Download k 1 - College of Arts and Sciences

Modeling 234Th
in the ocean
from scavenging to export flux
Nicolas SAVOYE
Vrije Universiteit Brussel
Photo: C. Beucher
Modeling 234Th
in the ocean
from scavenging to export flux
Th scavenging models
Estimating 234Th export flux
Steady vs non-steady state models
Toward 3D-models
Photo: C. Beucher
Modeling 234Th
in the ocean
from scavenging to export flux
Th scavenging models
Estimating 234Th export flux
Steady vs non-steady state models
Toward 3D-models
Photo: C. Beucher
Th scavenging models
estimating Th (total, dissolved, particulate, colloidal) residence time and
extrapolating the result to contaminant residence time (Th as contaminant
analogous)
understanding particle dynamics:
adsorption / desorption
aggregation / disaggregation
remineralization
sinking
determining Th fluxes and estimating biogenic fluxes (POC, PON, BSi) in ocean
One-box models
U
l
k
Tht
l
U
P = (l + k) [234Th]
Broecker et al (1973)
l
k
Tht
l
f
P + ([234Th]I – [234Th]) / f = (l + k) [234Th]
Matsumoto et al (1975)
P: production rate of 234Th from 238U
[234Th]I: 234Th concentration in the input water from the deeper layer
f: fluid residence time of the surface layer
l: decay constants
k: first-order removal rate constant
One-box models
U
l
k
Tht
l
U
l
k
Tht
l
f
P = (l + k) [234Th]
P + ([234Th]I – [234Th]) / f = (l + k) [234Th]
228Th/228Ra
t = 0.7 year
open ocean
234Th/238U
t = 0.38 year
open ocean
Knauss et al (1978)
228Th/228Ra
t = 0.52, 0.30 year
shelf water
Knauss et al (1978)
228Th/228Ra, 234Th/238U
t = 0.19 year
t = 0.03 year
Broecker et al (1973)
Matsumoto et al (1975)
t=1/k
shelf break
coastal water
One-box models
U
l
k
Tht
l
U
P = (l + k) [234Th]
l
k
Tht
l
f
P + ([234Th]I – [234Th]) / f = (l + k) [234Th]
Assumptions:
-k: first order
-steady state
-diffusion, advection negligible
two-box irreversible models
U
lU
Thd
lTh
Krishnaswami et al (1976)
d[Thp]
dt
k
=– S
d[Thp]
dz
lTh
Thp
S
+ k [Thd] – [Thp] lTh
[Ud] lU = – [Thd] (lTh + k)
d: dissolved; p: particulate; l: decay constants;
k: first-order rate constant for the transfer from dissolved to particulate phases;
S: settling velocity of particles
two-box irreversible models
U
lU
Thd
[Thp] lTh =
t = 0.40 year (from 234Th/238U)
S = 0.03 – 0.2 m/s (from 230Th/234U)
lTh
Thp
lTh
Krishnaswami et al (1976)
Steady state:
k
S
k [Ud] lU
k + lTh
1 – exp
z lTh
S
two-box irreversible models
U
l
Coale and Bruland (1985, 1987)
kd
Thd
l
Thp
l
kp
PTh
dATh,d
dt
= AU lTh- ATh,d lTh - JTh
=0
dATh,p
dt
= JTh - ATh,p lTh - PTh
=0
d: dissolved; p: particulate; l: decay constant;
kd, kp: first-order scavenging and suspended particulate removal rate constants, respectively;
A: radioisotope activity;
JTh: rate of removal of 234Th from dissolved to particulate form;
PTh: rate at which 234Th is transported out of the surface layer by the particle flux.
two-box irreversible models
U
l
Coale and Bruland (1985, 1987)
kd
Thd
l
Thp
kp
PTh
Assumptions:
- U is dissolved only
- kd, kp: first order
- steady state
- diffusion, advection negligible
- all particles have the same comportment
- irreversible scavenging
l
two-box reversible models
U
l
k1
Thd
l
Thp
k-1
l
Nozaki et al (1981)
[230Thd] + [230Thp] =
S
1+
k-1
P
k1
S
d: dissolved; p: particulate; l: decay constant;
k1: first-order adsorption/scavenging rate constant;
k-1: first-order rate constant for the transfer of 230Th from particles to solution;
S: settling velocity of particulate 230Th;
P: production rate of 230Th from 234U.
