Modelling particle residence times in agricultural river basins …livrepository.liverpool.ac.uk/2005520/3/Smith et al, 2014... · 2015-01-21 · Modelling particle residence times

EARTH SURFACE PROCESSES AND LANDFORMSEarth Surf. Process. Landforms 39, 1944–1959 (2014)© 2014 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.Published online 20 May 2014 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/esp.3589

Modelling particle residence times in agriculturalriver basins using a sediment budget model andfallout radionuclide tracersHugh G. Smith,1* William H. Blake2 and Alex Taylor21 School of Environmental Sciences, University of Liverpool, Liverpool, L697ZT, UK2 School of Geography, Earth and Environmental Sciences, Plymouth University, Plymouth, PL48AA, UK

Received 3 September 2013; Revised 14 April 2014; Accepted 15 April 2014

*Correspondence to: Hugh G. Smith, School of Environmental Sciences, University of Liverpool, Liverpool, L697ZT, UK. E-mail: [email protected]

ABSTRACT: Contemporary patterns in river basin sediment dynamics have been widely investigated but the timescales associatedwith current sediment delivery processes have received much less attention. Furthermore, no studies have quantified the effect ofrecent land use change on the residence or travel times of sediment transported through river basins. Such information is crucialfor understanding contemporary river basin function and responses to natural and anthropogenic disturbances or managementinterventions. To address this need, we adopt a process-based modelling approach to quantify changes in spatial patterns andresidence times of suspended sediment in response to recent agricultural land cover change. The sediment budget model SedNetwas coupled with a mass balance model of particle residence times based on atmospheric and fluvial fluxes of three falloutradionuclide tracers (7Be, excess 210Pb and 137Cs). Mean annual fluxes of suspended sediment were simulated in seven river basins(38–920 km2) in south-west England for three land cover surveys (1990, 2000 and 2007). Suspended sediment flux increased acrossthe basins from 0.5–15 to 1.4–37 kt y-1 in response to increasing arable land area between consecutive surveys. The residence timemodel divided basins into slow (upper surface soil) and rapid (river channel and connected hillslope sediment source area) transportcompartments. Estimated theoretical residence times in the slow compartment decreased from 13–48 to 5.6–14 ky with the increasein basin sediment exports. In contrast, the short residence times for the rapid compartment increased from 185–256 to 260–368 d asthe modelled connected source area expanded with increasing sediment supply frommore arable land. The increase in sediment residencetime was considered to correspond to longer sediment travel distances linked to larger connected source areas. This novel coupledmodelling approach provides unique insight into river basin responses to recent environmental change not otherwise available fromconventional measurement techniques. © 2014 The Authors. Earth Surface Processes and Landforms published by JohnWiley & Sons Ltd.

KEYWORDS: sediment budgets; sediment residence time; connectivity; fallout radionuclides; river basins

Introduction

Quantifying the timescales of sediment transfer through riversystems is fundamental for understanding river basin sedimentand associated contaminant dynamics. This timescale is repre-sented by the period of sediment residence or transit within a riverbasin that may encompass soil formation from bedrock, hillslopeerosion and delivery to streams, storage and remobilization inchannels and floodplains, and export from the basin outlet. Alter-natively, sediment residence time may be determined for a subsetof these components of the fluvial sediment cascade (Fryirs,2013). Information on the residence time of sediment for differentparts of a river basin is required to address research and rivermanagement questions of global importance. It has been used asa basis for interpreting the sedimentary response of river basins tochanges in land cover and climate over the past 100 ky (Dossetoet al., 2010). It can also be used to project timeframes for the re-moval of sediment-associated contaminants stored in river basins(Coulthard and Macklin, 2003; Malmon et al., 2005), thereby pro-viding valuable information to river managers.

This is an open access article under the terms of the Creative Commons Attribution-NonC

provided the original work is properly cited, the use is non-commercial and no modific

Investigations of sediment residence time in river basins canbe broadly divided into two categories, namely studies quanti-fying long-term weathering and denudation rates versus thosefocused on sediment dynamics in river channels and basinsunder recent environmental conditions. The first set of studiesuse cosmogenic or U-series isotopes to measure rates ofsediment production from bedrock (Heimsath et al., 2001;Fifield et al., 2010) or sediment transit times through riverbasins over 1 to several 100 ky timescales (von Blanckenburg,2005; Granet et al., 2010). Studies in the second categoryquantify sediment transit over short hydrological timescales ofmore relevance to management. Such studies have used thefallout radionuclides 7Be and excess 210Pb (210Pbex) to estimatefine sediment residence times or changes in sediment source inriver channels spanning days to months (Bonniwell et al., 1999;Matisoff et al., 2005) and over decades (Wallbrink et al., 1998,2002; Gartner et al., 2012). Fallout radionuclide tracers havealso been used to estimate sediment residence times at the riverbasin scale (Dominik et al., 1987; Le Cloarec et al., 2007;Evrard et al., 2010). Alternatively, the residence times of

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1945MODELLING SEDIMENT RESIDENCE TIMES IN RIVER BASINS

sediment stored in floodplains have been estimated probabilis-tically from computations of sediment mass balances forreach-scale storage units (Dietrich and Dunne, 1978; Kelseyet al., 1987; Malmon et al., 2003).The present study focuses on quantifying fine sediment

residence times in river basins under recent environmentalconditions. The objective was to model changes in spatialpatterns and residence times of suspended sediment in responseto contemporary agricultural land cover change. No studies haveexamined the effect of changes in land use on sediment residencetime. While many previous studies have quantified the impact ofland use change on the magnitude of sediment flux fromcatchments, changes to the timescales of sediment delivery incontemporary landscapes have been neglected. However, suchinformation is crucial to the fundamental understanding of con-temporary river basin sediment dynamics and the longer-termbenefits, or otherwise, or sedimentmanagement measures. In thiscontext, it also has important implications for residence times ofsediment-associated contaminants. For example, changes to theduration of sediment storage in particular landscape compart-ments could affect the level of contaminant mobility withnegative environmental consequences. Therefore, a new researchfocus is required to address this important knowledge gap.Changes in sediment residence times in response to land

cover change were, for the first time, modelled by combininga sediment budget model, SedNet, with a mass balance modelof particle residence times based on three fallout radionuclidetracers, namely 7Be, 210Pbex and 137Cs. SedNet is a spatially-distributed model that represents erosion, sediment transferand storage in steady state over a multi-decadal timescale(Prosser et al., 2001a; Wilkinson et al., 2004). It was developedin Australia and has been applied there to large river basins intropical and temperate environments (McKergow et al., 2005;Wilkinson et al., 2009; Hughes and Croke, 2011). There havebeen no previous applications of SedNet to river basins inEurope or the UK.

Figure 1. River Tamar study basin showing (a) the monitored sub-basins(10 m grid size) and the modelled floodplain.

© 2014 The Authors. Earth Surface Processes and Landforms published by John Wiley

Particle residence times were modelled using a mass balanceapproach based on atmospheric and fluvial fluxes of the falloutradionuclide tracers. The model was first proposed by Dominiket al. (1987) using only 7Be and 210Pbex. Subsequently, LeCloarec et al. (2007) revised the model by including the 137Cssoil inventory as an additional constraint. The model has beenapplied by Evrard et al. (2010) to investigate sediment dynam-ics in several small catchments in the tropical highlands ofMexico. In contrast, the present study differs from previousapplications of the residence time model by employing multi-decadal estimates of fallout and fluvial export. Previous appli-cations were based on short-term monitoring (1–2 years) thatis highly dependent on the specific hydroclimatic conditionsduring measurement periods. Furthermore, these studies did notaddress changes in residence times in response to land coverchange, which requires a dedicated model-based approach.The present study focuses on simulating residence times in sevenriver basins (38–920 km2) situated in south-west England for landcovers corresponding to three surveys produced from satelliteimagery between 1990 and 2007.

Methods

River basins

Modelling and field measurements were undertaken in sevenagricultural river basins located in south-west England(Figure 1). Six of the basins are nested within the River Tamarbasin upstream of the village of Gunnislake (920 km2) andinclude the Rivers Carey (67 km2), Inny (97 km2), Kensey (38 km2),Lyd (219 km2), Ottery (124 km2), and a second measurement siteon the main channel of the Tamar in the upper basin (TamarUpper; 238 km2). The River Tamar forms the main boundary be-tween the counties of Devon and Cornwall and drains south intothe Tamar Estuary at Plymouth. All measurements and modelling

with the modelled channel network and (b) digital elevation model

& Sons Ltd. Earth Surf. Process. Landforms, Vol. 39, 1944–1959 (2014)

1946 H. G. SMITH, W. H. BLAKE AND A. TAYLOR

were undertaken upstream of the tidal limit. The topography ischaracterized by short, steep hillslopes in the lower and midTamar basin, with lower relief terrain in the upper basin.Maximum elevations (up to 581 m) occur in the small areas ofgranitic moorland to the east and west.Most of the basins are underlain by fine sedimentary rocks

(mudstones, shales and sandstones). Soils are predominantlyloamy, with some peaty soils in upland areas. The extent offloodplain is limited and confined by narrow steep-sidedvalleys and shallow bedrock. The largest floodplain area islocated in the middle of the main Tamar basin. The section ofmain channel between the Inny and the basin outlet atGunnislake is extensively bedrock confined. Land cover ismostlyagricultural (grassland and arable) with a small area of woodland(<16%). Surveys of land cover based on satellite imagery werecompleted in 1990, 2000 and 2007 (Morton et al., 2011).Precipitation across the study basins falls predominantly as rain

and exhibits pronounced spatial variability with the highestannual totals occurring over the upland areas to the east andwest. Across the Tamar basin, mean annual precipitation was1284 mm based on 1×1 km gridded data for 1971 to 2000. Themean daily river flow measured at Gunnislake was 22.4 m3 s-1

and ranged between 0.58 and 482 m3 s-1 for the period from1956 to 2012. There is also pronounced seasonality in rainfalland river flows, with the highest discharge generally occurringfrom November to March in association with Atlantic cold fronts.

