Modeling of the coupled carbon, nitrogen and phosphorus
biogeochemical cycles in the coastal ocean during the
industrial era
Julien Bouchez
Pr Fred T. Mackenzie, advisor
February to August 2004
Contents
Abstract
3
Résumé
3
1
TOTEM, The Terrestrial Ocean aTmosphere Ecosystem Model : a FORTRAN version
1.1 Generalities about (bio)geochemical cycles modelling . . . . . . . . . . . . . . . . .
1.1.1 Fluxes and reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 The initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 The calculations and the interest of numerical modelling . . . . . . . . . . .
1.2 The Terrestrial Ocean aTmosphere Ecosystem Model, TOTEM . . . . . . . . . . . .
1.2.1 The main features of TOTEM . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 The main issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 The new TOTEM program . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.4 Some results of the new TOTEM model . . . . . . . . . . . . . . . . . . . . .
2
A new coupled C-N-P biogeochemical coastal ocean model
11
2.1 The global coastal ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Description of the coastal ocean biogeochemistry . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Definition of the coastal ocean in our model . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Definition of the model reservoirs and fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 The dissolved inorganic matter reservoir, MDIM . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 The biota reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 The dead organic matter reservoir, MDOM . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.4 The sediments reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 The initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Initial masses estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Initial fluxes estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Fluxes parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 The biological uptake during the photosynthesis : M FN P P . . . . . . . . . . . . . . . . . . 15
2.4.2 Grazing fluxes : M Fgraz,het and M Fgraz,bact . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.3 Respiration, excretion and death fluxes : M Fresp,het , M Fresp,bact , M Fexc,aut and M Fexc,het 16
2.4.4 Sedimentation Flux : M Fsed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.5 Exchange between pore water and seawater : M Fpw−wc . . . . . . . . . . . . . . . . . . . 17
2.4.6 Ocean output fluxes : M FDOM,oc and M FDIM,oc . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.7 Coastal upwelling flux : M Fupw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.8 Rivers input fluxes : M FDOM,riv , M FDIM,riv , M FROM,riv and M FP IM,riv . . . . . . . . 17
2.4.9 Burial (CFburial,org and CFburial,inorg ), carbonate transport to the slopes (CFtrans,slope )
and organic sediments oxidation (CFox,sed ) fluxes . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.10 Carbonate precipitation and dissolution (CFCaCO3 ,prec and CFCaCO3 ,diss ), biogenic carbonate production (CFCaCO3 ,bio ), and CO2 exchange across the sea-air interface (CFCO2 ,atm ) 18
2.4.11 N H4+ assimilation flux : N FN H + ass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4
2.4.12 Biologic N2 fixation flux : N FN2 f ix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.13 Atmospheric nitrogen deposition : N Fdep . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.14 Denitrification fluxes : N Fdenitr,wc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.15 Nitrogen volatilization flux : N Fvolat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 The carbonate chemistry in the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.1 Calculating the carbonate system concentrations . . . . . . . . . . . . . . . . . . . . . . . . 19
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Results and discussion
3.1 First results from the model over the past three centuries and the next fifty years
3.1.1 Evolution of the organic carbon balance . . . . . . . . . . . . . . . . . . . .
3.1.2 Evolution of the inorganic carbon balance . . . . . . . . . . . . . . . . . . .
3.1.3 Evolution of the CO2 flux . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Sensitivity analyses and influence of parameterizations . . . . . . . . . . . . . . .
3.2.1 Sensitivity analyses : biologic constants . . . . . . . . . . . . . . . . . . . .
3.2.2 Calcification equation for dependence on saturation state . . . . . . . . . .
3.2.3 Calculation of alkalinity change during photosynthesis and respiration .
3.3 Implications for global carbon cycle and discussion . . . . . . . . . . . . . . . . .
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2.6
2.7
2.8
3
2.5.2 The saturation state . . . . . . . . . . . . . . . . . . . . .
2.5.3 The biogenic carbonate production flux . . . . . . . . .
2.5.4 Carbonate precipitation and dissolution in pore water
CO2 flux across the air-seawater interface . . . . . . . . . . . .
2.6.1 Equilibration with atmospheric PCO2 : CFCO2 ,eq . . . .
2.6.2 Calcification CO2 flux : CFCO2 ,calc . . . . . . . . . . . .
2.6.3 Biogenic CO2 flux : CFCO2 ,bio . . . . . . . . . . . . . . .
2.6.4 Total CO2 flux, and initial values . . . . . . . . . . . . .
The two sets of initial values obtained . . . . . . . . . . . . . .
Residence times . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Conclusion
39
Acknowledgements
39
Appendix
40
List of figures
50
List of tables
51
References
55
2
Abstract
During the past three centuries, human activities such as fossil-fuel combustion, land-use change, usage of
fertilizers and sewage disposal, have strongly affected global biogeochemical cycles. Among others impacts
on the natural system, these activities led to an exponential incease in atmospheric carbon dioxide and to a
radical change in the concentration of terrestrial material brought by rivers to coastal ocean. As a consequence,
CO2 invasion into the coastal seawater may modify speciation of the carbonate system components; increased
inputs of nutrients such as nitrogen and phosphorus may increase primary production in the coastal zone and
change Net Ecosystem Production NEP, that is to say the balance between the uptake and the release of carbon
by the biota. In an attempt to simulate the past and future of the coastal carbonate system and biota (over the
period 1700-2050 A.D.), and their possible interactions, a coupled C-N-P biogeochemical model representative
of the global coastal ocean is developed. The results of the Terrestrial Ocean aTmosphere Ecosystem Model
(TOTEM) are used as forcings for rivers inputs and for atmospheric CO2 . Two different sets of initial fluxes
for the year 1700 are tested, each being representative of a possible pre-anthropogenic coastal trophic state,
following the litterature.
Numerical simulations show a decrease in seawater saturation state with respect to carbonate minerals
from 1700 through 2050, subsequently leading to a decrease in calcification by marine organisms, and to a
negative feedback to increasing atmospheric CO2 . NEP shows a great sensitivity to the initial conditions,
parameters and methods of calculations of the model, and does not present a clear trend over the period of
simulation. However, it seems to decrease during the twenty-first century. The role of the biota in the exchange
of CO2 betweeen the coastal ocean and the atmosphere then remains uncertain. These results emphasize the
lack of data in the litterature to constrain the coastal biota parameters.
Résumé
Au cours des trois derniers siècles, les activités humaines comme l’utilisation des combustibles fossiles, d’engrais,
l’installation d’égoûts et l’évolution des techniques d’agriculture, ont fortement affecté les cycles biogéochimiques, entraînant entre autres une augmentation exponentielle du dioxyde de carbone dans l’atmosphere ces
dernières décennies, et un changement drastique des concentrations dans les composés terrigènes transportés
par les rivières jusqu’à l’océan côtier. La dissolution du CO2 dans l’eau de mer côtière modifie la spéciation
des composés carbonatés, et l’apport accru de nutriments azotés et phosphatés modifie la production primaire dans la zone côtière. La photosynthèse et la respiration permettent aux êtres vivants d’interagir avec
le domaine inorganique; ce phénomène est quantifié par la NEP (Net Ecosystem Production), définie par le
bilan photosynthèse-respiration. Afin de simuler l’évolution passée et future du système carbonatés et de la
biomasse dans l’océan côtier de 1700 à 2050, ainsi que leurs éventuelles interactions, un modèle biogéochimique couplé carbone-azote-phosphore est construit, représentatif de l’océan côtier global, utilisant les résultats
du modèle TOTEM (Terrestrial Ocean aTmosphere Ecosystem Model) en forcages; deux ensembles de conditions initiales pour les valeurs des flux en 1700 sont testés, représentant chacun un état trophique pré-industriel
possible pour l’océan côtier.
Nos simulations indiquent une diminution de l’indice de saturation de l’eau de mer par rapport aux
minéraux carbonatés, et de la production de squelettes carbonatés par les organismes marins, source d’une
rétroaction négative sur le CO2 atmosphérique. La NEP présente une grande sensibilité aux conditions initiales, aux paramètres et aux méthodes de calcul utilisés, et aucune forte tendance ne résulte des calculs. La
tendance finale semble toutefois être une baisse de la NEP au cours du vingt-et-unième siècle. Le rôle des
organismes vivants dans l’échange de CO2 demeure donc incertain. Ces résultats soulignent le manque de
données dans la littérature nécessaires pour contraindre les paramètres de la biomasse côtière.
3
Chapter 1
TOTEM, The Terrestrial Ocean
aTmosphere Ecosystem Model : a
FORTRAN version
The understanding of biogeochemical cycles of light elements such as carbon, nitrogen or phosphorus, requires
to take in account the whole Earth surface system : biosphere, hydrosphere, atmosphere, lithosphere... On a
global scale, difficulties always rise when one tries to assess and understand transfer of elements.
In an attempt to gather the knowledge we have on Earth’s chemistry biogeochemical cycles, biogeochemical
models are developed. The purpose of such models is to simulate the evolution of Earth’s chemistry, under
given forcings, on regional or global scale. The outputs of the model can be tested by a comparison with data; a
well comparison is often a validity criterion of a model. Moreover, models use parameters that have sometimes
great uncertainties. Sensitivity analysis allows one to see whether making the parameter vary over the range
of uncertainty heavily changes model outputs or not, and points the parameters that have prioritarily to be
better known.
In this chapter, we sum up the methods used to build biogeochemical cycles model, and we explain the
rewriting of the TOTEM model that we have carried out, giving some results used further as forcings for our
coastal ocean model presented in S EC 3.
1.1
1.1.1
Generalities about (bio)geochemical cycles modelling
Fluxes and reservoirs
Knowing the elements and the time-scale we want to work on, we have to determine the reservoirs of Earth
where the studied elements are significantly present, with an approximately homogenous concentration : it’s
the "well-mixed" assumption. The transfers of elements between the N reservoirs are the fluxes. These fluxes
have to be identified and quantified, so as to calculate the instantaneous variation of an element M in a reservoir
i, following the equation of mass balance equation, we have :
!
dMi
dt
"
=
t
N
#
j=1,j"=i
M Fji (t) −
N
#
M Fij (t)
(1.1)
j=1,j"=i
where M Fab (t) is the M-element flux from reservoir a to reservoir b, at the time t. We can define now the
mean residence time τ of the element M in the reservoir i :
τMi = $N
1
j=1,j"=i M Fji (t)
= $N
1
j=1,j"=i
M Fij (t)
(1.2)
This definition is valid only when the sum of%the outgoing
fluxes is equal to the sum of the incoming fluxes.
&
i
In this case, the mass derivative of the element dM
dt t = 0, according to E Q 1.1. Here the Mi mass is constant
with the time : we are in a steady-state situation; if there is not any external forcings, the often masses-dependent
fluxes do not vary and their sum for each reservoir stays equal to 0, then the mass remain the same.
So it can be seen that with an appopriate method of integration, and knowing the values of the reservoir
mass of a given element at a time t0 , one can calculate this value at t0 + ∆ t, via the calculation of the fluxes at
4
t0 , and so on, from a time step to another, until the end of the simulation.
There are several ways to parameterize the fluxes of an element M from a reservoir i to a reservoir j are :
• the zeroth-order kinetics :
M Fij (t) = A
(1.3)
where A is a constant value, to be found in the litterature;
• the first-order kinetics :
M Fij (t) = kM Fij ∗ Mi (t)
(1.4)
where kM Fij is a constant, which could be obtained by the initial conditions, with the equation :
kM Fij =
M Fij (t0 )
Mi (t0 )
(1.5)
which is only a particular case of E Q 1.4. The initial values are to be found in the litterature. Assuming a
first-order kinetics relationship, we suppose that the flux is a linear function of the mass of the reservoir
it is coming from, which is a good approximation as a first approach in many cases.
• and many more complicated ways, some of them discussed in S EC 2.4.
