Modeling 234Th

1
Modeling 234Th in the ocean from scavenging to
export flux
Nicolas SAVOYE Vrije Universiteit Brussel
Photo C. Beucher
2
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
3
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
4
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 reminera
lization sinking
determining Th fluxes and estimating biogenic
fluxes (POC, PON, BSi) in ocean
5
One-box models
k
l
U
Tht
l
f
P (l k) 234Th
Broecker et al (1973)
P (234ThI 234Th) / f (l k) 234Th
Matsumoto et al (1975)
P production rate of 234Th from 238U 234ThI
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
6
One-box models
k
l
U
Tht
l
f
P (l k) 234Th
P (234ThI 234Th) / f (l k) 234Th
Broecker et al (1973)
228Th/228Ra
t 0.7 year
open ocean
Matsumoto et al (1975)
234Th/238U
t 0.38 year
open ocean
Knauss et al (1978)
t 0.52, 0.30 year
shelf water
228Th/228Ra
shelf break
t 0.19 year
Knauss et al (1978)
228Th/228Ra, 234Th/238U
t 0.03 year
coastal water
t 1 / k
7
One-box models
k
l
U
Tht
l
f
P (l k) 234Th
P (234ThI 234Th) / f (l k) 234Th
Assumptions

• k first order
• steady state
• diffusion, advection negligible

8
two-box irreversible models
Krishnaswami et al (1976)
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
9
two-box irreversible models
Krishnaswami et al (1976)
Steady state
t 0.40 year (from 234Th/238U) S 0.03 0.2
m/s (from 230Th/234U)
10
two-box irreversible models
l
kd
l
U
Thd
Thp
l
kp
Coale and Bruland (1985, 1987)
PTh
0
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.
11
two-box irreversible models
l
kd
l
U
Thd
Thp
l
kp
Coale and Bruland (1985, 1987)
PTh
Assumptions

• U is dissolved only
• kd, kp first order
• steady state
• diffusion, advection negligible
• all particles have the same comportment
• irreversible scavenging

12
two-box reversible models
k1
l
l
U
Thd
Thp
k-1
l
S
Nozaki et al (1981)
P
z
230Thd 230Thp
1
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.
13
two-box reversible models
k1
l
l
U
Thd
Thp
k-1
l
S
Bacon and Anderson (1982)
Steady state
k1 P
l (l k1 k-1)
1 exp
Thp

z
S (l k1)
l (l k1 k-1)
P k-1 Thp
Thd
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.
14
two-box reversible models
k1
l
l
U
Thd
Thp
k-1
l
S
Bacon and Anderson (1982)
Assumptions

• U is dissolved only
• k1, k-1 first order
• steady state
• diffusion, advection negligible
• all particles have the same comportment

15
three-box irreversible models
r1
l
k1
l
U
Thd
Thsp
Thlp
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.
16
modeling Th adsorption/desorption on mineral
particles
k1
k2
k3
Th
ThX
ThX
ThX
k-1
k-2
k-3
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 gtgt l The extent to which Th can desorb from
the particle decreases as the particle ages
17
three-box reversible models
k2
k1
l
l
U
Thd
Thsp
Thlp
k-2
k-1
S
l
l
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.
18
three-box reversible models
g
k1
r1
l
l
U
Thd
Thsp
Thlp
k-1
r-1
l
S
l
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.
19
three-box reversible models
b-1
k1
b2
l
l
U
Thd
Thsp
Thlp
k-1
b-2
l
w
l
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.
20
three-box reversible models the Brownian pumping
model
k1
k-1
k2
k1
l
l
U
Thd
Thc
Thfp
k-2
k-1
S
l
l
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.
21
four-box reversible model
R
k1
k3
k2
l
l
U
Thd
Thc
Thlp
Thsp
k-1
k-3
k-2
l
l
S
l
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
22
four (or more)-box irreversible model
h2
h3
l
U
Thd
Thc
Thlp
Thsp
k1
k-1
S3
S2
S1
k2
k-2
k-3
k3
Burd et al (2000)
l decay constant d dissolved c colloids
sp, lp small (0.5 lt lt 56 µm) and large (gt 56
µm) particles, respectively k adsorption or
desorption rate constants h aggregation rate
constants S settling loss.
23
five-box (ir)reversible model
Fd
Fp2
Fp1
Fp3
Fp4
l
Th
Thlp
Thsp
Thlp
U
Thd
0.5-1µm
1-10µm
10-53µm
gt53µm
l
l
l
l
l
Guo et al (2002)
d dissolved p particulate l decay constant
F flux.
24
Th scavenging models usual main assumptions
k1
b1
k2
l
l
U
Thd
Thc
Thlp
Thsp
k-1
b-1
k-2
l
l
S
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

25
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
26
Th scavenging models importance of the chemistry
of the particles
from 230Th sediment trap data
Kd,CaCO3 9.0 x 106 gt Kd,BSi 3.9 x 105 no
influence of lithogenics Chase et al (2002),
Chase and Anderson (2004)
Kd,lithogenics 2.3 x 108 gt Kd,CaCO3 1.0 x
106 gt Kd,BSi 2.5 x 105 Kuo et al (2004a, b)
27
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)
28
Importance of acid polysaccharides for 234Th
complexation
Quigley et al (2002)
29
Importance of uronic acid for 234Th scavenging
from Guo et al (2002)
y 0.577x-0.788
R2 0.66
30
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

31
Th scavenging models usual main assumptions
b1
k2
l
l
U
Thd
Thc
Thlp
Thsp
b-1
k-2
l
l
S
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