Field measurements and laboratory analysis

Suspended sediment samples were collected continuously atthe outlets of each river basin over a 12 month period. In situtime-integrated samplers based on the design by Phillips et al.(2000) were deployed in pairs at riffles. The samplers weremade from polyvinylchloride (PVC) tubes 1 m in length and0.11 m in diameter with sealed caps at both ends thatcontained 3 mm diameter inlet and outlet tubes. Water andsuspended sediment pass through the narrow inlet tube andenter the PVC tube where the change in cross-sectional areapromotes a reduction in flow velocity and sedimentation(Phillips et al., 2000). Under some conditions, these samplersmay under-sample the very fine fraction (<2 μm) of suspendedmaterial, although Phillips et al. (2000) noted that the transportof very fine particles as aggregates should reduce the level ofunder-sampling that was observed during laboratory experi-ments. Samples were collected at approximately monthlyintervals from September 2011 to October 2012. During thistime the mean daily flow for the River Tamar at Gunnislakewas slightly above average at 23.9 m3 s-1 and ranged between4.5 and 155 m3 s-1.All sediment samples were analysed for the three fallout ra-

dionuclides following freeze-drying and gentle disaggregation.Samples were sealed for 21 days in either 50 mm Petri dishes orin 4 mm vials for some low mass samples to allow equilibrationbetween 214Pb and its parent 226Ra. Activity concentrations ofthe radionuclides were measured using low backgroundEGandG Ortec planar (GMX50-83-LB-C-SMN-S) and well(GWL-170-15-S) HPGe gamma spectrometers at the PlymouthUniversity Consolidated Radio-isotope Facility within an ISO9001:2008-certified framework. 210Pbex was determined bysubtraction of 226Ra activity measured using 214Pb gammaemissions (295 and 352 keV) from total 210Pb (46.5 keV).137Cs and 7Be activities were determined from gamma emis-sions at 662 and 478 keV, respectively. Detector efficiency for7Be was determined by interpolation between the efficiencyvalues of 137Cs (662 keV) and 113Sn (392 keV). Count timeswere typically 86 ks, although some low mass sediment


samples were counted for 172 ks. Sample calibration wascarried out using standards of the same geometry and matrixas the experimental samples. Standards were prepared using amixed standard solution (G E Healthcare, Amersham, UK) whichwas distributed in a sediment matrix. Sample counts werecorrected for background emission, geometry efficiency anddecay. All values were decay corrected to the time of samplingand reported as activity concentration (Bq kg-1). Analytical perfor-mance was assessed by inter-laboratory comparison tests usingmaterials supplied by the International Atomic Energy Agency.

Sediment budget model

SedNet derives a river network from a Digital Elevation Model(DEM). This network is divided into river links that are formedbetween adjacent stream junctions and includes the internalcontributing area draining into each link. The mean annualsuspended sediment mass balance (t y-1) is computed for eachriver link from internal hillslope, gully and riverbank erosionand upstream tributary inputs less floodplain and reservoirdeposition losses. The net flux of suspended sediment is passedto the next downstream link. Transient storage of suspendedsediment within the channel network is neglected because thisis considered small relative to total yields over multi-decadaltimescales (Wilkinson et al., 2009).

Hillslope soil erosion is modelled using a spatially-distributedversion of the Revised Universal Soil Loss Equation (RUSLE,Renard et al., 1997). RUSLE is used to predict mean annual soilloss (A, t ha-1 y-1) from rill and interrill erosion based on theproduct of six empirically-derived factors:

A ¼ RKLSCP (1)

These are rainfall erosivity (R), soil erodibility (K), slope length(L) and steepness (S), cover (C) and management practice (P). Theprocedures for calculating each RUSLE factor are outlined inTable I. In the absence of specific information aboutmanagementpractices across the study basins, Pwas not explicitly included inthe computation ofA (i.e. it was set to 1). SedNet does not includerepresentation of small-scale features such as roads, tracks orditches that may either generate sediment or act as transportpathways. The RUSLE factors were produced as a set of rastergrids with three grids for C factors corresponding to the 1990,2000 and 2007 land cover surveys.

The proportion of sediment from hillslope erosion deliveredto the river network was represented using a hillslope sedimentdelivery ratio (HSDR). This is designed to account for thediscrepancy between plot-scale erosion rates and small basinsediment yields, reflecting short sediment travel distanceson hillslopes (Parsons et al., 2006) and storage opportunities(e.g. farm dams, contour banks) between slopes and thechannel network (Prosser et al., 2001b; Slattery et al., 2002).At larger basin scales, it is not practical to capture the smallscale variability in HSDR. Therefore, the HSDR was set to0.15 in the present study in accordance with field measure-ments made by Walling et al. (2002) in small agricultural basins(<4 km2) in central England. The mean annual supply ofhillslope-derived sediment (HSx, t y

-1) to the modelled channel

network in each river link is determined byHSx ¼ HSDRXj¼n

j¼1

Aj,

where Aj is the mean annual RUSLE erosion rate calculated foreach grid cell j in the internal drainage area containing n cellsfor each river link x.

Gully erosion was not observed in the study basins and thiscomponent of SedNet was not used. Riverbank erosion for each


TableI.

Summaryofdatainpu

tsan

dprocessingforcalculatio

noftheRUSLEfactors

foruse

intheSedNet

model

RUSLEfactor

Datainputan

dsource

Dataprocessing

Rainfallerosivity

(R)

Plymou

thUniversity,Princetownan

dSt

Maw

gan

(12–1

5years)sub-hou

rlyrainfallreco

rds;

Rainfallerosivity

(R,MJmm

ha-1h-

1y-1)was

calculatedusingthekinetic

energy

relatio

nship

ofMarshallan

dPalmer

(1948)reco

mmen

ded

fortheUKbyMorgan

(200

1):

BritishAtm

ospheric

DataCen

tre,

Plymouth

University

andtheUKMet

Office

KE=0.0895+0.0844log 1

0(I)

whereKEiskinetic

energy

per

unitrainfall(M

Jha-1mm

-1)an

dIisrainfallintensity

(mm

h-1).EI

30was

calculatedforeach

even

tas

the

produc

toftotalkinetic

energy

(E,MJha-1)an

dthemaxim

um

30-m

inrainfallintensity

(I 30,mm

h-1).Thelin

earregression

R=1.3723A

�551.27(R

2=0.95)betweenthean

nua

lsum

ofEI

30(R)an

dan

nual

rainfall(A,mm

y-1)fordatafrom

thethreerain

gauges

was

usedto

calculate

gridded

Rvalues

using

the1×1km

grid

of30-yearmeanan

nual

precipita

tion(1971–

2000)fortheriverbasins.

Soilerodibility

(K)

Digita

lsoilvectormap

andsoilattribute

data;

Soilerod

ibility

(K,thahha-1MJ-1

mm

-1)was

calculatedacco

rdingto

Wisch

meier

andSm

ith(1978):

Nationa

lSo

ilResources

Institu

te,

Cranfie

ldUniversity

aK¼

2:1x10�

412�O

Mð

ÞM1:14þ3

:25S�

2ð

Þþ2:5

P�3

ðÞ

7:59x100

whereOM

issoilorgan

icmatterco

nten

t(%

),M

=(%

silt+%very

finesand)x(100-%clay),Sisthesoilstructure

classan

dPisthe

permeability

class.