1.1.2
The initial conditions
The initial values for masses, fluxes and parameters, are classically obtained by a review of the litterature. But
it has to be emphasized that a great uncertainty lies on these values, coming both from the measurements and
the extrapolation of local data to global scale. Therefore, the outputs of global biogeochemical models should
be taken carefully.
1.1.3
The calculations and the interest of numerical modelling
In such a model using A boxes, up to 2A! fluxes might be calculated at each time step, sometimes as complicated functions of reservoirs masses, time... The number of calculations for a simulation is then set by :
• the duration of the simulation : seasonal, decadal, centuries, thousands or millions of years...
• the time step length (the two latters giving the number of time steps); the smaller it is, the more reliable
the calculations will be;
• the method of integration which is used; some implied several masses derivatives calculations for a same
time step.
This is why numerical modelling is often used for this kind of study.
1.2
1.2.1
The Terrestrial Ocean aTmosphere Ecosystem Model, TOTEM
The main features of TOTEM
TOTEM is a Earth biogeochemical model, composed of fourteen reservoirs of the terrestrial (living biota, humus, inorganic soil, soil water, shallow groundwater, lakes and rivers), oceanic (coastal waters, coastal organic
matter, coastal sediments, open ocean, ocean organic matter, deep ocean) and atmospheric realms. It links
the cycles of carbon, nitrogen, phosphorus and sulfur via a set of equations given in Ver [1999] and Ver et al.
[1999a], starting its calculations in the year 1700 A.D., with the initial fluxes shown on the conceptual diagram
on F IG 1.1, and following the calculations pattern explained in S EC 1.1. It takes in account natural and anthropogenic forcings. Many papers have been written about TOTEM and its results, over the last three hundred
years and the next century. For more complete TOTEM descriptions and results, see Mackenzie et al. [1998a],
Mackenzie et al. [1998b], Ver [1999], Ver et al. [1999a], Ver et al. [1999b] and Mackenzie et al. [2002].
The main features of TOTEM are :
5
• the coupling between elements, mainly carried out by the use of the (C:N:P) ratios, also called sometimes
Redfield ratios (see e.g. Redfield [1958]). These are the atomic proportions, in a given system, of carbon,
nitrogen, phosphorus. For example, when organic matter is remineralized, knowing the carbon flux, one
can calculate the nitrogen fluxes, dividing it by the (C:N) ratio (see E Q 2.5). There are other ways used in
TOTEM to couple the biogeochemical cycles, some are explained in S EC 2.4 for our coastal ocean model.
• the forcings : temperature, fossil fuel emissions, land-use change, sewage disposal and using of detergents. Based on data, fluxes are added at given time steps of the simulation to mass balance equations E Q 1.1 (for instance fossil-fuel combustion adds carbon and sulfur to the atmosphere), and/or
pre-existing fluxes paramerization are modified (for example land-use change enhances soil erosion, by
deforestation). For details about these forcings, see Mackenzie [2002].
1.2.2
The main issue
TOTEM was written on STELLATM , which is a graphically-based programming language, running on Winc The main problem with the STELLATM language is the fact that all the calculations results are
dows OS (#).
kept in RAM during the runs, so the memory can easily get overflown. That’s the main reason why it has been
decided to rewrite TOTEM in other languages, such as FORTRAN, running both on Unix and Windows OS.
Indeed, FORTRAN can handle much more calculations, so as the model is about to be extended (in complexity
and in time-scale length), it was important to transfer it to another platform (it is also being transferred on the
MATLABTM platform).
1.2.3
The new TOTEM program
Some modifications have been carried out to TOTEM during its rewriting in FORTRAN. The main one is the
change of method of integration. The previous version of TOTEM used the Euler method, which error term is
of h2 for a time step h. In the new version, we use the fourth order Runga-Kutta method, which is much less
divergent (the error term is h5 for a same time step). For details about these methods and their associated
errors, and to obtain the FORTRAN subroutines used in our program, see Press [1992]1 .
As the time step used in the whole study reported here is 0.01 yr, the calculations uncertainty is very small,
even after hundreds of years of simulation. Using this method would allow one to run the model on a larger
time scale in a dependable way (in addition of the fact of using FORTRAN instead of STELLATM ).
Compared to the previous papers where TOTEM has been used, we have not considered the sulfur cycle in
this study, regarding the uncertainties remaining on its actual cycle and interactions with the other elements.
1.2.4
Some results of the new TOTEM model
Results from TOTEM have already been presented in many papers such as Ver et al. [1999a], Ver et al. [1999b],
Mackenzie et al. [2002]. Here we present some results from the new version, which yields almost the same
outputs as the former one. The observed small differences are attributed to the change of method of integration,
and these differences are small compared to the uncertainties lying on the parameters and initial conditions
used in the model. TOTEM also yields projected fluxes and masses for the future (until 2050 A.D.), when
it is forced by scenarios of anthopogenic emissions (e.g. IPCC projections). Although these results are not
presented here, we use these projected outputs in the next chapters.
Atmospheric CO2
The increase of atmospheric carbon dioxide that has been observed especially during the last five decades
(Keeling and Whorf [2004]), makes the understanding of the carbon cycle an important issue. Moreover, the
measurements of global atmospheric CO2 are dependable and very continuous, especially for the twentieth
century. It is thus a very good way to check the results of a biogeochemical cycle model.
We present in F IG 1.2 a comparison between results from TOTEM and different measurements sets2 . The
trends compare very well, even if TOTEM’s atmospheric CO2 is a little above the data (+10.9 ppm above in
1995). But it stays within a very narrow range if we think about the uncertainty lying on the initial conditions.
Then on a century scale, TOTEM simulates well the behaviour of global carbon, especially atmospheric CO2 .
The atmospheric CO2 from TOTEM will be used in our coastal ocean model, in S EC 2.
1 the
subroutines are also available at http://www.library.cornell.edu/nr/bookpdf.html
at http://cdiac.esd.ornl.gov/trends/co2/contents.htm
2 available
6
Figure 1.1: Conceptual diagram of the new version of TOTEM.
Rivers inputs in coastal ocean
Our coastal oecan model (see S EC 2) needs rivers input simulated from 1700 to 2050 A.D., and the ones given
by TOTEM are assumed reliable as it takes in account forcings like land-use changes and sewage disposal, that
heavily affects rivers and streams chemistry (F IG 1.3, F IG 1.4, F IG 1.5).
Under anthropogenic forcings, due to land-use change, soil erosion has been increased, and the amount
of organic matter transferred from terrestrial realm to the oceans has been enhanced. The inorganic flux has
been rising as well, owing to the increase in the use of detergents and fertilizers. The values obtained here for
particulate input lie in the range of measurements made by Meybeck and Ragu [1995], as shown in Ver et al.
[1999b] and Mackenzie et al. [2002].
7
Figure 1.2: Comparison between TOTEM atmospheric CO2 and data from 1700 to 2005.
Comparison between TOTEM atmospheric CO2 and data (Keeling and Whorf [2004], Etheridge et al. [1998]
and Netfel et al. [2004]), from 1700 to 2005.
8
Figure 1.3: Carbon rivers input from TOTEM over the past three centuries.
Figure 1.4: Nitrogen rivers input from TOTEM over the past three centuries.
9
Figure 1.5: Phosphorus rivers input from TOTEM over the past three centuries.
10
Chapter 2
A new coupled C-N-P biogeochemical
coastal ocean model
In this chapter, we try to assess the evolution of organic and inorganic carbon balances of the global coastal
ocean in the past three centuries and in the next future, under anthropogenic forcings, and its possible role in
global caron cycle. We use a coupled C-N-P biogeochemical model following the steps explained in S EC 1.1.
We compare results obtained from two different initial states in the year 1700 A.D., each representing a possible
coastal ocean pre-industrial chemical state. Finally, sensitivity analysis are driven on crucial parameters of the
model.
2.1
The global coastal ocean
The coastal ocean is an important site in biogeochemical cycles studies, as it is the region where a large amount
of terrestrial material is deposited, after being transported by rivers and stream. Indeed, this zone is often
referred as the continental margin, and is the narrow transition domain between land and open oceans. It is
under control of both natural and anthropogenic fluxes, as the rivers has been loading pollutants during last
decades because of land-use change, detergents, sewage... (e.g. Mackenzie [2002]).
Finally, the coastal ocean is also socially important, as 40 to 60% of world population resides within 100
kilometers of the shore (Cohen et al. [1997]).
2.1.1
Description of the coastal ocean biogeochemistry
Owing to the load of inorganic terrestrial material, the coastal ocean is a region of high primary production,
that is to say reduction of inorganic matter into organic matter via photosynthesis. Thus, it is also a suitable
environment to sustain a food web of living organisms. The interactions between these organisms ans their
environment modify the carbon cycle (e.g. Mackenzie et al. [2004]). The coastal ocean also receives matter from
the deep oceans by coastal upwellings, and exports matter to the open oceans. Abiotic and biotic precipitation
of carbonates also occur in this zone : 25% of the global carbonate production, and almost 50% of the global
carbonate accumulation in the sediments, after Milliman [1993], Wollast [1994] and Wollast [1998].
Then, one can see that the reactions that heavily affect the carbon cycle via CO2 release or uptake in seawater will be :
• the photosynthesis (left to right) and respiration (right to left) reactions :
CO2 + H2 O ! CHOH
where CHOH stands for organic matter. The balance between photosynthesis (P ) and total respiration
(Rtotal ), also referred as trophic state or Net Ecosystem Productivity (N.E.P.) is :
N EP (t) = P (t) − Rtotal (t)
(2.1)
• The carbonates precipitation (right to left) and dissolution (left to right) reactions :
Ca2+ + 2HCO3− ! CaCO3 + CO2 + H2 O
11
(2.2)
From the magnitude of these fluxes, that modify the carbon chemistry in seawater, one can calculate the associated CO2 fluxes to/from the atmosphere. These calculations are explained in S EC 2.6.
In the following study, we build a box model of coastal ocean in S EC 2.2, adressing the question whether this
domain has been and is now a source or a sink of CO2 , via the calculations of NEP and carbonate production
during the past three centuries and the next fifty years. This model is forced by atmospheric PCO2 , and by
rivers inputs from TOTEM, from 1700 through 2050.
The program has been written on the FORTRAN platform, and we used the fourth-order Runge-Kutta method
to carry out the calculations.
2.1.2
Definition of the coastal ocean in our model
Many definitions of the coastal ocean can be found in the litterature. It is always the junction where the
land, ocean and atmospheric components interact (Ducklow and McCallister [2004]). It includes estuaries,
bays, lagoons, wetlands, mangroves and carbonate shelf, defined as an euphotic layer. In this study, we don’t
include continental slopes in the coastal ocean.
We use the definition of coastal ocean given in Ver [1999], Mackenzie et al. [1998a] and Ver et al. [1999a],
yielding a total volume of 0.3 ∗ 1016 m3 , and a surface of 36 ∗ 1012 m2 , which is approximately 10% of the total
ocean surface. This definition is used in sight of further development, such as including our coastal ocean
model into TOTEM.
2.2
Definition of the model reservoirs and fluxes
Notations used in this study are explained in TAB 3.5, TAB 3.9, TAB 3.10 and TAB 3.6. A summary of all the
mass balances equations are given in TAB 3.11, TAB 3.12 and TAB 3.13, and the conceptual diagram in F IG 2.1.
2.2.1
The dissolved inorganic matter reservoir, MDIM
The coastal ocean contains inorganic carbon compounds : dissolved CO2 , ion hydrogenocarbonate HCO3−
and ion carbonate CO32− (their sum is referred as DIC, standing for Dissolved Inorganic Carbon). Inorganic
nitrogen is present mainly as dissolved N2 , not taken in account here owing to its very low reactivity (except
in the case of dinitrogen fixation, see S EC 2.4.12). Nitrogen is also present as nitrate N O3− , nitrous oxide N2 O,
nitrite N O2− , and as ion ammonia N H4+ and its base ammoniac N H3 . Phosphorus is almost only under the
orthophosphate form P O43− . This reservoir is supplied by rivers load, coastal upwellings and respiration; its
output fluxes are the biological uptake and the export to the open ocean. It also exchanges matter with the
atmosphere and the sediments porewater. This reservoir will be referred in this study as DIM.
