharge was not explicitly experimented with in thepaper its influence is discussed. Finally, the research findingsare extended to show the dispersal implications for a speciespopulation distribution.

Dispersal Model

The advection–dispersion coupled transient storage model is asimplified one-dimensional, two compartments model: (i) mainchannel flow and (ii) storage zones (Figure 1) with a couplingterm which allows transfer between the storage zone and themain channel. This formulation is similar to transient storagemodels commonly used in pollutant tracer modeling in streamsand rivers to quantify the transport and fate of solutes (Bencalaand Walters, 1983). The model software, OTIS-S, is availableby the US Geological Survey (USGS) (http://water.usgs.gov/soft-ware/OTIS/). Downstream transport of buoyant seeds occurswithin the main channel where advection–dispersion carriesthe seeds at higher velocities than the slower moving storageareas. The storage areas temporarily detain seeds and lengthentransport times or strand the seeds by depositing them on thebank. The approach of this paper focuses only on surface riverflow and its interactions with the channel bank and thus has theadvantage of reducing averaging errors that occur in traditionalmodels where a single exchange parameter lumps both surfaceand subsurface flow processes (Briggs et al., 2009). The model

provides insights into how flow dynamics in river channels in-fluence transport and depositional locations of buoyant seeds.

Advective flow in the main channel provides effective trans-port of seeds while dispersive flow spreads and slows transportof seeds by a combination of shear stress and turbulent diffu-sion. Storage areas are responsible for the temporary detain-ment of solutes and encompass areas of divergent stream flow(back-eddies, recirculating flow, flow expansions), slack water(side-pools or embayments). The governing equations for themain channel and storage area in the one-dimensional modelare as follows:

Main channel :∂C∂t

¼ �Q∂CA∂x

þ 1A

∂∂x

ADL∂C∂x

� �

þ α C s � Cð Þ(1)

Storage zone :dC s

dt¼ αA

AsC � C sð Þ � λsC s (2)

where A is the cross-sectional area (in m2), C is the concentra-tion (in seeds m�3), DL is the longitudinal dispersion coefficient(in m2 s�1), Q represents the discharge (in m3 s�1), t is time(in seconds), x is the longitudinal distance (in meters), α is theexchange coefficient (in s�1) and the exponential decay term(in s�1), λ, accounts for seed deposition. Subscript ‘s’ indicatesthe storage zone while no subscript represents terms in themain channel. The principal assumption applied in the OTISderivation is based on tracer concentration that varies in thelongitudinal direction and not with depth; hence, particularlyapplicable to buoyant seed in river flow.

Research Site

The South Fork of the Eel River is an undammed, bedrock-gravelbed river situated in Mendocino County, California, USA. Thestudy area extends 400m upstream of the Elder Creek tributaryconfluence (39°43′N, 128°38′W) and is located within theAngelo Coast Range Reserve of the University of CaliforniaNatural Reserve System. The riverbed is composed of sandstoneand mudstone-shale bedrock with approximately 80% of thebed overlain with a mixture of fines to cobbles (d50=60mm)

Figure 1. Conceptual model of a control volume where mass is con-served. Advection and dispersion occur in the main channel while inthe storage area deposition occurs through an exponential decay term.The two zones are coupled by an exchange coefficient (amended fromRunkel, 1998).

616 A. CUNNINGS ET AL.

Copyright © 2015 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, Vol. 41, 615–625 (2016)

http://water.usgs.gov/software/OTIS/

http://water.usgs.gov/software/OTIS/

and intermittent boulders (Hodge et al., 2011). The meangradient is 0.005mm�1 with riffle and pool sequences alongthe research site. Within this area, the South Fork of the Eel Riveris confined by steep canyon walls with slopes primarily vege-tated by Douglas-fir (Pseudotsuga menziesii, Mirbel) and Coastredwood (Sequoia sempervirens, D. Don). The dominant ripar-ian vegetation consist of white alder (Alnus rhombifolia, Nutt.),Oregon ash (Fraxinus latifolia, Benth.), and bigleaf maple(Acer macrophyllum, Pursh) (see Power et al., 2004, for a fullvegetation description).The climate is Mediterranean, with the Pacific High remaining

