JGOFS REPORT No. 23
ONE-DIMENSIONAL MODELS OF
WATER COLUMN BIOGEOCHEMISTRY
Report of a Workshop held in Toulouse, France
November-December 1995
Geoffrey T. Evans and Véronique Garçon
Editors
FEBRUARY 1997
Published in Bergen, Norway, February 1997 by:
Scientific Committee on Oceanic Research
Department of Earth and Planetary Sciences
The Johns Hopkins University
Baltimore, MD 21218
USA
and JGOFS International Project Office
Centre for Studies of Environment and Resources
University of Bergen
5020 Bergen
NORWAY
The Joint Global Ocean Flux Study of the Scientific Committee on Oceanic Research (SCOR) is a Core
Project of the International Geosphere-Biosphere Programme (IGBP). It is planned by a SCOR/IGBP
Scientific Steering Committee. In addition to funds from the JGOFS sponsors, SCOR and IGBP, support is
provided for international JGOFS planning and synthesis activities by several agencies and organizations.
These are gratefully acknowledged and include the US National Science Foundation, the International
Council of Scientific Unions (by funds from the United Nations Education, Scientific and Cultural
Organization), the Intergovernmental Oceanographic Commission, the Research Council of Norway and the
University of Bergen, Norway.
Citation:
One-Dimensional Models of Water Column Biogeochemistry; Report of a Workshop held in
Toulouse, France; November-December 1995. Geoffrey T. Evans and Véronique Garçon,
Editors, February 1997.
ISSN:
1016-7331
Cover:
JGOFS and SCOR Logos
The JGOFS Reports are distributed free of charge to scientists involved in global change research.
Additional copies of the JGOFS reports are available from:
Ms. Judith R. Stokke, Administrative Assistant
JGOFS International Project Office
Centre for Studies of Environment and Resources
University of Bergen
High-Technology Centre
N-5020 Bergen, NORWAY
or, from our website: http://ads.smr.uib.no/jgofs/jgofs.htm
Tel: (+47) 55 58 42 46
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Table of contents
1
2
3
4
5
6
7
Introduction
Biogeochemical processes
Biogeochemical models
A common physical arena
Surface forcing
Running models, comparing with observations, interpreting
Comparative behaviour of 1-D physical and ecological models:
preliminary results
8 Equations and parameters
References
Participants
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1 Introduction
1.1 The role of local studies in a global project
The Joint Global Ocean Flux Study (jgofs) exists to \assess more accurately, and understand
better the processes controlling, regional to global and seasonal to interannual uxes of carbon
between the atmosphere, surface ocean and ocean interior, and their sensitivity to climate changes"
(SCOR 1992). Most of its eort in the eld is spent on local studies, sampling individual sites
either intensively for a limited period such as the North Atlantic Bloom Experiment of 1989
(Ducklow and Harris 1993), or at regular intervals for many years such as the Bermuda Atlantic
Time Series (Michaels and Knap 1996). Such local studies make sense in a global project only if
one can extrapolate their lessons to the rest of the ocean: jgofs is not about the local studies
but about the ocean in between them. \The carbon system in the surface ocean is so complicated,
and so rapidly varying in space and time, that global averages inferred by interpolation from
shipboard surveys are unreliable. Only if there is some underlying order that varies much more
slowly will jgofs goals be attainable. Process studies are conceived to seek this underlying order
. . . in particular by improving process models, estimating their parameters, and suggesting new
models." (SCOR 1992) The models and parameter values will then contribute to ux calculations
over larger regions of the ocean.
Biogeochemistry aects the ocean carbon cycle by converting inorganic carbon to organic
forms and by creating particles that sink through the water instead of moving with it. Local eld
programs measure biological variables, nutrients and carbon, and sometimes rates. Modelling can
address the questions: How well are the uxes and processes known; what alternatives can be
ruled out? What is the range of predicted exports; how constrained is it by physical forcing?
1.2 The purpose and achievements of the workshop
jgofs will be able to apply only a small number of biogeochemical (bgc) models in global contexts,
and so it should use models that have been examined in many locations, compared with other
candidates, and found good. A good model would be accurate (for things that matter) in dierent
locations, ecient, and sensible (degrading gracefully when pushed to extremes). jgofs, the
International Geosphere-Biosphere Programme, and the U.S. Oce of Naval Research sponsored
a workshop to evaluate how far modelling has progressed in addressing jgofs questions, and to
help it progress further. There were two general aims. The rst was to produce a systematic
comparison of a diverse and representative group of models that are being used for various jgofs
purposes, comparing both how they were formulated and how well they could reproduce sets of
observations. The second was to explore potential areas of agreement. There is currently no
consensus on how to represent ecological processes, or even on what processes jgofs needs to
have represented. It is neither probable nor desirable that there will ever be a consensus model
that all modellers will agree to apply in all circumstances. People who wish to explore the eects
of formulating some process in a new way may nevertheless nd it useful to have a standard
of comparison, where they can represent processes they are not especially interested in as other
people have agreed to represent them, and then see more clearly the eects of their particular
modication. (The model of Fasham et al. (1990), herein referred to as FDM, has to some extent
served as such a standard.)
In more detail, the workshop questions were: What do dierent models suggest about ecosystem structure and carbon ow? How are suggestions related to model formulation, especially
complexity? What model parameters are well constrained, and how does that vary across models? Do the data give us enough information to choose among candidate models? These questions
1
relate not only to dierent bgc models but also to dierent physical arenas, especially the degree
(even the presence) of vertical resolution.
The emphasis at the workshop turned out to be largely technical questions about how to formulate and explore models and how to formulate comparisons between models. Among fascinating
discussions and some frustrating failures, one can discern some tangible achievements. We produced a systematic comparison of the concepts underlying the diverse models that were present,
and made good progress towards a common notation for equations. (Considerably more progress
on this was made in the months following the workshop.) Data sets for driving the models were
assembled in a systematic way ready for use by other researchers. We produced a preliminary
comparison of how well dierent models can represent a single data set (although problems with
parameter estimation software prevented more than a preliminary comparison). We identied
some areas of growing agreement: notably the physical arena in which the bgc models run, ideas
about prior distributions for parameter values, and some high-quality numerical methods.
1.3 Summary of the report
This report presents work and thoughts in an unnished state. The workshop generated enthusiasm but did not complete its tasks; nor has it been possible to complete them in the months since.
We have judged it more useful to share the current state with the rest of the community than
to insist on a polished product. We have chosen to highlight (perhaps exaggerate) what dierent
models have in common; the original papers can be consulted for the counterbalancing view of
how each model is special.
Chapter 2 describes the concepts for describing individual in situ transformations, and presents
a comparison of process formulations. Chapter 3 describes how the processes are combined and
the uxes connected into bgc models.
The representation of biogeochemistry is only one part of the whole model, and so dierent
representations of bgc are most aptly made when the other parts are kept constant. The next three
chapters are devoted to accomplishing this. The models run in a 1-dimensional water column, and
depend on contrary gradients of light (attenuated with depth) and inorganic nutrients (brought
from deep water into the well-lit surface by mixing and upwelling). The common physical arena
that participants agreed on is described in Chapter 4. Chapter 5 describes the surface wind
and radiation data that are used in calculations of mixing. A model, once described, has to be
run to make predictions and compare with observations. How to run it (for example whether
to impose periodic or smooth forcing functions) is discussed in Chapter 6, along with issues of
estimating model parameters, what the estimates mean, and how they can be performed reliably
and eciently.
The progress referred to so far has been conceptual; what about results? As already mentioned,
these are all indicative rather than conclusive; at the same time, much valuable preparatory work
has been done and should be made widely available. In a major contribution to the success of
the workshop, the jgofs Scientic Steering Committee agreed to hire Cathrine Myrmehl for the
6 months preceding it, to assemble models and data sets and make sure they worked together.
Chapter 7 reports on the work she accomplished. This includes extracting meteorological data for
forcing the model at dierent sites around the world, deriving an agreed history of vertical mixing
and other physical variables as functions of time and depth, modifying computer codes so that all
of the models ran (with parameter values supplied by the authors) in the common physical arena,
and beginning to adjust parameter values to produce better ts to nitrate and chlorophyll data
from Station Papa.
Explicit equations for all the models, in a common notation, are collected in Chapter 8. This
chapter also contains a table of all the parameters, with `typical' values. Ideally these would be
the values for the dierent models tuned to the same data set, but this was not possible.
2
1.4 Future work
Model-data comparison, and model-model comparison, must be continued as part of jgofs.
We need to complete the task that was begun at the workshop, to compare whole models at a
given site, and also compare dierent subprocess formulations (for example ways to represent the
interactions of nutrients and light, or nitrate and ammonium, or dierent kinds of zooplankton
food) in an otherwise constant framework. (How stable are `irrelevant' or `distant' parameters
under changes in the formulation?)
The workshop began to develop a modelling workbench or toolkit, based on the WEB system
of structured documentation, for making such comparisons easier in future|comparing not just
whole models but also dierent ways of formulating a single process within a common framework
for the rest of the model. The workbench incorporates numerical analysis tools for running models
and estimating their parameters, to facilitate the computer-intensive work of estimating model
parameters and determining how well data sets have constrained parameter values.
A common move, when we know what a reputable solution to a modelling problem would look
like but lack the knowledge to implement one, is to use a stopgap instead. A slightly better move
in such circumstances would be to use two dierent stopgaps|perhaps concentrating on dierent
parts of what a reputable solution would contain|and evaluate the dierence between them as a
crude indication of how important it might be to achieve the reputable solution.
jgofs has not yet had the workshop at which local data sets and models are brought together
and their interplay studied, including how the idiosyncrasies of each aect the other. Problems
we know need to be addressed include accuracy of measurements, correlation of errors between
variables, process errors that lead to correlated residuals over time. There are other problems we
won't know about until such a workshop happens. We need to test the ability of data sets to
constrain estimates of parameters and uxes, as well as the ability of models to t data. This
leads into experimental design: what data set would be most informative about the quantities we
are interested in? This includes sampling times, depths, variables to sample, the value of a very
orthogonal measurement, even if relatively poor quality, compared to a very good measurement
of something that has been measured often before.
Given the need for more jgofs synthesis workshops, it is worth commenting on things that
contributed to the success of this one. It is a pleasure to acknowledge the cooperation of our
hosts the Observatoire Midi-Pyrenees, the UMR5566 laboratory and Jean-Francois Minster. The
facilities they provided included a large room with exible furnishings, four computer terminals,
and the cheerful support of computer and other professionals. Participation was deliberately
restricted to a small number of people. The emphasis was on tasks that small (3-5 people) groups
could usefully address, rather than set-piece presentations. A lot of the work of getting models
working in a new environment was done beforehand, so that participants arrived ready for scientic
interactions rather than details of coding.
The jgofs www site http://ads.smr.uib.no/jgofs/inventory/Toulouse/index.htm will
contain pointers to some of the work reported here, and also to follow-on work.
3
2 Biogeochemical processes
2.1 General considerations
This chapter considers the individual processes involved in in situ transformations of matter, the
issues involved, and the choices that dierent workshop models made. Although carbon is the
element of most interest to jgofs, the uptake of carbon by organisms is limited by some other
nutrient or by energy. All models therefore use nitrogen as a currency for matter ow among
organisms, and the symbols phy, zoo, etc. will denote the nitrogen content of the component.
Some models use carbon and occasionally silicon as well; this is important when the C:N ratio
can change. Consumption appears immediately as population growth: internal pools are ignored
or parameterized. This is appropriate to a study of seasonal to interannual changes.
Models generally represent a community, whose species composition changes with season, by
a single state variable. Hurtt and Armstrong (1996) take account of how community composition,
and therefore physiological rates, might be expected to change with community biomass. Temperature inuences many physiological rates, and some of the models include terms that take this
into account.
2.2 Light: nature, propagation and absorption
Before considering in detail the individual biogeochemical processes, we describe the energy driving
the conversion of inorganic to organic carbon.
2.2.1 At the sea surface
Much is known about the geometry and atmospheric physics of light reaching the surface of the
earth. One can try for as accurate as possible based on real measurements: for example the model
of Gregg and Carder (1990) that uses properties of atmospheric transmission, either for an average
solar elevation or integrated over the path of the sun through the sky, and perhaps including the
Earth's orbital eccentricity. At the other extreme, perhaps just getting the integrated light over a
day roughly right, say with the rst 3 terms of a Fourier series tted to the solstices and equinox, is
appropriate remembering the much larger inaccuracies there will be in representing the ecological
interactions. Models that do not try to predict the dynamics of phytoplankton chlorophyll, but use
it to compute primary production, may have a need for a more detailed and accurate treatment
of light.
2.2.2 Transmission
The main issue here is spectral dependence of transmission. The light in a spectral band decreases
exponentially with depth according to an attenuation coecient for that band, and the attenuated spectral bands at a given depth are added to give total light, perhaps weighted by the use
phytoplankton can make of it. The only dierence among models is whether they use one spectral
band, (Evans), or two (Denman), or 19 (Wolf), or 61 (Antoine). The attenuation coecient is
inuenced by chlorophyll. A further issue is the dierence between downwelling irradiance (the
quantity that is attenuated with depth) and scalar irradiance, which arrives from all directions
including upward scatter from below, and is the quantity that is used for photosynthesis.
David Antoine and Andre Morel Light propagation is modeled following Morel (1988):
par(z )
=
Z =700
=400
E (; 0) g(; chl) exp ,
4
Z z
0
Kw () + () Chl(z )e() dz d
The factor () and the exponent e() are from Morel (1988). g is a geometrical factor to convert
downwelling irradiance to scalar irradiance. Garcon, Ruiz-Pino and Prunet adapted Antoine and
Morel's approach for their models.