2.2.2
The biota reservoirs
A food chain has been implemented in the model, where the different boxes are defined and separated following the trophic type their components belong to. Indeed, the reservoirs are supposed to gather all the entities
having the same biogeochemical behaviour, and organisms having the same trophic type act the same way
concerning the biologically important elements such as carbon, nitrogen, phosphorus. This food web is inspired from pre-existing works such as the ones presented in Baretta et al. [1995], Laws et al. [2000], or Tanaka
[2002]. The reservoirs are :
Autotrophs reservoir, Maut
It contains all the organisms using solar light energy to convert inorganic matter into organic matter, such
as phytoplankton and benthic algae. They uptake carbon, nitrogen and phosphorus from the inorganic matter reservoir during the photosynthesis, are grazed by heterotrophic organisms, and release inorganic matter
during respiration and dead organic matter during excretion and death. Some organisms, called the nitrogen
fixers, are also able to uptake atmospheric dinitrogen.
Heterotrophs reservoir, Mhet
It contains all the eukaryotes unable to uptake inorganic matter, that is to say the zooplankton, the nekton and
the zoobenthos. Here they are supposed to graze only upon autotrophs, and release inorganic matter during
respiration and dead organic matter during excretion and death.
12
Figure 2.1: Conceptual diagram of the coastal ocean model, with the first set initial fluxes.
13
Heterotrophic bacteria reservoir, Mbact
They are separated from the other heterotrophs to emphasize the possible effect of a microbial loop (Azam
[1998]), and the possible autotrophic relationship concerning the nitrogen. Indeed, bacteria are able to uptake
ammonia instead of organic nitrogen, if the latter becomes too scarce. They feed upon dissolved inorganic
matter, and release inorganic matter during the respiration, and dead organic matter during excretion and
death. The importance of the microbial loop is discussed in S EC 2.4.3, and leads to the two different sets of
initial fluxes used in our simulations.
2.2.3
The dead organic matter reservoir, MDOM
The organic matter contains carbon, nitrogen and phosphorus under many forms. The dead organic reservoir
is defined to contain both particulate organic matter (coming from rivers load, excretion and death of living
organisms) and dissolved organic matter (coming from rivers load and excretion of living organisms). It should
be emphasized that this reservoir contains only the reactive part of particulate organic matter, the refractive
organic matter (ROM) brought by rivers being assumed to go straight into the organic sediments reservoir.
The main outlets of this reservoir are the sedimentation flux and the export to the open ocean. In this study,
DOM will stand for this reservoir.
2.2.4
The sediments reservoirs
For the three sediments reservoirs, only the carbon cycle is taken in account, as great uncertainties still stand on
nitrogen and phosphorus masses and fluxes in the sediments. Moreover, the N and P cycles in the sediments
are not important features of the model presented here.
The organic sediments reservoirs Corg,sed
The organic components of the surface sediments are gathered into the organic sediments reservoir, mainly
supplied by rivers and sedimentation of particulate organic matter. The reactive organic components are
respired by organisms living into the sediments, or are buried like the refractory components.
The pore water reservoir Cpw
The pore water is the liquid phasis of the sediment, circulating in the pores of sedimentary rocks. Its composition is quite different from the seawater composition, overall set by the organic sediments oxidation, abiotic
carbonate precipitation and dissolution, and by exchange of matter with the overlying water column.
The inorganic sediments reservoir Cinorg,sed
This reservoir contains the mineral part of the sediment such as carbonate rocks composed of calcite, magnesian calcite and aragonite (see Land [1967]). Abiotic and biotic carbonate precipitation form these minerals. This reservoirs interacts with seawater and pore water through the precipitation and dissolution phenomenons, receives matter from rivers, and exports material to the deep ocean via the continental slopes.
2.3
The initial conditions
We assume for the initial conditions in the year 1700 that each reservoir achieves steady-state :
"
!
dMi
=0
dt t0
(2.3)
This assumption allows to emphasize the variations of the masses and the fluxes relatively to the initial
values, and to decouple the variations due to forcings from any "natural" variation. Moreover, it gives a strong
constraint for initial fluxes estimates (see S EC 2.3.2).
14
Table 2.1: Initial masses used in the model.
Initial masses used in the model. In 1012 molM/yr.
System
Initial C Initial N Initial P
Dissolved inorganic matter
6000
60
0.45
Autotrophs
6
0.86
0.06
Heterotrophs
30
4.8
0.29
Heterotrophic bacteria
4
0.8
0.04
Dead organic matter
275
15.31
2.60
Organic sediments
110000
Pore water
54
Inorganic sediments
90000
2.3.1
Initial masses estimates
First, the carbon masses of each reservoir are estimated by a review of the litterature, as shown in TAB 3.2.
For the living reservoirs, an important assumption we make is that the deep ocean doesn’t contain neither
phytoplankton (which is strictly true, regarding the darkness in this area) nor zooplankton (which is a good
assumption, regarding the scarcity of primary producers that the heterotrophs could feed upon). When local
measurements are given in the litterature, we assume :
• that the mean published concentration is representative of the coastal ocean;
• an homogenous distribution of the element over the coastal ocean.
The dissolved inorganic nitrogen and phosphorus are taken from Ver [1999], where a complete review of
concentrations measurements is done. All others nitrogen and phosphorus masses are calculated from the
carbon masses using the (C:N) and (C:P) ratios given in TAB 3.7, following the equation :
Mi (t0 ) =
Ci (t0 )
(C : M )i
(2.4)
where M is N or P. The final values we use are given in TAB 2.1.
2.3.2
Initial fluxes estimates
The initial carbon fluxes are estimated the same way as the initial masses. Some nitrogen and phosphorus
fluxes can be calculated using the carbon fluxes and the (C:N) and (C:P) ratios, as follows:
M Fij (t0 ) =
CFij (t0 )
(C : M )k
(2.5)
where M is either N or P, and k is either i or j, depending on the type of flux (see S EC 2.4). Some nitrogen fluxes
cannot be estimated this way, like denitrification. A specific reviewing of the litterature is given in TAB 3.4.
Initial fluxes have sometimes to be balanced, so as to achieve the steady-state condition. The modification
is done on the fluxes where lie the greater uncertainties, for which the relative variation will be the smallest,
and with the most neglictible influence on global model trends.
As we show in S EC 2.4, we calculate two possible steady-state for the year 1700, depending on the intensity
of remineralization in the water column. We summarize the values in TAB 3.5. More details about the way we
obtain these values and the equations are given in S EC 2.4.
From the fluxes given in TAB 3.5 and masses given in TAB 2.1, residence times are calculated and shown in
TAB 3.8, following E Q 1.2.
2.4
2.4.1
Fluxes parameterization
The biological uptake during the photosynthesis : M FN P P
The photosynthesis is the mean by which some organisms are able to convert inorganic matter into organic
matter, using solar energy light; it is then a way to incorporate inorganic matter into the food chain. The
15
amount of carbon uptaken during the photosynthesis by a system is often referred as the Gross Primary Production (GPP). The NPP (standing for Net Primary Production) is often given in the litterature and is equal to
:
N P P (t) = GP P (t) − CFresp,auto (t)
(2.6)
CFGP P (t) = CFGP P (t0 ) ∗ fN (t) ∗ fP (t) ∗ fT (t)
(2.7)
that is to say the reduction-oxidation balance of photosynthesizers.
It has been shown that photosynthesis strongly depends on the photosynthesizers mass, but is also limited
by available N O3− and P O43− . In this model, we will assume that this dependance is on total nitrogen and total
phosphorus. The temperature enhances photosynthesis as well. We model photosynthesis using MichaelisMenten functions, as in Ver et al. [1999a], Laws et al. [2000], Tyrell [1999] :
fN (t) =
N (t)
kN +N (t)
N (t0 )
kN +N (t0 )
;
fP (t) =
P (t)
kP +P (t)
P (t0 )
kP +P (t0 )
;
T (t)−T (t0 )
10
fT (t) = Q10
(2.8)
This way, the function fM (M here standing for N or P ) reaches a maximum value, when M (t) increases.
This traduces the fact that for a given amount of photosynthesizers, the GPP cannot increase indefinitely.
However when M (t) is quite inferior to kM , the relation 2.7 can be approached by a linear dependence in
N and P. This accounts for the limiting role of nitrates and phosphates in photosynthesis. The dependence
in temperature is modeled here as often using Q10 factor, quantifying by how many times is multiplied the
photosynthesis flux for an increase of 10◦ C in temperature.
The values we use for kN , kP and Q10 are given in 3.6, and are tested during sensitivity analysis (see
S EC 3.2). The constant kCFGP P is determined using E Q 1.4.
We take as initial carbon flux the value used in Mackenzie et al. [1998a], Ver et al. [1999a], Andersson and
Mackenzie [2003], a value lying in the common range of estimates of the NPP. The nitrogen and phosphorus
fluxes are calculated following E Q 2.5.
2.4.2
Grazing fluxes : M Fgraz,het and M Fgraz,bact
The grazings are the fluxes by which the elements are going from a trophic level to another into the food chain,
when heterotrophic organisms feed upon organic matter. Here we use the same parameterization as in Laws
et al. [2000] :
CFgrazing (t) = CFgrazing (t0 ) ∗ fprey (t) with fprey (t) =
Cprey (t)−kprey
Cprey (t)
Cprey (t0 )−kprey
Cprey (t0 )
(2.9)
The grazing value reaches a saturation state for a strong prey abundance. When Cprey (t) = kprey , then
CFgrazing (t) = 0, that is to say the grazing stops when the prey is too scarce.
The values for kprey are arbitrarily set as 20% of the initial prey value (TAB 3.6), and will be tested during
sensitivity analysis (see S EC 3.2).
The initial carbon flux for heterotrophs grazing values are taken from Wollast [1991], and the initial nitrogen
and phosphorus fluxes are calculated following E Q 2.5. The initial carbon flux for bacteria grazing is obtained
assuming the steady-state for the bacteria reservoir. This yields two different values, following the initial NEP
assumed (this is discussed in S EC 2.4.3). It has to been said that the bacteria grazing flux is actually the net
transfer of matter from the DOM reservoir to the bacteria reservoir, as bacteria both feed upon and release
DOM. The values for carbon fluxes are taken from Wollast [1991]. The total nitrogen and phosphorus grazings
are calculated following E Q 2.5, but ammonia assimilation flux magnitude (see S EC 2.4.11) is substracted to
this total for the nitrogen.
2.4.3
Respiration, excretion and death fluxes : M Fresp,het , M Fresp,bact , M Fexc,aut and M Fexc,het
The release of inorganic matter during respiration, carried out by all living organisms, is here modeled as a
first-order kinetics flux (E Q 1.4). The release of particulate organic matter during the death of living organisms
and of dissolved organic matter during the excretion is also parameterized as a first-order kinetics flux. We
refer below in this study as "excretion" the sum of both excretion and death fluxes. The values for carbon
fluxes are taken from Wollast [1991]. The total nitrogen and phosphorus respiration and excretion fluxes are
calculated following E Q 2.5.
16
For the heterotrophs box, carbon respiration and excretion are taken from Wollast [1991]. Autotrophs excretion is calculated to achieve steady-state for autotrophs box (giving a value close to the one given by Wollast
[1991]).
We set up the bacteria respiration flux with two different values, both tested as inputs of the model. Indeed,
fB is referred in the litterature as the fraction of NPP going through grazing then respiration by bacteria. fB
shows a great spatial and temporal variability, as said in Azam [1998]. Here we take fB = 0.5 in the first set
of value and fB = 0.75 in the second set, two values reported as possible by Azam [1998], and yielding total
respiration magnitudes (combined with estimates from Wollast [1991]) in the range given by litterature. The
first set of values uses a total respiration close to the one given in Ver et al. [1999a]; the second set of value uses
one lying in the range of Wollast [1991]. We summarize the features of each set of initial values obtained in
TAB 2.3
2.4.4
Sedimentation Flux : M Fsed
The sinking rate of particulate organic matter from the water column to the seafloor is assumed to be mainly
dependent on the dead organic matter reservoir size. It is thus modelled as a first-order kinetics flux (E Q 1.4).