over the region between May to September resulting in littleprecipitation. Most of the precipitation occurs between Octoberand April when the Pacific High moves south. The South ForkEel gauging station recorded daily discharge and was operatedfrom 1947 to 1970 by the USGS Branscomb gauge site(11475500) and from 2008 to present by the University ofCalifornia Natural Reserve System (http://sensor.berkeley.edu/).Missing data from 1971 to 2007 was calculated by correlatingthe USGS Leggett (11475800) station for 1965 to present(R2 =0.96) and the remainder of the missing data with the USGSElder Creek (11475560) station from 1967 to present (R2 =0.94).A bankfull value of 120m3 s�1 with a recurrence interval of1.5 years (Dunne and Leopold, 1978) was calculated using peakstreamflow data from the USGS gauging station (1947–1977).The bankfull value for the longer period 1947–present is then70m3 s�1 with a recurrence interval of 1.5 years. The differencein bankfull levels suggests that the earlier time period(1947–1970) was wetter than from 1970 onwards and is empha-sized by extreme floods events in 1955 (322.8m3 s�1), 1964(475.7m3 s�1) and 1966 (314.3m3 s�1).

Characteristic species

White alder (Alnus rhombifolia) is the dominant riparian tree atthe study site. It grows primarily within the bankfull region and

undergoes annual inundation during the rainy season. Whitealder disperses light weight, buoyant seeds (6.18×10�4 g,standard error [SE] =3.68×10�5 g) in large numbers fromapproximately mid-April to the end of May. Average dischargefor the month of April is 5.4m3 s�1 (SE=0.15m3 s�1) and2.4m3 s�1 for May (SE=0.07m3 s�1) (Figure 2). For the periodof 1947 to 2012 there is only a 5% probability in the month ofApril that the flow exceeds a bankfull value of 70m3 s�1 whilein the month of May a bankfull level has never been exceededsince 1947 and has an exceedance probability of 0.3% basedon an exponential fit. Most bankfull flow regimes occur inJanuary or December before white alder seeds are mature ordispersed.

Alder seeds are too small (~1.9 × 10�9 m3) to directly observein the river flow and recover on river banks and thus a mimicwas necessary. Our aim was to find a mimic that had similarproperties of the alder seeds: light enough to not disturbstreamflow lines; affects the meniscus in a similar manner asalder seeds are hydrophobic and create a negative meniscus;does not sit high above the stream level; and roughly similarto the shape of the seeds. Coloured Tyvek™ material waschosen as the seed mimic as it retains the above criteria.Furthermore, the mimic retained similar density to that of thewhite alder seeds. The density, estimated based on an ellipsoidvolume, was calculated to be on average 0.32 g cm�3 for a drywhite alder seed. When wetted for 24 hours in both stagnantand agitated water, the seeds slowly began to retain water butremained buoyant with an approximate density of 0.52 g cm�3.The mimic had a similar density of 0.30 g cm�3 when dry and0.39 g cm�3 after wetting for 24 hours and confirmed that themimics would remain afloat akin to the seed. It is not possibleto retain exact seed size and shape as the mimic would notbe visible in the flow. To allow for visibility in the field themimics were cut to average dimensions (in centimetres) of 1.9(length) × 1.5 (width) × 0.025 (height) but varied to reflect thevariability found in seed size. Even with mimics that wereroughly 7× larger than the seed there still remained difficulties

Figure 2. The average monthly discharge for the months of April (top) and May (bottom) on the South Fork Eel River. Bars represent the range inmaximum and minimum discharge. Data is regressed from 1970 to 2008 (see text for explanation).

617FLUVIAL SEED DISPERSAL OF RIPARIAN TREES


http://sensor.berkeley.edu

in 100% retrieval of the mimics which will be further consid-ered in the Discussion section. It is important to note that themodel does not predict exact locations of deposited seeds butrather the size of the storage area in each reach, allowing theTyvek pieces to be a suitable mimic, which increases the gener-ality of the model to other types of tree species with floatingseeds.