z
two-box reversible models
U
k1
l
Thd
l
Thp
k-1
l
Bacon and Anderson (1982)
S
Steady state:
[Thp] =
[Thd] =
k1 P
l (l + k1 + k-1)
1 – exp –
l (l + k1 +k-1)
S (l + k1)
P + k-1 [Thp]
l + k1
d: dissolved; p: particulate; l: decay constant; z: depth;
k1, k-1: first-order adsorption and desorption rate constants;
S: settling velocity of particulate 230Th; P: production rate of Th from its parent.
z
two-box reversible models
U
l
k1
Thd
l
Thp
k-1
Bacon and Anderson (1982)
l
S
1.4
1.2
Assumptions:
- U is dissolved only
k1 (yr-1)
1.0
0.8
0.6
0.4
- k1, k-1: first order
- steady state
- diffusion, advection negligible
- all particles have the same comportment
0.2
0
0
5
10
15
[SPM] (µg/l)
20
25
three-box irreversible models
U
l
k1
Thd
r1
Thsp
Thlp
l
r-1
l
l
Tsunogai and Minagawa (1978)
cited by Moore and Hunter (1985) and Moore and Millward (1988)
d: dissolved; sp, lp: small and large particles, respectively; l: decay constant;
k1: first-order scavenging rate constant;
r1, r-1: aggregation, disaggragation rate constants, respectively.
modeling Th adsorption/desorption on mineral particles
Th
k1
k-1
ThX
k2
k-2
ThX’
k3
k-3
ThX’’
Moore and Millward (1988): in vitro experiments
X: surface binding site for Th;
ThX: weakly-bound Th on the particle surface;
ThX’: more strongly bound form or form held within the structure of particle;
ThX’’: most strongly bound form of particulate Th;
k: first-order adsorption/desorption rate constants.
k-1 >> l
The extent to which Th can desorb from the particle decreases as the particle ages
three-box reversible models
U
l
k1
Thd
k2
Thsp
k-1
l
Thlp
l
k-2
l
S
Bacon et al (1985), Nozaki et al (1987)
d: dissolved; sp, lp: small and large particles, respectively; l: decay constant;
k1, k-1: adsorption and desorption rate constants, respectively;
k2, k-2: aggregation and disaggragation rate constants, respectively;
S: sinking speed.
three-box reversible models
g
U
l
k1
Thd
r1
Thsp
k-1
l
Thlp
l
r-1
l
S
Clegg and Whitfield (1991)
d: dissolved; sp, lp: small and large particles, respectively; l: decay constant;
k1, k-1: adsorption and desorption rate constants, respecitvely;
r1, r-1: aggregation, disaggragation rate constants, respectively;
g: remineralization rate constant;
S: sinking.
three-box reversible models
b-1
U
l
b2
k1
Thd
Thsp
k-1
l
l
b-2
Thlp
l
w
Murnane et al (1994)
d: dissolved; sp, lp: small and large particles, respectively; l: decay constant;
k1, k-1: second order adsorption and first order desorption rate constants, respecitvely;
b2, b-2: first order aggregation and disaggragation rate constants, respectively;
b-1: first order remineralization rate constant;
w: sinking velocity.
three-box reversible models: the Brownian pumping model
k1
k-1
U
l
k1
Thd
k2
Thc
Thfp
k-1
l
l
k-2
l
S
Honeyman and Santschi (1989)
d: dissolved; c: colloids; fp: flitrable particles; l: decay constant;
k1, k-1: adsorption and desorption rate constants, respectively; fast equilibrium;
k2, k-2: aggregation and disaggragation rate constants, respectively; slow step
S: sinking.