For the first set of values, we assess the sedimentation fluxes achieving steady-state in DOM reservoir, which
yields values close to the ones used in TOTEM, except for nitrogen, rather big here. However, the fate of
nitrogen in the sediments is not a feature of the model presented here. For the second set of values, as the
uptake of dissolved organic matter by bacteria is weaker than in the first set, more matter has to get out
from the DOM reservoir (150 Tmol/yr for carbon, for example). This imbalance is fixed assuming the ratio
M FDOM,oc (t0 )
M FDOM,oc (t0 )+M Fsed (t0 ) is the same than in the first set of initial values. That method gives values of sedimentation close to the ones given by Rabouille et al. [2001] and values for the sum of sedimentation and export to
the open ocean closer to the range assesed by Wollast [1991].
2.4.5
Exchange between pore water and seawater : M Fpw−wc
The net transfer of an element between the pore water system and the water column is mainly determined
by the concentration gradient of the considered element. For carbon, this flux is estimated achieving steadystate in the pore water reservoir, and is parameterized as a first-order kinetics flux (E Q 1.4). For nitrogen and
phosphorus, fluxes are set achieving steady-state in the DIM reservoir, and are assumed to be zeroth-order
kinetics fluxes (E Q 1.3).
This yields two different sets of values, following the intensity of respiration in water column.
2.4.6
Ocean output fluxes : M FDOM,oc and M FDIM,oc
The export of organic and inorganic matter from the coastal ocean to the open ocean is mainly directed by
advection of water. We assume here that these fluxes are first-order kinetics fluxes (E Q 1.4), depending on the
amount of matter (organic or inorganic) in the coastal ocean. This is strictly true if the dynamics of the ocean
does not change.
For the DOM export, see S EC 2.4.4.
For the DIM export, in both sets of initial values, we take nitrogen and phosphorus fluxes equal to the
ones used in TOTEM. For carbon, the export flux is always assumed to balance the DIM reservoir so as to
achieve steady-state. This allows to link the magnitude of remineralization in the coastal ocean to the amount
of inorganic matter exported to the open ocean, and then gives different values following the set of initial
values.
2.4.7
Coastal upwelling flux : M Fupw
Due to ocean dynamics, inorganic matter is brought from the deep ocean to the coastal ocean during upwellings. This phenomenon is local, and induces phytoplanktonic blooms where it occurs. Here we use the
results from TOTEM to force our model.
2.4.8
Rivers input fluxes : M FDOM,riv , M FDIM,riv , M FROM,riv and M FP IM,riv
As we said in S EC 2.3.2, we use the results of simulation by TOTEM from 1700 to 2050 as rivers input.
17
2.4.9
Burial (CFburial,org and CFburial,inorg ), carbonate transport to the slopes (CFtrans,slope )
and organic sediments oxidation (CFox,sed ) fluxes
The organic matter sinking to the sediments may follow two different paths : it can be either oxidized by in situ
respiring organisms, or buried into the deep sediments, where it cannot be oxidized anymore (Wollast [1991]).
The burial rate is thus a function of the sedimentation rate, and of the rate of oxidation taking place into the
sediments.
For the first set of values, the oxidation flux is taken from Andersson and Mackenzie [2003], and the burial
flux in both organic and inorganic sediments reservoir is calculated achieving steady-state assumption, giving
a quite small value for organic burial and a value lying in the range given by litterature for inorganic burial. For
the second set of values, the imbalance coming from the increase in the organic sedimentation rate (compared
CFox,sed (t0 )
to the first set) is fixed assuming the ratio CFox,sed (t0 )+M
Fburial,org (t0 ) is the same than in the first set of initial
values. This gives a value for organic carbon burial closer to the one given in Rabouille et al. [2001]. The burial
and oxidation fluxes are modeled as first-order kinetics fluxes (E Q 1.4).
An important amount of sediments is also exported to the continental slopes by ocean dynamics (Wollast
[1991]). Here we assume that phenomenon only concerns inorganic matter, as done in TOTEM (Ver [1999]).
This flux is assumed to be a zeroth-order kinetics fluxes (E Q 1.3).
2.4.10
Carbonate precipitation and dissolution (CFCaCO3 ,prec and CFCaCO3 ,diss ), biogenic
carbonate production (CFCaCO3 ,bio ), and CO2 exchange across the sea-air interface
(CFCO2 ,atm )
These fluxes are discussed in S EC 2.5.
2.4.11
N H4+ assimilation flux : N FN H4+ ass
Bacteria use nitrogen from both dissolved organic and inorganic matter, if they become depleted in the first
one, relying primarily on it. Fasham et al. [1990] (reported by Tanaka [2002]) described the mechanism of
ammonia assimilation. Using the quantity c =
N FN H + ass
N Fgraz,bact ,
4
they demonstrated that :
(C : N )DON
c=
− 1 and N FN H + ass = N Ftotal,bact ∗
4
(C : N )bacteria
!
c
1+c
"
(2.10)
which yields with our ratios (see TAB 3.7) approximately c = 0.6. N Ftotal,bact is the total amount of nitrogen
uptaken by the bacteria (that is to say N FN H + ass + N Fgraz,bact ), equal to bacteria respiration, following the
4
mass balance with respect to the bacteria reservoir. This yields two differents initial values, following the
magnitude of bacteria respiration.
2.4.12
Biologic N2 fixation flux : N FN2 f ix
The biologically-mediated dinitrogen fixation occurs when available nitrogen as nitrate in the water is too
scarce; it is only used by a few organisms, mainly from the genus Oscillatoria (Fogg [1982]). This is thus a small
flux, dependent on total available nitrogen in the water column, modeled here as a zeroth-order kinetics flux
(E Q 1.3).
2.4.13
Atmospheric nitrogen deposition : N Fdep
Atmospheric nitrogen as gazeous N Hx and N Oy can be deposited onto the ocean, either by wet transport or by
a dry processus. Atmospheric N2 can also be fixed by lightnings. The total flux is assumed to be a zeroth-order
kinetics flux following E Q 1.3.
2.4.14
Denitrification fluxes : N Fdenitr,wc
Denitrification is carried out by microbes in oceanic realm, and allows these organisms to reduce nitrates
in nitrites and in dinitrogen, instead of using oxigen. Denitrification is inhibited by O2 , which is not taken in
account in the model. So we cannot set a built-in dependence of denitrification on oxygen, as done in Rabouille
et al. [2001] for instance. Denitrification is then set as a zeroth-order kinetics flux (E Q 1.3).
18
2.4.15
Nitrogen volatilization flux : N Fvolat
Oceanic nitrogen volatilizes from the ocean as N2 O from nitrification, or as N H3 gas. Here we take it as a
zeroth-order ninetics fluxes (E Q 1.3).
2.5
The carbonate chemistry in the model
In order to assess anthropogenic perturbations on the coastal carbonate system, calculations of carbonate speciation are incorporated into the model. These calculations are carried out at each time step, assuming that the
thermodynamical equilibrium is achieved :
• precipitation and dissolution fluxes, following what is explained in S EC 2.5.3 and S EC 2.5.4;
• CO2 flux across the sea-air interface, depending on the difference between atmospheric pCO2 and dissolved CO2 in seawater, on the magnitude of CaCO3 precipitation and on NEP.
2.5.1
Calculating the carbonate system concentrations
The simplified carbonate system has basically (Zeebe and Wolf-Gladrow [2001]) :
• six variables : [CO2 ], [HCO3− ], [CO32− ], [H + ], DIC and T A (total alkalinity1 ).
• four equations, as follows :
CA = [HCO3− ] + 2[CO32− ]
DIC
= [CO2 ] + [HCO3− ] +
[H + ][HCO3− ]
K1 =
[CO2 ]
[CO32− ][H + ]
K2 =
[HCO3− ]
[CO32− ]
(2.11)
(2.12)
(2.13)
(2.14)
where CA is carbonate alkalinity , and K1 (respectively K2 ) is the thermodynamic constant for CO2
(respectively HCO3− ) dissociation, and is dependent on temperature, salinity and pressure2 .
So knowing two variables, one can come up to the four others using the equations of the system. As previously
seen, coastal dissolved inorganic matter is a reservoir of our model, so we can access the total DIC concentration, assuming its distribution is homogenous over the coastal ocean. Using PCO2 from TOTEM, we obtain the
dissolved CO2 concentration, by Henry’s law :
KH =
[CO2 ]diss
PCO2
(2.15)
where KH is the solubility constant of CO2 in seawater. We assume here that the equilibrium between air and
seawater concerning carbon dioxide is reached instantaneously.
A subroutine3 calculating the thermodynamics constants as functions of temperature (salinity and pressure are assumed constant in this study; however, the influence of salinity has been implemented for further
developpement) is incorporated in the program (calculations from Zeebe and Wolf-Gladrow [2001]). Other
subroutines4 using matrix algebra are implemented to find roots of polynomials appearing when one calculates the equilibrium variables of the carbonate system.
T A ! CA + BA + W A, with BA borate alkalinity and W A water alkalinity
the thermodynamics constants used here are stoechiometric constant, obtained from empirical equations; then we can use molalities in our calculations, assuming a constant density of seawater of 1.026.
3 This
subroutine has been adapted from MATLAB to FORTRAN for this study,
and is available at
http://www.awi-bremerhaven.de/Carbon/co2book.html.
4 the subroutines are also available at http://www.library.cornell.edu/nr/bookpdf.html
1 then,
2 All
19
2.5.2
The saturation state
For a given solid phasis, the saturation state of a solution is the product of the ions reacting to give the solid,
on the solubility product Ksp of this solid (for given temperature, pressure and composition). For instance, for
calcite :
[CO32− ][Ca2+ ]
Ω=
(2.16)
Ksp,calc
When Ω ≥ 1, the solution is saturated and solid precipitates. If Ω < 1, the solution is undersaturated and
the solid dissolves. The more a solution is saturated ("the more Ω > 1"), the "easier" and "faster" will be the
precipitation.
2.5.3
The biogenic carbonate production flux
We relate the biogenic carbonate production, used by some of the phytoplanktonic organisms to build their
skeleton, to the total DIC content.
Carbonate production is also modified by changes in temperature, via an effect on kinetics constants. We
use the following equation from Andersson and Mackenzie [2003] and Mackenzie and Agegian [1989] :
RT (t) = 100 − 0.00013∆ T (t) − 1.3∆ T (t)2
(2.17)
where RT is the relative biogenic carbonate production in relation to temperature (in %), and T is temperature
(in ◦ C).
The abundance of reactive components enhances the speed of the reaction; thus, saturation state also has an
effect on this flux, as shown in Andersson and Mackenzie [2003], from Gattuso et al. [1999] (eqnrefeqn:precsat1)
or Gattuso et al. [1998] (eqnrefeqn:precsat2):
RΩsw (t) = 21.3Ωsw (t) + 12
'
(
Ωsw (t)
or RΩsw (t) = 228 1 − exp− 0.69 − 128
CFCaCO3 ,bio (t) = kCFbio,CaCO3 ∗ CDIM (t) ∗ RT (t) ∗
RΩsw (t)
RΩsw (t0 )
(2.18)
(2.19)
(2.20)
where RΩsw is the relative biogenic carbonate production in relation to seawater saturation state with respect
to calcite. The consequence of using one or another of these equations are discussed in S EC 3.2. For "regular"
runs, we will use the linear equation, as it emphasizes variations in calcification.