Slopelength(L)

10m

DEM

Slope

length(L)was

calculatedonthebasisofco

ntributin

gareasacco

rdingto

Desmet

andGovers

(1996):

UKOrdnan

ceSu

rvey

L i;j¼

Ai;j;inþD

2ð

Þmþ1

�Amþ1

i;j;in

Dmþ2

xm i;j22:13

ðÞm

whereAi,j,inistheco

ntributin

garea

(m2)to

thegrid

cellwith

coordinates

(i,j),

Disthegrid

cellsize

(10m),x i,j=sinα i,j+co

sαi,j,w

hereα i,j

istheaspectdirectio

nforthegrid

cellwith

coordinates

(i,j),

misavariab

leslope

lengthexponen

trelatedto

theratio

εofrillto

interrill

erosionbym=ε/(1+ε)in

whichεiscalculatedforsoilthat

ismod

eratelysuscep

tible

toboth

rillan

dinterillerosionby

ε=sinθ/(0.0896

[3.0(sinθ)

0.8+0.56]),whereθ

istheslope

angle(Ren

ardet

al.,1997).In

thepresentstudy,

themaxim

um

slopelengthwas

limite

dto

300m

toreduce

thelik

elihoodofch

annel

form

ationwith

increasingco

ntributin

garea

(Ren

ardet

al.,1997).

Slopesteepness(S)

10m

DEM

Slope

steepne

ss(S)was

calculatedusing

theeq

uationreco

mmen

ded

byMcC

oolet

al.(198

7)whereθisslopean

gle:

UKOrdnan

ceSu

rvey

S¼

10:8sinθ

þ0:03;

s<

9%

16:8sinθ

�0:50;

s≥9%

�

Cover(C)

UKlandco

versurveysfor1990,

2000an

d2007(25m

raster

grids).

Cover(C)values

werebased

ontherang

eofvalues

estim

ated

byMorgan

(2005);Fu

etal.(2006);Van

Rompa

eyan

dGovers

(2002)

andWisch

meier

andSm

ith(1978):

Cen

treforEcology

andHyd

rology

Arable

landC=0.25;pasture

C=0.01;forestC=0.001;shrub/heath

C=0.01;urban

andinlandbaregroundC=0.03.

aSo

ilsdata©

Cranfie

ldUniversity

(NSR

I)an

dfortheControlle

rofHMSO

2012


© 2014 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd. Earth Surf. Process. Landforms, Vol. 39, 1944–1959 (2014)

TableII.

SummaryofSedN

etmodel

datainpu

tsan

dparam

eter

values

Mode

linput

Datasetsan

dparam

eters

Datasource

Topograp

hy

10m

DEM

UKOrdnan

ceSu

rvey

Flood

plain

extent

MRV

BFinde

x>3.5

clipped

by100year

recu

rren

ceinterval

flood

extent

100year

flood

layer:UKEn

vironmen

tAgenc

yMeanan

nual

precipita

tion

1×1km

grid

of30year

meanan

nua

lprecipita

tion(197

1–2000)

UKMet

Office

Potentia

levap

oration

MOREC

S40×40km

grid

UKMet

Office

River

flow

Unregu

latedflo

w:5rivergaug

es(18–2

6years);Regulated

flow:6rivergauges(22–

37years)

UKEn

vironmen

tAgency/Cen

treforEcology

andHyd

rology

Ban

kfullrecu

rren

ceinterval

1.5

yearsonthean

nua

lmaxim

um

series

Davidsonan

dHey

(201

1)

Meanban

kheigh

t(H

)H=0.93±0.22m

Chan

nel

network

survey

(n=20sites)

Chan

nel

width

(W)-catchmen

tarea

(A)

W=1.346A0.4885(R

2=0.94)

Chan

nel

network

survey

(n=20sites)

Proportionfin

evs.co

arse

sedim

ent

(ban

kerosion)

0.74vs.0.26:Meanclay,siltan

dvery

finesandvs.remainingsandco

ntentforripariansoils.

Themeanfractio

nofsampledsuspen

ded

material<63μ

mwas

0.89±0.06.

Digita

lsoilmap

;Nationa

lSo

ilResources

Institu

te,

Cranfield

University

a

Riparianvegetatio

n(ban

kerosion)

Clip

ped25m

buffe

reither

sideofmodelledch

annel

network

for1990,

2000an

d2007landco

versurveys

UKCen

treforEcology

andHyd

rology

Hillslopesedim

entdeliveryratio

(HSD

R)

0.15

Wallin

get

al.(2002)

aSo

ilsdata©

Cranfie

ldUniversity

(NSR

I)an

dfortheControlle

rofHMSO

2012.


river link (BEx, t y-1) is modelled by relating link stream power

(pgQbfSx) to bank erodibility (Wilkinson et al., 2005), which isrepresented as a function of riparian vegetation and floodplainwidth, as in the following equation:

BEx ¼ cρgQbf Sx 1� PRxð Þ 1� e�0:008Fx� �

Lxhρspsð Þ (2)

where c is a coefficient that is set to limit the maximum bankretreat rate (c=0.0001), ρ is the density of water, g is accelera-tion due to gravity, Qbf is bankfull discharge (m3 s-1), Sx is theenergy slope approximated by channel gradient, PR is theproportion of intact riparian vegetation along a river link(defined here as forest or woodland cover in 1× 25 m cell eitherside of the modelled channel network ), Fx is floodplain width(calculated as floodplain area divided by river link length), Lxis the link length (m), h is mean bank height (0.93 m), ρs is soilbulk density (1.5 t m-3 for the full bank profile) and ps is theproportional bank contribution of fine sediment to suspendedload (Table II). Bankfull discharge was defined as the flow witha recurrence interval of 1.5 years on the annual series based ona survey of UK rivers (Davidson and Hey, 2011). The increasingproportion of riparian forest or woodland along a river link wasconsidered to reduce bank erodibility through the effect of treeroot reinforcement increasing bank stability (Thorne, 1990;Abernethy and Rutherfurd, 2001). Floodplain width was usedas a surrogate for exposure to bedrock such that there was anexponential decline in bank erodibility with decreasingfloodplain width corresponding to increased bedrock exposure(Wilkinson et al., 2005).Floodplain deposition (FDx, t y

-1) is computed as a functionof floodplain area and the median value of daily overbank flow(Prosser et al., 2001b):

FDx ¼ Qf

QIxð Þ 1� e

� vAfQf

� � !(3)

where Qf is the median of the set of daily overbank dischargesdetermined from the amount by which total daily discharge (Q)exceeds bankfull discharge (Qbf), Ix is the total suspendedsediment supply to the link x, Af is the floodplain area and vis the particle settling velocity (1 × 10-6 m s-1) based on StokesLaw for particles with diameters 1–4 μm such that that largerparticles can be expected to have settled during the period ofoverbank flow (Wilkinson et al., 2009). It is assumed that theproportion of sediment delivered to the floodplain equates tothe proportion of discharge that goes overbank relative to totaldischarge. The floodplain extent was defined by the Multi-Resolution Valley Bottom Flatness (MRVBF) terrain indexdeveloped by Gallant and Dowling (2003). Reservoir deposi-tion is calculated as a function of the mean annual reservoirinflow and its total storage capacity based on a revised versionof the Brune Rule that is used to determine sediment trappingefficiency (Brune, 1953; Heinemann, 1981).Hydrological regionalization is required to provide esti-

mates of mean annual discharge (MAD), bankfull discharge(Qbf), and median overbank discharge (Qf) for each river linkfor use in erosion and deposition modelling. This is based onlong-term gauge records of unregulated discharge (Table II)for which MAD, Qbf and Qf were calculated. The runoffcoefficient (Rc) is estimated by combining a simplified waterbalance where Rc= (P� E)/P with a rational function relatingmean annual precipitation (P), evapotranspiration (E) andpotential evaporation (E0) (Zhang et al., 2004), to give Equation(4) (Wilkinson et al., 2006):



Rc ¼ 1þ E0

P

� � a E0=Pð Þþbð Þ" #1= a E0=Pð Þþbð Þ� E0

P(4)

The parameters a and b are fitted by least squares regression forE0/P versus Rc for the gauged river basins. Rc was estimated for allriver links based on the mean of the gridded E0/P for each link andthen used to calculateMAD for all links, whereMAD=RcPA andA is the internal drainage area for each link. Qbf and Qf areregionalized as a function of MAD using gauge data where Qbf=g(MAD)h andQf= j(MAD)k and g, h, j and k are fitted parameters(Wilkinson et al., 2004). Flow in the Tamar basin is affected by theoperation of Roadford Reservoir (built 1989; capacity 34.5 GL) inthe Lyd sub-basin and to a lesser extent the Upper Tamar Lake(built 1975; capacity 1.48 GL) in the north (Figure 1(a)). Rivergauge data available for the period following reservoirconstruction (Table II) was used to adjust the regionalized MADfor river links affected by reservoir diversions and this changewas propagated to downstream links.