Ken Denman
= par(0) V1 e,1:67 z + (1 , V1 ) e,0:05 z
Solar radiation is partitioned into long-wave and visible, with long wave having a much higher
attenuation coecient. Phytoplankton concentration does not aect the attenuation coecients.
par(z )
Scott Doney
par(z ) = 0:45E (0) exp
(Morel, 1988).
chl
,0:121 chl 0:428 z
is the mean chlorophyll concentration within the euphotic zone.
Geo Evans
= par(0) exp (,Kw + kc chl)
Bannister (1974). Hurtt and Armstrong, Sharada, McGillicuddy compute
way.
par(z )
Olaf Haupt and Uli Wolf
par(z )
=
par(0)
nX
=19
n=1
Z z =ze
Vn exp ,
z=0
par(z )
(Kw;n + kc chl(z )) dz
in the same
Vn are partitioning factors for 19 wavelength domains. kc is constant and Kw;n is from Jerlov.
2.3 Primary production and growth of phytoplankton
Primary production, the conversion of inorganic carbon to organic or particulate forms in which
it cannot readily exchange with the atmosphere, is a main route by which biological processes
inuence ocean geochemistry. The processes and factors controlling it are better understood than
for, say, zooplankton grazing. It is therefore both possible and perhaps desirable that models be
more sophisticated here than at higher trophic levels.
2.3.1 Use of light
A nutrient molecule that is not used now is still there to be used perhaps later; a photon that is
not used now is gone forever. Therefore light is measured as a ux rather than a concentration.
Primary production is carried out by chloroplasts, not by total phytoplankton nitrogen. The
fraction of cell biomass that is chlorophyll can vary; some models take it to be constant, while
others model phytoplankton nitrogen (phy) and chlorophyll (chl) as coupled dynamical variables, obeying either separate dierential equations or some algebraic relation that may change
with time. Phytoplankton acclimate or photoadapt to low light (nutrient) levels by increasing
(decreasing) their cellular Chl:C and Chl:N levels. If we are modelling chl then we want primary production per unit chlorophyll as a function of photons in terms of the maximum rate of
B , traditionally measured in units of gC gChl,1 h,1 and the initial slope B
photosynthesis Pmax
,
1
,
1
in g C gChl h (E m,2 s,1 ),1 where E is an einstein, a mole of photons. If we are modelling
phy alone, then we want the population growth rate as a function of light (often expressed as
energy rather than photons) in terms of the maximum specic growth rate in d,1 and the initial
slope in d,1 (W m,2 ),1 . There are of course no constant conversions between the dierent sets
of parameters, but the following values are not atypical:
5
1 g Chl = 0:5 mol N
1 mol N = 12 106 = 16 = 79:5 g C
1 Wm,2 = 2:5 1018 Q m,2 s,1 = 106 2:5 1018 = 6:022 1023 = 4:15 E m,2 s,1
B = 0:5 79:5=24 = 1:656 Pmax
B = 0:5 79:5=4:15=24 = 0:4 Photosynthesis-light curve The wavelength of light aects how eective it is in photosynthe-
sis. Many models treat light as a scalar quantity, but it is more accurate to take account of its
spectral character, either in detail (Sathyendranath et al. 1989, Morel 1991) or in a computationally ecient approximation of an eective light, E (Anderson 1993). The function describing how
phytoplankton use E is typically described in terms of its initial slope, , and maximum value,
. Candidates include
E Michaelis-Menten
+ E
E
p
Smith (1936)
2
+ 2 E 2
1 , e,E=
Webb et al. (1974)
1 , e,E= e,E= Platt et al. (1980)
In the last formulation, which describes inhibition of photosynthesis in strong light, is no longer
the maximum growth rate; growth attains a maximum value which is hard to interpret as a
function of the parameters, at a nite value of E which is equally hard to interpret. is still
the initial slope. The dierences between the Smith and Webb curves with the same and are
not large, and would be even smaller if, instead of using the same parameters, one were to use
parameters for each tuned to the same representative data set.
Time and space averaging When we are studying seasonal to interannual changes, the day-
night cycle is a nuisance to be averaged over if possible. Evans and Parslow (1985) combined
Smith's equation with an assumed triangular daily light function with day length D and total
light L during the day. If light is so high that photosynthesis is saturated whenever there is any
daylight then the growth in a day is GD = D; if light is so low that photosynthesis is always
in the linear range then growth in a day is GL = L. The concepts GD and GL are meaningful
for all equations that are described by an initial slope and a maximum value, not just the Smith
equation. If the light attenuation coecient k is constant over a layer of thickness M , then the
average over a numerical layer of the total growth during the day is
2
G
2
G
G
D
L
L
,
kM
G=
,
e
(1)
kM
where
GD
GD
p
2
, 1 +uu , 1 :
(2)
In the limit as u ! 0, (u) ! u=2 so that G ! GL(1 , e,kM )=kM , which in turn ! GL as
kM ! 0. As u ! 1, (u) ! ln(2u) , 1 so that G ! GD . A useful approximation for (u) is
p
(u) = ln u + 1 + u2
0:555588u + 0:004926u2 :
1 + 0:188721u
6
It has a maximum percentage error of almost 12% at the origin, and a maximum absolute error of
0.01 between u = 0 and u = 20. It also degrades slowly when pushed beyond the range for which
it was designed. Polynomial approximations, such as that used by Platt and Sathyendranath
(1993), behave somewhat worse than rational functions.
The formula for G is universal in the following sense: if G is a 2-parameter function determined
by its initial slope and maximum value, and E decreases with depth at a constant exponential
rate, then, whatever the functional forms of G and of daily light variation, G is given by (1) for
some function which has the same large and small limits as (2) (Platt & Sathyendranath 1993).
Anderson (1993) has extended this approach to take account of the change in the spectrum
of light
with depth. He obtains a similar result with a function that can be written as A 2aG#DGL where
a# , a dimensionless function of depth and chlorophyll concentration, accounts for the change in
spectrum.
2.3.2 Nutrients
Growth as a function of nutrients is most often expressed as a Michaelis-Menten (Monod) function
parameterized by its maximum value and half-saturation abscissa K :
no3
K + no3 :
Dissolved inorganic nitrogen comes in two forms. Nitrate is generally associated with water
newly brought into the well-lit surface layer whereas ammonium is produced in situ by processes
of regeneration. There is interest within jgofs in how much production is due to each (new
and regenerated production), and therefore many models include expressions for computing the
uptake of no3 and nh4 when both are present. One form for the uptake of nitrate and ammonium
respectively (the ow into phytoplankton is the sum of the two):
no3e, nh4 ;
nh4
KN + no3 KA + nh4
was proposed by Wroblewski (1977) and used in FDM. Its main drawbacks are that the total
growth can be greater than the supposed maximum , and for some values of no3 and nh4 the
total uptake can be a decreasing function of nh4. Hurtt and Armstrong take nh4 uptake to be a
function of nh4, and total uptake to be a function of no3+nh4, to obtain the forms
nh4 :
K no3
;
(K + nh4) (K + nh4 + no3) K + nh4
Here the single parameter K means many dierent things. In these formulas
nh4 uptake is
unaected by no3 concentrations whereas no3 uptake is inhibited by the presence of nh4. There
are also formulas that allow phytoplankton to take up nh4 preferentially but also allow some
reduction of nh4 uptake at high no3 concentrations. Ruiz-Pino, following Lancelot et al. (1993),
makes uptake a switching, weighted average of the no3-only and nh4-only uptakes (see Chapter
8 for details). Evans and Fasham (1993) take a mechanistic, queuing theory approach in which
the use of no3 requires an extra, reduction step whereas nh4 is already reduced. Although simple
enough in its own terms, this ends up looking complicated in ; K terms. For one thing, there is
not a single : the maximum growth rate is less on no3 alone than on nh4 alone because of the
time required for the reduction step.
2.3.3 Interaction of light and nutrients
When growth is a function of many resources, there is a large range of functional forms that might
express the joint dependence (and the number of experiments required to determine the correct
7
one is correspondingly large). To control this explosion of possibilities, it is common to think of
separate resources as limiting factors reducing some theoretical maximum growth rate|factors
that can be determined separately and then combined in one of a small number of ways. For
example we might take the product of light and nutrient limitation terms, as in FDM, or their
minimum. But in principle it is just as easy to imagine that nutrient limitation reduces the
parameter in the P -I curve (or GD ) but does not aect (GL ), or vice versa. This would
provide a form of interaction intermediate between product and minimum. We might have to
think, at least temporarily, about internal storage pools. Nutrient limitation of the instantaneous
photosynthetic rate might be less relevant if the nutrients can be obtained also at night when
there is no photosynthesis to limit. Hurtt and Armstrong (1996) use the minimum of two separate
growth functions, each with its own maximum value, instead of two separate limiting factors for
a single maximum growth rate.
We have dealt so far only with nitrogen as a limiting nutrient. None of the models considered
at the workshop considers carbon or iron as a limiting nutrient. Ruiz-Pino does consider silicate
limitation.
2.4 Bacteria
Bacteria contain both nitrogen and carbon, and we assume that they contain them in a constant
ratio BNC (abbreviated, for this section only, as ). The following description of the issues is
conceptually simple, and none of the models described in Chapter 8 treats bacteria in exactly this
simple way. A dierent account, paying more careful attention to physiological issues, is given
in Anderson (1992). Consider rst the mass balances implied in producing bacteria. Carbon is
available as doc, nitrogen as don + nh4. Thus the amount of bacteria bac (in nitrogen units)
that can be produced is
min( doncar; don + nh4):
Second assumption: although don and doncar are written separately, they are two aspects of
a single substance so that the ratio of the amounts processed is the same as the ratio of the
amounts present. (That is, a dissolved organic molecule is completely broken into its constituents
if it is processed; the bacteria do not simply strip out the nitrogen (if that is what they need)
and leave behind a dissolved organic molecule enriched in carbon. It is not clear how realistic this
assumption is given observations of relatively carbon-rich detritus.) There are then 3 ranges:
1. doncar < don: Carbon is limiting, and there is more than enough nitrogen in dissolved
organic matter to use all the carbon to make bacteria. The excess nitrogen when doncar
is used has to go somewhere, and it is simplest to assume that it becomes nh4.
2. don < doncar < don + nh4: Carbon is limiting, and there is enough extra nitrogen in
nh4 to go with the doncar left over after don is used up.
3.
don + nh4 < doncar: Nitrogen is limiting, and the extra carbon that is processed becomes
CO2 .
When we turn from the amount of product to the rate of production, we make a convenient
and plausible, though by no means logically necessary, assumption: nitrogen and carbon limit
production rate in the same ratio that they limit product. Thus the rate of growth of bac is
doncar
don + nh4
min K + doncar ; K + don + nh4 bac:
N
N
The rst term in the minimum corresponds to the carbon-limited ranges 1 and 2. What are
the rates of use of the constituents (suppressing the common factor bac which multiplies all of
them)? When carbon is limiting, the use of doncar is equal to the carbon growth of bacteria,
8
which is 1= times the nitrogen growth, giving doncar=(KN + doncar). Then the rate of
use of don is don=(KN + doncar). When nitrogen is limiting, we can assume that there is
no preference between don and nh4 so that the rate of use of don is don=(KN + don + nh4).
Combining the two gives don uptake rate:
don
KN + min( doncar; don + nh4)
and doncar uptake rate:
doncar
KN + min( doncar; don + nh4)
The rate of use of nh4 is then what is needed to ensure nitrogen mass balance: the growth of bac
minus the use of don. This works out to
doncar , don
nh4
min K + doncar ; K + don + nh4
N
N
which will be negative (a source of nh4) in range 1.
FDM do not model doncar explicitly; instead they assume that doncar=don is a constant
(1 + ) and that > 0, excluding range 1.
Drange takes a dierent approach in range 1. He assumes that only as much don is processed
as is needed for the amount of doncar instead of processing the two in proportion to their
abundance and `wasting' the excess don as nh4.
Anderson makes the additional point that bacteria use organic carbon as an energy source as
well as a structural material, so that the amount of doncar that appears as new bacteria is less
than the amount used. In range 3, bacteria respond separately to don and nh4 rather than to
their sum. That is, uptake of one form can be saturated while uptake of the other is still in the
linear range.
2.5 Zooplankton
Within these models, each type of zooplankton is modelled as a single variable following a dierential equation. This is believed to be appropriate for protozoa, which are the zooplankton most
active in carbon ux, but it might be less appropriate for copepods with a complicated life history.
The functional forms for grazing as a function of food concentration are not as well established,
either in theory or experimentally. When we are comparing dierent possible functional forms,
it is important that, to the extent possible, parameters are chosen to have the same meaning for
the dierent forms. This will not always be possible, and even when it is the choice will not be
unique. Do two dierent Holling Type I curves have \the same" parameters if they have the same
initial slope and maximum value, or if they have the same maximum value and half-saturation
concentration? If there are two dierent functional forms possible, then the parameters should
ideally have the same meaning for each. For example, Michaelis-Menten and Ivlev forms of grazing are both linear for small food concentrations and constant for large ones. They might be
parameterized by their initial slope, , and maximum value, , (as photosynthesis-light curves
traditionally are):
x and 1 , e,x= + x
or by their maximum value and half-saturation abscissa, K , (as nutrient uptake curves traditionally are):
x
x=K :
and
1
,
0
:
5
K +x
Often grazing is assumed to decrease to zero, or nearly, at small positive food concentrations, either
9
with an explicit threshold or with a functional form whose the slope at the origin is identically
zero. The half-saturation form is more useful here, for example a form that is quadratic for small
concentrations and constant for large ones:
x2 :
K 2 + x2
There are other classes of function, characterized most easily by behaviour at small and large
food concentrations: for example the rational and Mayzaud-Poulet forms that are quadratic for
small concentrations and linear for large:
x2
,cx=
and
x
1
,
e
x + =c
parameterized in terms of their initial curvature c and nal slope .
