**The GFDL TOPAZ ocean biogeochemical model**

*Overview*

The GFDL Tracers for Ocean Phytoplankton with Allometric Zooplankton
(TOPAZ) model is designed to reproduce diverse interactions between the
marine ecosystem and the physical environment as accurately as possible,
while incorporating as little complexity as possible. The model has been
tested and calibrated against global nutrient and satellite observations
in the GFDL global, one-degree resolution ocean model.

The model is constructed according to the same principles as most other
biogeochemical/ecosystem models, but also has some important
distinctions. All major nutrient elements are considered (N, P, Si and
Fe), placing this model at the high end of available global models in
terms of nutrient complexity. The model includes both labile and
semi-labile dissolved organic pools, and parameterizations to represent
the microbial loop. Although there is a heterotrophic biomass component,
its concentration does not affect grazing rates, which are determined
solely by phytoplankton concentrations. The ecosystem does not
explicitly trace detritus, in contrast to many NPZD models (e.g.
Schmittner), but instantaneously distributes sinking particles through
the water column and to the sediment, employing a particle ballast
scheme involving opal, CaCO~3~ and lithogenic material (which affects
remineralization profiles). The model also traces dissolved oxygen, DIC
and alkalinity, and includes the option of using highly flexible
phytoplankton stoichiometry and variable Chl:C ratios.

Three classes of phytoplankton form the base of the global ecosystem.
"Small" phytoplankton represent cyanobacteria and picoeukaryotes,
resisting sinking and tightly bound to the microbial loop. "Large"
phytoplankton represent diatoms and other eukaryotic phytoplankton,
which sink more rapidly. "Diazotrophs" fix nitrogen directly rather than
requiring dissolved forms of nitrogen. All phytoplankton are
simultaneously limited by the availability of light and multiple
nutrients, but each class has its own set of tunable parameters for
determining growth rates and its own nutrient stoichiometry. Grazing is
calibrated as described in Dunne et al. (2005).

*Growth*

Light is the ultimate limiting nutrient. The average light level is
calculated for the mixed layer (as defined in the KPP routine plus one
level), and this value is used for all levels within the mixed layer.
The actual level of irradiance phytoplankton exploit is that of the
irradiance memory, which is delayed relative to changes in local
irradiance with a relaxation timescale of 1d.

For N and P, a limitation term is calculated at each time step, and the
combined effect is expressed through the growth rate. The P limitation
follows simple Michaelis-Menten kinetics. The N limitation represents
the dual availability of NO~3~ and NH~4~ while inhibiting the use of
NO~3~ in the presence of high concentrations of NH~4~, following Frost
and Franzen (1992) as modified by Sharada et al. (2006):

NO~3~lim = NO~3~ \* (1 + NH~4~ / k_NO~3~) / ((k_NO~3~ + NO~3~) \* (1 +
NH~4~ / k_NH~4~))

NH~4~, P, Si and Fe limitation are given by standard Michaelis-Menten
equations. In all cases, the half saturation constants of Lg and Di
phytoplankton are determined by multiplying those of the small
phytoplankton by a constant, representing the decreased uptake
efficiency due to the larger effective size.

The C:N ratio of all organic matter is constant throughout the model,
hence organic N is directly proportional to the organic C implicitly
contained in any organic component. The carbon-specific growth rate,
P^C^, is calculated as

P^C^ = P^C^~max~ \* e^kT^

which includes the Eppley (1972) temperature dependence, e^kT^.

Iron has a special role as a limiting nutrient in the model, in that its
availability determines the ability of phytoplankton to synthesize
chlorophyll, as indicated by Sunda and Huntsman (1997) based on culture
studies of diatoms and here assumed to by typical of all phytoplankton.
Fe deficiency produces low Chl:N, causing light limitation to have more
of an impact on growth rates. The Fe deficiency, Q~Fe:N~**,** is
calculated as

Q~Fe:N~ = (Fe:N)^2^ / ((k~Fe:N~)^2^ + (Fe:N)^2^)

where Fe:N is the elemental ratio within the existing biomass of the
given phytoplankton class, and k~Fe:N~ is the ratio at which the
phytoplankton capacity to use Fe is saturated. The chlorophyll to N
ratio of the phytoplankton class, θ, is then determined at each
time-step from a combination of light and nutrient limitation using a
parameterization adapted from Geider (1997),

θ = θ~max~ \* Q~Fe:N~ / (1 + θ~max~ \* Q~Fe:N~ ∗ α ∗  I~mem~ / (2
P^C^)) + θ~min~

where θ~max~ is the maximum value, θ~min~ is the minimum, I~mem~ is the
irradiance memory, α** **is the initial slope of the photosynthesis vs.
irradiance curve, and P^C^ is the maximum nitrogen-specific
photosynthesis rate previously calculated. The degree of light
limitation is then calculated,

I~lim~ = 1 -- *e* -α I θ / P^C^~m~

where I is the irradiance. The growth rate is then given by

μ = P^C^~m~ / (1 + ζ) \* I~lim~ \* (P:N)^2^ / ((k~P:N~)^2^ + (P:N)^2^)

where ζ represents the metabolic cost of organic matter synthesis,
following Geider (1997), and P-limitation is represented in a method
analogous to that of Fe, following Christian (2005).