Radionuclide residence time model

The residence timemodel computes radionuclide mass balancesusing basin inputs and fluvial export of 7Be, 210Pbex and

137Cs forriver basins divided into slow and rapid transport compartments.The compartments are defined according to transport velocity(Dominik et al., 1987). The slow compartment represents the up-per soil profile containing the fallout radionuclide inventories(<0.30 m soil depth). It is characterized by long residence timesthat correspond to the period of storage and transfer of radionu-clides from the upper soil profile to the rapid compartment. Therapid compartment represents river and reservoir surfaces as wellas the immediate surroundings that have much shorterradionuclide residence times. This includes runoff and sedi-ment-generating areas on hillslopes that are connected to theriver network. Rapid compartment residence times were consid-ered to represent the mobilization and transfer of radionuclidesfrom connected source areas to the basin outlets over approxi-mately seasonal to annual timescales. Model estimates of resi-dence times should be interpreted as mean values under steadystate conditions for each land cover.The fallout radionuclides employed here have been widely

used as soil erosion and sediment source tracers (see reviewsby Wallbrink and Murray, 1993; Walling, 2003; Mabit et al.,2008; Taylor et al., 2013). 7Be (t1/2=53 days) is a naturallyoccurring radionuclide produced by cosmic ray spallation ofnitrogen and oxygen in the upper atmosphere. Fallout occurspredominantly in association with precipitation (Wallbrinkand Murray, 1994). 210Pbex (t1/2=22 years) refers to the amountof 210Pb derived from atmospheric fallout that exceeds thatsupported by decay of its lithogenic parent 226Ra in situ.137Cs (t1/2=30 years) was produced by atmospheric nuclearweapons testing during the 1950–1960s and dispersedglobally, with subsequent less extensive releases from theChernobyl and Fukushima nuclear power plant accidents.The main basis for use of these fallout radionuclides as sedi-ment tracers is their tendency to strongly adsorb to fine particles(Cremers et al., 1988; He and Walling, 1996). This is reflectedin the high partition coefficients (Kd). In the present study, Kd

values of 1.0 × 105, 1.0 × 106 and 8.4 × 104 L kg-1 for freshwaterconditions were used for 7Be, 210Pbex and

137Cs, respectively,based on the summary of values presented by Le Cloarecet al. (2007). Use of these values assumes that environmentalconditions which may affect radionuclide mobility betweenthe particulate and dissolved phases remain unchanged acrossthe study basins (Taylor et al., 2012).


The model requires estimates for the atmospheric input of7Be and 210Pbex, the soil inventory of 137Cs (since fallout isnow negligible) and fluvial export of particulate and dissolvedfractions. Atmospheric fallout was estimated using meanannual rainwater concentrations for 7Be and 210Pbex of1.97±0.3 Bq L-1 (Taylor, 2012) and 0.1 ± 0.008 Bq L-1 (Peirsonet al., 1966), respectively. 7Be in rainwater was measured southof the Tamar basin at Plymouth during 2009-2010, while210Pbex was measured between 1962 and 1964 at MilfordHaven in south Wales. Mean annual rainwater concentrationswere combined with 1 × 1 km gridded data for 1971–2000mean annual precipitation to compute mean annual falloutfor each river basin (Table III). The 137Cs soil inventory (ICs,Bq m-2) was estimated using the regression relationship ICs=4.16R+1400, where R is mean annual rainfall. This was de-rived by Appleby et al. (2003) using soil inventory data (to0.3 m depth) from locations across Great Britain that weresampled in 1977 (Cawse, 1983). This relationship was appliedto the gridded mean annual precipitation data to estimate the137Cs inventory for each river basin, which was corrected forradioactive decay to 2012. There was negligible fallout fromthe 1986 Chernobyl nuclear accident in south-west England(Walling et al., 1989).

The proportional contribution of sediment from hillslopesurface and channel bank erosion affects the activity concentra-tions of fallout radionuclides in suspended sediment (Wallbrinket al., 2003; Smith et al., 2011). This reflects the soil profiledistribution of the radionuclides, where maximum concentra-tions occur at or near the surface and decrease exponentiallywith depth to negligible levels (Wallbrink et al., 1999). Therefore,the effect of changes in modelled hillslope and channel banksediment contributions on radionuclide activity concentrationsrequired consideration. The measured activity concentrations(Table III) were considered closest to values for suspended sedi-ment exported under 2007 land cover because of a consistenttrend of increasing arable land from 1990 to 2007 that increasedmodelled hillslope sediment contributions. Suspended sedimentactivity concentrations for the 1990 and 2000 simulations werescaled by the modelled proportion of hillslope sediment supply(HS) relative to total supply (TS) for each river basin. This ratiowas then divided by the equivalent ratio for 2007 and multipliedby the measured activity concentrations for each radionuclide(Cm) to give the estimated concentrations (Cet) for survey yearst (1990, 2000):

Cet ¼ Cm HS=TSð Þt= HS=TSð Þ07

(5)

Fluvial export of radionuclides associated with suspendedsediment was calculated by multiplying the estimated (1990,2000) or measured (approximating 2007) concentrations withthe respective modelled mean annual suspended sedimentoutput for each river basin. The factor changes in estimatedactivity concentrations for 1990 and 2000 compared withmeasured values equated to 0.62–0.78 and 0.91–0.98, respec-tively. The effect of earlier radionuclide activity concentrationson subsequent estimates for suspended sediment were consideredminimal because of the frequency of higher magnitude flowsthat could be expected to remove fine sediment fromstorage within the channel network over approximately seasonalto annual timescales. The dissolved radionuclide flux (Fd) wasdetermined using the literature-based Kd values for fresh waterwith activity concentrations for suspended sediment (C) andregionalized mean annual discharge (MAD) for each river basin(where Fd=C(1/Kd)MAD).

The residence time model requires solutions to fourEquations (6)-(9). The fraction of the basin area represented


TableIII.

Studybasin

characteristics,estim

ated

fallo

utan

dmeanactiv

ityco

ncentratio

nsobtained

from

time-integrated

suspen

ded

sedim

entsamplin

g

Estim

ated

mean

fallo

ut,F a

(MBqy-1)

Meansuspen

ded

sedim

entactiv

ityco

ncen

tration±SE

(Bqkg

-1)d

River

basins

Basin

area

(km

2)

Meanan

nual

precipita

tion,

MAP(m

m)

Modelledmean

annual

disch

arge,

MAD

(mm)

Reliefratio

,RRa

Norm

alised

MAD.RRb

7Be(×

105)

210Pb e

x(×

105)

137Cs,M

(MBq,×105)c

7Bee

210Pb e

x137Cs

Tamar

Upper

238

1214

658

0.006

0.12

5.7

0.29

6.9

127±13

42.1±2.9

4.8±0.9

Otte

ry124

1255

740

0.011

0.27

3.1

0.16

3.7

131±13

47.0±5.8

4.6±0.9

Carey

67

1180

669

0.011

0.24

1.6

0.08

1.9

113±11

48.4±4.5

5.9±0.7

Ken

sey

38

1333

832

0.014

0.39

0.99

0.05

1.2

255±21

104±8.3

8.3±0.9

Lyd

219

1325

733

0.029

0.69

5.7

0.29

6.8

152±25

60.6±12

10±1.3

Inny

97

1488

1070

0.014

0.49

2.8

0.14

3.3

207±13

91.5±5.9

8.5±0.4

Tamar

Gunnislake

920

1284

750

0.012

0.30

23

1.2

28

166±14

53.8±3.5

6.6±0.2

aReliefratio

isameasure

ofbasin

slopean

disdefined

asthemaxim

umbasin

relie

fdivided

bythemaxim

umhorizo

ntallengthmeasuredparallelto

themainriverch

annel.

bMAD

andRRwerenorm

alised

bydividingbytheirrespectiv

emaxim

umvalues

andthen

multip

lied(ran

ge0–

1).

cFo

r137Cs,theestim

ated

totalfallo

utinventory

(M)foreach

basin

was

based

onarelatio

nship

betweensoilinventory

andmeanan

nual

rainfall(App

lebyet

al.,2003).

dMeansuspen

ded

sedim

entactiv

ityco

ncen

trations

werecalculatedfrom

measuremen

tsof12monthly

time-integrated

suspen

ded

sedim

entsamples(w

ith10monthly

samplesfortheRiver

Carey).

eMeanmon

thly

measured

7Beactiv

ityco

ncen

trationsweredecay-correctedbyap

portio

ningactiv

ityacco

rdingto

thedaily

propo

rtional

flow

duringeach

month

andthen

correctin

gforthenumber

ofd

aysuntil

thesam-

plin

gdate.