What if there is more than more one source of food? One possibility is to form a single
variable called food and make grazing a function of that. food is often not a linear combination
of individual concentrations: for example FDM use the formula
food
K + food
where
phy2 + pbac bac2 + pdet det2
= pphy
pphyphy + pbacbac + pdetdet
Notice that this food is not a monotone increasing function of its components: increasing a scarce
prey type decreases the total amount of grazing. The formula was devised to achieve switching of
grazing to the most abundant food type, in the interest of stability. Evans (unpublished) proposed
food
food
= phy (1 + phy c=K ) + bac (1 + bac c=K ) + det (1 + det c=K )
grazing = K (1 + food
c) + food
which accomplishes switching if c > 0 while at the same time making grazing a monotone function
of food density. If there is just one type of prey, then K is the half-saturation concentration. The
formula reduces to Michaelis-Menten when c = 0; when 1 + c is the golden ratio ( 1:62) the
curvature at the origin is zero (the borderline between Holling types II and III).
2.6 Losses to non-living matter
A number of processes can lead to the loss of material from living to non-living pools, for example
natural mortality, cell lysis and virus production, consumption of zooplankton by higher trophic
levels. Although they are generally poorly understood, not directly measured in the eld and
parameterized only crudely in current ecosystem models, the treatment of losses to non-living
pools can profoundly aect the character of numerical simulations. Any transfer may be diverted,
and any compartment tapped, to contribute to one or more non-living components. In the simplest
case the rate of contribution is proportional to the ow (dimensionless allocation fraction bounded
above by 1) or compartment (dimensions of inverse time) but more complicated, non-proportional
functions have been considered, especially for losses from the zooplankton compartment that
might either saturate or increase faster than linearly at high concentrations. There is no reason
in principle why the fraction of a ow diverted might not also change as the ow increases.
10
The functional form of loss terms, and where they are lost to, is almost arbitrary and is best
conveyed by a table with transfers (the arrow indicating what it is transferred to) or compartments
as rows, destinations of losses as columns, and functional forms that have been used in some model
as entries.
!phy
phy
!bac
don
L
det
nh4
no3
L, Q, QL, LE
L
L
L
L
L
L
L
zoo
L
L, Q
QL, L, LQ Q, L
In this table, L denotes a linear (proportional) loss, Q a quadratic loss, LQ a loss that is linear for
small values and quadratic for large like ax + bx2, and QL a loss that is quadratic for small values
and linear for large, like ax2 = (1 + bx). The loss from phytoplankton to detritus can take almost
any form: LE describes the a(ebx , 1) form of Hurtt and Armstrong (1996) that is linear for small
values and exponential for large. In the model of Anderson the fraction of primary production of
carbon lost to dissolved organic carbon increases when inorganic nitrogen concentration is low.
Losses from the zooplankton compartment generally represent the eect of carnivore populations
rather than physiological losses. The quadratic loss term that is common in describing zooplankton
mortality is often justied on the grounds that a large zooplankton population engenders a large
population of carnivores to graze on it, although it omits the time lag that might be expected with
real population dynamics of carnivores. Also, in a vertically resolved model, it is not immediately
clear whether the quadratic dependence should be on the zooplankton at a given level or on the
vertically integrated zooplankton (if the carnivores are capable of changing their depth at will).
bac
!zoo
2.7 The dynamics of non-living matter
The distinction between don and det is easily blurred|they are fed in the same way and decay
in the same ways; the only dierence is that detritus can have a sinking velocity and is more likely
to be used by zooplankton as food. Decay of detritus to smaller classes is modelled; aggregation
of non-living particles to larger classes is not a feature of any of the models considered at the
workshop.
Sinking of particles is the other main reason why biology is important for ocean geochemistry.
Without it, carbon that is locked up in organic or particulate forms would oxidize or dissolve
soon enough and once more be available for exchange with the atmosphere. Sinking particles are
removed from contact with the atmosphere much faster than if they simply moved with the water.
The size, and therefore sinking rate, of particles can change seasonally. For example, following
a spring diatom bloom when there are many small particles ready to collide and aggregate into
larger, rapidly sinking particles. In models with more than one size class of detritus, the relative
abundance and therefore the average sinking rate can change dynamically. Hurtt and Armstrong
(1996) have a single class with a sinking rate that changes according to the biomass in that
component.
A model of the whole water column should include the nitrication of ammonium into nitrate.
This happens mainly at depth, and in Uli Wolf's model the rate is explicitly inversely proportional
to par.
2.8 Inorganic carbon chemistry
Dierent formulations of the equilibrium among bicarbonate, carbonate and dissolved CO2 (Antoine and Morel 1995, Bacastow 1981, Peng et al. 1987) all give much the same answer and cause
11
no great controversy, compared to issues of modelling ecology. There is less consensus about the
role of biology in adding or removing total CO2 and alkalinity.
CO2 is taken up by primary production and some of what is taken up is returned by respiration (the rest is respired at depth and re-enters the surface layer with the water movement).
The production and loss terms are specied in the individual dynamical models (those that have
an explicit carbon component). The most common assumption is that transfers between organic
and dissolved inorganic carbon are the same as between organic and dissolved inorganic nitrogen,
multiplied by a constant Redeld ratio. For the change in alk we need to take account of the
formation of CaCO3 . This is taken as a fraction of primary production: either a constant (20%
on a C-mole basis) or reduced at low temperature by a fraction
:6 (T , 10)]
fCaCO3 = 1 +exp[0
exp[0:6 (T , 10)] ;
where T ( C) is the water temperature. The factor fCaCO3 ranges from 0 to 1; for T =5, 10, 15,
and 20 C, fCaCO3 is close to 0.05, 0.5, 0.95 and 1, respectively. Therefore, at water temperatures
close to 10 C, the biogenic formation of CaCO3 is 10% of the organic material that sinks out of
the euphotic zone.
The total biologically-induced change in alkalinity is then
dalk = ,dno3 + dnh4 , 2 dCaCO3 :
dt
dt
dt
dt
Not all models consider the eect of taking up no3 and nh4.
12
3 Biogeochemical models
This chapter looks at ways to assemble processes into models that predict quantities important
to jgofs. Diagrams describe how nitrogen ows are linked. Their purpose is not to describe
each model precisely (the original papers can be read for that) but to make it easy to compare
the structure of dierent models. The text then describes special features of each model. Tables
of equations, lists of state variables and of parameters are in Chapter 8. In the diagrams, solid
lines represent recipient-controlled ows (uptakes by organisms) from left to right; dotted lines
represent donor-controlled losses, from right to left. The ows are labelled with letters indicating
their behaviour at small and large concentrations. In Ken Denman's model, for example, the
loss from zoo to no3 is a quadratic (Q) function of zoo; the functional response of zoo to phy
approaches quadratic at small phy concentrations and constant at large ones (QC). Responses of
phytoplankton to a single inorganic nutrient in the absence of others are always Michaelis-Menten
functions (LC); other unlabelled uxes are by default linear throughout their range. The det
variable (in all models that have one) also sinks through the water.
3.1 Ken Denman
NO3
PHY
QC
Q
ZOO
This NPZ model (Denman and Gargett 1995) would give answers to most of the questions
that jgofs asks of biology. There may be a case for more elaborate models, once one had
demonstrated that this simplest one was inadequate for some purpose. Even then, a simple model
is an important tool for exploring elaborations of physical structure, parameter estimation, etc.
Primary production is limited by the minimum of light and nutrients. A fraction of all the losses
disappears immediately, as if it had been converted to detritus with an innite sinking rate.
3.2 Scott Doney
DET
NO3
Q
PHY
QL
ZOO
LQ
This 4-compartment NPZD model (Doney et al. 1996) was designed to explore the interaction
of upper ocean physics and biology at the Bermuda Atlantic Time Series (BATS) site on seasonal
time scales, addressing in particular the factors aecting the vertical distribution of chlorophyll and
nutrients, vertical nutrient and particulate uxes, and aphotic zone remineralization. The ratio of
phytoplankton chlorophyll to nitrogen is a dynamic variable depending on light level; this is found
to be important for simulating the subsurface chlorophyll maximum. The eects of nutrients,
13
photoadaptation and light on the phytoplankton growth rate are multiplied. Zooplankton grazing
does not saturate at high food concentrations.
3.3 Dennis McGillicuddy
NH4
PHY
LC
LQ
ZOO
NO3
This 4-compartment model was implemented in a one-dimensional physical model to examine
aspects of the bloom during the 1989 jgofs North Atlantic Bloom Experiment that are primarily controlled by local forcing (McGillicuddy et al. 1995). The inuence of mesoscale dynamical
processes was then studied with the same biological model embedded into a quasi-geostrophic
physical model with a fully coupled surface boundary layer. Primary production uses the Wroblewski formulation for the interaction of no3 and nh4. The use of light is modelled by the Platt
equation, and the light and nutrient limitations are multiplied. The LQ loss from zoo is critical
in maintaining stability in the balance between phy and zoo in cases when the rate of grazing
approaches the rate of phytoplankton growth. Detritus is not treated explicitly in this model,
regeneration of the nitrogen content of this material is assumed to occur instantaneously. Phytoplankton have a sinking speed. A fraction of the losses is lost completely to the system, and is
accounted for in a sediment trap component.
3.4 George Hurtt and Rob Armstrong
NH4
NO3
DET
LE
PHY
There are predictable seasonal changes in the relative abundance of phytoplankton species and
this makes it problematic to represent them by a single phy. As an alternative to simply adding
more phytoplankton components representing dierent species groups, Hurtt and Armstrong's
(1996) model has a small number of carefully parameterized components. They assume that as
phytoplankton biomass increases the relative proportion of larger cells also increases, and they
use allometric relationships to work out the average physiological rates of an assemblage with a
given biomass. Their model was selected, from among many parameterizations attempted, for its
ability to t the 1988-1991 BATS data.
14
Phytoplankton growth is the lesser of light and nutrient functions, and the chlorophyll-tonitrogen ratio adjusts, in response to light and nutrient availabilities, to make the two functions
equal when possible. Day-night dierences in light were integrated out. The use of no3 and
nh4 is described in Chapter 2. Zooplankton are not modelled explicitly; instead a recycling pool
represents the eects of zooplankton, bacteria and non-living organic matter. It is labelled det in
the diagram because the ow into it is donor controlled, but the LE loss function (near linear at
low concentrations and near exponential at high) is chosen to represent the population dynamics
of grazers. Similarly, the sinking rate of det is an LE function (all other models have constant
sinking rates) to account for the preponderance of larger particles when detritus (or zooplankton
making fecal pellets) is abundant.
The model was available at the workshop in a 0-d version. In extending it to vertically resolved
models, it will be interesting to decide if the phytoplankton species composition (and therefore
rates) should be appropriate to the biomass at a given depth or to the average biomass in the
water column (thus leading to partial integro-dierential equations).
3.5 Olaf Haupt and Uli Wolf
NH4
DET 2
Q
LC
NO3
ZOO
QL
PHY
The detritus box in this diagram represents two similar but separate state variables in the
model: large (mostly fecal pellets) and small particles. Large particles sink faster. The model was
designed to simulate particle uxes in the water column in the Norwegian Sea. The nitrication
term and the zooplankton quadratic mortality term are modelled as light dependent functions.
3.6 Veronique Garcon, Isabelle Dadou and Francois Lamy
DON 2
LC DET 2
L
NO3
ZOO
PHY
This is the pelagic component of a coupled pelagic-benthic model of the oligotrophic site of the
eumeli program in the northeast tropical Atlantic ocean (Dadou and Lamy 1996). Zooplankton
15
grazing does not saturate at high food concentrations. The det and don boxes each represent
two state variables in the model. Refractory don is the major form of organic matter in the
water column at the site. Bacterial processes are represented implicitly by the transformations
of detritus to dissolved organic matter and the remineralization of labile don. The eect of
nutrients and light on the phytoplankton growth rate is multiplicative. Light absorption and use
by phytoplankton is modelled according to Morel (1991).
FDM
Although there was no explicit 1-d version of FDM at the workshop (Geo Evans had the original
0-d version working in an optimizing framework; see Fasham and Evans (1995)) there were many
of its descendants with the same `topology' of nitrogen ow. There were subtle dierences as
indicated by the footnotes.
DON
BAC
NH4
(1)
(5)
PHY (2)
(1)
NO3
LC
(4)
ZOO (2)
(5)
(3)
DET (2)
(1) In Tom Anderson's and Helge Drange's models these losses are QL; in other models they
are linear. Tom Anderson's model has no loss from zooplankton biomass to don (but see (4)).
(2) Diana Ruiz-Pino has two compartments for each of these components.
(3) Diana Ruiz-Pino also has silicate as a dynamical variable, which limits the uptake of one
of the phytoplankton boxes. It is supplied only from deep water, not from in situ regeneration.
(4) Tom Anderson's grazing losses also go to don and nh4.
(5) Diana Ruiz-Pino's model only.
FDM was originally designed to investigate what controls the ratio of new to regenerated
production, and also the role of bacteria in producing regenerated nutrients. In contrast to other
models considered at the workshop, it has two dierent production processes|one obtains its
carbon and energy from light, the other from dissolved organic matter. It has been widely used
in jgofs; the quantities it predicts correspond closely to the list of jgofs core measurements.
Primary production uses the Wroblewski formulation for the interaction of no3 and nh4. The
use of light is modelled by the Smith equation, with response to diel variation integrated under the
16
assumption that light varies during the day according to a triangle with the correct base and area
to represent day length and total light. Light and nutrient limitations are generally multiplied.
3.7 M.K Sharada
The grazing of zooplankton in this model diers from FDM. Although it has an LC form, it does
not exhibit switching to the more abundant prey. It has been applied in the Arabian Sea.