Methods

Field experiment

In the field experiment, mimics were released and observedduring an average discharge of 9.5m3 s�1 (Figure 3a). Onethousand mimics were released over 27minutes, approxi-mately one mimic every two seconds. The mimics werereleased mid-stream near the end of a pool (Figure 3b) whichrepresents the zero meter mark. The travel times of the seedswere visually observed at 140m (Figure 3c) and 360m(Figure 3d) downstream from the starting point and the cumu-lative number of seeds passing by was recorded each minute.After four hours the observers stopped recording as eachobserver had at least a 15minute interval with no mimicspassing. The right-hand side bank was then inspected tolocate and record the number of deposited seeds; due tohigher discharge it was not possible to reach the other bankand binoculars were used to identify seeds on the oppositebank. However, it should be noted that previous test runs inlower flow resulted in the bulk of deposited seeds on theright-hand side bank as the left bank was largely bedrockrather than depositional features such as gravel bars. Figure 4provides a description of the river geomorphic characteristicsalong with width measurements.To compare the standing vegetation with deposition patterns,

the number of established white alders (> five years) werecounted on the right bank and compared to deposited mimics.Juvenile trees (< approximately five years) were not counteddue to the lack of confidence in identification as foliage hadnot yet appeared and bark patterns are indiscernible at the

species level. However, the juvenile establishment patternappeared similar to that of the established trees.

Model considerations

The advection–dispersion with coupled transient storage wassolved using the OTIS(-P) code (Runkel, 1998; http://water.usgs.gov/software/OTIS/doc/). Tracer concentration was con-sidered as Cseed =NseedV

�1 where Cseed is the seed concentra-tion (number seeds m�3), Nseed is the number of seeds(number seeds), and V is the flow volume (in m3). Seeds canbe transported from the main channel into the storage areawhere they may be deposited on the bank or returned to themain flow. It was assumed that seeds were not deposited inthe main channel. The study site was modeled as two reaches,where a reach was treated as an area in which the modelparameters are constant. Each reach was further subdividedinto 10m control volumes that include a main channel andstorage area where mass is conserved. The model boundaryconditions were defined by an upstream and downstreamboundary. The upstream boundary condition had a fixedconcentration that varied with time and was represented bythe seed concentration entering at 0m for the duration of thefield experiment. The first reach ended at 140m which coin-cided with the first field observer. The downstream boundarywas defined by a dispersive flux with a zero gradient implyingthat the downstream boundary was equal to that of the lastmodeled segment. Due to this assumption, the second reachin the model extended 40m beyond the second field observerlocated at 360m. OTIS-P uses a nonlinear least squares tech-nique to estimate the dispersion term, channel and storageareas, and exchange coefficient (α). In order for the model toconverge, the deposition term was fixed to reduce the numberof estimated parameters. Deposition was calculated in eachreach as an exponential decay, ln(N/No) = λseedt, where N isthe number of seeds exiting the reach, No is the number ofseeds entering the reach, λseed is the seed decay term (in s�1),and t is time length (in seconds) that corresponds with themodel’s integration time step of 18 seconds.

Figure 3. (a) The March 26, 2012 hyetograph, (b) arrow shows where mimics were released into the flow, mid-stream, (c) picture taken at 130m inan upstream direction, (d) photograph taken at 280m in an upstream direction.



http://water.usgs.gov/software/OTIS/doc/

http://water.usgs.gov/software/OTIS/doc/

To ensure the model values were of the same order of magni-tude as the field values, the model results were compared tofield values by empirically calculating the total channel area(AT) and longitudinal dispersion (DL). The total channel area(AT, in meters), which is the sum of the main channel and stor-age cross-sectional areas, was estimated using the discharge(Q, in m3 s�1) and velocity relationship (U, in m s�1),AT =QU�1. The average channel velocity was calculated bythe travel time of the first mimics passing the observation pointswhich occurred at four minutes at 140m and 12minutes at360m. Thus the total channel area in the field was estimatedto be 16.3m2 in the first reach and 19.0m2 in the second reach.Longitudinal dispersion can be empirically estimated by the

equation (Fischer, 1975):

DL ¼ 0:011 U2 � W 2� �

=d gdSð Þ1=2h i

(3)

where U is the average velocity of the main channel (in m s�1),W is the average channel width (in meters), d is the averagedepth (in meters), g is acceleration due to gravity (in m s�2),and S is the channel slope (in m m�1). To determine the aver-aged depth of each reach, a simple volume relationship wasused, d=ATW

�1. River width measurements were recorded inthe field every 10m and averaged over each reach; Reach 1had an average width of 17.7m while Reach 2 had an average

width of 19.3m. Using Equation 3, the longitudinal dispersionwas calculated as 1.23 and 1.08m2 s�1 in Reach 1 and Reach2, respectively.