four-box reversible model
R
U
l
k1
Thd
k2
Thc
Thsp
k-1
l
k3
k-2
l
Thlp
l
k-3
l
S
Honeyman and Santschi (1992)
cited by Baskaran et al (1992)
d: dissolved; c: colloids; sp, lp: small and large particles, respectively; l: decay constant;
k1, k-1: adsorption and desorption rate constants, respectively;
k2, k-2: coagulation and repeptization rate constants, respectively;
k2, k-2: aggregation and disaggregation rate constants, respectively;
S: sinking; R: remineralization
four (or more)-box irreversible model
h2
U
l
Thd
Thc
l
k-1
k1 S1
Thsp
l
k-2
k2 S2
h3
Thlp
l
k-3
Burd et al (2000)
l: decay constant; d: dissolved; c: colloids;
sp, lp: small (0.5 < < 56 µm) and large (> 56 µm) particles, respectively;
k: adsorption or desorption rate constants;
h: aggregation rate constants;
S: settling loss.
k3 S3
l
five-box (ir)reversible model
U
l
Thd
Fd
Th
0.5-1µm
l
Guo et al (2002)
d: dissolved; p: particulate;
l: decay constant;
F: flux.
l
Fp1
Thsp
1-10µm
l
Fp2
Thlp
10-53µm
l
Fp3
Thlp
>53µm
l
Fp4
U
Th scavenging models: usual main assumptions
l
k1
Thd
b1
k2
Thc
Thsp
k-1
l
k-2
l
- U is dissolved only
- rate constants are (pseudo) first-order
- steady state conditions
- diffusion, advection negligible
-remineralization negligible
- adsorption on colloids or small particles only
l
b-1
Thlp
S
l
Th scavenging models: ideas for future directions
-increasing the number of particle size classes (i.e. of boxes);
-including biology (e.g. food web)
-including physical properties of particles like density and stickiness
Th scavenging models: importance of the chemistry of the particles
Thd
Thp
Partitioning coefficient:
Kd =
[Thp]
[Thd]
from 230Th sediment trap data:
Kd,CaCO3 = 9.0 x 106 > Kd,BSi = 3.9 x 105; no influence of lithogenics
Chase et al (2002), Chase and Anderson (2004)
Kd,lithogenics = 2.3 x 108 > Kd,CaCO3 = 1.0 x 106 > Kd,BSi = 2.5 x 105
Kuo et al (2004a, b)
Importance of acid polysaccharides for 234Th complexation
Polysaccharides:
-highly surface-reactive exudates excreted by phytoplankton and bacteria
-composed of deoxysugars, galactose and polyuronic acids
- main component of transparent exopolymer particles (TEP)
Importance of acid polysaccharides for 234Th complexation
Quigley et al (2002)
Importance of uronic acid for 234Th scavenging
from Guo et al (2002)
4
y = 0.577x-0.788
R2
y = 1.70x-0.192
3
= 0.66
R2= 0.07
2
2
1
1
234Th
residence time (day)
3
0
>53µm
0
0
0.5
1
1.5
2
2.5
0
2
4
y = 0.577x-0.788
5
234Th
residence time (day)
5
R2= 0.47
3
2
1
1
0
0
10
20
[uronic acid] (nM)
R2= 0.85
y = 528x-2.31
R2= 0.63
3
2
0
y = 53.9x-1.94
8
4
y = 37.9x-1.37
4
R2= 0.66
6
30
0
10
20
[uronic acid] (nM)
30
10-53µm
1-10µm
Th scavenging models: ideas for future directions
-increasing the number of particle size classes (i.e. of boxes)
-including biology (e.g. food web)
-including physical properties of particles like density and stickiness
-including the chemistry of the ‘particles’
U
Th scavenging models: usual main assumptions
l
k1
Thd
Thc
Thsp
k-1
l
b1
k2
k-2
l
- U is dissolved only
- rate constants are (pseudo) first-order
- steady state conditions
- diffusion, advection, horizontal transport negligible
-remineralization negligible
- adsorption on colloids or small particles only
l
b-1
Thlp
S
l
Th scavenging models: reversibility / irreversibilty of Th adsorption
U
l
k1
Thd
Thc
Thsp
k-1
l
b1
k2
k-2
l
l
b-1
Thlp
l
S
Quigley et al (2001)
Th scavenging models: reversibility / irreversibilty of Th adsorption
U
l
k1
Thd
Thc
Thsp
k-1
l
b1
k2
k-2
l
l
b-1
Thlp
l
S
Quingley et al (2001)
Modeling 234Th
in the ocean
from scavenging to export flux
Th scavenging models
Estimating 234Th export flux
Steady vs non-steady state models
Toward 3D-models
Photo: C. Beucher
estimating 234Th export flux: steady vs non-steady state models
U
l
Th
k
dATh
l
dt
Tanaka et al (1983)
0.3 < tNSS/tSS < 3.8
ATh2 =
l AU
l+k
= AU l - ATh l - ATh k
ATh1 -
l AU
l+k
(data from the Funka Bay, Japan)
l: decay constant; k: removal rate constant; A: radioisotope activity;
1, 2: first and second samplings; T: time interval between 1 and 2;
t: residence time
SS, NSS: steady and non-steady state models.