3.8 Tom Anderson; Helge Drange
The models described so far have had nitrogen as their sole currency, and the implications for
carbon have been through constant Redeld ratios. The models of Anderson and Drange consider
non-living forms of carbon and nitrogen as separate state variables. They are produced by dierent
organisms in dierent ratios. Because bacteria require don as a carbon source, the growth of
bacteria is a more complicated function of the element ratios in dissolved organic matter, and the
availability of ammonium as a supplement if required.
3.9 Diana Ruiz-Pino; Pascal Prunet
These closely-related models investigate coupled element cycles. Diana Ruiz-Pino's model (Pondaven et al. in press) computes the nitrogen (and implicitly carbon) content of 5 living compartments and 2 sizes of particulate detritus, the silicon content of large phytoplankton and the
2 detritus classes, and 4 dissolved variables (3 forms of N plus silicate) for a total of 14 state
variables. Pascal Prunet's model (Prunet et al. 1996a) omits the large phytoplankton variable
and does not model Si in any form, but adds a third detrital size class for a total of 10 state
variables. Both models consider dissolved oxygen consumption and production.
3.10 David Antoine
Instead of predicting the dynamical changes of state variables, the model of Antoine and Morel
(1995) is designed to compute concentrations and uxes of CO2 and other quantities given the
chlorophyll concentration. The model provides the annual cycles of CO2 and oxygen concentrations and uxes at the air-sea interface, and of organic carbon, oxygen and nitrate within the upper
water column and exported to deeper levels. Variations in the physical environment are computed
with a turbulent kinetic energy model forced by meteorological data. The biological submodel
computes photosynthetic carbon xation, by making use of a spectral light-photosynthesis model.
The fate of the organic carbon produced through photosynthesis is evaluated from the temporal
evolution of the chlorophyll biomass (for instance as detected from space), combined with the
Eppley factor (the \f-ratio"). This \tethered" model has been designed to be mainly driven by
satellite data (chlorophyll, irradiance, temperature, wind speed).
17
4 A common physical arena
Comparing the behaviour of ecosystem models is more dicult if each is driven by its own onedimensional mixed layer model. Participants decided to develop a common physical arena, in
which each ecosystem model in turn would be embedded. This section starts with a brief account
of current 1-dimensional models of vertical mixing, and then describes conceptual and practical
progress before and during the workshop towards a common physical arena.
4.1 Current state of physical models
The air-sea exchange of momentum, heat and fresh water drive mixing in the surface ocean through
physical mechanisms such as Langmuir cells, shear instability and buoyancy-driven convection
(Large et al., 1994; Archer, 1995). Fortunately, the details of the physics are not always important
and are often condensed into a single measure of the vertical mixing prole, the turbulent eddy
diusivity Kz (z ). The time evolution of the mean prole of a species X (z ) is then given by:
@X = ,r~u X + @ K @X + Source
@t
@z z @z
with terms for mean advection, vertical turbulent mixing, and sources such as in situ biological
transformations. The classic depth prole for Kz includes a surface mixed layer with large (O(500)
cm2 s,1 ) diusivities above a stratied interior with small (O(0.1) cm2 s,1 ) diusivities generated
by internal wave breaking and double diusion (Gregg, 1987; Ledwell et al., 1993, Large et al.,
1994). Most models capture the basic seasonal mixed layer structure, though they can dier greatly
on specic details. The two regimes are separated by a transition region where the entrainment
into the mixed layer actually occurs, and it is in this transition region where the behavior of the
physical models tends to diverge. The choice of model depends in part on the application and
level of desired sophistication of the physics. More in-depth discussions are presented in a recent
series of review articles and model intercomparisons (Martin, 1985; Large et al., 1994; Archer,
1995).
Many upper ocean models do not compute an upper Kz but instead assume that there is a
homogeneous \mixed layer", the equivalent of setting Kz to a very large value; this class of models
then focuses on computing the entrainment/detrainment rate across the base of the mixed layer
(Kraus and Turner 1967, Price et al. 1986). Mixed layers are not always present in the ocean and
may be well mixed for some species, for example temperature, but not others depending on the
relative timescales of turbulence and the local source/sink terms; this may be particularly relevant
for biological species that undergo signicant diurnal cycles (Stramska and Dickey, 1994; Doney et
al., 1996). Turbulence closure (Mellor and Yamada 1982; Gaspar et al. 1990; Kantha and Clayson
1994) and K-Prole (Large et al. 1994) approaches, in contrast, compute large nite mixing rates
near the surface that increase with surface wind stress and unstable surface buoyancy forcing (i.e.
net cooling and evaporation).
The development of a 1-D physical model for use in biogeochemical simulations is not a trivial
task, involving the collection of the appropriate forcing and verication data sets as well as the
actual model simulations (Doney, 1996). One alternative that has been suggested is to use historical temperature and salinity proles to diagnose a mixed layer depth, and then use that depth
as one would in a bulk mixed layer model (e.g. Bisset et al., 1994).
In a further simplication, several models at the workshop (Evans, Hurtt & Armstrong, Anderson) ran the biogeochemical model in a so-called 0-D or bulk mixed layer arena. Here the mixed
layer depth changes with time, and one must account for entrainment and detrainment across the
bottom boundary. The physical exchange is specied from the rate of change of the boundary layer
18
depth hml , the background upwelling/downwelling velocity w, a turbulent exchange velocity wt
across the base of the mixed layer, typically taken as order a few tenths of m d,1 , and the species
concentration X0 below the mixed layer. Vertical advection is often treated as an asymmetrical
process with mixing of surface and subsurface water occurring during entrainment or upwelling
(w > 0) and no concentration change for detrainment (w < 0). The rate of change for the average
concentration over the mixed layer is then given by:
dX = wt + max(w + dhml =dt; 0) (X , X )
0
dt
hml
(1)
An exception is generally proposed for zooplankton, which are assumed to concentrate in shoaling
mixed layers (Evans and Parslow, 1985).
4.2 Activities prior to the Workshop
Various one-dimensional mixed layer models were run with the same surface forcing for the period
1975-77 at Ocean Station P in the subarctic North Pacic Ocean, with the aim of choosing single
mixed layer physical model in which to compare and optimize the various biogeochemical models
(see Chapter 7).
It was decided to provide a common kinematics rather than dynamics. This gives the option
of exploring a dynamically incorrect model, for didactic purposes. Also the dynamics requires a
shorter time step than the bgc does, and fast-running models are an asset for parameter estimation.
The common output should include vertical mixing rate, vertical velocity, temperature, and light as
functions of time and depth. We turn o one feedback: the eect of phytoplankton concentration
on the penetration of radiant heat from the surface and thence on vertical mixing. This was
a deliberate choice that enabled us to compare all biogeochemical models in the same physical
framework.
4.3 Activities During the Workshop
It was obvious from the collected behaviour of the bgc models that modelled vertical diusion
below the mixed layer is too small to supply nutrients to the euphotic layer at Station P. An extra
physical mechanism, such as Ekman upwelling, is needed to supply nutrients to the surface to
replenish those lost to exported production.
One complication was that the models do not use a common bottom boundary condition. The
0-D models could probably easily implement a common bottom boundary condition, but it would
be less straightforward with 1-D models. Obvious questions are whether the models specify nitrate
ux or nitrate concentration as the bottom boundary condition and whether the bottom boundary
condition for temperature and salinity was the same as for nitrate and other state variable.
We discussed several possible mechanisms for supplying nitrate to the surface layer:
(i) Increase Kz below the mixed layer arbitrarily, to values greater than are physically acceptable, in order to achieve a larger upward diusive ux of nitrate from the bottom boundary.
(ii) Specify isopycnal (essentially horizontal) diusion by estimating the isopycnal nitrate gradient (at scales greater than the mesoscale) and the isopycnal (or horizontal) turbulent diusion
coecient Kh along isopycnals.
(iii) Specify Ekman upwelling at the base of the model. This option would be appropriate
for Station P, but might not suce at Bermuda where part of the year the surface ocean ow is
convergent with presumably a downwelling transport.
The simplest implementation is to specify a nitrate concentration immediately below the model
and a vertical upwelling current speed decreasing linearly from some value w = w,h at the base
of the model z = z,h , to w = 0 at the ocean surface z = 0. Such a recipe is divergent everywhere
within the model domain, removing the need to specify values or horizontal gradients outside the
19
model column itself. Within the model the conservation equation (without sources or sinks), for
the nutrient N can be written as:
@N + r(u N ) = 0:
@t
(2)
@N = ,w @N
@t
@z
(3)
If we assume incompressibility and horizontal homogeneity, this reduces to vertical advection:
If we specify the state variable n at the gridpoint at the centre of each layer k and the upward
advection at each interface, as in the diagram, then we can use an upstream nite dierence
equation for the nutrient advection:
Nk = ,t wk+1(Nk , Nk+1 )=z:
(4)
Below the bottom interface, we specify a deep reservoir value for the nutrient Nd . Therefore, for
the bottom layer m, eq. (5) becomes
Nm = ,t w,h(Nm , Nd )=z:
(5)
interface
mid-layer
wk , (log10 Kz )k
Nk
wk+1 , (log10 Kz )k+1
Nk+1
After the workshop, Ken Denman implemented this algorithm in his NPZ model coupled to a
non-diusive mixed layer model. A reasonable value for w,h of 30 m/yr in the Alaskan gyre (e.g.
Gargett 1991) more or less balanced losses for an eective f-ratio of about 0.2
(iv) Restore or reset the nitrate values below the mixed layer to climatology. This option,
chosen during the workshop because it makes the fewest assumptions about the underlying physical
processes, allowed the recharging of nitrate in the surface layer during autumn and winter as the
mixed layer deepens to its maximum winter penetration. This raises the issue of whether it makes
sense to use a climatological mean vertical prole of nitrate without also using climatological
forcing and mixed layer depth. For example, the 1976 nitrate observations had large variations
below the mixed layer (eddies?) which showed little resemblance to the climatological annual
nitrate cycle from Matear (1995). Do we use a mean annual prole or an annual climatological
cycle, although Matear's plot did not show a clear annual cycle? Resetting rather than restoring
(relaxing to climatology according to some specied timescale) is easy to implement but may
cause problems with ordinary dierential equation solvers and the optimisation scheme. During
the workshop, we eventually settled on resetting the nitrates below the mixed layer to a mean
vertical prole estimated from Matear (1995).
4.4 Implementing a Common Physical Arena
During the workshop, we discussed in detail several specic aspects of implementation of a common
physical arena; the results of these discussions are summarized below.
20
(i) Atmospheric forcing. For surface solar radiation, winds, heat uxes, the options (for station
P) are (a) the 3-year time series (1975-77), (b) a mean annual cycle derived from the three years
1975-77, or (c) a long term climatological annual cycle, if available.
(ii) Mixed layer depth. The same three options are available, where the rst two would be
calculated from the Ruiz-Pino model output (see Chapter 7). The climatological annual cycle in
mixed layer depth could be taken from Matear (1995), but his summer mixed layer depth seemed
too spikey, without an expected level or gradually deepening plateau as summer progressed. The
diagnosed climatological mixed layer depth provided by Howard Freeland (Institute of Ocean
Sciences, Sidney, B.C.) seemed too deep in spring and summer because it tracked that maximum
gradient in density rather than the initial increase at the base of the mixed layer.
(iii) Annual cycle in Kz (z; t). The mixed layer depth from the models was not used directly.
The Kz (z; t) eld was used to choose which physical model to use to drive the ecosystem models. If
we were to use a climatological annual cycle of mixed layer thickness, and say there is one constant
Kz within the upper mixed layer (we chose 3 10,2 m2 s,1 above zM ) and another constant Kz
in deep water (we chose 3 10,5 m2 s,1 below zD ), then Kz (z ) within the transition zone could
be specied as follows:
log Kz (z ) , log Kz (zM ) = 2 (3 , 2 ) where = z , zM :
log Kz (zD ) , log Kz (zM )
zD , zM
The cubic function of scaled depth ensures a smooth, spline-like join to the assumed constant
mixing rates above and below; the logarithmic transformation is appropriate because the mixing
rates above and below dier by several orders of magnitude.
(iv) Restoring or resetting nitrate below the mixed layer. Restoring rather than resetting
nitrate below the mixed layer reduces the possibility of introducing problems with the integrator/solver method used. We thought that a restoring time scale of 1 day would be appropriate with
a restoring coecient of 1 in deep water and 0 in the upper mixed layer, with a cubic polynomial
transition in between.
21
5
Surface forcing
Surface forcing inuences marine ecosystems both directly (e.g. solar radiation, nutrient inputs)
and indirectly through modications of the physical environment and upper ocean boundary layer.
This chapter discusses the air-sea uxes of momentum, heat, fresh water and dissolved gases airsea uxes of heat and solar radiation; although, dened more broadly, forcing could include the
vertical turbulent mixing eld as well as any ux (e.g. momentum, energy, or material) across
the top, sides and bottom of the model domain. From a biogeochemical perspective, the most
important outputs from the physical model solutions are the elds of temperature T and vertical
diusivity K (m2 s,1 ) as functions of time and depth (see Chapter 4). Moreover, compared to a
dynamical model of mixing, a bgc model needs to know these quantities at relatively infrequent
intervals, which is more ecient.
Most one dimensional physical models require at a minimum the net surface uxes of heat Qnet ,
freshwater Fnet and, in most cases, momentum . Air-sea uxes are dicult to measure directly,
and the spatial and temporal variability of atmosphere-ocean exchanges are one of the more poorly
known aspects of the climate system (e.g. Weller and Taylor, 1993). More often surface forcing is
specied using an empirical formula, calibrated at a few locations, and surface atmospheric data
taken from observations (e.g. meteorological buoys and drifters, research vessels, merchant ships;
e.g. Weller, 1990), climatologies (e.g. Isemer and Hasse, 1985a) or operational weather models
(e.g. Kalnay et al., 1996). Some uxes, in particular downward solar radiation and precipitation,
are frequently calculated from satellite- or atmospheric-model-derived data products. A basic
framework for how air-sea uxes are computed for physical models is presented below, followed
by a limited outline of available surface forcing and upper ocean data sets.