2.5.4
Carbonate precipitation and dissolution in pore water
The abiotic carbonate precipitation and dissolution within the sedimentary system are parameterized in the
model by the following equations (Andersson and Mackenzie [2003], Zhong and Mucci [1989] for the precipitation equation and Walter and Morse [1985] for the dissolution one), following whether Ω ≶ 1 :
CFCaCO3 ,diss (t) = kdiss (1 − Ωpw (t))ndiss
CFCaCO3 ,prec (t) = CFprec (t0 ) ∗ RΩpw ,prec (t)
with RΩpw ,prec (t) =
(Ωpw (t) − 1)nprec
(Ωpw (t0 ) − 1)nprec
(2.21)
(2.22)
(2.23)
where RΩpw ,prec is the rate of change in precipitation in relation to saturation state in pore water. Indeed,
calculating the initial CO32− from an initial pH in pore water equal to 7.615 yield Ωpw = 3.13 (with respect to
calcite). The initial net flux is thus a precipitation. However, the very upper part of the sediments porewater is
known to be undersaturated owing to the intense oxic respiration (and the subsequent low pH). This leads to a
net dissolution of carbonates minerals, nonetheless limited to the upper few centimeters of the sediments (see
Morse and Mackenzie [1990]). This flux is assumed to be constant, supplying the entire pore water reservoir,
and has to be added to the fluxes calculated above. Its value is taken from Wollast [1994].
kdiss , ndiss and nprec are kinetics constants. Their values are given in 3.6.
These equations are valuable for different carbonates such as calcite, aragonite or magnesian calcite; however, the parameters change for each compound. Here we will only consider calcite, but results for aragonite
are also given, in 3.1.
5 estimated
from Morse and Mackenzie [1990] and Andersson and Mackenzie [2003]
20
Figure 2.2: Calculation method for CFCO2 ,calc .
2.6
CO2 flux across the air-seawater interface
The CO2 flux across the ocean surface is the sum of three contributions : change in atmospheric PCO2 ("equilibration" flux), CO2 from carbonate precipitation ("calcification CO2 flux"), and CO2 from photosynthesis/respiration
("biogenic CO2 flux"). In this study, we consider that a positive CFCO2 ,atm is from the ocean to the atmosphere.
2.6.1
Equilibration with atmospheric PCO2 : CFCO2 ,eq
The increase in atmospheric PCO2 induces an invasion of CO2 into the coastal seawater, and modifies DIC. At
each time step, the subsequent variation in DIC is given by :
dDIC
= f ([H + ], [CO2 ], T )
d[CO2 ]
!
"
dDIC
CFCO2 ,eq (t) =
∗ (PCO2 (t) − PCO2 (t − ∆t)) ∗ KH
d[CO2 ] t
(2.24)
(2.25)
dDIC
where d[CO
is a complicated function of pH, dissolved CO2 concentration and thermodynamics conditions
2]
(Zeebe and Wolf-Gladrow [2001]).
2.6.2
Calcification CO2 flux : CFCO2 ,calc
As shown in E Q 2.2, CaCO3 precipitation ends up forming CO2 . To estimate the amount of carbon dioxide
emitted to the atmosphere, we calculate the variations in alkalinity and DIC following the precipitation of
CaCO3 , as done in Lerman and Mackenzie [in press], and explained in F IG 2.2 :
T ACalc (t) = T A(t) − 2 ∗ CFCacO3 ,bio (t)
DICCalc (t) = DIC(t) − CFCaCO3 ,bio (t)
(2.26)
(2.27)
Then, from T Acalc (t) and [CO2 ](t), one can come up with a new DICeq (t), in equilibrium with the postprecipitation system. We assume that DIC value goes from DICCalc (t) to DICeq (t) exchanging carbon with atmospheric CO2 reservoir; this does not modify alkalinity. We obtain CFCO2 ,CaCO3 (t) = DICeq (t)−DICcalcif (t).
CF
2 ,CaCO3
This method gives an initial Ψ = CFCO
= 0.63, close to the values given by Frankignoulle et al. [1994].
CaCO ,bio
3
2.6.3
Biogenic CO2 flux : CFCO2 ,bio
Trophic state of the biota in the coastal ocean affects the CO2 concentration in seawater, ending up in a flux
across the air-seawater interface, which direction depends on NEP.
It has been shown by Brewer and Goldman [1976] that one can model changes in alkalinity during photosynthesis removing N O3− and releasing OH − in seawater, obtaining thus electroneutrality in algae cells.
Even if it is not clearly demonstrated for phosphorus (Brewer and Goldman [1976]), we will assume the same
relationship about the uptake of P O43− . Contrariwise, respiration will decrease alkalinity by uptaking OH − .
Nothing is really known about N H4+ assimilation influence on alkalinity (Karl, pers. comm.). We suppose here
that each mole of N H4+ uptaken by bacteria decreases alkalinity alkalinity by one mole, releasing H + . This
relationship is discussed in S EC 3.2.
21
T Aphot−resp = T A(t) − (N FN P P (t) − N Fresp,het (t) − N Fresp,bact (t))
− (P FN P P (t) − P Fresp,het (t) − P Fresp,bact (t)) + N FN H + ass (t) (2.28)
4
DICphot−resp (t) = DIC(t) − (CFN P P (t) − CFresp,het (t) − CFresp,bact (t))
(2.29)
Then, following the same rationale as in S EC 2.6.2, we calculate the subsequent CO2 flux from/to the atmosphere, CFCO2 ,bio 6 .
These calculations, used to estimate initial CO2 flux, yield interesting results : indeed, in both sets of initial
values we use, we assumed a net autotrophy. But in the first case, the CO2 flux following E Q 2.1.1 is from
the atmosphere to the ocean, whereas the biota is removing CO2 from seawater; indeed, the release of H +
(following the high N H4+ uptake rate, and the low NEP) acidifies the solution and produces CO2 .
2.6.4
Total CO2 flux, and initial values
Then, the total flux is :
CFCO2 ,atm (t) = CFCO2 ,eq (t) + CFCO2 ,calc (t) + CFCO2 ,bio (t)
(2.30)
The initial values calculated in both cases are reported in TAB 2.2, as well as in F IG 2.1 and F IG 3.13 :
Table 2.2: Initial values of CO2 flux, and different contribution, in the two different sets of initial values.
Initial values of CO2 flux, and different contribution, in the two different sets of initial values (positive value
means out of the ocean). In 1012 molC/yr.
Flux
CFCO2 ,eq CFCO2 ,CaCO3 CFCO2 ,bio CFCO2 ,atm
First set
0
15.43
26.83
42.26
Second set
0
15.43
-157.92
-142.49
2.7
The two sets of initial values obtained
Assuming as a starting point two different rates of respiration, based on different estimates and agreeing with
two possible intensities of bacteria respiration, as explained in S EC 2.4.3, we came up with two sets of initial
fluxes, which results are presented and compared in S EC 3. In TAB 2.3, we summarize the main features of
each set of initial values. The initial fluxes values are also given on the conceptual diagrams in F IG 2.1 and
F IG 3.13.
Table 2.3: Comparison of the two sets of initial fluxes used as inputs of the coastal ocean model.
Set of initial fluxes
First
Second
fB
0.75
0.5
Bacteria respiration
High
Low
Total respiration
High
Low
NEP
Slightly autotroph
Strongly autotroph
Biogenic CO2 flux
Slightly from the ocean Strongly from the atmosphere
Coastal ocean and CO2
Source
Sink
Export fluxes
Low
High
Sedimentation flux
Low
High
2.8
Residence times
Calculated residence times from initial masses and fluxes are reported in TAB 3.8. Logically, residence times
in each biota reservoir are the same for the three elements, as organisms are supposed to uptake and release
6 at steady-state, we suppose that other mechanisms (upwellings, export to the coastal ocean) restore alkalinity to its initial value after
this calculation
22
matter in the same atomic ratios as the ones of their body. These residence times are small, accounting for the
high turn-over rate of marine biota, mainly plankton.
The small residence time of DOM accounts for the high rates of remineralization by bacteria in the coastal
ocean, and this residence time is dependent on the set of values, then on the magnitude of bacteria respiration. Finally, the solid phasis of the sediments, have a long residence time, owing to the important mass they
represent.
23
Chapter 3
Results and discussion
In this chapter we present results from our coastal ocean biogeochemical model, lead sensitivity analysis, and
discuss the outputs of the model in terms of global carbon cycle.
3.1
3.1.1
First results from the model over the past three centuries and the next
fifty years
Evolution of the organic carbon balance
As a first result, we show in F IG 3.1(a) and F IG 3.1(b) the evolution of the NEP for each set of initial values :
the model predicts in 2050 a trend towards heterotrophy for the first set (variation of -2.5 TmolC/yr from 1700
through 2050, -12.5%), and a neglictible increase in autotrophy for the second set (+0.2%). But in both case,
the final trend is a decreasing NEP after the year 1950, showing that the respiration rate becomes greater, and
slowly tends to balance the increased photosynthesis due to following nutrients inputs by the river.
In the first set of initial values, the high rate of bacteria respiration, enhanced by the increase in dissolved
organic matter, yields a very high total respiration rate that largely balance the increase in photosynthesis. The
present NEP (18.5 TmolC/yr) is close to the value given in Rabouille et al. [2001] (+20 TmolC/yr).
With the second set, the total respiration is too low to allow this phenomenon to occur clearly before the
year 2050, but the same final trend is observed. The present NEP value (approximately +170 TmolC/yr) agree
well with estimates from Wollast [1998] (+200 TmolC/yr) or Gattuso et al. [1998] (+231 TmolC/yr), but we do
need to start from a strongly autotrophic pre-industrial environment (+170 TmolC/yr) to obtain this range of
values. This disagrees with many estimates for pre-industrial state considering even a slightly heterotrophic
pristine coastal ocean : Wollast and Mackenzie [1989] (-3.3 TmolC/yr), or Smith and Hollibaugh [1993] (-7
TmolC/yr).
Moreover, the small variations observed with our model over the period of simulation do not allow one
to conclude about the actual evolution of NEP, especially for the second set of values. The final decreasing
autotrophy trend is contrary to many results of the litterature, which often predict an increased NEP during the
past three centuries. Andersson and Mackenzie [in press], from the results of TOTEM, predicted an increased
autotrophy from 1700 through 2050 from -7 TmolC/yr to +18 TmolC/yr. This can be accounted by the use
in TOTEM of a global organic box, and of a total respiration flux proportionnal to the organic mass. Then,
respiration is strongly coupled with primary production. In our model, the high respiration rate mainly caused
by kDOM allows the remineralization flux not to follow the increase in primary production, but rather the
increased DOM mass, exponentially increasing in the late twentieth century. The value we chose for kDOM
make bacteria uptake very sensitive to variations in dissolved organic matter, and this value is not constrained
by litterature (see S EC 3.2.1).
3.1.2
Evolution of the inorganic carbon balance
Our numerical simulations show a quite important increase in DIC (see F IG 3.2 : +250 TmolC in 2050, +4%)
in both sets of initial values, with not any remarkable difference in the evolutions. This increase is obviously
driven by the load of inorganic material by rivers during industrial era, rather than by the small change in the
NEP observed in our model, and has been measured in tropical waters1 and reported in Winn et al. [1998],
1 data
available at http://hahana.soest.hawaii.edu/hot/hot_jgofs.html
24
(a) Net Ecosystem Production, first set of initial values
(b) Net Ecosystem Production, second set of initial values
Figure 3.1: Results from the coastal ocean model : NEP.
between 1998 and 2000. Even if data are sparse, this conclusion seems very reliable as it is a straightforward
consequence of anthropogenic forcings.
The increase in atmospheric CO2 during simulations induces a raise in [CO2 ], scavenging ions CO32− , and
then reducing the saturation state in respect with calcite and aragonite, as shown in F IG 3.3(a), from 4.9 to 3.3
(30%) in 2050. So, in spite of the increasing DIC content in seawater, the calcification flux (F IG 3.3(b)) has been
decreasing by 7 TmolC/yr in 2050, or 30%. The results are the same for both sets of initial values, consistent
with the fact that the saturation state depends on DIC, which is the same with the two sets, and on [CO2 ],
25
Figure 3.2: Results from the coastal ocean model : DIC.
determined by the forced atmospheric PCO2 .