During the field experiment, the observers recorded 32.0%and 27.6% of the mimics at 140m and 360m respectivelypassing in the flow. Along the bank 35.3% of the mimicshad been deposited between 0 and 140m while 11.3% werefound between 140m and 360m. Thus 32.7% and 25.8%went unaccounted for in each section due to a combinationof visibility issues during transport (mimics obscured byturbulences or unnoticed at far bank) or by deposited mimicsthat were not visible (perhaps due to being hidden under-neath rocks or not visible on opposite bank). Thus, to ensurethat a mass balance was conserved in the model, the startingconcentration was reduced to the sum of mimics of the firstobserver and the number of mimics found along the bank.As noted earlier, there was a further discrepancy betweenthe two observers where the second observer recorded6.9% more seeds (including both deposited and transportedmimics) than the first observer due to human error. Onceagain, to ensure that a mass balance was conserved, the num-ber of mimics deposited in the second control volume wasreduced. These amendments kept the observed travel timesand number of mimics recorded by the observers unchanged.Figure 5 provides a conceptual view of the amendmentsmade to the model.

Figure 4. (Top) Overhead map of river reach, image courtesy of Google Earth. R = riffle, P = pool, B = bedrock constriction. (Bottom) Cross-sectionriver width measurements at 10m intervals. (Right) Variation in river width around the mean width with the locations of the fluvial geomorphicfeatures.

Figure 5. Conceptual view of the resulting model areas. Reach 1 has a large storage area and Reach 2 is dominated by the main channel. In Reach 1,the modeled channel area was 10.24m2 and the storage area was 6.18m2. In Reach 2, the modeled channel area was 18.24m2 and the storage areawas 1.93m2.



Results

Channel areas, dispersion and exchange coefficient wereapproximated using non-linear estimation techniques in theOTIS-P model (Table I). The main channel area (advectionand dispersion area) was estimated in the model to be10.24m2 representing 62.4% of the total channel area while6.18m2 (37.6%) was allocated as the storage area in the firstreach (0–140m). The second reach (140–360m) had an esti-mated main channel area of 18.24m2 (90.4%) and a smallerstorage area of 1.93m2 (9.6%) (Figure 5). The total modeledarea was estimated to be 16.42m2 in the first reach and20.17m2 in the second reach supporting the empirically esti-mated values of 16.3 and 19.0m2, respectively. Longitudinaldispersion had a modeled value of 9.77m2 s�1 in Reach 1and 14.83m2 s�1 in Reach 2. While the empirically calculateddispersion values were lower (~1m2 s�1), the values are realis-tic (Wallis and Manson, 2004). Wallis and Manson (2004)showed considerable scatter in numerous empirically deriveddispersion coefficients values (2.0–72.3m2 s�1) based on a sim-ilar discharge level lending support to modeled and calculated

results. The exchange coefficient (α) was faster in Reach 1(7.11 × 10�3 s�1) than Reach 2 (6.26 × 10�3 s�1).

The dispersal curve in Figure 6 shows that the model hada reasonable fit with the field observations based on rootmean square error (RMSE) calculations. In Reach 1, theRMSE between the model and field observations was 5.97mimics while Reach 2 had a RMSE of 10.77 mimics. Themodel had difficulties in capturing the tail of the dispersalcurve and could only be approximated to field results whenthe storage area in the model was forced to unrealisticvalues (102m2). As a consequence, the tail of the secondreach was smoothed at a larger time interval allowing stor-age area parameters to be within acceptable margins. InReach 2, the larger error and high standard deviation inthe exchange coefficient is believed to be the result of float-ing debris piles in dead flow areas. Mimics were observedto be detained and released in simultaneous clumps backinto the main channel. These clumps of mimics transferredback into the main channel causing spikes in the actualdata rather than continuously decreasing as suggested bythe model.