Flow

was

usedas

asurrog

atefordaily

suspen

ded

sedim

entan

dassociated

7Beinpu

tto

thesamplers.210Pbexan

d137Csweredecay-correctedto

thesamplin

gdate.



by the slow (Ss) and rapid (Sr) transport compartments is used topartition atmospheric fallout (Equation (6)):

Ss þ Sr ¼ 1 (6)

The mass balance for the slow compartment is representedby input from atmospheric fallout (Fa) with losses from the soilradionuclide inventory (Is) dependent on the rate of transportout of the slow compartment (ks) and radioactive decay (λ):

FaSs ¼ Is ks þ λð Þ (7)

The transport rate out of the slow compartment is related tothe residence time (τs) by ks=1/τs. For the rapid compartment,atmospheric input is added to the flux from the slow compart-ment which is balanced by losses due to fluvial export or radio-active decay:

FaSr þ Isks ¼ Ir kr þ λð Þ (8)

where Ir is the radionuclide inventory in the rapid compartmentand kr is the rate of export from the rapid compartment. Thefluvial export of radionuclides from the river basin (Fr) iscalculated as

Fr ¼ Ir kr (9)

Solutions to Equations (6–9) for the unknown variables Sr, ks,kr, Is and Ir can be obtained using estimates of atmosphericfallout, soil inventory (137Cs only) and fluvial export for all threefallout radionuclides (Dominik et al., 1987; Le Cloarec et al.,2007). However, these solutions require several assumptions.The first is that most 7Be in the slow compartment will be lostto radioactive decay rather than be exported from this compart-ment given its short half-life of 53 d (i.e. ks≪ λBe). Export fromthe slow to the rapid compartment is considered negligiblecompared to atmospheric fallout to the rapid compartment(i.e. ks(Is)Be≪ Sr(Fa)Be). It is also assumed that the duration ofsediment storage in the rapid compartment does not result innet decay of 7Be to levels below the limit of detection.Furthermore, the decay rate of 210Pbex is considered negligiblecompared to the export rate from the rapid compartment(i.e. λPb≪ kr).

The rapid compartment area (Sr) can be determined bycombining Equations (8) and (9) based on the first assumptionsuch that Sr is a function of the ratio Fr/Fa for 7Be and the exportrate (kr=1/τr):

Sr ¼ Fr

Fa

� �Be

λBekr

þ 1

� �(10)

The slow compartment residence time (τs) is then computedby solving Equations (6)-(9) for 210Pbex with the assumption thatλPb≪ kr and combining this with Equation (10):

τs ¼1λPb

� �1� Fa

Fr

� �Pb

h iRrRa

� �1þ λBeτrð Þ � 1

(11)

where Rr= (Fr)Be/(Fr)Pb and Ra= (Fa)Be/(Fa)Pb.Slow compartment residence time can also be calculated

using the mass balance equations for 137Cs with basin-scaleinventory (M) rather than fallout (Le Cloarec et al., 2007) to give:

τs ¼M� Frð ÞCsτr� �Frð ÞCs λCsτr þ 1ð Þ (12)

where M= (Is)Cs+ (Ir)CsThe rapid compartment residence time (τr) may then be

obtained by combining Equations (11) and (12) and finding a



solution to the equation:

a τrð Þ2 þ b τrð Þ þ c ¼ 0 (13)where

a ¼ � Frð ÞCsRr

Ra

� �λBeλPb

b ¼ MRr

Ra

� �λBeλPb � Frð ÞCsλPb

Rr

Ra� 1

� �� Frð ÞCsAλCs

c ¼ λPbMRr

Ra� 1

� �� A Frð ÞCs

in which

A ¼ 1� Fa

Fr

� �Pb

A sensitivity analysis similar to that employed by Le Cloarecet al. (2007) was used to determine the effect of changes ininput parameter values on τs, τr and Sr. Factor changes of 0.5and 1.5 were applied to suspended sediment flux (SS), Fa(210Pbex), Fa (

7Be) and M (137Cs) for the Tamar basin upstreamof Gunnislake under 2007 land cover. Changes in model outputsthat resulted from effectively ignoring Kd (set to 1 ×1012 L kg-1) aswell as varying radionuclide activity concentrations by±2standard errors were also examined. Factor changes in modeloutputs were determined by the equation:

Table IV. Summary of suspended sediment budgets for the River Tamar bas

Land coversurvey

Arable landarea (%) HSDR

Inputs (kt y-1)

Hillslope Channel banks

1990 6.3 0.05 2.9 7.72000 22 0.05 7.8 7.72007 36 0.05 11 8.41990 6.3 0.15 8.8 7.72000 22 0.15 23 7.72007 36 0.15 32 8.4

Figure 2. Modelled suspended sediment yields for each river link (n=92) fothe River Tamar basin upstream of Gunnislake. This figure is available in col


FC ¼ 1þ Ov �Oið ÞOi

(14)

where FC is the factor change in model outputs (O) resulting fromthe relative difference between outputs based on varied parametervalues (Ov) and initial parameter values (Oi).

Results and Discussion

Sediment budgets and land cover change

Suspended sediment budgets were modelled for the entireTamar River basin for land covers corresponding to the 1990,2000 and 2007 surveys. These basin-wide budgets show alarge increase in hillslope sediment contributions between1990 and 2007 in response to an increasing proportion ofarable land (Table IV). The mean annual hillslope sedimentcontribution range for 1990–2007 was 8.8–32 kt y-1 with anHSDR of 0.15. The bank erosion contribution to suspendedsediment was between 7.7 and 8.4 kt y-1. Total sediment stor-age in reservoirs and floodplains was minor (1.3–3.6 kt y-1)resulting in mean annual basin suspended sediment exports of15–37 kt y-1, which equated to a range in yields of 16–40 t km-2 y-1

based on the HSDR of 0.15. The increase in river link(n=92) suspended sediment flux between consecutive landcover surveys was distributed across the Tamar basin (Figure 2).

in upstream of Gunnislake for three land covers and two HSDR values

Outputs (kt y-1)

Reservoir Floodplain Basin export Basin yield (t km-2 y-1)

0.15 0.6 9.9 110.23 0.8 14 160.40 1.1 18 190.42 0.9 15 160.67 1.7 29 311.2 2.4 37 40

r the (a) 1990, (b) 2000 and (c) 2007 land covers with HSDR=0.15 forour online at wileyonlinelibrary.com/journal/esp



The highest modelled fluxes occurred in the headwaters of theRiver Lyd sub-basin (Figure 1(a)), which was characterized bythe highest rainfall erosivity, local slope gradients and basinrelief ratio values.Uncertainty in change detection between land cover surveys

represents an important challenge in the use of remotely senseddatasets (Fuller et al., 2003). Accuracy in the detection of landcover changes is of less concern if the focus of modelling wereto use only these data to characterize land cover scenarios formodelling. However, accurate detection of land cover changesduring the survey period (1990–2007) is important if modeloutputs are to be interpreted as a meaningful representationof the effects of recent change. The large increase in arable landcover (6.3 to 36%) represented the main change during thesurvey period. It was mostly offset by a reduction in the areasclassified as grassland. Other land uses such as forest/woodland (11–16%), urban (1–3%) and shrub/heath/bog (all1%) were reasonably consistent between surveys.The trend of increasing arable land cover for the Tamar basin

can be assessed by comparison with land use data from county-scale farm surveys for Devon and Cornwall (Department ofEnvironment, Food and Rural Affairs (DEFRA), 2010). Betweenthe 1995 and 2005 surveys, there was an 8% and 6% increasein cropped land area in Devon and Cornwall, respectively. In-terpolating between farm survey years suggests an increase of13% and 24% for Devon and Cornwall from 1990 to 2007compared with 30% for the Tamar basin. There was also aconsistent trend of increasing arable land area between consec-utive farm surveys spanning the full land cover survey period(1985–2009). This provides increased confidence in thechanges in arable land cover recorded in the Tamar basin bysatellite imagery. It also indicates that model simulations arerelevant for understanding the effect of recent land coverchanges on erosion and sediment transfer.

Particle residence times

Modelled slow compartment residence times for the riverbasins were 13–48, 7.7–17 and 5.6–14 ky for the 1990, 2000and 2007 land covers, respectively (Table V). The decline inthe theoretical mean residence times of radionuclides in theupper soil profile was related to the increase in arable land areaand associated increase in modelled suspended sedimentexports with consecutive land cover surveys (Table V). Between1990 and 2007, arable land cover in the river basins increasedfrom 3.7–7.7 to 26–43% while modelled suspended sedimentexports increased from 0.5–15 to 1.4–37 kt y-1. Slow compart-ment residence times decreased because there was negligiblechange to the modelled atmospheric flux (FaSs) or

137Cs inven-tory (M) and increased fluvial export associated with increasedsuspended sediment output. This corresponds to an increase inthe radionuclide transport rate out of the slow compartment (ks)that results in a decrease in the residence time (i.e. τs=1/ks).Slow compartment residence times cannot represent deeply

eroded sediment from channel banks (i.e. sediment from belowthe depth of the 137Cs inventory). This is because the model isunable to estimate the residence time of sediment that containsnegligible levels of the fallout radionuclide tracers. Such sedi-ment may come from deep colluvial or floodplain deposits thathave not been exposed to fallout for long periods and whereinitial radionuclide activity has decayed to negligible levels.Therefore, the residence time estimates do not apply to parti-cles stored in and subsequently eroded from these deposits.Combining the modelled hillslope erosion rates with the

slow compartment residence times produced an estimate ofsoil denudation depths. This was calculated using the mean


RUSLE-derived hillslope erosion rate for the entire Tamar basinwith the estimated HSDR of 0.15 to give net hillslope erosionrates for each land cover survey. The resulting range in meandenudation depths was 0.28–0.36 m, which equated todenudation rates of 11–39mmky-1. These valueswere determinedusing a mean area-weighted soil bulk density of 0.9 t m-3. This wascalculated from spatially-distributed particle size and organic mat-ter data for upper surface soils (mean maximum depth 0.23 m) inthe Tamar basin using the method of Rawls (1983). The range indenudation depths was consistent with the depth of the upper soilprofile containing the 137Cs inventory (~0.3 m).