Perhaps the most straightforward forcing method is to restore the model surface temperature
T and salinity S elds to observed values (T0 , S0 ) with a relaxation timescale :
s
s
Qnet =
zc
(T0 , T )
s
Fnet =
p
s
z
(S , S )
S 0
s
s
s
where z is the thickness of the surface layer and c and are the heat capacity and density of
seawater, respectively. Surface restoring accounts for both air-sea uxes and ocean advection, and
remains a common, stable method for forcing 3-D ocean circulation models. A major drawback
with restoring, however, is that the uxes are identically zero when the model elds match the
observations, leading to weak seasonal cycles that lag those in the data. Numerous improvements
to the restoring method have been proposed (Haney, 1971), but the use of surface restoring is
currently not widespread for 1-D upper ocean models.
A more common approach is to compute the air-sea uxes of momentum, heat and freshwater
using traditional, bulk surface formulas. The bulk formulas require estimates of wind speed, air
temperature, air humidity, cloud cover and sea surface temperature. The air-sea uxes can be
computed using either xed observed values or predicted elds from the 1-D upper ocean model,
which can lead to feedbacks between the model solution and air-sea uxes (e.g. Large et al., 1994;
Doney, 1996). A third alternative is to use uxes specied from atmospheric climate or weather
models (e.g. Dadou and Garcon, 1993); it should be noted, however, that the turbulent uxes from
the models are computed with formulas very similar to those given below. For long integrations,
care should be taken to ensure that over the annual cycle the net air-sea uxes combined with
any subsurface horizontal and/or vertical uxes balance to near zero.
The general bulk form for the ux F of property X is:
s
p
X
F
X
/ C W10(X , X )
X
a
22
s
where C is a property-specic empirical drag coecient, W10 is the 10 m wind speed, and X and
X are the air and surface values of X . The drag coecients vary both with wind speed and lower
atmospheric stability, and appropriate corrections can be applied based on the air-sea temperature
and humidity dierences (e.g. Arya 1988). When the atmospheric boundary layer is unstable, i.e.
the surface potential air temperature is warmer than that of the air above, convection within the
atmospheric boundary layer can ensue, and the eective transfer rates increase for the same wind
speed and atmosphere-ocean gradient. Conversely, stable conditions damp atmospheric boundary
layer turbulence, reducing air-sea exchange.
X
a
s
5.1 Momentum
The downward transfer of momentum from the atmosphere to the ocean plays an important
role in mixing the surface ocean through the production of near-surface turbulence and shear
instability mixing. The winds also generate the surface wave eld, which may play a role in
Langmuir circulation (Weller and Price, 1988), and contribute to the exchange of trace gases (e.g.
Wanninkhof, 1992). The zonal and meridional wind stress components and can be computed
from bulk formulas (Large and Pond, 1981):
x
y
= C U10 W10
x
a
D
= C V10 W10
y
a
D
where U10 and V10 are the 10m zonal and meridional wind components, is the air density and
C is an empirical drag coecient. One form of the neutral, 10 m drag coecient is given by:
2
:70
+ 0:142 + 0:0764W 10,3 :
C =
a
D
N
10
W10
D
The drag coecient C is then increased (decreased) when the atmospheric surface layer is unstable (stable) based on similarity theory (Large and Pond, 1981; Arya, 1988).
D
5.2 Heat
The net air-sea heat ux Qnet can be partitioned as the sum of the sensible, latent, net longwave,
and net shortwave uxes:
net
Qnet = Qsen + Qlat + Qnet
lw + Qsw :
The turbulent heat uxes, Qsen and Qlat , are typically computed from empirical air-sea transfer
relationships (Large and Pond, 1982):
,T )
Qlat = LC W10 (q , q )
Qsen = c C W10 (T
a
a
a
p
H
E
a
a
s
s
where c and L are the specic heat of air and latent heat of water, and T and q are the sea
surface temperature and saturated specic humidity. C and C are the transfer coecients for
heat and water, and one set of neutral forms is given by:
a
p
s
H
C
C
C
s
E
= 32:7C 1 2 10,3 when the lower atmosphere is unstable
= 18:0C 1 2 10,3 when it is stable
= 34:6C 1 2 10,3 :
=
H
D
=
H
D
=
E
D
Drag coecients for the bulk formulae are traditionally computed for a reference height of 10 m,
and atmospheric data from other levels should be adjusted to 10 m height using Monin{Obukov
similarity theory with appropriate stability corrections (Large and Pond, 1982; Arya, 1988).
23
The net longwave radiation Qnet
lw is the dierence between large upward and downward infrared
uxes and depends upon the atmospheric water vapor prole and vertical cloud distribution. One
approach is to compute the net longwave ux from a full column 1-D atmospheric radiative transfer
model (e.g. Fung et al., 1984). Several empirical formulas based solely on surface properties have
also been proposed (Fung et al., 1984; Breon et al., 1991), an example of which is that of Berliand
and Berliand:
4
05
3
Qnet
lw = , T [0:39 , 0:05(e ) ]F (C ) + 4T (T , T )
where T and T are in Kelvin, e (mbars) is the surface water vapor pressure, is the surface
emissivity taken as 1.0, and is the Stefan-Boltzmann coecient equal to 56710,10 W m,2 K,4 .
F (C ) is a cloud correction factor following Budyko (1974):
a
a
s
a
:
a
s
a
a
F (C ) = 1 , a C 2
c
where the cloud fraction C varies from 0 to 1, and a is a latitude-dependent empirical coecient
adapted by Fung et al. (1984) from Bunker (1976). As estimators for the instantaneous net longwave ux, the empirical formulas generally fare poorly; but they may be adequate for monthly
mean values, especially when the cloud height data required for the radiative-transfer models is
not often known (e.g. Breon et al., 1991). Under limited circumstances, direct measurements of
the upward and downward longwave uxes may be available from buoys (e.g. Weller, 1990).
Similarly, the net shortwave ux is a function of both the clear and cloudy sky transmission
and can be computed from atmospheric radiative transfer models (e.g. Bishop and Rossow, 1991;
Pinker et al., 1995) or from empirical relationships (e.g. Reed, 1977; Dobson and Smith, 1988).
The radiative transfer models can be formulated to predict the bulk shortwave ux or the full
spectral distribution if needed (see Chapter 2). With the advent of the International Satellite
Cloud Climatology Project (Rossow and Schier, 1991), the spatial and temporal coverage for
cloud cover is sucient to fully use the power of the radiative transfer model approach. The
presence of clouds has an opposite and partially compensating eect on longwave (warming)
and shortwave (cooling) forcing of the ocean surface, and it is important, therefore, to have a
consistent treatment of clouds for both radiative components. In addition, direct measurements
of the downward shortwave ux are available in some locations from research ships, meteorological
buoys, and more recently surface drifters (e.g. Weller, 1990).
The ocean surface albedo :
down
Qnet
sw = (1 , )Qsw
can vary from 3% up to 45% for low zenith angles and calm conditions; however, the albedo for
diuse radiation under overcast skies is only about 6%, which is also a typical value for general
use (Payne, 1972). Shortwave radiation penetrates into the water column producing subsurface
heating. Many models have specied the heating rate prole using a two-band approximation
(a red and infrared band absorbed within the upper meter and a deeper penetrating blue-green
band) (e.g. Paulson and Simpson, 1977; Simpson and Dickey, 1981), though more sophisticated
approaches are available (e.g. Kantha and Clayson 1994; Morel and Antoine, 1994).
c
5.3 Fresh water
The net air-sea freshwater ux Fnet is the sum of the evaporation (< 0) and precipitation rates.
Evaporation is given directly from Qlat by dividing by the latent heat of freshwater as a function of
temperature. Ocean precipitation rates are not well known in general, and climatological estimates
have been created by combining precipitation frequency ship observations with coastal and island
rain-gauge data (e.g. Dorman and Bourke, 1979; 1981; Schmitt et al., 1989; Montgomery and
Schmitt, 1994). Satellite precipitation algorithms (e.g. Spencer, 1993) oer the prospect of
knowing the temporal variability better, but the uncertainty is still rather large (Schmitt, 1994).
Unlike the heat ux, there is no direct negative feedback from surface salinity to freshwater ux.
24
Despite several decades of research, the uncertainties in present air-sea heat and freshwater
ux estimates generally remain signicantly above those required for ocean boundary layer and
climate models (total heat ux 10-15 W m,2 , net freshwater ux 0.15 m y,1 (e.g. Weller and
Taylor, 1993; OODSP, 1995), though signicant advances have been made for limited duration,
intensively sampled eld campaigns such as TOGA-COARE. In part, this problem arises from a
fundamental mismatch in the space and time scales of satellite data versus direct measurements
from ships and buoys. Future gains may depend heavily on the assimilation of these diverse
measurement techniques into numerical weather prediction models.
5.4 Gas exchange
Depending on their complexity, biogeochemical models may require a number of additional surface forcings beyond the standard set used by physical models. The discussion of the surface and
subsurface photosynthetically active radiation (par) was presented in the context of the biogeochemical processes that use it (Chapter 2.) Other important biogeochemical uxes include air-sea
gas exchange (e.g. DMS, CO2 , O2 ), wet and dry nutrient deposition (e.g. Knap et al., 1986), and
aerosol input of trace metals. The details of air-sea gas exchange are still under debate|related
to the surface wave, ocean turbulence, surface lms, and bubble elds|but for many situations
empirical wind-speed dependent parameterizations (e.g. Liss and Merlivat, 1986; Wanninkhof,
1992) will suce. The current scatter in the empirical wind speed{gas exchange relationships
is approximately a factor of two, though this may in part reect dierent methods for scaling
between gas species and for averaging wind speed over time (Wanninkhof, 1992). The processes
controlling nutrient input and aerosol deposition depend more on terrestrial source patterns and
large-scale atmospheric transport and are thus more dicult to estimate from local data alone.
5.5 Data sets
Adequate atmospheric and water column observational data are crucial for 1-D numerical models
both to drive the physical simulations and to verify the physical/biogeochemical solutions. Even
with the recent intensive jgofs eld programs, the number of sites with sucient meteorological
and water column observations for detailed upper ocean modeling remains limited.
Not surprisingly, much of the 1-D modeling eort to date has focused on the ocean weathership data sets, in particular Station P in the subpolar North Pacic (145 W, 50 N) (e.g. Denman,
1973; Denman and Miyake, 1973; Martin, 1985; Gaspar et al., 1990; Large et al., 1994). Available
meteorological and oceanographic data for Station P include all of the standard surface measurements (e.g. SST, air temperature) on 3 hour time scale (Martin, 1985; Tabata, 1965) from which
the turbulent surface heat and freshwater ux estimates can be derived (e.g. Tricot, 1985; Large et
al., 1994). Additional ancillary forcing data including surface solar irradiance (Dobson and Smith,
1988) and precipitation (1954-1970; Knox, 1991) were also measured at Station P. Further, many
of the empirical air-sea relationships discussed above were developed and calibrated using Station
P data (e.g. Dobson and Smith, 1988). A variety of long-term biogeochemical datasets were also
collected at Station P including chlorophyll, nutrients, primary production, surface pCO2 , and
oxygen (e.g. Thomas et al., 1990; Archer et al., 1993; McClain et al., 1996).
Other weathership data sets include OWS Bravo in the Labrador Sea (56 N 51 W; meteorological data 1946-1974, hydrographic data 1964-1973) (Smith and Dobson, 1984), OWS November in
the subtropical Pacic (30 N 140 W) (Martin, 1985), and OWS India in subpolar Atlantic (59 N
19 W, biogeochemical data, 1971-1975) (Williams and Robinson, 1973).
The weathership data are unique because of their continuous coverage over extended time
periods. Several other local time-series sites exist, though of more limited temporal duration and
in many cases lacking the supporting meteorological data. These include, but are not limited to,
the jgofs-supported time series sites near Bermuda (BATS; Michaels and Knap, 1996), Hawaii
25
(HOT; Karl and Lukas, 1996), the kerfix station near the Kerguelen Islands in the Indian part of
the Southern Ocean (Pondaven et al., in press; Jeandel et al., 1996), and the Canary Islands. The
jgofs process studies (e.g. NABE, 1989-1990; Ducklow and Harris, 1993; EUMELI, 1991-1992;
Morel, 1996; EqPAC, 1992, Murray et al., 1995; Arabian Sea, 1995) may also provide a resource
for seasonal timescale modelling, though it is usually dicult to reconstruct more than one- or
two-year records.
Surface meteorological moorings oer continuous coverage with temporal resolution of approximately 15-30 minutes: an attractive alternative to ship-based time-series stations (e.g. Dickey,
1991; Dickey et al., 1992). Mooring data are often supplemented with water column physical
(e.g. velocity, temperature) and bio-optical measurements that are also valuable for assessing 1-D
models. Examples of biogeochemical mooring data sets of seasonal to multi-year duration include
the LOTUS and BIOWATT experiments in the subtropical North Atlantic and the MLML experiment in the subpolar North Atlantic south of Iceland (Dickey, 1991). As mooring technology
progresses, they are also becoming a more common component of jgofs process studies. An
extension of the mooring concept, the deployment of the operational TOGA-TAO array in the
Equatorial Pacic has opened up a new era in ocean monitoring, greatly expanding the quantity
and character of surface atmosphere and ocean data available for ocean modeling.
In many instances, however, detailed local measurements are not available, and one must
rely on either climatological data, operational weather forecast models or satellite data sets (e.g.