Table I. OTIS-P model results when deposition rate (decay) held constant

Reach length,L (m)

Dispersion,DL (m

2 s�1)Main channel area,

A (m2)Storage area,

As (m2)

Total area,AT (m

2)Exchange coefficient,

α (s–1)Deposition,

λ (s–1)

Reach 1Model 140 9.77 (5.18) 10.24 (0.62) 6.18 (1.88) 16.42 7.11 × 10–3 (8.05 × 10–4) 4.15 × 10–2

Empirical 140 1.23 — — 16.3 — -Reach 2Model 220 14.83 (6.66) 18.24 (1.09) 1.93 (0.35) 20.17 6.26 × 10–3 (6.71 × 10–3) 8.25 × 10–3

Empirical 220 1.08 — — 19.0 — —

Note: Standard deviation shown in parentheses. Model estimates dispersion, main channel area, storage area, exchange coefficient.

Figure 6. Dashed line corresponds to initial mimic release at 0m. Field observers recorded the transport of mimics at 140m and 360m. The soliddiamonds represent field data, and solid lines are the model results. Storage area concentration do not have corresponding field observations and arebased on modeled results.



While field observations do not record the movementbetween the main channel and storage area, the model pro-vides some insight. For example, in the storage area of Reach1 the model calculates 153 mimics entering then exiting backto the main channel, implying that only 19% of the totalmimics remained exclusively in the main channel, 23%entered and returned into the main channel while 58% weredeposited. In Reach 2, the proportion of mimics staying in themain channel drops to 9% with 65% entering and exitingstorage and 26% being deposited. This high percentage ofmimics entering and exiting the two channel areas is shownin Figure 6 (Reach 2) by the similar curves modeled in the mainchannel and storage area.The Damkohler number (DaI) is a dimensionless number

used to evaluate the uncertainty in the modeled exchangeparameter (Briggs et al., 2010):

DaI ¼ α 1þ A=Asð ÞL½ � =U (4)

Erroneous exchange coefficient values may occur when (i) ex-change rates are rapid relative to average flow velocitycausing the exchange coefficient to become inseparable fromdispersion in the main channel or (ii) equilibrium in theconcentration between the two areas has been reached(Harvey et al., 1996). The DaI value for the first reach was1.05 and the second reach was 0.32, which falls within theacceptable sensitivity range for the DaI values being between0.1–10 (Briggs et al., 2010) which provides confidence in themodel’s estimation of the exchange coefficient parameter.

Bank deposition

In the field experiment, a greater proportion of seeds weredeposited in the first 140m which corresponds to Reach 1(Figure 7a). These deposition numbers were based on the rightbank due to the limited access to the left bank. However, previ-ous experiments where both bank sides were accessible, duringlow discharge rates, showed that a majority of the mimicsdeposited on the right bank due to the bend in the river.The bend remained a dominant geomorphic feature at the

experimental discharge level of 9.5m3 s�1. On average, 2.5mimics m�1 were deposited in the first reach and 0.5 mimicm�1 in the second reach. However, seeds were not found alongthe entire reach but were preferentially deposited at particularlocations on the bank (Figure 7b). The largest percentage ofdeposition was found adjacent to and near the end of a rifflewhere the river bends and causes a large re-circulating flow.There was minimal deposition of mimics in pools. A largebedrock outcrop from 190 to 210m provides a similar structureto that of a riffle (but lacks a bar formation) and deposition isfound in the transitional area where the flow expands into thepool once again, creating re-circulating flows. Interestingly,when recovering the mimics along the banks clumps of smallseeds (species not identified) would be found while turningover rocks in the same locations of the retrieved mimics. Depo-sition patterns were further compared to established aldersbased on a stem count and reflect a similar percentage betweenthe two reaches (Figure 7c) with the vast majority of mimicsand alders found in the first reach.

Discussion

To model the dispersal of buoyant seeds the following fieldobservations provided guidance when selecting a numericalformulation. When a large number of mimic seeds are releasedat the same time in the middle of a heterogeneous stream andobserved at a cross-section point downstream the followingoccurs: (1) seeds do not pass the observation point at the sametime and spread longitudinally in the steam; (2) seeds extendhorizontally in the flow and do not follow the same streamline;(3) some seeds are captured in eddies (transient storage) alongthe edge of the stream and are deposited on the banks. Theseobservations support the use of the advection–dispersion equa-tion for seed transport and transient storage to convey seeddeposition. While the model is not definitive, it provides asimple first approximation to seed transport and defines storageareas for seed deposition. The model output parametersprovide insight into seed transport and deposition by examin-ing the ratio between the storage area and the main channelarea (As:A ratio), along with the exchange between these two

Figure 7. Field deposition shown as (a) total percentages and (b) at 10m intervals. (c) The percent deposition of mimics was compared withestablished alders to highlight the distribution pattern.



areas. While the results model a single discharge event, wealso consider the effect of variable flow conditions on As:Aratio.