32
Th scavenging models reversibility /
irreversibilty of Th adsorption
k1
b1
k2
l
l
U
Thd
Thc
Thlp
Thsp
k-1
b-1
k-2
l
l
S
l
Quigley et al (2001)
33
Th scavenging models reversibility /
irreversibilty of Th adsorption
k1
b1
k2
l
l
U
Thd
Thc
Thlp
Thsp
k-1
b-1
k-2
l
l
S
l
Quingley et al (2001)
34
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
35
estimating 234Th export flux steady vs
non-steady state models
0.3 lt tNSS/tSS lt 3.8 (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.
36
estimating 234Th export flux steady vs
non-steady state models
0.3 lt tNSS/tSS lt 3.8 (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

37
estimating 234Th export flux steady vs
non-steady state models
Tanaka et al (1983)
20
11
15
Wei and Murray (1992) data from Dabob Bay, USA
10
SS residence time (day)
5
0
0
5
10
15
20
NSS residence time (day)
38
estimating 234Th export flux steady vs
non-steady state models
Buesseler et al (1992)
39
estimating 234Th export flux steady vs
non-steady state models
Pi-1
Buesseler et al (1992)
l
Ji
U
Thd
Thp
l
l
Pi
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.
40
estimating 234Th export flux steady vs
non-steady state models
Pi-1
Buesseler et al (1992)
l
Ji
U
Thd
Thp
l
l
Pi
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.
41
estimating 234Th export flux steady vs
non-steady state models
Pi-1
Pi-1
l
Ji
l
U
Thd
Thp
U
Tht
l
l
l
Pi
Pi
Buesseler et al (1992)
Assumptions

• - Pi is constant within the period t2-t1
• diffusion and advection are negligible

42
estimating 234Th export flux steady vs
non-steady state models
Buesseler et al (2001), Southern Ocean

43
estimating 234Th export flux steady vs
non-steady state models
Benitez-Nelson et al (2001), Aloha station,
Pacific Ocean

44
estimating 234Th export flux steady vs
non-steady state models
Schmidt et al (2002), Dyfamed, Mediterranean Sea
45
estimating 234Th export flux steady vs
non-steady state models
Savoye et al (preliminary data), EIFEX, Southern
Ocean

46
estimating 234Th export flux steady vs
non-steady state models
Savoye et al (preliminary data), EIFEX, Southern
Ocean

47
estimating 234Th export flux steady vs
non-steady state models
Checking the validity of the steady state
assumption
-49 /- 216 dpm/m2/d

-2001 /- 264 dpm/m2/d

Savoye et al (2004), Southern Ocean
48
estimating 234Th export flux steady vs
non-steady state models
Limit of the non-steady state model
/- 0.02dpm/l
49
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?

50
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
51
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.
52
estimating 234Th export flux toward 3D-models
Ky
3D model
v
l
U
l
Tht
u
(Thd Thp)
Kx
S
w
Kz
d dissolved p particulate t total l decay
constant S sinking velocity u, v, w
advection velocities Kx, Ky, Kz diffusion
constants.
53
estimating 234Th export flux toward 3D-models
3D model steady state conditions
?ATh
0 AU l ATh l P V
?t
?ATh
?ATh
?ATh
V u
v
w
advection term
?x
?y
?z
?2ATh
?2ATh
?2ATh
Kx
Ky
Kz
diffusion term
?x2
?y2
?z2
54
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)
55
estimating 234Th export flux toward 3D-models
importance of advection and diffusion in coastal
area

Charette et al (2001) Gulf of Maine, USA
56
estimating 234Th export flux toward 3D-models
k
l
Matsumoto et al (1975)
U
Tht
l
P (234ThI 234Th) / f (l k) 234Th
f
l (RI R) / f (l k) R
P production rate of 234Th from 238U 234ThI
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
57
estimating 234Th export flux toward 3D-models
k
l
Matsumoto et al (1975)
U
Tht
l
P (234ThI 234Th) / f (l k) 234Th
f
l (RI R) / f (l k) R
R 0.8 RI 1.0 f 5 yr (RI R) / f 0.04
yr-1 ltlt l 10.5 yr-1
58
estimating 234Th export flux toward 3D-models
Pi-1
wi-1
l
wi wi-1
U
Tht
Bacon et al (1996)
l
Pi
wi
Steady state conditions Pi Pi-1 l (AU
AiTh) wi (Ai1 Ai)
t total l decay constant A radioisotope
activity i layer of interest P particulate
234Th flux w upwelling velocity.
59
estimating 234Th export flux toward 3D-models

Bacon et al (1996), equatorial Pacific
60
estimating 234Th export flux toward 3D-models
Ky
Ky
v
v
U
l
Dunne and Murray (1999)
k1
l
Thd
Thp
l
k-1
w
S
w
Kz
Kz
Zonal (W-E) advection and diffusion negligible
d dissolved p particulate l decay constant
k1, k-1 adsorption and desorption constants S
sinking velocity v, w advection velocities Ky,
Kz diffusion constants.
61
estimating 234Th export flux toward 3D-models

Dunne and Murray (1999), equatorial Pacific
62
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?...
63
summary toward 5D-models?
?ATh
Sc V
Sc scavenging V physic
?t
?ATh
non-steady state term (t)
?t
Sc adsorption/desorption, aggregation/disaggregat
ion (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
64
summary toward 5D-models?
Ky
Ky
Ky
v
v
v
l
U
l
l
R
l
k2
ki1
k1
ki
k-1
k-i
k-2
k-i1
Thd
Ths1
Thsi
u
u
u
Kx
Kx
Kx
w
Kz
S
w
Kz
S
w
Kz
65
What, when, where?
66
What, when, where?
67
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