This agrees with results obtained by Kleypas et al. [1999], who predicts a decrease from approximately 4.5
in 1800 to 3 in 2100, by Winn et al. [1998], Mackenzie et al. [2000] and Andersson and Mackenzie [2003], whose
model predicts a decrease in saturation state in seawater with respect to calcite from approximately 6.7 in 1700
to 4.8 in 2100 (30%). Even if the saturation index remains well above the critical value of 1, the calcification
becomes harder to carry out for marine organisms such as corals which produce mainly aragonite (Kleypas
et al. [1999]).
In pore water, saturation state evolution seems mainly driven by the enhanced oxidation and release of DIC
from the organic sediments (which mass increases after the DOM increase), presented on F IG 3.4 : following
increased oxidation flux, saturation state raises of approximately 2%, which is a small change compared to the
one occuring in the water column. This results do not agree with Andersson and Mackenzie [2003], who ended
up with the conclusion that the saturation state in porewater in respect with all carbonate minerals has been
decreasing over the same period of simulation. This could lead to the dissolution of unstable minerals such as
magnesian calcite, a minor buffer effect to increasing atmospheric CO2 .
Nonetheless, the direction of the change we obtained for the precipitation/dissolution in pore water with
both our sets of initial values is not very dependable, as its magnitude is small (+8%) relatively to the uncertainty lying on the initial values and methods of calculation for pore water.
3.1.3
Evolution of the CO2 flux
The equilibration flux (F IG 3.5(a)) with the atmosphere is about -4 Tmol/yr around the year 2030, increasing
over the simulation as the atmospheric PCO2 increases owing to anthropogenic emissions. This being dependent on the capacity of seawater DIC to buffer [CO2 ], for a given increase in atmospheric carbon dioxide, the
equilibration flux becomes smaller and smaller. The seawater is indeed acidified by the invasion of CO2 ; thus,
during the twenty-first century, the flux begins to decrease (E Q 2.24).
The calcification flux decreases from 1700 to 2050, especially in the last fifty years, reaching a value approximately 15% lower than the initial one. This has been noticed by Zondervan et al. [2001] and Andersson and
Mackenzie [2003], and could act as a negative feedback against rising atmospheric CO2 .
The biogenic CO2 flux (F IG 3.6(a) and F IG 3.6(b)) is very different in magnitude and direction following
the set used, emphasizing its dependence on NEP : for the first set, more and more CO2 is released to the
atmosphere (+30%), consistent with the decreased autotrophy (F IG 3.1(a)); for the second set, the flux variation
is small (0.5%), but the coastal ocean seems to uptake less and less CO2 following photosynthesis and respira26
(a) Saturation state in respect with calcite and aragonite in seawater
(b) Biogenic calcification (for calcite)
Figure 3.3: Results from the coastal ocean model : carbonates in seawater.
tion, as its autotrophy decreases by the twenty-first century. So in both cases, biota uptake does not seem to be
enhanced by human-induced perturbations on nutrients concentrations in the coastal ocean.
The sum of these three fluxes gives the results shown in F IG 3.7(a) and F IG 3.7(b). As one can see, the
total flux is overall driven by the biogenic CO2 flux, especially for the second set of initial values. Even for
the first set, seeing a total CO2 flux variation of 30%, one can conclude that the influence of the equilibration
and calcification fluxes is small. Especially during the twenty-first century, the coastal ocean seems to be an
enhanced source (or a weakened sink) of CO2 . But here again, the variations observed in our outputs are very
27
(a) Saturation state in respect with calcite in pore water
(b) CaCO3 production
Figure 3.4: Results from the coastal ocean model : carbonates in pore water.
small compared to the uncertainties lying on the initial fluxes.
Several attempts to measure the CO2 flux between the coastal ocean and the atmosphere have been made,
yielding a great spatial and temporal variability, and difficulties to draw a global conclusion. However, the
surface specific value we find in the year 2000 with the first set of initial values (15 gC/m2 /yr) is within the
range of values found for some sites, such as 30 gC/m2 /yr for the South Atlantic Bight (Cai et al. [2003]), or
upwelling regions with 11 gC/m2 /yr in Goyet et al. [1998]. With the second set, this value (-46 gC/m2 /yr)
agrees more with the upper range (-35 gC/m2 /yr) for the North Atlantic shelf from Frankignoulle and Borges
[2001], or for East China Sea (-34 gC/m2 /yr) from Chen and Wang [1999]). It is then hard to conclude about
the validity of the model or of one or other of the initial states.
28
(a) Equilibration flux
(b) Calcification flux
Figure 3.5: Results from the coastal ocean model : equilibration and calcification CO2 fluxes.
29
(a) Biogenic flux, the first set of initial values
(b) Biogenic flux, second set of initial values
Figure 3.6: Results from the coastal ocean model : biogenic CO2 fluxes.
30
(a) Total flux, first set of initial values
(b) Total flux, second set of initial values
Figure 3.7: Results from the coastal ocean model : total CO2 fluxes.
31
3.2
3.2.1
Sensitivity analyses and influence of parameterizations
Sensitivity analyses : biologic constants
In this section, we drive sentivity analysis on some not well-constrained parameters used in the model, making
vary one parameter at a time. If results were the same for both of our sets of initial values, only one of them is
shown.
Control of photosynthesis constants : kN , kP and Q10 factor
We made kN and kP vary by a factor of 10, and we tested Q10 ± 0.5, regarding the uncertainty lying on these
parameters, and we present here the results for NEP, for the first set of initial fluxes.
The model does not seem to be very sensitive to kN (F IG 3.8(a)), mainly because common concentrations
of nitrogen in the coastal ocean are well above the half-saturation constant range of possible values. However,
with a great kN , the autotrophy is obvioulsy less decreased, showing the great positive dependence of primary
production to nutrients input in this case.
kP (F IG 3.8(b)) has a greater influence on the outputs than kN , even cancelling the decreased autotrophy
trend for its maximum tested value. It is indeed closer to the total phosphorus mass in the costal ocean (where
the derivative of the Michaelis-Menten function is great). We can conclude that we built a coastal margin
limited in phosphorus rather than in nitrogen on over-a-year-time-scales, agreeing with conclusions of Tyrell
[1999], and that the increase in photosynthesis in mainly due to the phosphorus inputs in our model.
Sensitivity analysis outputs for the Q10 factor are not shown here, but led to a small variability in outputs;
we made this parameter vary on the whole narrow range of uncertainty, and as the absolute output variation
is small, the Q10 factor is more sensitive than important. Finally, variation of temperature are small over the
period of simulation (about 1◦ C).
Grazing constants : kaut and kDOM
Sensitivity analysis has been driven on kaut , but this parameter does not seem to be crucial for our model, as it
acts only on the heterotrophs box. This can be explained by the small size of this box, and its small contribution
to the total respiration and then to the NEP.
kDOM , tested with the values of 4% (11 TmolC/yr) and 50% (137.5 TmolC/yr) of the initial DOM mass,
acts strongly on the NEP. It even yields two different trends following its value (F IG 3.9), showing the same
importance for this output as kP does, with an even greater sensitivity. The NEP could even increase during
the whole period of simulation, with a low value for kDOM .
3.2.2
Calcification equation for dependence on saturation state
Using either a linear or curvilinear (E Q 2.18 or E Q 2.19) relationship for the rate of change of calcification as
a function of seawater saturation state in respect with carbonate minerals radically modifies the evolution
of calcification over the past three hundreds years (F IG 3.10(a)). If we use the curvilinear relationship, the
calcification rate remains constant until the twenty-first century, where it begins to decrease, but always staying
well superior to the calcification obeying to the linear relationship. This well agrees with results obtained by
Andersson and Mackenzie [2003], who even show a slight increase in calcification over the past three centuries
when he uses the curvilinear relationship, and then observe the same decrease after 2050. Indeed, the threshold
value (0.69) in E Q 2.18 is well very low compared to the common saturation state of seawater.
The subsequent release of CO2 (F IG 3.10(b)) to the atmosphere can even increase when the biogenic CaCO3
production is constant. This is due to the raise in atmospheric PCO2 , which consumes all buffer effect from
carbonate system, even with an increased DIC; then, any "surproducted" CO2 molecule has to get out the
ocean, tending towards a value of Ψ of 1.
3.2.3
Calculation of alkalinity change during photosynthesis and respiration
The role of phosphate uptake during photosynthesis in alkalinity change is not well-known (Brewer and Goldman [1976]), but it represents anyway a small change of alkalinity. But the role of ammonia assimilation is not
better known (Karl, pers. comm.), and is very important in our model2 .
2 indeed, even if during photosynthesis, a vegetal organism uptakes both nitrate and ammonium, on a more global scale, one can
consider that only nitrate is consumed (Broecker and Peng [1982])
32
(a) Influence of kN on NEP
(b) Influence of kP on NEP
Figure 3.8: Sensitivity analyses on the coastal ocean model : influence of kN and kP on the NEP, for the first set
of initial values.
Assuming two different relationships between alkalinity change and N H4+ from the one given in E Q 2.28,
we recalculate two initial biogenic CO2 fluxes, the imbalance created being assumed to be fixed by a change
in open ocean inorganic export, so as to achieve steady-state in DIM reservoir. The new initial fluxes are pre-
33
Figure 3.9: Sensitivity analysis on the coastal ocean model : influence of kDOM on NEP, for the first set of initial
values.
sented in TAB 3.1.
Table 3.1: New steady-state fluxes for different ∆ T A = f (N H4+ ).
New steady-state fluxes for different ∆ T A = f (N H4+ ). In 1012 molC/yr.
Relationship
Initial set
CFCO2 ,bio CFCO2 ,atm
∆ T A(CFN H + ,ass ) = −CFN H + ,ass (E Q 2.28) First
26.83
42.26
4
4
Second
-157.92
-142.49
∆ T A(CFN H + ,ass ) = 0
First
-0.68
14.75
4
Second
-176.26
-160.83
∆ T A(CFN H + ,ass ) = CFN H + ,ass
First
-28.18
-12.75
4
4
Second
-194.58
-179.15
CFDIM,oc
450.68
563.95
478.19
582.29
505.69
600.62
∆ T A(CFN H + ,ass ) = 0 could mean that mechanisms such as nitrification occur and balance the loss in al4
kalinity by producing N O3− , and ∆ T A(CFN H + ,ass ) = CFN H + ,ass means that this kind of mechanism would
4
4
only lead to the production of N O3− , as in photosynthesis/respiration. We should add that using these relationship leads to greater and "less realistic" values of inorganic carbon export. Results for biogenic CO2 flux
and total CO2 fluxes are presented in F IG 3.11.
As one can see on F IG 3.11 and F IG 3.12, variations in CO2 fluxes are lessened compared to the ones given
in S EC 3.1.3 (2 and 4 TmolC/yr instead of 8 for the first set, for instance), obtained with E Q 2.28. Indeed,
with the equations used here, the total effect of photosynthesis/respiration is a removal of H + (or a increase in
alkalinity), although with E Q 2.28, alkalinity was strongly decreased by N H4+ assimilation (and the subsequent
release of H + ). This increased alkalinity allows the system to buffer the CO2 produced by respiration, and then
reduces the CO2 flux to the atmosphere, compared to the "regular" runs. For the second set of initial fluxes,
using one or another of the new equations even makes the ocean becomes a more and more efficient sink of
CO2 in the twentieh century.
34
(a) Biogenic calcification in seawater
(b) CO2 flux following CaCO3 precipitation
Figure 3.10: Influence of the calcification parameterization on the coastal ocean model, for the first set of initial
values.
35
(a) First set of initial values
(b) Second set of initial values
Figure 3.11: CO2 flux, with ∆ T A(CFN H + ,ass ) = 0.