e-(l + k)T
estimating 234Th export flux: steady vs non-steady state models
U
l
Th
k
dATh
l
dt
Tanaka et al (1983)
0.3 < tNSS/tSS < 3.8
ATh2 =
l AU
l+k
= AU l - ATh l - ATh k
ATh1 -
l AU
l+k
e-(l + k)T
(data from the Funka Bay, Japan)
Assumptions:
- k is first order
- removal and input rates of 234Th are constant within the observational period
- diffusion and advection are negligible
estimating 234Th export flux: steady vs non-steady state models
l
U
Th
k
dATh
l
dt
Tanaka et al (1983)
ATh2 =
SS residence time (day)
20
l AU
l+k
= AU l - ATh l - ATh k
ATh1 -
l AU
l+k
e-(l + k)T
1:1
15
10
Wei and Murray (1992); data from Dabob Bay, USA
5
0
0
5
10
15
NSS residence time (day)
20
estimating 234Th export flux: steady vs non-steady state models
Layer 1 (surface)
U
l
Thd
J1
l
Layer 2
U
l
Thd
J2
l
Thp
P1
l
Thp
P2
l
Pi-1
Layer i
Buesseler et al (1992)
U
l
Thd
Ji
l
Thp
Pi
l
estimating 234Th export flux: steady vs non-steady state models
Pi-1
Buesseler et al (1992)
U
∂AiTh,d
∂t
∂AiTh,p
∂t
∂AiTh,t
∂t
=
Ai
U
l- Ai
Th,d
l-
l
Thd
Ji
Ji
l
Thp
Pi
i
i-1
i
i
= J + P - A Th,p l - P
i
i-1
i
i
= A U l + P - A Th,t l - P
d: dissolved; p: particulate; t: total; l: decay constant; A: radioisotope activity;
J: net flux of all forward and reverse exchange reactions;
P: particulate 234Th flux.
l
estimating 234Th export flux: steady vs non-steady state models
Pi-1
Buesseler et al (1992)
U
∂AiTh,t
∂t
=
Ai
U
l+
Pi = Pi-1 + l
Pi-1
- Ai
Th,t
l-
l
Thd
Ji
Thp
l
Pi
Pi
AiU (1- e-l(t2-t1)) + Ai,t1Th,t e-l(t2-t1) – Ai,t2Th,t
1- e-l(t2-t1)
d: dissolved; p: particulate; t: total; l: decay constant; A: radioisotope activity;
t1, t2: time of the first and second sampling, respectively; i: layer of interest;
J: net flux of all forward and reverse exchange reactions;
P: particulate 234Th flux.