Significance of storage area

Our results suggest that the extent of the transient storage areaplays an important role in seed transport and deposition. Whenconsidering As:A ratio, the first reach had a relatively high ratio(0.6) and was responsible for the majority of mimics capturedalong the bank, while the second reach had a low ratio (0.1)and fewer deposition numbers. The model approach is novelin terms of seed dispersal and at present can only be comparedto traditional application based on solute tracer studies. Forinstance, solute tracer studies (Battin et al., 2003; Ensign andDoyle, 2005; Jin and Ward, 2005; Argerich et al., 2008) havefound the ratio of As:A to be an important parameter to under-stand nutrient transport and retention in streams. This wasshown by Argerich et al. (2008) where leaves accumulating atthe head of a riffle caused a dam-like feature wherein upstreamwater pooled resulting in an increased storage area and waterresidence time to increase the opportunity for nutrient uptake.In stream systems dominated by surface storage rather thanhyporheic storage, an increased storage area and As:A wasattributed to greater complexity in geomorphic structures. Thiswas shown physically by Ensign and Doyle (2005) whomounted flow baffles in both a canal and creek that resultedin larger storage areas and an increased As:A ratio comparedto their natural straight channel. Similar findings, connectinga high As:A ratio with channel complexity, are prominent inhyporheic exchange studies (Harvey and Bencala, 1993;Cardenas et al., 2004; Gooseff et al., 2006; Gooseff et al.,2007). In this study, the first reach had a large riffle (adjacentto the cobble/gravel bar) along with a bend (due to confiningbedrock wall) that created large divergent flow as the flowexpanded towards the pool. These geomorphic features likelycontributed to the larger storage area modeled in Reach 1.Furthermore, Gooseff et al. (2005) reasoned that solute mean

residence time in transient storage areas had a linear relation-ship with eddy size and implied that larger eddies led to greatersolute concentration in the storage area. Similarly, if largereddies caused a greater number of seeds to accumulate in thestorage areas this may provide more opportunity for seed depo-sition. To quantify the strength of eddies, Merritt and Wohl(2002) introduced a dimensionless number termed the ‘recircu-lation index’ (Uavg/Umax where Uavg represents the mean veloc-ity [in m s�1] in the flow for a specific fluvial feature andUmax isthe maximum point velocity [in m s�1] within the main chan-nel) to provide a measure of recirculation strength caused byvarious fluvial features where a low index indicates a strongrecirculation. A low recirculation index was associated withslack water, an eddy, or a flow expansion. In their flume study,over 80% of early dispersing seeds were deposited in areaswith a low recirculation index when discharge was decreasedby a continuous and stepped flow regime. Our results, whilein steady state conditions where discharge was held constant,corroborate that of Merritt and Wohl’s (2002) findings thatsuggested a reduced flow velocity (represented by storage areain our study) and a low recirculation index (represented by ahigh exchange coefficient) are dominant hydraulic factors thatfavor deposition. In the numerical model, the storage areasare not defined by a single flow type. At the study site, the firstreach was dominated by divergent flow types while the secondreach was predominantly slack water. Similar to the flume resultsof Merritt and Wohl (2002), storage areas dominated by diver-gent type flow were more successful at depositing mimics.