The slow compartment residence times were related to abasin-scale index of sediment transport capacity to support aphysical interpretation of model outputs. This index was basedon the representation of sediment transport capacity (qs) as afunction of discharge per unit slope width (q) and surface gradi-ent as an approximation for energy slope (S ), where qs= kq βS γ,and k, β and γ are empirical or theoretically derived constants(Prosser and Rustomji, 2000). At the basin scale, modelledmean annual discharge per unit basin area was multiplied bythe energy gradient approximated by basin slope using therelief ratio (RR), while the constants were set to 1.0. Bothvariables were normalized by their respective maximumvalues to produce a new index (MAD.RR) that varied between0 and 1 (Table III).

Slow compartment residence time varied as a negativepower function of MAD.RR for each land cover survey(Figure 3). The fitted power functions exhibited R2 values rang-ing between 0.69 and 0.84 (P< 0.05). As sediment transportcapacity (MAD.RR) approaches zero the slow compartmentresidence time goes to infinity, whereas at MAD.RR=1 the co-efficient equates to the minimum residence time associatedwith each land cover for the set of basins analysed. These min-imum values were 13044, 6162 and 5392 years for the 1990,2000 and 2007 land cover surveys, respectively. The decreasein the value of the coefficient and increase in the exponentcaptured the increase in basin-scale erodibility with increasingarable land area. With the increase in sediment available fortransport, the range in slow compartment residence times asso-ciated with each function declined from 35 000 to 8400 yearsas sediment supply approaches basin-scale transport capacity.A theoretical minimum slow compartment residence time foreach river basin would occur when sediment supply reachedtransport capacity assuming steady state conditions.

Mean residence times for the rapid transport compartmentwere 185–256, 243–362 and 260–368 days for the 1990,2000 and 2007 surveys, respectively (Table V). The modelledarea of the rapid transport compartment (Sr) also increased from0.2–0.6 to 1.0–2.5% between 1990 and 2007. The modelledrapid transport area is dependent on the river output of 7Be rel-ative to atmospheric input to the rapid compartment (i.e. Fr /Fa)based on the assumption of negligible 7Be input from the slowcompartment compared with direct atmospheric input to therapid compartment. Hancock et al. (2013) estimated that directfallout of 7Be onto wetted channels was insignificant comparedwith 7Be exported with suspended sediment during a flowevent for two large catchments in north-east Australia. Thissuggests most 7Be associated with suspended sediment maybe derived from connected source areas outside the channelnetwork. Furthermore, the rapid transport compartment is un-likely to capture the contribution from channel bank erosionbecause sediment contributed by banks tends to contain negli-gible 7Be (Wallbrink and Murray, 1993; Hancock et al., 2013).

The increase in Sr related to the increase in Fr /Fa with consec-utive land covers equated to an effective increase in theatmospheric input (FaSr) to the rapid compartment, which wasproportionally larger than the increase in modelled 7Be river


TableV.

Modelledsuspen

ded

sedim

enta

ndfallo

utrad

ionu

clide(FRN)e

xportan

dassociated

residen

cetim

esfortheslow

(upper

surfacesoils)a

ndrapid

(river

andco

nne

cted

hillslopesource

area)c

ompartm

entsforthe

sevenriverbasinsan

dthreelandco

versurveys

ModelledFR

Nexpo

rt,F r

(MBqy-1)a

Modelledpartic

leresiden

cetim

esRap

idco

mpartm

ent

area,S r

(%)

River

basin/

survey

year

Arable

landarea

(%)

Modelledsuspen

ded

sedim

entexport(kty-1)

7Be(×

102)

210Pbex(×

102)

137Cs(×

102)

Slow,τ supper

soil

profile(ky)

Rap

id,τ rriveran

dco

nnectedarea

(d)

1990

Tamar

Uppe

r7.0

3.0

3.9

0.90

0.16

43

185

0.2

Otte

ry6.1

1.5

2.0

0.48

0.08

48

204

0.2

Carey

6.6

0.9

1.0

0.30

0.06

33

256

0.3

Ken

sey

5.6

0.5

1.5

0.39

0.05

22

248

0.6

Lyd

7.7

4.7

7.4

2.3

0.52

13

241

0.5

Inny

3.7

1.2

2.8

0.75

0.13

26

231

0.4

Tamar

Gunn

islake

6.3

15

25

5.7

1.0

27

188

0.4

2000

Tamar

Uppe

r25

5.6

8.4

2.2

0.33

21

244

0.6

Otte

ry27

3.9

6.0

1.8

0.22

17

297

0.9

Carey

21

1.5

2.0

0.67

0.11

17

322

0.7

Ken

sey

22

1.3

3.9

1.3

0.13

8.6

362

2.3

Lyd

14

7.0

12

4.1

0.86

7.7

280

1.0

Inny

17

2.7

7.3

2.5

0.31

10

344

1.4

Tamar

Gunn

islake

22

29

56

15

2.3

12

243

1.0

2007

Tamar

Uppe

r43

8.3

13

3.6

0.49

14

273

1.0

Otte

ry43

5.2

8.1

2.5

0.29

12

317

1.3

Carey

37

2.1

2.9

1.0

0.15

12

357

1.0

Ken

sey

33

1.4

4.3

1.5

0.15

7.8

368

2.5

Lyd

29

9.7

17

6.0

1.2

5.6

307

1.5

Inny

26

3.0

8.1

2.8

0.35

9.2

358

1.6

Tamar

Gunn

islake

36

37

73

20

3.0

9.2

260

1.4

aModelledFR

Nexport(F

r)co

mbined

suspen

ded

sedim

ent-associated

FRN

expo

rtwith

theestim

ated

dissolved

fluxcalculatedusingregionalized

annua

lflo

wan

dpartitionco

effic

ients(K

d)foreach

radionuclide.



Figure 3. Slow compartment residence time versus the MAD.RR(Mean Annual Discharge multiplied by Relief Ratio) index (see text fordetails) for each river basin for the 1990, 2000 and 2007 land covers.


output (Fr). This led to an increase in the 7Be inventory (Ir) of therapid compartment. Therefore, the rapid compartment trans-port rate (kr= Fr/Ir) decreased and the residence times (τr = 1/kr)increased with consecutive land cover surveys.Model estimates of rapid compartment residence times

assume that the duration of sediment storage will not result innet decay of 7Be to levels below the limit of detection. In theTamar basin, detectable levels of 7Be were measured insuspended sediment samples collected using thetime-integrated samplers over monthly intervals. The durationof in-channel storage of fine sediment would be unlikely toreduce 7Be activity concentrations to negligible levels due tothe frequency of flushing flows. Also fine sediment stored in-channel should not accumulate significant amounts of unat-tached 210Pbex. This has previously been used as a measureof in-channel residence time where storage times span a mini-mum of several years up to decades (Wallbrink et al., 2002).The monthly suspended sediment samples collected over a12 month period were assumed to capture the variability asso-ciated with 7Be accumulation and decay in surface soils. Thisvariability was reflected in the coefficient of variation for 7Beactivity concentrations on suspended sediment, which rangedbetween 28 and 58%.The increase in Sr may be considered to reflect the expansion

of connected near-channel source areas with increasing sedi-ment supply. This is consistent with an increase in the area ofarable land intersecting with the channel network that couldsupply more sediment. In the modelled scenarios for the Tamarbasin, this equated to 0.6, 2.9 and 4.1 km2 of riparian arableland within an arbitrarily defined 25 m buffer surrounding themodelled channel network for 1990, 2000 and 2007, respectively.The increase in rapid compartment residence times may also beinterpreted in the context of the increase in Sr. Larger source areasare likely to correspond to longer sediment travel distances andhence increased residence times.Temporary sediment storage on-slope is important for under-

standing timescales associated with hillslope sediment deliveryprocesses. Particles move by a series of transport steps that maynot scale with slope length (Parsons et al., 2006). Runoff ratiostend to decline with increasing slope length (Sheridan et al.,


2013), which also contributes to increased particle residencetimes on longer slopes. Owing to the frequency of highermagnitude flows in the river network, the storage duration formost fine sediment within channels is probably short. There-fore, rapid compartment residence times may be largely associ-ated with the number of runoff events required to deliver aparticle to the channel network and the duration of particlestorage between runoff events within connected slope sourceareas. The increase in rapid compartment residence timesrelated to the expansion of connected source areas isconceptually linked to the increase in near-channel arable landthat generates more sediment for transport.

Model evaluation and sensitivity

Sediment budgetsModelled sediment budget components were examined in rela-tion to available regional datasets in the absence of basin-specificvalidation data. The components considered were dividedaccording to budget inputs that included RUSLE hillslope erosionrates, the hillslope sediment delivery ratio (HSDR) and channelbank erosion, and budget outputs, namely floodplain storageand basin-scale suspended sediment exports.