l
estimating 234Th export flux: steady vs non-steady state models
Pi-1
U
l
Pi-1
Tht
Pi
Pi = Pi-1 + l
U
l
Thd
l
Ji
Thp
l
Pi
l
AiU (1- e-l(t2-t1)) + Ai,t1Th,t e-l(t2-t1) – Ai,t2Th,t
1- e-l(t2-t1)
Buesseler et al (1992)
Assumptions:
- Pi is constant within the period t2-t1
- diffusion and advection are negligible
estimating 234Th export flux: steady vs non-steady state models
Buesseler et al (2001), Southern Ocean
SS
NSS
4000
3000
2000
13-Mar
27-Feb
13-Feb
30-Jan
16-Jan
02-Jan
19-Dec
05-Dec
21-Nov
0
07-Nov
1000
24-Oct
234Th
flux (dpm/m2/d)
5000
estimating 234Th export flux: steady vs non-steady state models
Benitez-Nelson et al (2001), Aloha station, Pacific Ocean
SS
NSS
2000
1500
1000
Mar-00
Feb-00
Jan-00
Dec-99
Nov-99
Oct-99
Sep-99
Aug-99
Jul-99
Jun-99
0
May-99
500
Apr-99
234Th
flux (dpm/m2/d)
2500
estimating 234Th export flux: steady vs non-steady state models
Schmidt et al (2002), Dyfamed, Mediterranean Sea
1500
NSS
1000
SS
500
29 mai
27 mai
25 mai
23 mai
21 mai
19 mai
17 mai
15 mai
13 mai
11 mai
9 mai
0
7 mai
234Th
flux (dpm/m2/d)
2000
estimating 234Th export flux: steady vs non-steady state models
Savoye et al (preliminary data), EIFEX, Southern Ocean
inpatch 234Th, 238U (dpm/l)
Depth (m)
1.0
1.5
2.0
out patch 234Th, 238U (dpm/l)
2.5
1.0
0
0
50
50
100
100
150
238U
200
1.5
2.0
150
200
day -1
day 20
day -1
day 4
day 23
day 5
day 9
day 28
day 10
day 11
day 32
day 16
day 15
day 18
day 36
day 25
day 34
2.5
estimating 234Th export flux: steady vs non-steady state models
Savoye et al (preliminary data), EIFEX, Southern Ocean
in-patch
NSS 234Th flux (dpm/m2/d)
4000
out-patch
3000
2000
10000
SS
NSS
in-patch
5000
0
-1
5
10
15
20
25
30
36
30
36
-5000
1000
0
-1
5
10
15
20
25
days after infusion
30
36
NSS 234Th flux (dpm/m2/d)
SS 234Th flux (dpm/m2/d)
15000
10000
SS
NSS
out-patch
5000
0
-1
-5000
5
10
15
20
25
days after infusion
estimating 234Th export flux: steady vs non-steady state models
Checking the validity of the steady state assumption
234Th, 238U
0
1
234Th, 238U
(dpm/l)
2
0
3
51°S
100
50
234Th
150
Depth (m)
Depth (m)
65°S
100
238U
150
200
250
300
200
250
300
350
350
400
400
450
2
0
0
50
1
(dpm/l)
-49 +/- 216 dpm/m2/d
500
450
500
-2001 +/- 264 dpm/m2/d
Savoye et al (2004), Southern Ocean
3
estimating 234Th export flux: steady vs non-steady state models
Limit of the non-steady state model
234Th, 238U
1.5
(dpm/l)
2.0
2.5
0
SS '+/-' fluxes
NSS 'true' fluxes
NSS '+/-' fluxes
2
4
6000
+/- 0.02dpm/l
234Thflux
100
(dpm/m2/d)
50
Depth (m)
SS 'true' fluxes
150
5000
4000
3000
2000
1000
0
-1000
-2000
200
238U
day 1
day 3
day 5
1
3
days
5
steady vs non-steady state models: some remaining questions
- To what extent the actual steady and non-steady state models
can be used?
- How to test the validity of these models (especially the SS
model)?
- To what extent the assumption of constant Pi over the
observation period is valid? Need to use a Pi = f(t)
relationship?
Modeling 234Th
in the ocean
from scavenging to export flux
Th scavenging models
Estimating 234Th export flux
Steady vs non-steady state models
Toward 3D-models
Photo: C. Beucher
estimating 234Th export flux: toward 3D-models
1D model
U
l
l
Tht
(Thd + Thp)
S
d: dissolved; p: particulate; t: total; l: decay constant;
S: sinking.
estimating 234Th export flux: toward 3D-models
3D model
v
Ky
l
U
l
u
Tht
Kx
(Thd + Thp)
Kz
w
S
d: dissolved; p: particulate; t: total; l: decay constant;
S: sinking velocity; u, v, w: advection velocities; Kx, Ky, Kz: diffusion constants.