Storage flow structure

The coefficient (α) is the coupling term of the exchange ofmass between the main channel and storage area. It is attrib-uted to varying flow velocities and turbulent dynamics andis thought to be a measure of lateral dispersion with morerapid exchange (by an order of magnitude) occurring insurface storage compared to hyporheic transient storage(Briggs et al., 2009; Gooseff et al., 2011). In this study themean storage residence time (ts =As/αA) was much longer(84.9 seconds) in Reach 1 compared to Reach 2 (16.9 seconds).However, a large standard deviation in the exchange coeffi-cient in Reach 2 suggests that a single surface storage modelmay not accurately describe the exchange capacity (Table I).Floating debris piles in Reach 2 were observed to detainmimics for long periods of time (typically 101minutes) andsporadically released mimics back into the flow. Systems thatcontain exchange flux at multiple temporal scales may bemore appropriately modeled by multiple storage zones. Choiet al. (2000) demonstrated in wetlands the appropriatenessof a two-zone storage model where vegetation was responsi-ble for detaining solutes for hours as opposed to the quickerexchange in non-vegetated flow. While longer residencetimes suggest a greater chance of deposition of buoyant seeds,detainment by floating mats or large woody debris would notbe suitable establishment sites for some species such as whitealder. Thus, longer residence times should be positively corre-lated with deposition, although these features associated withdetainment may make these sites unsuitable for later stages inthe population dynamics (i.e. establishment and survival). Theresults suggest that pools have a shorter residence time whichdecreases the opportunity for deposition, but contain featuressuch as debris piles that may effectively delay transportprocesses.

Velocity profile to estimate channel areas

A secondary analysis using stream velocity profiles was under-taken to ensure model results supported the field observations.In the field, the ratio between the main channel and storagecan be estimated by analysing the direction of the surface flowvelocity where positive flow values indicate main channel flowand negative flow values suggest flow in storage areas (Briggset al., 2009). To corroborate the ratio of the storage and mainchannel areas (As:A) between the model and the field it is possi-ble to examine the cross-sectional surface velocity profile byusing a handheld acoustic Doppler velocimeter. Cross-sectionallengths of negative velocity (water flowing upstream) can thenbe used to estimate approximate areas of surface storage (Briggset al., 2010) and help validate model results.

Only one location, a pool at 300m, was accessible when theflows were at 9.5m3 s�1 (Figure 8). The velocity profile in thepool at 300m recorded backflow only on the right-hand sidebank (facing downstream) and accounted for 2.2% of the overalllength, suggesting a small storage area and corroborating withmodel results where storage area was calculated to be 10% ofthe total area. Unfortunately, cross-section measurements werenot possible in the riffle due to safety concerns with the strongflow. However, surface flow measurements at the end oftwo riffles (90m and 220m) were taken during low flow(<1m3 s�1) when wading across the stream was possible(Figure 8). Much larger backflows were recorded at the end ofeach riffle where 33.1% and 53.2% of the overall cross-sectionallength had a negative velocity at 90m and 220m, respectively,implying a large storage area which is attributed to the geomor-phic feature where flow expansion occurs at the end of the riffle.



Similarly, the modeled area at 9.5m3 s�1 had a 38% storage areaimplying that the geomorphic feature results in similar storagepercentage areas but does not necessarily scale at the varyingflow conditions as geomorphic features may become submergedwith larger discharge.

Variable flow considerations

While not explicitly examined in this paper, discharge andchannel morphology control hydraulic conditions, which inturn affect model parameters. Few studies to date have investi-gated the relationship between surface storage area andchanges in discharge. In a lumped parameter study, where sur-face storage was not separated from hyporheic flow, the As:Aratio decreased with increasing discharge in a second-orderstream, with discharges ranging from 0.006 to 0.029m3 s�1

(Argerich et al., 2008). Increasing discharge has further beenexamined by moving study sites down the channel networkrather than observing a varying discharge at a single location.For instance, in base flow conditions, Briggs et al. (2010) sepa-rated surface storage and hyporheic flow along a coastal stream

network and found that As:A had a weak positive relationshipwith discharge. However, when these researchers consideredcontributing area as an independent variable, deeming it moregeomorphologically significant than discharge, no relationshipto As:Awas found.

Basin confinement in river valleys may further dictate thechanging nature of As:A as discharge varies. A decreasing As:A trend was found in mountain streams with increasing streamorder with the exception of unconstrained, fifth-order sites thatresulted in higher As:A ratios; however, this trend was observedon lumped parameters that did not separate out the surface tohyporheic areas which may affect the ratio calculations(D’Angelo et al., 1993). Additionally, studies that move alonga stream network to identify the relationship between dischargeand As:A ratios may misinterpret the results as retention mech-anisms and morphological features do not stay constant alongthe stream network (Briggs et al., 2010). It is also acknowledgedthat research conducted by D’Angelo et al. (1993) and Briggset al. (2010) was based on tracer studies rather than mimicsand further research would be required to verify the effects ofa varying discharge on buoyant seed deposition patterns.