Mean RUSLE hillslope erosion rates calculated at the gridscale for forest, arable areas and grassland were 0.05–0.07,6.0–6.8 and 0.29–0.31 t ha-1 y-1, respectively. These erosionrates represent the range in mean values for each land coverrecorded at the basin-scale for the three cover simulations.Combined, the three land cover types equate to 95–98% ofthe Tamar basin area. Therefore, the mean erosion rates capturethe spatial variation in rainfall erosivity, soil erodibility, slopecontributing area and gradient for the three land cover typesacross the basin. Model performance was assessed againstregional datasets as well as a large-scale compilation ofEuropean erosion plot data.

Modelled mean erosion rates were generally consistent withpublished data. At the local scale, monitoring (1 year) in a smallfirst-order grassland basin (0.46 km2) located in Devon producedan estimated net erosion rate between 0.5 and1.2 t ha-1 y-1 forclayey soils (Bilotta et al., 2010). These rates exceed long-term(11 years) plot-scale measurements for sandy soils under grasscover in central England, which gave a mean of 0.23 and range0.1–0.5 t ha-1 y-1 (Fullen, 1998). Measurements in cultivatedand pasture fields with clay-loam soils in south Devon using137Cs indicated erosion rates of 8.0 and 0.16 t ha-1 y-1, respec-tively (Owens et al., 1997). Furthermore, erosion rates estimatedusing 137Cs for arable and pasture fields were 1.2–8.5 and0.2–5.3 t ha-1 y-1, respectively, in two small lowland basins(Walling et al., 2002). However, comparison between modellederosion rates and those measured using 137Cs was limited by (i)difficulty in directly relating field-scale erosion measured using137Cs to soil loss estimates for slope segments based on RUSLEand (ii) untested assumptions in the use of 137Cs to measure soilerosion that could produce erroneous results (Parsons and Foster,2011). Analysis of a compilation of erosion plot data from acrossEurope that excluded the Mediterranean zone produced meanforest, cultivated and grassland erosion rates of 0.003, 6.3 and0.29 t ha-1 y-1, respectively (Cerdan et al., 2010). The modelledarable and grassland erosion rates are consistent with this plotdata. The much lower forest erosion rate was based on only 60plot-months of data compared with 6635 and 1535 plot-monthsfor cultivated and grassland plots (Cerdan et al., 2010).

The modelled suspended sediment budgets were highly sen-sitive to change in the HSDR. An increase in HSDR from 0.05to 0.15 corresponded to an approximately 3-fold increase inthe basin-wide hillslope sediment contributions and a 1.5–2-



fold increase in the basin suspended sediment exports(Table III). The HSDR of 0.15 was selected on the basis of thedetailed sediment budgets developed by Walling et al. (2002)for two small basins in central England (<4 km2). These budgetsmeasured in-field and field-to-channel deposition relative togross erosion estimated using 137Cs. While subject to theaforementioned uncertainties in the use of 137Cs to measuresoil erosion, these HSDR values provide the only availableestimates of hillslope-to-channel sediment delivery in compa-rable agricultural basins and at a spatial scale equivalent to thatof the individual river link drainage areas (mean± SD=9.96±7.7 km2) used in SedNet modelling of the Tamar basin. TheHSDR of 0.15 was also chosen with reference to the resultingbasin suspended sediment yields, which were consistent withregional yield estimates, as shown below.Modelled link-average bank erosion rates ranged between

0 and 0.19m y-1 (mean=0.02m y-1) based on a coefficient valueset to 0.0001 (Equation (2)) to limit the maximum rate of bankretreat (Wilkinson et al., 2004). These bank retreat rates are inthe low range ofmean rates (0.03–1.18m y-1) from fieldmeasure-ments (1–3 y) for streams and rivers with basin areas ranging from4.8–620 km2 in south-west England (Hooke, 1980; Murgatroydand Ternan, 1983). Longer-term (1840–1975) bank retreat ratesmeasured from historic maps ranged from 0–1.79 m y-1 (Hooke,1980). However, the comparatively low modelled bank erosionrates may be reasonable for several reasons. First, bank monitor-ing locations in the study by Hooke (1980) were biased towardsareas of likely maximum erosion, particularly open floodplainsites. In contrast, the modelled channels have mean riparian for-est cover ranging over 26–33% of the length of river links,thereby reducing bank retreat rates. Second, channel networkconfinement by bedrock and steep hillslopes occurs in manylocations across the Tamar basin and limits lateral channelchange. Third, low bank retreats rates are consistent with thepreservation of small areas of floodplain in the Tamar basin.The modelled floodplain occupies 2.8% of the total basin areaand has a mean width of only 70±62 m. The largest area offloodplain occurs in the mid-basin where four tributaries jointhe main channel (Figure 1(b)). This represents productive agri-cultural land and hence bank stabilization measures have beenadopted in some locations. It should be noted that modelledfloodplain storage inputs do not offset channel bank losses(Table III). This should not be interpreted to imply a net loss fromfloodplain units. Channel bank erosion includes contributionsfrom non-floodplain areas such as colluvial footslopes, whilefloodplains also receive inputs from adjacent hillslopes. Noexplicit calculation of hillslope-derived sediment inputs tofloodplain storage units is made by the SedNet model.Modelled floodplain deposition rates were low. Mean (and

maximum) deposition rates for the 1990, 2000 and 2007 landcovers were 0.04 (0.1), 0.08 (0.2) and 0.12 (0.3) mm y-1,respectively. Measurement of floodplain deposition rates using137Cs in five river basins (276–3717 km2) in southern Englandyielded a range in mean reach-scale values of 0.7–1.6 mm y-1

since the mid-1950s (Walling and He, 1998). Inundation ofthese floodplain reaches was estimated to occur several timesper year. In another study set in northern England, the meansedimentation rates for floodplain transects extending fromthe channel margin to the outer floodplain were 0.07–3.7 and0.1–1.5 mm y-1 for the River Ouse and River Tweed, respec-tively (Walling et al., 1999). These rates were converted fromg cm-2 y-1 to mm y-1 using a sediment bulk density of1.5 g cm-3. The lower modelled floodplain deposition rates prob-ably result in part from the effect of averaging annual overbanksediment deposition across the entire modelled floodplain areafor each river link. Floodplain deposition is not spatially uniform,as shown by declining sedimentation rates with distance from


channels (Walling et al., 1999). The comparison with mean ratesfor transects spanning most of the floodplain reduces thisdisparity. Floodplain inundation frequency is also an importantfactor distinguishing sedimentation rates. SedNet simulationsused a basin-wide bankfull discharge frequency of 1.5 years onthe annual series to determine the proportion of overbank flow.Inundation frequency will be higher in some near-channellocations, as was the case for floodplain reaches measured byWalling and He (1998).

Modelled suspended sediment yields for the Tamar basin atGunnislake were 16–40 t km-2 y-1 using an HSDR of 0.15 forthe three land covers. This range in yields is comparable withsuspended sediment yields obtained from longer-term(1994–2003) monitoring of three agricultural river basins(226–601 km2) in Devon (Harlow et al., 2006). These measuredyields range from 24 to 45 t km-2 y-1, and provide a goodcomparison with modelled yields on the basis of generalsimilarities in basin land use and hydroclimatic conditions.Such longer-term measurements of yield are preferable for usein assessing model performance given that SedNet computesmean annual budgets over a timescale of several decades.The modelled yields were also consistent with an earlierregional compilation of river basin suspended sediment yieldsfrom south-west England (Walling and Webb, 1987). In thiscompilation, the range in suspended sediment yields was16–58 t km-2 y-1 for basins with areas ranging between 46and 422 km2, excluding the three basins with more recent datareported by Harlow et al. (2006) and those basins <10 km2.This is also consistent with the modelled suspended sedimentyields for the Tamar sub-basins (38–238 km2) which rangedfrom 12–21, 22–34 and 31–44 t km-2 y-1 for the 1990, 2000and 2007 land covers, respectively. Notably, the range inmodelled yields spanning the three land cover surveys isconsistent with the range in measured yields. This indicates thatthe effect of land use change on modelled yields in the Tamarbasin does not exceed regional variability in mean annualsuspended sediment yields.

Particle residence timesThe performance of the particle residence time model cannotbe examined directly due to (i) the absence of independentvalidation datasets and (ii) the difficulty in validating estimatesof slow compartment residence times for specific land coversthat do not change through time. Instead we use a sensitivityanalysis to identify those parameters which exert greater influ-ence on model outputs and compare estimates of parametervalues with available measurements.