Dadou and Garcon, 1993; Doney, 1996). Climatologies are primarily derived from the volunteer
merchant ship reports (e.g. Bunker, 1976), with the COADS data representing the most up to
date and extensive archive (Woodru et al., 1987). The data is concentrated in regions of heavy
ship trac such as the North Atlantic and North Pacic, and there is, for example, generally
only poor coverage in the South Pacic and Southern Ocean. Regional (e.g. Isemer and Hasse,
1985a,b) and global (e.g. Esbensen and Kushnir, 1981; Oberhuber, 1988) surface elds and air-sea
heat and freshwater uxes are available generally with monthly resolution. Several wind stress
climatologies have also been created (Hellerman and Rosenstein, 1983; Trenberth et al., 1989).
Monthly climatologies are also available for surface ocean temperature (Levitus and Boyer, 1994)
and surface salinity (Levitus et al., 1994). Other resources include cloud cover (e.g. Warren et al.,
1988), ocean precipitation (e.g. Legates and Wilmott, 1990; Jaeger, 1976) and nutrient (Glover
and Brewer, 1988) climatologies.
The archived analysis data and forecasts from several operational meteorological models are
available (e.g. National Meteorological Center; European Center for Mid-range Weather Forecasting ECMWF; Fleet Numerical Oceanographic Center). Two products are available from the
operational centers, an analysis data product which combines previous model forecast elds and
observations through 4-d data assimilation and the actual model forecast elds, which include
air-sea ux estimates as well as surface properties. The analysis data is typically provided at 6
hour resolution on a coarse global grid (1.125 by 1.125 for ECMWF).
Satellite data products provide a data resource complementary to numerical models and ship
observations, particularly for the more remote, data-poor regions of the global ocean. The algorithms used to derive surface data from satellite measurements are generally empirical and may
depend heavily upon atmospheric transmission corrections; further, satellite measurements in the
visible and infrared bands may be often obscured by clouds. Nevertheless, satellites provide a
powerful tool for exploring ocean behaviour on spatial and temporal scales that are simply not
observable from local platforms. Satellites are currently providing estimates for a wide range of
surface properties (e.g. Weller and Taylor, 1993) including wind speed (Etcheto and Merlivat,
1988), sea surface temperature, latent heat ux (Liu, 1988), daily cloud fraction (Rossow and
Schier, 1991), surface insolation (Bishop and Rossow, 1991), and precipitation (Spencer, 1993).
In terms of biogeochemical models, ocean color measurements are invaluable as large-scale observable quantities for model verication, and with the imminent launch of both SeaWifs and OCTS,
the historical CZCS database (Feldman et al., 1989) will soon be greatly augmented.
26
6 Running models, comparing with observations, interpreting
6.1 Running a model
We compare observations not with a model, but with one realization of it, determined partly
by the model structure, but also by the parameter set, driving variables, initial conditions, and
algorithm for numerically approximating the solution of the model equations. There is a further
question of whether the observations play any explicit role in the model realization. In the model
of David Antoine, for example, chlorophyll concentration is determined from observations, and
the model is used not to compute the changes in chl but instead to compute one component
of the bgc uxes associated with the variable, namely primary production. We might say that
chl is tethered: the model indicates one component of how fast it changes, but doesn't follow it.
CO2 and O2 are free dynamical variables. It would be a useful additional step to compute the
forces on the tether: given the rate of change implied by the primary production calculations, how
large must the loss terms be in total to produce the observed trajectory of chl? A more exible
option is to let the model run freely in between observations but then make adjustments to the
state variables to bring them back towards available observations. Activities at the workshop were
concentrated on model runs that were not explicitly aected by observations after they started.
6.1.1 Driving variables
In addition to the physical considerations of the previous two chapters, there is a more philosophical question. The ocean does not repeat itself exactly year after year; do we wish to use
real forcing that varies between years? There are advantages to this approach. That's the way
the ocean was, why pretend otherwise? It is the real ocean with its between-year dierences that
generated the variables that were observed, with which we want to compare model results. Yearto-year variations exercise the model in a wider range of conditions and thereby provide more
stringent tests of its performance.
Nevertheless, there are arguments for exploring the response to periodic forcing indenitely
prolonged. The questions that jgofs poses are more about the behaviour of an average ocean
than about the accidents of a particular year: how does the ocean work, in general; not how
exactly did it work in 19XX? Long-term persistence is as much an observation as the results of
a particular eld program, and just as important for a model or model parameter set to predict.
(Multi-year time-series like BATS will impose a requirement for persistence).
In addition to the philosophy, there are technical issues either way. If we are going to run
the model for a few years with real forcing, we must establish initial conditions; for a vertically
resolved model this means initial proles for all the state variables. Typically there are not
enough observations to enable one to do this, and if they are initialized wrongly the period of
adjustment can easily be 30 years: longer than the time series we aim to match. Estimating, as
model parameters, all the numbers that would be required to specify the starting proles creates
problems. If we run the model with eternally repeating forcing, then the long-term behaviour is
usually independent of initial conditions and so there is no need to know or estimate them. But
we do not know the climatological cycle to use for driving: we can only hope that the average of
the few years we do have is close to the long term average cycle. Because of non-linear eects, it
is probably best to make the average as late as possible, and construct a climatology of mixing
rates, not of surface forcing, if we can. It is probably best to try both approaches { real and
average forcing { and acknowledge the weaknesses of each. When it makes a big dierence to
goodness-of-t or parameter estimates, we have an indication of where the whole of jgofs needs
to do more work.
27
Similar issues arise over the question of how smooth we make the driving variables. Do we
want to take account of day-night dierences? storms? Again, we are pulled in the direction of
more detail by the data sets we want to compare with, which have been aected by all the detail
there is. We are pulled in the direction of less detail by the nature of jgofs and the questions
it wishes to address. jgofs contains the assumption that we know enough about the ocean at a
coarse, smoothed scale to be able to make statements about global carbon ow abstracted from
all the details. So models abstracted from all the details are in a sense more true to the nature
of jgofs than detailed data sets are. We want to capture the essential variability for addressing
jgofs questions, rather than all the variability there is. This requires some experimenting to
determine which variability should be explicitly represented, which parameterized, and which left
unresolved. If we do choose to represent day-night dierences in light, consistency would suggest
taking account also of dierences in mixing caused by nighttime cooling and convection (Wolf and
Woods 1992).
6.1.2 Algorithms for solving the model equations
One dierence among common algorithms is whether they use a xed time step or let the algorithm
adjust the time step to be as great as possible consistent with desired accuracy and times of output.
Aside from gains in eciency, automatic time step adjustment can also provide more accuracy
when required; model runs that don't use it not uncommonly end up with negative concentrations:
a warning that even when they are not negative they are likely to be inaccurate. However, when
a model is run with two slightly dierent parameter sets it will probably choose slightly dierent
series of time steps for each, and this introduces a small random component into the solution:
not enough to be important for people examining the output, but sometimes important enough to
confuse other software, for numerical optimization, that thinks it is dealing with a smooth function
of its parameters. Another dierence is between forward- and backward-dierence (explicit and
implicit) methods. Vertically resolved models are typically sti: mixing in the upper mixed layer
equilibrates more quickly than the ecological processes of interest. Backwards dierence methods
can often get away with much large time steps.
There is another advantage to dealing with smoothed driving variables: the state variables
we wish to predict will as a consequence vary more gradually and routines that approximate
solutions of systems of dierential equations can reach their answers with less computing eort|
often orders of magnitude less. This does not matter much if the model is to be run just once;
but if it is to be run repeatedly, for example with many dierent parameter sets seeking a best
set, then the time a single model run takes can determine whether the research can be carried out
practically or not. This is an advantage one should be careful of invoking, because of the danger
that the scientic questions we wish to address will be steered by considerations of what we can
compute easily rather than what we believe to be true. On the other hand, if the distance between
a quick-to-compute model and a slow-to-compute model is small compared with the distance of
either from the full complexity they seek to represent, then it may make sense to explore the cheap
model rst and more fully.
6.2 Comparing with data
We are approaching the key question: How do we combine models and data to address the
questions of jgofs? What data are available and suitable for comparison with model output,
what (beyond visual comparison) is a good measure of the degree of t or mist between model
and data, how do we use the data to help select model parameter values, and how do we use the
data to help select among dierent models?
28
6.2.1 What data?
The issue of what jgofs measurements correspond to what model variables is not always simple.
For example, what zooplankton measurements correspond to the microzooplankton variable of
FDM? What in the model corresponds to particulate organic nitrogen measurements? What
fraction of dissolved organic nitrogen takes part in the reactions that the models are concerned
with? What is the correspondence between detrital ux and collections in sediment traps at
dierent depths? (We have in mind here both the performance of traps at shallow depths and
the wide potential collection area of traps at deep depths.) Sediment trap measurements have
integrating properties that make them especially appropriate to jgofs time and space scales; so
that eorts to understand their properties and uncertainties would be rewarded.
How seriously should we take the depth of the observations, when there are internal waves
that aect the observations but not the models? Again, if the model predicts that observation
but at a slightly dierent depth, is that pretty good? Although most globally available data will
be at the surface, we expect that the few places where there are vertically resolved observations
will have a lot of ability to constrain.
The issues of how to compare data with model results are suciently complicated and varied
to require a workshop all their own.
Other model-data comparison work has been done by Matear (1995) and Prunet et al. (1996a,
b) at Station P, Fasham and Evans (1995) at NABE, and Hurtt & Armstrong (1996) at BATS.
6.2.2 Measure of mist
There is an underlying `right' way to measure mist, which we don't know enough to implement.
It entails making a statistical model where every observation has an associated error, and then
computing the probability of obtaining the observed results if the model, with its error structure,
were true. To do this correctly requires the jgofs community to know a lot about its data
set: intrinsic measurement variances, intrinsic small-scale variation in space of the process being
measured, covariances among measurements (e.g. chlorophyll and primary production), serial
correlation of variables (if an unmodelled process creates a perturbation in the system that lasts
long enough to aect successive observations). When we have such a model of the errors in the
data, then a simulation model run can be judged by its likelihood: the probability (density) of
obtaining the observed data had the model been true.
Intuition says that for nutrient measurements the intrinsic spatial variation is the largest part
of the error, whereas for zooplankton grazing rates actual measurement error is comparable.
A stopgap measure is to use some sort of sum of squared deviations. If at the same time we
can convey to the jgofs community how the conclusions we can draw change drastically as one
changes measures of likelihood, models of error, etc., it may be possible to induce jgofs (or any
successor project) to put more eort into understanding its variances.
Comparing real data with an average model may produce phase problems: a real peak that
appears at a dierent time in dierent years will appear in the averaged data as a qualitatively
dierent low, broad rise. Do we compare strictly model predictions and observations at the same
time? Or times at which the model prediction and observation give the same value? This leads
into some of the issues in errors-in-variables regression. For predictions, jgofs can only use
averages (possibly with statistically average noise like storminess), not real data. Matear (1995)
and Hurtt and Armstrong (1996) used averages of several years of data. Fasham and Evans (1995)
used a single year of data as if were steadily repeating. Prunet et al. (1996a, b) used two years of
real observations.
There are important issues of mist that the workshop did not address except in passing. Is
a `good' model t one that does a number of dierent things adequately, so that the mist is
more appropriately a minimax than sum of squares? What about requirements that the model
behave `reasonably', in the sense of agreeing with informal or anecdotal information about its
29
site (say about winter values, vertical uxes, annual seasonal amplitudes) as well as the specic
observation program? How do we weight explicit and anecdotal observations? The workshop also
did not address issues of goodness-of-t and model rejection, although the Hurtt & Armstrong
model was selected, out of many, as the only one to t the BATS data.
6.3 Estimating parameters
One view of the world would say that we already know parameter values, and we just do the local
studies to conrm that we know them and they are the same globally. We can run models with
the parameters that the authors suggest, and compare their outputs, for example compare values
of the mist function for a particular set of data. But a large mist need not indicate a poor
model; it might indicate a poor choice of undetermined parameters. It therefore makes sense to
compare models when each uses the parameter values that gives the best t we can nd to the
data. In a sense the question is how much we are prepared to learn from a particular measurement
program, and if we think this program tells us all we will ever know or if we have learned things
in the past that we will not reject without good reason. This is a question for the whole jgofs
community: what do they think they know already (e.g. parameter priors) and what new things
was the study designed to learn?
There are dierent techniques, with dierent strengths and weaknesses, for nding the parameter set that produces minimum mist. The mist function of the parameters may have local
minima, so that a routine like simulated annealing (used by Matear 1995 and Hurtt & Armstrong
1996), which tries to explore wide areas of parameter space before concentrating on the most
promising areas, may be indicated. Or the function may not be smooth (if for example it is derived from numerical approximations to solutions of dierential equations) so that gradient-based
methods can fail. Press et al. (1992) discuss many approaches briey, and Dennis and Schnabel
(1983) discuss gradient-based methods (by far the quickest when they work) in detail.
But we don't know nothing about the parameters before we start. We have a fair knowledge
of ranges and likely values, from years of experimenting, that the results of a particular set of
data should not be able to totally override. Especially when the data set may not be very informative about some of the parameters. It therefore makes sense to start with a prior distribution
for parameters, and minimize the sum of a model-data mist and a parameter-prior mist? At
a pragmatic level, a numerical optimization routine that knows no science can try meaningless
parameter values even when it is going to converge on sensible ones: a prior distribution incorporating bounds on possible values can avoid this. And a structure than allows for prior distributions
allows also for making them non-informative over a huge range if that is desired. The prior or
penalty function approach has been used by Fasham and Evans (1995). Another way to make
parameter estimates more denitive is to use models with a small number of parameters. Here the
very model structure contains decisions that are more rigid than decisions about prior parameter
distributions. This is the approach of Hurtt and Armstrong (1996).