4
36
(a) First set of initial values
(b) Second set of initial values
Figure 3.12: CO2 flux, with ∆ T A(CFN H + ,ass ) = CFN H + ,ass
4
37
4
3.3
Implications for global carbon cycle and discussion
Our numerical simulations agree with many other models results and existing data concerning the evolution
of the carbonate system in coastal seawater. Anthropogenic activities induce three main changes in coastal
carbonate system :
• an increase in DIC, mainly induced by rivers input, its variation not being dependent on the change in
NEP;
• a decrease in saturation state with repect to carbonate minerals, in spite of the increase in DIC. As a
result, calcification flux could be inhibited, leading to severe consequences to coastal ecosystems. The
possible following decrease in CO2 flux can be seen as a negative feedback to rising atmospheric carbon
dioxide (Kleypas et al. [1999], Andersson and Mackenzie [2003]). But this change is really dependent on
the calcification equation (E Q 2.18 or E Q 2.19), and could even lead to a positive feedback (S EC 3.2.2).
• a decrease in buffering effect of seawater, induced by its acidification following CO2 invasion. This yields
a positive feedback to increasing atmospheric CO2 .
These results seem yet independent from any change in the very sensitive NEP, suggesting a strong decoupling between the biota system and the carbonate system in our model; this effect is attributed to the huge
size of the DIC reservoir. The change of the magnitude of rivers DIC during industrial era is then a first-order
cause of change in coastal ocean chemistry. Moreover, our assumption of a coastal ocean in instantaneous
equilibrium with atmospheric CO2 following Henry’s law gives a strong constraint on carbonate speciation
and then to saturation state, not depending on any constant or other forcing.
However, the decoupling is probably not so strong in the actual coastal ocean. The calcification flux must
also depend on the total mass of calcifying organisms.
The evolution of NEP during the past three centuries and its present value seem more controversal, both
in the litterature and in our model. With each of our sets of initial fluxes, we obtain a final trend towards a
decreased autotrophy; but this is only allowed by a high rate of remineralization of dissolved organic matter
by bacteria, via kDOM (see S EC 3.2). The implementation of several biota boxes leads to a complex response of
NEP, but very sensitive to the model constants. It is clear that the value of NEP greatly depends on the values
of the uptake constants, but then also on the magnitude of rivers input, which have their own uncertainties,
and are difficult to assess on a global scale. Regarding these doubts we still have on crucial values, and
the small variations of the NEP given by our model, we should take these results carefully. It is however
possible that the NEP has not been affected so much by nitrogen and phosphorus inputs in coastal ocean : the
primary production is probably not limited in these nutrients on a global scale, and the respiration rate has
been enhanced as well as the primary production, following the increase of the biota. The sparse litterature
data prevents one from confirming or infirming any of the present values obtained by the model.
Finally, the uncertainty lying on the methods of calculation of alkalinity change does not allow one to
conclude about a possible role of the coastal biota in atmospheric CO2 uptake. It could be yet the main contribution to the total CO2 flux, especially if the hypothesis of a great net autotrophy is to be true. Regarding the
difficulties to measure the global CO2 flux between the coastal ocean and the atmosphere, experimental data
are needed to assess the response of biota to change in nutrients concentration.
38
Conclusion
Following our models results, human activities has been affected the coastal ocean during the past three centuries in two major ways : a decrease in saturation state with respect to carbonate minerals, and an increase
in primary production. The effect on the Net Ecosystem Production seems to be difficult to assess, regarding
the great uncertainties we still have on the parameters needed to calculate the NEP and the the lack of robust
global data to constrain its value during the past three centuries. But the model suggests that present coastal
ocean could tend towards a less and less autotrophic state.
Beyond the possible lethal consequence on shallow-water ecosystems, reducing calcification in seawater
does not necessarily lead to a negative feedback on increasing atmospheric CO2 . The reaction of pore water
system to these perturbations could be insignificant. Moreover, the capacity of the coastal ocean to buffer
carbon dioxide has been decreasing during the pas three centuries. The evolution of the Net Ecosystem Production and then of the organic carbon cycle under human forcings remains uncertain, but could be of the first
order in CO2 exchanges between coastal ocean and atmosphere.
Acknowledgements
Mahalo to you all at SOEST, University of Hawaii at Manoa, especially to my advisor, Fred Mackenzie, who
gave me the wonderful opportunity to come to Hawaii for my internship; to all the faculty and grad students
who helped me : Abraham Lerman, Andreas Andersson, Richard Zeebe, Dan Hoover, Dave Karl; to Kathy
Kozuma for administrative support and to Pat Townsend for technical support. Special thanks to Northwestern University, Geological Science Department, who welcomed me as a visitor for a very interesting week.
And thanks to the Hawaiian Islands for being what it is.
39
Appendix
Table 3.2: Litterature data for the carbon masses in the coastal ocean.
Litterature data for the carbon masses in the coastal ocean. In 1012 molC/yr.
System
Carbon Mass Reference
Inorganic Matter
6000
Computed from Broecker and Peng
[1982]
Biota
42.1
Lerman et al. [1989]
50
Scaled up from Rabouille et al. [2001]
Phytoplankton
5.47
Scaled down from R.H. and Likens
[1973]
4.93
Computed from Tyrell [1999], using
(C:N) ratio from TAB 3.7
Autotrophs
5.872
Scaled down phytoplankton from
Bazilevitch [1974]
2.65 to 6.05
Scaled down phytoplankton from Moiseev [1969]
13.85
Computed from Smith et al. [1981] (reported by Tanaka [2002]), using (C:N)
ratio in TAB 3.7
Heterotrophs
26.1
Scaled down zooplankton + zoobenthos from Moiseev [1969]
26.4
Heterotrophic Bacteria
3.7
Computed from Bendtsen et al. [1999]
1.18
Computed from Smith et al. [1981], reported by Tanaka [2002], using (C:N)
in TAB 3.7
Dead Organic Matter
274.9
Murray [1992]
250 to 900
Computed from Cauwet et al. [1997]
(concentrations given for the Mediterranean Sea)
Organic Sediments
134100
Andersson and Mackenzie [2003]
107700
Computed from Ingall et al. [1993]
Pore Water
54
Andersson and Mackenzie [2003]
Inorganic Sediments
72900
Andersson and Mackenzie [2003]
99300
Using Ver [1999] and Ingall et al. [1993]
40
Table 3.3: Litterature data for the carbon fluxes in the coastal ocean.
Litterature data for the carbon fluxes in the coastal ocean. In 1012 molC/yr.
Flux
Carbon
Reference
Transfer
Rate
Primary production
460
Scaled up from Rabouille et al. [2001]
696
Scaled up from Wollast [1991]
600
Mackenzie et al. [2004], Ver [1999], Andersson and
Mackenzie [2003]
363.2
Computed from Tyrell [1999], using (C:N) ratio in
TAB 3.7
228 to 426
Computed from Lefevre et al. [1997]
Total respiration
596
Ver [1999], Andersson and Mackenzie [2003]
307.6
Scaled up from Rabouille et al. [2001]
607
Mackenzie et al. [1998a]
324.2
Computed from Tyrell [1999], using (C:N) ratio in
TAB 3.7
372
Scaled up from Wollast [1991]
Herbivores respiration
132
Wollast [1991]
Microplankton respira- 240
Wollast [1991]
tion
Phytoplankton excretion 324
Wollast [1991]
and death
Herbivores excretion and 60
Wollast [1991]
death
Microplankton excretion 72
Wollast [1991]
and death
Sedimentation
324
Wollast [1991] (not scaled up, taking in account
transport to the open ocean)
154.25
Scaled up from Rabouille et al. [2001]
32
Ver [1999]
Exchange between pore- 42
Andersson and Mackenzie [2003]
water and seawater
Organic carbon burial
9
Ver [1999] and reference therein, Mackenzie et al.
[1998a], Mackenzie et al. [2004], Andersson and
Mackenzie [2003]
17.5
Scaled up from Rabouille et al. [2001]
Inorganic carbon burial
14.5
Ver [1999] and reference therein
68.4
Scaled up from Wollast [1991]
24.5
Andersson and Mackenzie [2003]
Organic sediments oxi- 31
Andersson and Mackenzie [2003]
dation
Carbonate precipitation
0.05
Wollast [1994]
Carbonate dissolution
11
Wollast [1994]
Biogenic carbonate pro- 24.5
Wollast [1994]
duction
14
Ver [1999] and reference therein
41
Table 3.4: Litterature data for the nitrogen fluxes in the coastal ocean.
Litterature data for the nitrogen fluxes in the coastal ocean. In 1012 molN/yr.
N2 fixation
2.37 Ver [1999] and reference therein
0.44 Scaled down from Tyrell [1999]
3.15 Computed from the mean value from
Seitzinger [1988]
N Atmospheric deposition
0.92 Ver [1999] and reference therein
0.27 Scaled down from Tyrell [1999]
Total denitrification
4.78 Ver [1999], Mackenzie et al. [2004]
Denitrification in the water column 1.19 Ver [1999] and reference therein
0.19 Scaled down from Tyrell [1999]
1.1 Computed from Shaffer and Rönner
[1984] (concentrations given for the
Baltic Sea)
4.68 Computed from the mean value from
Seitzinger [1988]
Denitrification in the sediments
3.57 Ver [1999] and reference therein
23.5 Computed from Shaffer and Rönner
[1984] (concentrations given for the
Baltic Sea)
9.46 Computed from the mean value from
Seitzinger [1988]
Nitrogen volatilization
0.85 Ver [1999] and reference therein
42
Table 3.5: Fluxes of the coastal ocean model : initial values, parameterization equations, and their signification.
Fluxes of the coastal ocean model : initial values, parameterization equations, and their signification. In 1012
molM/yr. When two values are indicated : value for the first set or value for the second
Flux
C
N
P
Equation Signification
M FN P P (t0 )
600
83.74
5.6
E Q 2.7
Photosynthesis (-autotrophs respiration)
M Fgraz,het (t0 )
190
27.27
1.76
E Q 2.9
Autotrophs grazing by heterotrophs
M Fgraz,bact (t0 )
450
or 56.25 or 4.17
or E Q 2.9
Dissolved DOM grazing by bac300
37.5
2.78
teria (-bacteria excretion)
M Fresp,het (t0 )
130
18.09
1.18
E Q 1.4
Heterotrophs respiration
M Fresp,bact (t0 )
450
or 90 or 60
4.17
or E Q 1.4
Bacteria respiration
300
2.78
M Fexc,aut (t0 )
410
58.84
3.80
E Q 1.4
Autotrophs excretion
M Fexc,het (t0 )
60
9.61
0.58
E Q 1.4
Heterotrophs excretion
M Fsed (t0 )
28
or 11.02 or 0.19
or E Q 1.4
Sedimentation of DOM
119.30
26.15
0.93
M Fpw−wc (t0 )
40.44 or 8.02
or 0.46
or E Q
1.4 Porewater-seawater exchange
103.54
26.77
1.51
and
E Q 1.3
M FDIM,oc (t0 )
450.68 or 9
0.38
E Q 1.4
Export of DIM to the open ocean
548.53
M FDOM,oc (t0 )
18
or 2.64
or 0.17
or E Q 1.4
Export of DOM to the open
76.70
6.26
0.82
ocean
M Fupw (t0 )
465
10.76
0.46
TOTEM
Upwelling input in DIM
M FDIM,riv (t0 )
32
0.32
0.01
TOTEM
Rivers input of DIM
M FDOM,riv (t0 )
26
1.46
0.15
TOTEM
Rivers input of DOM
M FROM,riv (t0 )
8
0.75
0.13
TOTEM
Rivers input in refractive organic matter
set M F
(t
)
15
0.04
0.39
TOTEM
Rivers input in particulate inorP IM,riv 0
ganic matter
CFburial,org (t0 )
5 or 18.9
E Q 1.4
Burial of organic sediments
CFburial,inorg (t0 ) 26.06
E Q 1.4
Burial of inorganic sediments
CFox,sed (t0 )
31 or 94.1
E Q 1.4
Oxidation of organic sediments
by respiring organisms
CFCaCO3 ,prec (t0 ) 1.56
E Q 2.22
CaCO3 precipitation in the sediments
CFCaCO3 ,diss (t0 ) 11
E Q 2.21 CaCO3 dissolution in the sediand
ments
E Q 1.3
CFCaCO3 ,bio (t0 ) 24.5
E Q 2.20
Biogenic calcification in seawater
CFCO2 ,atm (t0 )
42.26 or see
CO2 exchange across the air142.49
S EC 2.6
seawater interface
CFtrans,slope
4
E Q 1.3
CaCO3 transport to the continental slope
N FN H + ass (t0 )
33.75 or
E Q 2.10
N H4+ assimilation by bacteria
4
22.5
N FN2 f ix (t0 )
2.37
E Q 1.3
Atmospheric N2 biologically
mediated fixation
N Fdep (t0 )
0.92
E Q 1.3
Nitrogen deposition onto the
ocean
N Fdenitr,wc (t0 )
0.34
E Q 1.3
Denitrification in the water column
N Fvolat (t0 )
0.85
E Q 1.3
Nitrogen volatilization
43
Figure 3.13: Conceptual diagram of the coastal ocean model, with the second set of initial fluxes.