estimating 234Th export flux: toward 3D-models
3D model – steady state conditions
∂ATh
∂t
= 0 = AU l – ATh l – P + V
V=–u
+ Kx
∂ATh
∂x
∂2ATh
∂x2
–v
∂ATh
∂y
+ Ky
–w
∂2ATh
∂y2
∂ATh
advection term
∂z
+ Kz
∂2ATh
∂z2
diffusion term
estimating 234Th export flux: toward 3D-models
importance of advection and diffusion in coastal area
McKee et al (1984)
Gustafsson et al (1998)
Santschi et al (1999)
Benitez-Nelson et al (2000)
Charette et al (2001)
estimating 234Th export flux: toward 3D-models
importance of advection and diffusion in coastal area
Charette et al (2001)
Gulf of Maine, USA
estimating 234Th export flux: toward 3D-models
U
l
k
Tht
f
Matsumoto et al (1975)
l
P + ([234Th]I – [234Th]) / f = (l + k) [234Th]
l + (RI – R) / f = (l + k) R
P: production rate of 234Th from 238U
[234Th]I: 234Th concentration in the input water from the deeper layer
f: fluid residence time of the surface layer
l: decay constants
k: first-order removal rate constant
R: ATh / AU = l [234Th] / P
A: radioisotope activity
estimating 234Th export flux: toward 3D-models
U
l
k
Tht
f
l
Matsumoto et al (1975)
P + ([234Th]I – [234Th]) / f = (l + k) [234Th]
l + (RI – R) / f = (l + k) R
R = 0.8; RI = 1.0; f = 5 yr
(RI – R) / f = 0.04 yr-1
<< l = 10.5 yr-1
estimating 234Th export flux: toward 3D-models
Pi-1
wi-1
U
l
wi – wi-1
Tht
Bacon et al (1996)
l
wi
Pi
Steady state conditions:
Pi = Pi-1 + l (AU – AiTh) + wi (Ai+1 – Ai)
t: total; l: decay constant; A: radioisotope activity; i: layer of interest;
P: particulate 234Th flux; w: upwelling velocity.
estimating 234Th export flux: toward 3D-models
Bacon et al (1996), equatorial Pacific
El Niño conditions
non-El Niño conditions
estimating 234Th export flux: toward 3D-models
v
Ky
v
Ky
U
Dunne and Murray (1999)
l
l
k’1
Thd
Kz w
k-1
Thp
Kz w S
Zonal (W-E) advection and diffusion negligible
d: dissolved; p: particulate; l: decay constant;
k’1, k-1: adsorption and desorption constants
S: sinking velocity; v, w: advection velocities; Ky, Kz: diffusion constants.
l
Dunne and Murray (1999), equatorial Pacific
estimating 234Th export flux: toward 3D-models
estimating 234Th export flux: toward 3D-models
Advection and/or diffusion are not negligible:
in coastal areas and continental marges
in upwelling systems
What about frontal systems (cf Coppola et al, accepted), eddies, etc?...
Need to identify peculiar regions and/or physical conditions where
advection and diffusion processes are not negligible (model
simulation may be useful)
summary: toward 5D-models?
∂ATh
∂t
∂ATh
∂t
= Sc + V
Sc: scavenging; V: physic
: non-steady state term (t)
Sc: adsorption/desorption, aggregation/disaggregation (s), remineralization
V = diffusion (x, y, z) + advection (x, y, z)
t: time dimension
s: particle size dimension
x, y, z: longitude, latitude and depth dimensions, respectively
summary: toward 5D-models?
v Ky
l
U
l
u
v Ky
l
R
k1
Thd
Kx
Kz w
k-1
u
Kx
Ths1
Kz w S
v Ky
l
k2
ki
k-2
k-i
u
Kx
ki+1
Thsi
Kz w S
k-i+1
What, when, where?
Do we need complex models?
how many boxes (dissolved phase, colloids, particle spectrum)?
what fluxes (remineralization, advection, diffusion, desorption)?
including particle composition (chemistry, biology)?
including the physical properties of particles (density, stickiness)?
Depends on
scientific questions
scales (time, space)
conditions (physic, biology)
What, when, where?
What do we need to improve models?
peculiar experiment to better parameterize models?
development of new techniques?
Need of model simulations
to check the validity of the assumptions
to design the sampling strategy
Need to identify ocean regions and physical and biological
conditions where some assumption can be made