The important issue of how much information the data contain about which parameters was
addressed in many ways during the workshop, both in discussions and in working models. The
parameter estimation technique of Prunet et al. (1996a) also assesses which linear combinations
of parameters can be estimated. Assume that the parameter and observation vectors have been
scaled so that the components have equal prior error estimates. If we have a current estimate pk
of the parameter vector p, and if the predictions c(p) of the model are linearized around pk :
c(pk + p) c(pk ) + Ap
where A is the jacobian matrix of partial derivatives @c=@p, and if the cost function we wish to
minimize is a sum of squares between observations and predictions:
F (p) = (o , c(p))T (o , c(p))
30
then the value of p that minimizes the linear approximation is
,1
p = AT A
AT (o , c(pk )):
That is, the linear approximation to the model, combined with the quadratic form of the penalty
function, produces a paraboloid in parameter space whose minimum we can compute in a single
step. However, the paraboloid may be so at in certain directions, and the step in those directions
therefore so large, that the linear approximation on which it was based becomes useless and the
mist value at the predicted point can even become larger than at pk . Conventional minimization
practice when this happens is to take a smaller step in the same direction (which is initially a
descent direction) to remain in the neighbourhood where the linear approximation is valid. In
the initial stages of seeking the minimum this is still the recommended technique. However, near
the minimum, Prunet et al. attempt to extract more information concerning the nature of the
problem and how much of a solution can be expected. Singular value decomposition allows one
to identify directions along which the quadratic surface has a very shallow curve that leads to
large and meaningless steps, and then nd a `nearby' surface that is exactly at and horizontal
in these directions, so that no step at all is taken. Deciding which directions should be retained
and which should be cancelled can be subjective. Prunet et al. make the decision as follows:
starting with the eigenvector corresponding to the largest singular value, and then adding the
eigenvectors of successively smaller eigenvalues, produces a succession of estimates of p for which
the model is run and the mist computed. As long as the mist is a decreasing function of the
number of eigenvectors, they judge that the approximation is reasonable. When increasing the
number of eigenvectors leads to an increase in the mist, they judge that the linear approximation
is breaking down and the data contain no information about the remaining linear combinations.
In other words, the approximation is being chosen not directly on the size of the singular values,
but on the eect of the singular vectors on the mist.
It is useful to express the imposition of prior parameter distributions in the same notation. It
amounts to augmenting the cost function to
F (p) = (o , c(p))T (o , c(p)) + (p , p0)TS ,1(p , p0)
where S represents how certain we are about dierent parameters. The solution to the new
minimization problem is then
p = (AT A + I ),1 AT (o , c(pk ) , Ap) + S , 12 (p0 , pk )
and the replacement of (AT A),1 by (AT A + I ),1 provides some protection against ill-conditioning.
6.4 Interpreting results
Even if we can t models to data modestly well, so what? What would make us believe that the
data have enabled us to constrain parameter values? Do we really believe that we have determined
parameters that can be carried condently to other parts of the ocean? This at least can be tested:
estimate parameters for one data set and then use them in dierent physical surroundings and
compare the model's predictions with what is observed there. A less ambitious plan is to estimate
the parameters that enable the best t to two dierent data sets in dierent places. [Or at
dierent times in the same place if, as in McGillicuddy et al. (1995), we determine that a ship
has drifted from one eddy to another and therefore in some sense the model should be restarted
with new initial conditions.] But note that this is less ambitious: what we want of jgofs is that
it converge|that the next major measurement program would not vastly change the estimates of
parameters|not that we can go on changing our minds as more evidence comes in.
Even a good t need not indicate a good model. In particular, it may be possible to t
some measurements (nitrate, chlorophyll) well with a model that turns out to represent primary
31
production measurements badly. There is a case for reserving part of any data set to see how well
it is predicted by the best t to the rest of the data. A poor t, and a need to adjust parameter
values substantially to obtain a good t, would indicate that the model investigation process has
not converged and we should be unwilling to trust the answers obtained so far. It often happens
that simple models extrapolate better than complicated ones. Think of polynomial tting to a
set of slightly noisy data: a suciently high-order polynomial can t all of the data exactly, by
writhing in between the observations in a way that has absolutely no predictive power; whereas a
low order polynomial (an average or a linear regression) will probably t new observations much
better.
At a second level of comparison, how do we compare the model-data mist of two dierent
models that have dierent numbers of parameters? Akaike's information criterion and likelihood
ratio are possibilities. We might use a null model (Fourier series with the same number of parameters?) to assess skill of models. It makes sense to develop new models with a level of complexity
that is quantitatively justied by the available data, if this can be determined.
Although the workshop did not get this far, one of the purposes of jgofs modelling (for
successor programmes if not for jgofs itself) is to determine the eects of dierent sampling
frequencies, depths, dierent types of variables, etc. on the ability of a data set to constrain
parameter values. An example of the sort of question that only modelling studies can answer:
Is it worth spending a lot of eort on (or devoting scarce shipboard resources to) measurements
that are intrinsically low precision (think of microzooplankton grazing rates)? Do the merits of
constraining from a dierent direction outweigh the merits of high accuracy that extra nutrient
measurements would have?
32
7 Comparative behaviour of 1-D physical and ecological models:
preliminary results
Cathrine Myrmehl1
One goal of the workshop was to compare the behaviour of dierent models at dierent sites in
the ocean: Station P, Eumeli, NABE and BATS. This requires us to do the following at each site.
1. Agree on common physical framework:
(a) develop atmospheric surface forcing
(b) decide on lower boundary conditions
(c) run physical models to determine Kz (z; t)
(d) choose a single representation of Kz (z; t)
2. Run models with standard parameter values as given:
(a) choose biological initial conditions
(b) agree on N closure (possible restoring or resetting) within the modelled region
(c) compile \observed data" for comparisons
(d) run models for particular years and extract appropriate model results
3. Optimize model parameters:
(a) choose form of cost function to be minimized
(b) choose numerical method for optimization
(c) run optimizer
None of the three tasks was accomplished completely. The rst was accomplished for Station
P and partly for Eumeli; the second, for all the models at Station P; and the last was partly
accomplished at Station P. All the data that were assembled and processed in the course of
preparing the results of this chapter will be made available to the general community through a
jgofs www site (http://ads.smr.uib.no/jgofs/inventory/Toulouse/index.htm).
7.1 Atmospheric forcing data
The four atmospheric forcing data sets are available at three-hour resolution and include values
of incoming solar radiation, non-solar heat uxes, two-dimensional wind stress, wind speed and
sea surface temperature. The European Center for Medium-Range Weather Forecasting (ecmwf)
data sets are analysis products created from 4-dimensional data assimilation of near real-time
observations with a 6-hour model forecast from the previous state. The analysis surface elds
include the components of the air-sea ux estimates, of the zonal and meridional 10 m winds, the
sea surface temperature, and the surface (2 m) air and dew point temperatures. Some of the models
need forcing data every three hours, and the ecmwf data was therefore interpolated linearly to
give the required frequency. The time and eort spent by Christophe Herbaud, LODYC, in the
extraction of the ecmwf elds are very much appreciated. The ecmwf has performed a reanalysis
back to 1979 in order to ensure a consistent data set, with the same parameterization for all the
model years; this will avoid bias corrections such as those we report here for Eumeli.
1
Nansen Environmental and Remote Sensing Center, Edvard Griegsvei 3a, 5037 Solheimsviken, Norway
33
Year
1986
1987
1988
Solar Infrared Sensible Latent Total
130.72 -65.98 -16.59 -87.55 -39.40
141.94 -72.31 -18.29 -87.16 -35.82
138.80 -71.87 -19.07 -85.12 -37.25
Table 1: Yearly mean values for the atmospheric heat uxes at NABE.
7.1.1 Station P
At Station P (50 N, 145 W) atmospheric forcing was computed from 1975 through 1977 from
3-hourly records of sea surface temperature, air temperature, wind speed at 10 m height, sealevel barometric pressure and total cloudiness index (Antoine and Morel 1995). The average heat
budget over the three years is -0.5 Wm,2 , which is suciently close to zero for our purposes.
Evolution of the various air-sea heat uxes (net = solar + (non-solar = infrared + latent +
sensible)) at Station P over the three year period is shown in Figure 1, together with the x- and
y-components of the wind stress. During the workshop an average atmospheric forcing for the 3
years was put together as shown in Figure 2.
7.1.2 Eumeli
The atmospheric forcing used to run the models at the oligotrophic site at Eumeli (21 N, 31 W)
is derived from the operational Atmospheric General Circulation Model of the ecmwf (data from
1986 to 1990 were extracted, but only data from 1990 to 1992 were used in this study). Data
from the four ecmwf grid points closest to the site were interpolated to give the atmospheric
forcing at the study site. Incoming solar radiation, infrared, latent and sensible heat uxes, sea
surface temperature, wind velocity vector, and wind stress vector were extracted. Gleckler and
Taylor (1993) found, by comparing with existing climatologies, that the ecmwf model short wave
radiation in 1990 was systematically larger than the observations in the eastern part of the oceans.
It could be in part explained by little model cloud cover over o the west coast of every continent.
The root-mean-square (RMS) dierence between the modeled ecmwf and observed short wave
radiation is 50 Wm,2 ; the Eumeli oligotrophic site is aected by this error. Correcting the ecmwf
1990 incoming solar radiation made the SST computed from a 1-D upper ocean model (Gaspar et
al. 1990) comparable with the SST eld from ecmwf 1990 (Dadou and Garcon 1993). However,
applying this correction in 1990 resulted in mixed layer depths far too deep in January/February
1991. After some experimenting, the best t between model and observations was found with
corrections of -42 Wm,2 in 1990 (giving a net budget for that year of -6 Wm,2 ), -10 Wm,2 in
1991 (net budget +3 Wm,2 ), and no correction in 1992 (net budget 0). Siefriedt (1994) compared
ecmwf output with existing climatologies and suggested a similar correction for 1990. The heat
imbalance averaged over the 3 years is close enough to zero (-1 Wm,2 ). Figure 3 gives the monthly
means of the components of the atmospheric heat uxes, after correcting the solar uxes.
7.1.3 NABE
At the NABE site at 47 N, 20 W, the atmospheric forcing was also derived from ecmwf. Data
from 1986 to 1988 indicated a large heat imbalance (Table 1). It was not feasible to use 1989
ecmwf data (the year of the NABE program) because the model algorithm was changed in the
middle of the year. The heat imbalance indicated a large horizontal contribution, but this was
not incorporated in our 1-D models due to lack of time, and therefore precluded further analysis
at NABE. The atmospheric uxes of the three years, 1986 { 1988 are plotted in Figure 4.
34
Incoming solar radiation
Nonsolar flux
180
-20
160
-40
140
-60
-80
W/m^2
W/m^2
120
100
-100
80
-120
60
-140
40
-160
20
-180
6
12
18
Months
24
30
36
6
12
Infrared heat flux
18
Months
24
30
36
24
30
36
24
30
36
30
36
Sensible heat flux
-30
5
0
-35
-5
-40
W/m^2
W/m^2
-10
-45
-50
-15
-20
-25
-55
-30
-60
-35
-65
-40
6
12
18
Months
24
30
36
6
12
Latent heat flux
18
Months
Surface net heat flux
0
150
-10
100
-20
50
-40
W/m^2
W/m^2
-30
-50
-60
0
-50
-70
-100
-80
-90
-150
6
12
18
Months
24
30
36
6
12
Wind stress, u-component
18
Months
Wind stress, v-component
0.1
0.05
0.05
0
0
-0.05
-0.1
N/m^2
N/m^2
-0.05
-0.15
-0.2
-0.1
-0.15
-0.25
-0.2
-0.3
-0.35
-0.25
6
12
18
Month
24
30
36
6
12
18
Month
24
Figure 1: Monthly means of the components of the atmospheric heat uxes and wind stress,
computed from 3-hourly records at Station P for the years 1975{1977.
35
Incoming solar radiation
Nonsolar flux
180
-50
-60
160
-70
140
-80
-90
W/m^2
W/m^2
120
100
-100
-110
80
-120
60
-130
40
-140
20
-150
1
2
3
4
5
6
7
Months
8
9
10
11
12
1
2
3
4
5
Infrared heat flux
6
7
Months
8
9
10
11
12
8
9
10
11
12
9
10
11
12
9
10
11
12
Sensible heat flux
-35
-10
-20
-40
-30
W/m^2
W/m^2
-45
-50
-40
-50
-55
-60
-60
-70
-65
-80
1
2
3
4
5
6
7
Months
8
9
10
11
12
1
2
3
4
6
7
Month
Surface net heat flux
5
150
0
100
-5
50
W/m^2
W/m^2
Latent heat flux
5
-10
0
-15
-50
-20
-100
-25
-150
1
2
3
4
5
6
7
Months
8
9
10
11
12
1
2
3
4
Wind stress, u-component
5
6
7
Months
8
Wind stress, v-component
0
0
-0.02
-0.02
-0.04
-0.06
-0.04
N/m^2
N/m^2
-0.08
-0.1
-0.06
-0.12
-0.08
-0.14
-0.16
-0.1
-0.18
-0.2
-0.12
1
2
3
4
5
6
7
Month
8
9
10
11
12
1
2
3
4
5
6
7
Month
8
Figure 2: Monthly means of the components of the average forcing at Station P during 1975{77.