The total chlorophyll concentration in each grid cell is then calculated
as

Chl = C:N \* 12000 \* Σ~classes~ θ \* N

Where N is the concentration of N in a given phytoplankton class and C:N
is the global ratio of carbon to nitrogen in biomass, a constant among
all organic matter.

The production terms are calculated individually for each element in a
manner similar to that of Geider et al (2002):

Jprod_NO~3~ = μ \* N \* NO~3~lim

Jprod_NH~4~ = μ \* N \* NH~4~lim

Jprod_PO~4~ = μ \* N \* PO~4~lim \* (P:N~max~ -- P:N)

Jprod_Fe = μ \* N \* Felim \* (Fe:N~max~ -- Fe:N)

where P:N~max~ and Fe:N~max~ represent the prescribed maximum
incorporation rates of P and Fe relative to N, respectively.

Diazotrophs do not take up nitrate or ammonia but implicitly fix new N,
have low photosynthesis efficiency and high N:P (Letelier & Karl, 1998).
Large phytoplankton have difficulty reducing NO~3~ when strongly iron
limited, and therefore become enriched in P.

The fraction of Lg phytoplankton that represents diatom is equal to the
Si limitation term, SiO~4~lim. CaCO~3~ production depends on the
potential growth rate of small phytoplankton, multiplied by a constant
Ca:N, similar to Moore et al. (2002):

Jprod_CaCO~3~ = μ~Sm~ \* N~Sm~ \* Ca:N

Note that with this formulation, N, P and Fe limitation do not prevent
calcifiers from forming CaCO~3~ (although it is reduced, through the
effects of P and Fe on μ). This reflects the tendency of
coccolithophorids to produce liths even in the absence of growth.

*Food web processing and remineralization*

Grazers are implicitly assumed to maintain steady state with respect to
the phytoplankton, so that grazing rates depend only on phytoplankton
concentrations and temperature. Small and diazotophic phytoplankton are
grazed at a rate proportional to the square of their concentrations,
while large phytoplankton are grazed at a rate equal to their
concentration to the 4/3^rd^ power. These rates are constrained by a
defined maximum of 1 per timestep and by a Michaelis-Menton term to
prevent phytoplankton extinction at low concentrations. A lag in the
response of grazers to large phytoplankton population changes is
parameterized by a memory lag in the large phytoplankton, more
pronounced at low temperatures.

Fixed fractions of the grazed biomass are converted to nonredfieldian
semilabile dissolved organic nitrogen and phosphorus (SDON, SDOP) and
redfieldian labile dissolved organic matter (LDOM) following the
observations of Libby and Wheeler (1997). Of the remaining grazed
biomass, a temperature-dependent fraction is converted to particulate
organic N and P, with a higher fraction of detritus generated from large
than from small/diazotrophs, and a higher fraction at low temperature. A
fraction of the grazed organic matter is converted to heterotroph
biomass, which does not affect grazing rates, but serves only to
temporarily sequester organic matter and, in this sense, is virtually
identical to LDOM. DOM remineralization is parameterized in order to be
consistent with Abell et al. (2000), with a 3 month timescale for LDOM
after Archer et al. (1997). Grazed N not converted to detritus, DON or
NHET is converted to ammonia, while the equivalent P is converted to
PO~4~. Nitrification of ammonia is inhibited by light after Ward (1982).

Fe is recycled in parallel to N, achieved by multiplying the N specific
grazing rates by the instantaneous Fe:N of each component. A fraction of
the grazed Fe is converted to particulate Fe. The dissolution of grazed
SiO~2~ depends on temperature, as observed by Katami (1982), and was
globally tuned to fit Nelson et al. (1995). CaCO~3~ solubility is
calculated from Sayles (1985) and, where undersaturated, CaCO~3~
dissolves with a characteristic length scale. CaCO~3~ that reaches the
sediments dissolves slowly.

The concentrations of lithogenic material, SiO~2~, and CaCO~3~ are used
to determine the amount of organic matter that is protected from
remineralization, to simulate mineral ballasting of organic matter
(Klaass and Archer, 2002). Unprotected organic matter, i.e. that not
associated with lithogenic material, SiO~2~ or CaCO~3~, decays following
an exponential that approximately matches the Martin curve over the
upper portion of the water column. Under oxic conditions the decay uses
a short length scale and consumes oxygen, while below 5 μM decay
consumes nitrate with a longer length scale. Organic matter that reaches
the bottom box is instantly remineralized, and sedimentary
denitrification is parameterized from the organic flux reaching the
bottom box and the water depth, according to the metamodel of Middelburg
et al. (1996).