44
Table 3.6: Parameters values used in the coastal ocean model, and their signification.
Parameter
Value
Reference
Signification
kN (in 1012 1.5
Fasham et al. [1990], for Half-saturation constant
molN)
both ammonium and of primary production
nitrates, used in Tyrell relatively to nitrogen
[1999] and in Tanaka
[2002]
kP (in 1012 0.09
Tyrell [1999]
Half-saturation constant
molN)
of primary production
relatively to phosphorus
Q10
2.0
Ver et al. [1999a]
Q10 f actor
kaut (in 1012 1.2
this study
Mass of autotrophs at
molC)
which their grazing by
heterotrophs ceases
kDOM
(in 55
this study
Mass of DOM a which its
1012 molC)
grazing by bacteria ceases
[Ca2+ ]
in 0.01028
DOE [1994]
seawater (in
mol/kg)
nprec
2.8
Andersson and Macken- Calcite precipitation reaczie [2003] and Zhong and tion order
Mucci [1989]
ndiss
2.86
Andersson and Macken- Calcite dissolution reaczie [2003] and Walter and tion order
Morse [1985]
kdiss
102.82
Andersson and Macken- Calcite dissolution rate
zie [2003] and Walter and constant
Morse [1985]
Table 3.7: C:N:P ratios in various systems.
System
C
N
P References
Phytoplankton
108 15.5 1 Murray [1992], Lerman et al. [in
press]
Zooplankton
103 16.5 1 Murray [1992], Lerman et al. [in
press]
Bacteria
108 21.6 1 Fenchel and Blackburn [1979],
Murray [1992]
Dissolved inorganic matter in surface ocean 1312 0.7
1 Mackenzie et al. [1993], Lerman
et al. [in press]
Dissolved organic matter in surface ocean
106
6.3
1 Mackenzie et al. [1993], Lerman
et al. [in press]
Particulate organic matter in surface ocean
105
1.9
1 Mackenzie et al. [1993], Lerman
et al. [in press]
45
Table 3.8: Residence times of the different reservoirs of the coastal ocean model, calculated from the masses
and fluxes that have been used in the model.
Residence times of the different reservoirs of the coastal ocean model, calculated from the masses and fluxes
that have been used in the model. In yrs. When two values are indicated : value for the first set or
Reservoir
τC
τN
τP
DIM
5.37 or 5.05
0.47
0.08
Autotrophs
0.010
0.010
0.011
Heterotrophs
0.16
0.17
0.16
Bacteria
0.008 or 0.013
0.009 or 0.013 0.009 or 0.014
value for the second set
DOM
0.55
0.22
0.57
Organic sediments
3055.56 or 864.1
Pore water
1.29 or 0.45
Inorganic sediments
2191.91
Table 3.9: Masses notations of the coastal ocean model.
Symbol
Signification
Mi
Mass of element M in the reservoir i
DIM
Dissolved inorganic matter
aut
Autotrophs
het
Heterotrophs
bact
Bacteria
DOM
Dead organic matter
org, sed
Organic sediments
pw
Porewater
inorg, sed
Inorganic sediments
46
Table 3.10: Symbols and notations of the coastal ocean model.
Symbol Signification
DIM
Dissolved inorganic matter
PIM
Particulate inorganic matter
DOM
Dead organic matter
ROM
Refractive organic matter
GPP
Gross Primary Production, photosynthetic flux
NPP
Net Primary Production, GPP minus
autotrophs respiration
NEP
Net Ecosystem Production, trophic
state, GPP minus total respiration
PCO2
Atmospheric partial pressure in carbone dioxide
DIC
Dissolved inorganic carbon
CA
Carbonate alkalinity
TA
Total alkalinity
K1
First dissociation constant of carbonic
acid
K2
Second dissociation constant of carbonic acid
KH
Henry’s constant
Ωsw
Saturation state in respect with calcite
in seawater
Ωpw
Saturation state in respect with calcite
in porewater
c
Ratio ammonia assimilation flux on
DOM grazing flux by bacteria
Ψ
Ratio calcification CO2 flux on calcification flux
fB
Fraction of Net Primary Production
that goes through the microbial loop
47
Table 3.11: Carbon mass balance equations used in the coastal ocean model.
!
dCDIM
dt
"
= CFresp,het (t) + CFresp,bact (t) + CFpw−wc (t) + CFupw (t) + CFDIM,riv (t)
t
!
!
!
dCDOM
dt
"
dCinorg,sed
dt
"
− CFN P P (t) − CFCaCO3 ,bio (t) − CFDIM,oc (t) − CFCO2 ,atm (t)
dCaut
= CFN P P (t) − CFgraz,het (t) − CFexc,auto (t)
dt
t
!
"
dChet
= CFgraz,het (t) − CFresp,het (t) − CFexc,het (t)
dt
t
!
"
dCbact
= CFgraz,bact (t) − CFresp,bact
dt
t
t
= CFexc,auto (t) + CFexc,het (t) + CFDOM,riv (t) − CFgraz,bact (t) − CFsed (t) − CFDOM,oc (t)
"
dCorg,sed
= CFsed (t) + CFROM,riv (t) − CFox,sed (t) − CFburial,org (t)
dt
t
!
"
dCpw
= CFox,sed (t) + CFCaCO3 ,diss (t) − CFCaCO3 ,prec (t) − CFpw−wc (t)
dt
t
"
!
= CFCaCO3 ,prec (t) + CFCaCO3 ,bio (t) + CFP IM,riv (t)
t
− CFCaCO3 ,diss (t) − CFburial,inorg (t) − CFtrans,slope (t)
48
Table 3.12: Nitrogen mass balance equations used in the coastal ocean model.
!
"
dNDIM
dt
= N Fresp,het (t) + N Fresp,bact (t) + N Fpw−sw (t) + N Fupw (t) + N Fdep (t) + N FDIM,riv (t)
t
− N FN P P (t) − N Fdenitr,wc (t) − N FN H + ass (t) − N Fvolat (t) − N FDIM,oc (t)
4
!
!
dNDOM
dt
"
dNaut
dt
!
"
t
= N FN P P (t) + N FN2 f ix (t) − N Fgraz,het (t) − N Fexc,het (t)
"
dNhet
= N Fgraz,het (t) − N Fresp,het (t) − N Fexc,het (t)
dt
t
!
"
dNbact
= N Fgraz,bact (t) + N FN H + ass (t) − N Fresp,bact (t)
4
dt
t
= N Fexc,auto (t) + N Fexc,het (t) + N FDOM,riv (t) − N Fgraz,bact (t) − N Fsed (t) − N FDOM,oc (t)
t
Table 3.13: Phosphorus mass balance equations used in the coastal ocean model.
!
dPDIM
dt
"
= P Fresp,het (t) + P Fresp,bact (t) + P Fpw,sw (t) + P Fupw (t) + P FDIM,riv (t)
t
− P FN P P (t) − P FDIM,oc (t)
!
!
dPDOM
dt
"
"
dPaut
= P FN P P (t) − P Fgraz,het (t) − P Fexc,het (t)
dt
t
!
"
dPhet
= P Fgraz,het (t) − P Fresp,het (t) − P Fexc,het (t)
dt
t
!
"
dPbact
= P Fgraz,bact (t) − P Fresp,bact (t)
dt
t
t
= P Fexc,auto (t) + P Fexc,het (t) + P FDOM,riv (t) − P Fgraz,bact (t) − P Fsed (t) − P FDOM,oc (t)
49
List of Figures
1.1
1.2
1.3
1.4
1.5
Conceptual diagram of the new version of TOTEM. . . . . . . . . . . . . . .
Comparison between TOTEM atmospheric CO2 and data from 1700 to 2005.
Carbon rivers input from TOTEM over the past three centuries. . . . . . . .
Nitrogen rivers input from TOTEM over the past three centuries. . . . . . .
Phosphorus rivers input from TOTEM over the past three centuries. . . . . .
.
.
.
.
.
7
8
9
9
10
2.1
2.2
Conceptual diagram of the coastal ocean model, with the first set initial fluxes. . . . . . . . . . .
Calculation method for CFCO2 ,calc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
21
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Results from the coastal ocean model : NEP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results from the coastal ocean model : DIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results from the coastal ocean model : carbonates in seawater. . . . . . . . . . . . . . . . . . . . .
Results from the coastal ocean model : carbonates in pore water. . . . . . . . . . . . . . . . . . . .
Results from the coastal ocean model : equilibration and calcification CO2 fluxes. . . . . . . . . .
Results from the coastal ocean model : biogenic CO2 fluxes. . . . . . . . . . . . . . . . . . . . . .
Results from the coastal ocean model : total CO2 fluxes. . . . . . . . . . . . . . . . . . . . . . . . .
Sensitivity analyses on the coastal ocean model : influence of kN and kP on the NEP, for the first
set of initial values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sensitivity analysis on the coastal ocean model : influence of kDOM on NEP, for the first set of
initial values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Influence of the calcification parameterization on the coastal ocean model, for the first set of
initial values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CO2 flux, with ∆ T A(CFN H + ,ass ) = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
CO2 flux, with ∆ T A(CFN H + ,ass ) = CFN H + ,ass . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
4
Conceptual diagram of the coastal ocean model, with the second set of initial fluxes. . . . . . . .
25
26
27
28
29
30
31
3.9
3.10
3.11
3.12
3.13
50
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.
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.
33
34
35
36
37
44
List of Tables
2.1
2.2
2.3
Initial masses used in the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Initial values of CO2 flux, and different contribution, in the two different sets of initial values. .
Comparison of the two sets of initial fluxes used as inputs of the coastal ocean model. . . . . . .
15
22
22
3.1
3.2
3.3
3.4
3.5
New steady-state fluxes for different ∆ T A = f (N H4+ ). . . . . . . . . . . . . . . . . . . . . . . . .
Litterature data for the carbon masses in the coastal ocean. . . . . . . . . . . . . . . . . . . . . . .
Litterature data for the carbon fluxes in the coastal ocean. . . . . . . . . . . . . . . . . . . . . . . .
Litterature data for the nitrogen fluxes in the coastal ocean. . . . . . . . . . . . . . . . . . . . . . .
Fluxes of the coastal ocean model : initial values, parameterization equations, and their signification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters values used in the coastal ocean model, and their signification. . . . . . . . . . . . . .
C:N:P ratios in various systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Residence times of the different reservoirs of the coastal ocean model, calculated from the masses
and fluxes that have been used in the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Masses notations of the coastal ocean model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Symbols and notations of the coastal ocean model. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Carbon mass balance equations used in the coastal ocean model. . . . . . . . . . . . . . . . . . . .
Nitrogen mass balance equations used in the coastal ocean model. . . . . . . . . . . . . . . . . . .
Phosphorus mass balance equations used in the coastal ocean model. . . . . . . . . . . . . . . . .
34
40
41
42
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
51
43
45
45
46
46
47
48
49
49
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