Complex channels, such as Reach 1, that are both confinedand compound and where the base flow has a different geom-etry than at bankfull flow, would be expected to have a varyingAs:A ratio at different discharge levels. In high discharges abovethe bankfull level, we expect a low As:A as the width to depthratios would begin to decrease due to the confining valleyand bedform structures becoming inundated due to the highflow volume. For base flow conditions in our study area(<1m3 s�1), the As:A ratio may also remain low due to the re-duced eddy size and stream power that have been shown tobe positively correlated to α (Zarnetske et al., 2007). Base flowconditions may also lack connections with side pools or em-bayments that would otherwise increase storage areas. How-ever, a higher As:A ratio would be expected if aquaticvegetation was present, such as tussocks and sedge that growon riffles during summer base flow conditions along the SouthFork Eel River within the reserve. Therefore, it is during moder-ate flows that we might expect the highest As:A ratio as agreater portion of the cross-sectional area interacts with theflow and is combined with faster exchange coefficients, thusleading to longer residence times (or stronger recirculation)and, correspondingly, more opportunity for deposition. In thesecond reach that is dominated by pools and that is lessgeomorphologically complex, we expect the As:A ratio to fluc-tuate only marginally as bedrock outcrops become more/lessexposed with varying discharge. Low seed deposition in thepools is probable even at varying discharge. More field basedresearch is necessary to understand the influence of dischargeon As:A ratio and exchange coefficients, with consideration ofascending and descending flow regimes also being necessary.In the Merritt and Wohl (2002) flume study, a descending flowregime resulted in higher deposition numbers. Conversely, as-cending flows played a larger role in entraining and transportingseeds as the flume geomorphic features where inundated collab-orating with the idea that low As:A ratios are associated withsparse deposition.

Conclusion

Here we have used a one-dimensional model of a coupledadvection–diffusion equation to a transient storage equationto highlight the two primary flow patterns in rivers and streams:advective and dispersive flow in the main river/stream whichtransport buoyant seed down river/stream, transient storageareas which hold buoyant seeds for varied period of time and

Figure 8. Cross-sectional velocity profiles at 90m, 220m, and 300m.Circles represent actual velocity measurements. Positive velocities rep-resent downstream movement and negative velocities represent back-flow in the upstream direction. Measurements at 90m and 220mwere taken in December, 2011 at the end of a riffle when stream wad-ing was possible. The measurement at 300m was located in a pool aday prior to the release with similar discharge values.



strand some. Fluvial geomorphological structures within theactive channel play a primary role in seed deposition by caus-ing divergent flows which are responsible for preferential seeddeposition. Consequently, the initial deposition location affectsthe distribution of riparian trees and overall population dynam-ics. A greater understanding of seed depositional locations andpatterns as dictated by flow structure may benefit riparian resto-ration efforts which seek to rebuild a riparian tree population.Linking depositional patterns with observed vegetation

remains difficult and requires further consideration of popula-tion dynamics (Nilsson et al., 2002; Levine and Murrell, 2003;Merritt and Wohl, 2006; Merritt et al., 2010). Dispersed seedsmay still be subject to germination limitations, seedling mor-tality, inappropriate substrate type, and the constant riskof uprooting by a flood. However, depositional location maybe viewed as a template when considering the populationstructure for a species. Once seeds are deposited, germinationrequirements need to be met for establishment to occur. Seedsdeposited at high water levels have the advantage of not beingwashed away in subsequent floods, yet may be at risk ofdesiccation/quiescence if ground water levels descend withdecreasing discharge. This paper has shown the associationof the deposition pattern with standing vegetation at a partic-ular discharge that favors preferential deposition but acknowl-edges the limitations in concluding a direct causal effect dueto the many life history stages that may also shape a popula-tion’s distribution structure.

Acknowledgements—This research was supported by an NSERCDiscovery Grant. The authors thank the Angelo Coast Range Reservefor providing accommodation and Mary Power’s lab for their assis-tance. The authors also thank Peter Bezeau, Jim Cunnings, JocelynHirose, D’Arcy Kroeker, Diane Tan and Yulia Tsinko for their help asfield assistants. Unnamed reviewers provided helpful and thoughtfulcomments.

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