QUANTIFYING ECOSYSTEM SERVICES PROVIDED BY HYPORHEIC EXCHANGEStanley B. Grant and Morvarid Azizian

Civil and Environmental Engineering, University of California Irvine & Infrastructure Engineering, University of Melbourne

Objectives•Present an analytical model of benthic exchange and reactionPumping of solute across bedformsAdvection-dominated mass transportFirst-order reaction in sediment•Evaluate modelCompare to numerical solutionDerive solution for solute flux into the sediment•ApplicationCorrelations for mass transfer coefficientTrade-off between volume of water processed in the sediment and extent of reaction

streamline geometry

J τ R( )=JMTL 1−Cf τ R( ) C0⎡⎣ ⎤⎦

pressure head

velocity field

Elliot and Brooks Velocity Model

h x , y( )=h hm =sinxey

normalize by wave numberx =2πx λ y =2πx λ

ux x , y( )=ux um =−cosxey

uy x , y( )=uy um =−sinxey

um =−2πKhhm λKh =hydrauλic conducτiviτyλ =bed fo rm wave leng th

x =horizonτaλ disτancey=verτicaλ d isτance

hm =m axim um πressure head

ux =x-veλociτyvariable definitions

uy =y-veλociτyum =m ax−veλociτy

predicted concentration field

C f τ R( )=C0 exπ −τ Rx0

π 2 cosx0

⎡⎣⎢

⎤⎦⎥0

π /2

∫ sin x0dx0

C x , y,τ R( )=C x,y,τ R( )

C0

=exπ −τ R cos−1 eycosx⎡⎣ ⎤⎦−x( )

2π 2eycosx

⎡

⎣⎢⎢

⎤

⎦⎥⎥, −π 2 < x <π 2, y< 0

predicted concentration field (analytical)

Solution approach (neglect dispersion & diffusion) Numerical simulation results

∇⋅uC θ −D ⋅∇C( ) = −krC

C0 =sτream concenτraτionτ R =

trans i t t imereac t ion t ime

=krλ θ πum

kr =1sτ-order reacτion raτe

θ =sed imen t po rosi ty

variable definitionsC =sedim enτ concenτraτion

C f =fλow-weighτed uπweλλing conc.

JMTL =−C0um θπ( )

flux into sediment bed

mass-transfer-limited flux

D=

um ey

θaL cos

2 x +aT sin2 x( )+ ′D m

um ey

θaL −aT( )

sin2x2

um ey

θaL −aT( )

sin2x2

um ey

θaLsin

2 x +aT cos2 x( )+ ′D m

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

Numerical approach (governing equations)

u=−um cosxeyi −um sin xe

y j

variable definitionsa L = long i tud ina l d i spers iv i tyaT = transverse d i spers iv i ty

advection/dispersion equation

dispersion tensor

predicted concentration field (numerical)

Numerical and analytical solutions near-identicalNumerical simulation carried out with COMSOLMechanical dispersion & molecular diff. negligibleDirichlet b.c. at surface causes gradient artifact

ApplicationsAnalytical model supports use of mass transfer coefficient

J =−km C0 −Cf( ) km =um θπ( )

Flux ~ conc. diff. in upwelling & downwelling zonesMass transfer coefficient = downwelling velocity

Ecosystem services

Flux into sediment = mass removal in sedimentMass removal in sediment = ecosystem service (N, P, C processing; CEC removal)Model identifies trade-off between volume of water processed by hyporheic zone and extent of reaction in sediment (hard to optimize both)

AcknowledgementsFunding by the National Science Foundation Partnerships for International Research and Education (PIRE) Award No. OISE-1243543. A huge THANK YOU to Keith Stolzenbach (UCLA), Megan Rippy (UCI), Mike Stewardson (UoM), and Perran Cook (Monash Univ).

′Dm = τ Dm = di ffus ion / to r tuos i ty