quantifying ecosystem services provided by hyporheic exchange
DESCRIPTION
Stanley 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 reaction Pumping of solute across bedforms - PowerPoint PPT PresentationTRANSCRIPT
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