The sensitivity analysis showed that a factor change of 0.5and 1.5 to individual model parameters could result in factorchanges to slow and rapid compartment residence timesranging between 0.4 and 2.6 (Table VI). However, mostchanges in residence time estimates remained within the range0.5–1.5. Slow compartment residence time was most sensitiveto changes in suspended sediment flux and basin-scale 137Csinventory (M), whereas the rapid compartment residence timeand Sr were most sensitive to changes in Fa (

210Pbex). Changesto Fa (

7Be) affected only the rapid compartment residence time.Slow compartment residence times were unaffected by changesin Fa for

7Be or 210Pbex. Ignoring the partitioning of the radionu-clides between the dissolved and particulate forms (i.e. Kd→∞)increasedmodel estimates of Sr, slow and rapid compartment res-idence times, by factors of 1.0–1.3 (Table VI). This was equivalentto the effect of increasing Fa (

7Be) orM, with a negligible effect forFa (

210Pbex) due to its already high Kd (Le Cloarec et al., 2007).The sensitivity analysis indicated that the estimates of

suspended sediment flux, M and Fa for7Be and 210Pbex exert an

important control on model outputs. Modelled mean annual


Table VI. Summary of factor changes in τs, τr and Sr in response to changes in residence time model parameters for the Tamar basin upstream ofGunnislake under the 2007 land cover

Model inputFactor change inparameter values

Factor changes in model outputs

Slow compartment (τs) Rapid compartment (τr) Rapid compartment area (Sr)

Suspended sediment flux 1.5 0.7 1.1 1.50.5 1.7 0.8 0.5

Increase parameter Decrease Increase IncreaseRadionuclide activity concentrationa + 2SE 0.9 1.0 1.1

– 2SE 1.1 1.0 0.9Increase parameter Decrease Negligible change Increase

Fa (210Pbex) 1.5 1.0 0.5 0.6

0.5 1.0 2.6 2.3Increase parameter Negligible change Decrease Decrease

Fa (7Be) 1.5 1.0 1.6 1.0

0.5 1.0 0.4 1.0Increase parameter Negligible change Increase Negligible change

M (137Cs) 1.5 1.5 1.1 1.10.5 0.5 0.7 0.8

Increase parameter Increase Increase IncreaseIgnore Kd 1.2 1.3 1.0Most sensitive parameters SS and M Fa (

210Pbex) Fa (210Pbex)

aRadionuclide activity concentrations were varied by ±2 standard errors (SE) reported in Table III.


suspended sediment yields were shown to be comparable withlonger-term measurements from agricultural river basins in theregion. Uncertainty in the measured mean radionuclide activityconcentrations (Table III) used in calculating Fr was constrainedby the use of continuous time-integrated sampling that captureda range of flow conditions over a 12 month period. Varying theseactivity concentrations by ±2 standard errors had only a minoreffect on model outputs (Table VI). However, the necessaryscaling of activity concentrations to reflect changes in modelledhillslope and channel bank sediment contributions introducedadditional uncertainty in residence time estimates. Decreasingthe estimated suspended sediment activity concentrations forthe 1990 and 2000 land cover simulations was consistent withlower modelled sediment contributions from hillslope surfaceerosion.M was estimated for each river basin using the relation-ship between soil 137Cs inventory and mean annual rainfallderived by Appleby et al. (2003) with the 1×1 km gridded1971–2000 precipitation data. This produced a range in areal137Cs inventories of 2820–3390 Bq m-2. This approach capturedthe spatial variability associated with precipitation patterns.Higher inventories occurred across elevated areas of the Tamarbasin in the east and west compared with lower inventories inthe centre and northern part of the basin.Possibly the largest source of uncertainty in model inputs

relates to the estimates of Fa for7Be and 210Pbex. The range in

areal fallout values used to derive Fa for 7Be was 2330–2930Bq m-2 y-1 (mean precipitation= 1180–1488 mm y-1). Thiswas consistent with measurements of 2750 (Dominik et al.,1987) and 2670 Bq m-2 y-1 (Schuler et al., 1991) in Switzerlandfor precipitation of 1100–1200mm y-1 which is comparable withthe study basins. However, it is higher than 1618 Bq m-2 y-1

(precipitation=1328 mm y-1) at Milford Haven in south Wales(Peirson et al., 1966) and 1200 Bq m-2 y-1 (precipitation notreported) for the Seine River basin (Le Cloarec et al., 2007), butlower than 3912±120 Bq m-2 y-1 (precipitation=1884 mm y-1)in Cumbria, northern England (Short et al., 2007). In additionto annual rainfall amount and latitude, solar activity is animportant control of 7Be production, which varies by ~25%with the 11 year solar cycle (Kaste et al., 2002). Therefore,differences between studies may in part reflect solar variability.Variation in Fa (7Be) affects only the rapid compartmentresidence times (Table VI). The large range in reported annual


atmospheric fallout and the effect of solar variability indicatesthat rapid compartment residence times are probably subjectto greater uncertainty than slow compartment residence timeswhich are unaffected by variation in Fa (

7Be). However, it canbe anticipated that this uncertainty was reduced to some extentby the use of 30 year mean annual precipitation data tocompute 7Be fallout.

The range in estimated mean areal fallout values used toderive Fa for 210Pbex was 118–149 Bq m-2 y-1. These valueswere less than 165± 8 Bq m-2 y-1 based on measurements of210Pbex concentration in rainwater for 1997–1998 in Cumbria(Short et al., 2007). However, this is consistent with highermean annual rainfall (1884 mm) for the Cumbrian site as wellas the proximity of the Tamar study basin to the east coast ofthe Atlantic (i.e. air mass with reduced geogenic 222Rn activity).The range in 210Pbex atmospheric flux in the present study liesbetween the mean of 117 Bq m-2 y-1 estimated for the 30–60° Nlatitude zone based on a compilation of data (Preiss et al.,1996) and 161 Bq m-2 y-1 from soil inventories in Devon(Walling and He, 1999). These comparisons suggest thatestimates of Fa for

210Pbex were reasonable.

Conclusions

This is the first study to combine a sediment residence timemodel with multi-decadal estimates of mean annual dischargeand suspended sediment export from river basins. In contrast,previous applications have been based on short-term monitor-ing (1–2 years) that is highly dependent on the specifichydroclimatic conditions during measurement periods. Thismay have an important effect on estimated residence timesdue to model sensitivity to suspended sediment exports. Thenovel combination of a river basin sediment budget model witha mass balance model of particle residence times that uses fall-out radionuclide tracers identified changes in spatial patternsand timescales of suspended sediment transfer in response torecent agricultural land cover change. With increased pressureon soil systems to meet global food security targets, such infor-mation is highly valuable to catchment managers and policymakers who need to balance food production against protec-tion of downstream water resources and aquatic ecosystems.



The SedNet model was used to simulate mean annualsuspended sediment fluxes for three land cover surveysspanning a period of recent change in agricultural land use inthe study basin. Modelled basin-scale suspended sedimentyields ranged between 16 and 40 t km-2 y-1 and were consistentwith longer-term measurements from the region. Likewise,hillslope and channel bank erosion rates were comparable toavailable data suggesting that the SedNet model provided areasonable representation of suspended sediment transfer.Comparison of modelled sediment budgets between land coversurveys showed a pronounced increase in suspended sedimentyields in response to an increase in the area of arable land from6.3 to 36% between 1990 and 2007.Modelled particle residence times were estimated for seven

sub-basins that were divided into slow (upper surface soil)and rapid (river and connected hillslope source areas) transportcompartments. Modelled slow compartment residence timesfor the river basins were 13–48, 7.7–17 and 5.6–14 ky for the1990, 2000 and 2007 land cover surveys, respectively. Theresidence times decreased in response to the increase inmodelled suspended sediment exports with increasing arableland area. It was also shown that slow compartment residencetimes were related to a basin-scale index of sediment transportcapacity by a negative power function for each land cover.Both the residence times and estimated source areas of therapid transport compartment increased with consecutive landcover surveys. Conceptually, this was considered to reflectthe expansion of connected hillslope source areas with increas-ing sediment supply from more arable land situated near thechannel network. Larger source areas correspond to longersediment travel distances and hence increased residence times.The coupled sediment budget-residence time modelling

approach provides unique insight into river basin responses torecent environmental change not otherwise available fromconventional measurement techniques. Quantifying residencetimes of fine sediment and associated contaminants indegraded river basins may yield valuable information onpotential recovery rates from pollution under current environ-mental conditions. Future environmental changes could alsobe modelled. For example, the use of a sediment budget modelwith hydrologic parameters such as SedNet would allowexamination of the potential impact on sediment residencetimes of projected changes in precipitation and evaporationassociated with future climate scenarios.

Acknowledgements—HGS acknowledges the support of a Marie CurieFellowship (PIIF-GA-2010-273069) within the 7th European Commu-nity Framework Programme. This paper also represents a contributionto the International Atomic Energy Agency Coordinated ResearchProgramme D1.20.11 under Research Agreement IAEA contract UK/15538 (WB). We thank staff from the Westcountry Rivers Trust for helpwith site selection and arranging access for river monitoring. We alsoacknowledge the contribution of Professor Geoff Millward to gammaspectrometry analysis and for lively discussion. We thank two anony-mous reviewers whose comments helped improve the manuscript.

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