36
Incoming solar radiation
Nonsolar flux
300
-100
280
-150
260
-200
220
W/m^2
W/m^2
240
200
180
-250
-300
160
-350
140
120
-400
6
12
18
Months
24
30
36
6
12
Infrared heat flux
18
Months
24
30
36
24
30
36
24
30
36
30
36
Sensible heat flux
-45
0
-50
-5
-55
-10
-65
W/m^2
W/m^2
-60
-70
-75
-15
-20
-80
-25
-85
-90
-30
6
12
18
Months
24
30
36
6
12
Latent heat flux
18
Months
Surface net heat flux
-60
150
-80
100
-100
50
-120
W/m^2
W/m^2
-140
-160
-180
-200
0
-50
-100
-220
-150
-240
-260
-200
6
12
18
Months
24
30
36
6
12
Wind stress, u-component
18
Month
Wind stress, v-component
-0.02
0.1
-0.03
0.08
-0.05
0.06
-0.06
0.04
N/m^2
N/m^2
-0.04
-0.07
-0.08
0.02
-0.09
0
-0.1
-0.02
-0.11
-0.04
-0.12
-0.13
-0.06
6
12
18
Month
24
30
36
6
12
18
Month
24
Figure 3: Monthly means of the components of the total energy ux and wind stress at the
ocean-atmosphere interface from ecmwf at Eumeli for the years 1990{1992, correction applied.
37
Incoming solar radiation
Nonsolar flux
250
-40
-60
-80
200
-100
-120
W/m^2
W/m^2
150
100
-140
-160
-180
-200
50
-220
-240
0
-260
0
6
12
18
Month
24
30
36
0
6
12
Infrared heat flux
30
36
24
30
36
24
30
36
30
36
5
-50
0
-55
-5
-60
-10
-65
-15
W/m^2
W/m^2
24
Sensible heat flux
-45
-70
-20
-75
-25
-80
-30
-85
-35
-90
-40
0
6
12
18
Month
24
30
36
0
6
12
Latent heat flux
18
Month
Surface net heat flux
0
150
-20
100
-40
50
0
W/m^2
-60
W/m^2
18
Month
-80
-50
-100
-100
-120
-150
-140
-200
-160
-250
0
6
12
18
Month
24
30
36
0
6
Wind stress, u-component
12
18
Month
Wind stress, v-component
0.3
0.14
0.12
0.25
0.1
0.2
0.08
0.06
N/m^2
N/m^2
0.15
0.1
0.04
0.02
0.05
0
0
-0.02
-0.05
-0.04
-0.1
-0.06
0
6
12
18
Month
24
30
36
0
6
12
18
Month
24
Figure 4: Monthly means of the components of the total energy ux and wind stress at the
ocean-atmosphere interface from ecmwf at NABE for the years 1986 { 1988.
38
7.1.4 BATS
The physical forcing from the Bermuda Atlantic Timeseries Station (BATS) (32 N, 64 W) from
1987 to 1994 was calculated by Doney (1996) using ecmwf and ISCPP (International Satellite
Cloud Climatology Project) data. For BATS, the state variables from ecmwf (wind speed,
temperature, etc.) were used to compute new uxes (either with prescribed SST or interactively
with the model SST). The forcing data are based primarily on the uninitialized, 6-hourly TOGA
global surface analysis from ecmwf. The elds are supplemented by daily cloud fraction and
surface insolation estimates from ISCPP and monthly satellite precipitation estimates from the
Microwave Sounding Unit (MSU). The uxes are shown in Figure 5. The average heat budget
over the eight years is -21.5 Wm,2 .
7.2 Kz history
In order to compare the biogeochemical parts of the models, it was necessary to agree upon a
common physical framework. The 1-D models in which the physics were explicitly computed were
run with the same physical forcing, to see which gave the best results according to observed mixed
layer depth and temperature. The 1-D models that were run were those of Scott Doney, Dennis
McGillicuddy, David Antoine, Diana Ruiz-Pino, Veronique Garcon and Pascal Prunet. The four
latter are all based on the physical model of Gaspar et al. (1990), with a minimum turbulent
kinetic energy imposed below the upper mixed layer. Some of the 0-D models needed a smooth
mixed layer depth (MLD) history, so the Kz and MLD were averaged over seven days. Thereafter,
a boxcar-lter of 3 was passed twice, also for temperature and salinity. Applying a boxcar lter
of 3 gives a sliding mean with weights 1/3, 1/3, 1/3; applying it again gives weights 1/9, 2/9,
3/9, 2/9, 1/9 (a triangle). In 2 dimensions, applying it twice gives a pyramid-weighted mean
of the nearest 25 points. Other smoothing procedures (e.g. cubic spline interpolation) failed to
reproduce the original structure .
7.2.1 Station P
The workshop concentrated its attention on Station P. One reason for picking this site is that
most of the physical mixing models have been studied there, so it was a good location where to
compare physical models and to get diverse bgc models to run in the same physical arena. It is
not a perfect choice. Iron limitation is quite likely an important factor there, and it is absent
from the models considered at the workshop. In addition, only nutrient and chlorophyll data were
available for validating or constraining parameter sets.
All the model output plots at Station P were sent to the physical oceanographers participating
at the workshop, along with the bathythermographic records of Station P for the years 1975 { 1977,
provided by David Antoine (Figure 6). Visually, Scott Doney's and Diana Ruiz-Pino's models
matched the data best, and so the root-mean-square dierences in SST were computed for these
two models (Table 2).
Of the two models compared, Scott Doney's reproduces the SST cycle better for the three years
(see Table 2). The dierence was not overwhelming, however, and we decided to proceed with
Diana Ruiz-Pino's model on the practical ground that people in Toulouse who would be involved in
preliminary work were more familiar with it. Temperature, salinity, MLD and turbulent diusion
coecient are plotted in Figure 7, and for comparison Scott Doney's are found in Figure 8.
Two models (Geo Evans, which is simply FDM built into an optimizing shell, and Tom
Anderson) that assume a steady cyclic forcing and are run to a steady cyclic solution were driven
by the 3-year average MLD cycle given in Figure 9. During the workshop we also produced a
1975 { 1977 average radiation forcing for the 0-D models (Figure 2).
39
Incoming solar radiation
Nonsolar flux
350
-50
-100
300
-150
-200
W/m^2
W/m^2
250
200
-250
-300
150
-350
100
-400
50
-450
6
12
18
24
30
36
42
48 54
Months
60
66
72
78
84
90
96
6
12
18
24
30
36
Infrared heat flux
42
48 54
Months
60
66
72
78
84
90
96
66
72
78
84
90
96
66
72
78
84
90
96
66
72
78
84
90
96
Sensible heat flux
-50
10
-100
-10
0
-20
W/m^2
W/m^2
-150
-30
-40
-200
-50
-60
-250
-70
-300
-80
6
12
18
24
30
36
42
48 54
Months
60
66
72
78
84
90
96
6
12
18
24
30
Latent heat flux
36
42
48 54
Months
60
Surface net heat flux
-35
200
-40
150
100
-45
50
0
-55
W/m^2
W/m^2
-50
-60
-50
-100
-150
-65
-200
-70
-250
-75
-300
-80
-350
6
12
18
24
30
36
42
48 54
Months
60
66
72
78
84
90
96
6
12
18
24
30
Wind stress, u-component
36
42
48 54
Month
60
Wind stress, v-component
0.16
0.1
0.14
0.08
0.1
0.06
0.08
0.04
N/m^2
N/m^2
0.12
0.06
0.04
0.02
0.02
0
0
-0.02
-0.02
-0.04
-0.04
-0.06
-0.06
6
12
18
24
30
36
42
48 54
Month
60
66
72
78
84
90
96
6
12
18
24
30
36
42
48 54
Month
60
Figure 5: Monthly means of the components of the total energy ux and wind stress at the
ocean-atmosphere interface from ecmwf and ISCPP at BATS for the years 1987 { 1994.
40
4
4
4
4
4
4
4
4
4
4
4
5
5
4
5
5
5
5
6
5
5
5
5
5
4
4
7
5
5
6
5
5
5
6
5
5
5
5
5
4
5
36
33
8
9
8
6
6
8
5
6
5
5
5
5
5
6
5
9
8
5
8
7
6
5
12
10
9
1011
7
11
10
8
8
6
6
7
5
5
5
5
4
250
30
27
24
21
18
Month
15
9
7
9
6
12
9
6
7
11
7
5
5
100
7
5
4
5
8
7
6
10
10
9
5
5
5
4
8
12
0
7
10
50
7
6
6
6
200
3
300
5
150
depth (m)
(1975 to 1977)
41
Figure 6: Bathythermographic records, for comparison with the model outputs of temperature.
STATION P : Contour plot of temperature (Bathythermographic records)
1975
1976
1977
Global
Diana Ruiz-Pino Scott Doney
0.55
0.53
1.24
0.72
1.34
0.57
1.10
0.61
Table 2: RMS between SST and model output.
7.2.2 Eumeli
At Eumeli, no common Kz history was chosen before or during the workshop, but some of the
results are shown in Figures 10, 11, 12 and 13.
7.2.3 NABE
No models were run at NABE, due to the heat imbalance in the atmospheric forcing.
7.2.4 BATS
Scott Doney's model has been run at BATS with the same atmospheric forcing and initial conditions as in this study; see Doney (1996).
7.3 Data for initializing bgc models and comparing their outputs
This section presents the data used for initialization of the models and the data used for parameter
estimation. Total CO2 and total alkalinity are presented as well, although the carbon systems of
the models where this is included were not run during the workshop.
7.3.1 Station P
Initial proles At Station P, the temperature were bathythermographic records, salinity from
Levitus and oxygen data were taken from in situ measurements, see Figure 14 (Antoine & Morel
1995). For the biology, dierent sources were also involved. The phytoplankton data were the
equilibrium of the NPZD-model of Prunet et al. (1996a) (see Table 3), the nanophytoplankton
variable in Ruiz-Pino's model was set to zero. The zooplankton, detritus, labile DOM and bacteria
were in situ measurements provided by Diana Ruiz-Pino (Table 3). For the refractory DOM pool,
a value of 70 mmol C m,3 was assumed, giving the same fraction between the labile and refractory
DOM pool as at Eumeli. For nitrate, in situ measurements were used (Antoine & Morel 1995)
For Ruiz-Pino's model, an initial value of silicate was also needed. According to Frank Whitney
(personal communication), Si was in the range 22 to 28 mmol Si m,3 for the years 1975 to 1977,
depending on the year, and winter levels were increasing year by year. In this study a homogeneous
value of 22 mmol Si m,3 was chosen. The ammonium data was that of Wheeler & Kokkinakis
(1990). For total CO2 and total alkalinity, a prole after one year of spin-up of David Antoine's
model was used.
Data used for parameter estimation The surface phytoplankton and nitrate data, used for
the parameter estimation were in situ measurements from 1975 and 1976 (Figures 15 and 16), as
reported in Prunet et al. (1996b).
42
Figure 7: Station P, 1975 { 1977. Diana Ruiz-Pino's model. The coecient of turbulent diusion
and the depth of the mixed layer have been averaged over a week. Thereafter a boxcar-lter of 3
is applied twice. For temperature and salinity, only the boxcar-lter has been used.
Figure 8: Station P, 1975 { 1977. Scott Doney's model. The coecient of turbulent diusion has
been averaged over a week. Thereafter a boxcar-lter of 3 is applied twice. For temperature, only
the boxcar-lter has been used.
43
Figure 9: \Climatology" of the mixed layer history.
Figure 10: Eumeli, 1990 { 1992. Veronique Garcon's model. The coecient of turbulent diusion
and the depth of the mixed layer have been averaged over a week. Thereafter a boxcar-lter of 3
is applied twice. For temperature and salinity, only the boxcar-lter has been used.
44
Figure 11: Eumeli, 1990 { 1992. Pascal Prunet's model.
Figure 12: Eumeli, 1990 { 1992. Diana Ruiz-Pino's model.
Figure 13: Eumeli, 1990 { 1992. Scott Doney's model.
45
Salinity
0
-50
-50
-100
-100
Depth (m)
Depth (m)
Temperature
0
-150
-150
-200
-200
-250
-250
-300
4.2
4.4
4.6
4.8
5
5.2
5.4
Degrees Celsius
5.6
5.8
6
-300
32.8
6.2
33
33.2
0
-50
-50
-100
-100
-150
-200
-250
-250
150
200
250
O2 mmol/m3
300
-300
2090
350
2100
2110
2120
2130
TCO2 mmol/m3
34
2140
2150
2160
Nitrate
0
-50
-50
-100
-100
Depth (m)
Depth (m)
Total alkalinity
0
-150
-150
-200
-200
-250
-250
-300
2270
33.8
-150
-200
-300
100
33.6
Total carbon dioxide
0
Depth (m)
Depth (m)
Oxygen
33.4
PSU
-300
2280
2290
2300
meq/m3
2310
2320
2330
10
15
20
Figure 14: Initial conditions at Station P.
46
25
mmolN/m3
30
35
40
Figure 15: Surface data of phytoplankton used for model-data comparison, 1975 and 1976.
Figure 16: Surface data of nitrate used for model-data comparison, 1975 and 1976.
47
Variable
Phytoplankton
Zooplankton
Microzooplankton
Bacteria
Very small detritus
Small detritus
Large detritus
Labile DOM
Refractory DOM
Nitrate
Ammonium
Silicate
Initial Value { surface
0.18 mmol N m,3
0.14 mmol N m,3
0.14 mmol N m,3
0.14 mmol N m,3
0.14 mmol N m,3
0.0001 mmol N m,3
0.0001 mmol N m,3
1.67 mmol C m,3
70 mmol C m,3
14.50 mmol N m,3
0.15 mmol N m,3
22 mmol Si m,3
Initial Value { bottom
0.18 mmol N m,3
0.0001 mmol N m,3
0.0001 mmol N m,3
0.0001 mmol N m,3
0.0001 mmol N m,3
0.0001 mmol N m,3
0.0001 mmol N m,3
1.67 mmol C m,3
1.67 mmol C m,3
38.9 mmol N m,3
0.15 mmol N m,3
22 mmol Si m,3
Table 3: Initial values for the dierent variables at Station P.
7.3.2 Eumeli
Initial proles The temperature, salinity and oxygen data to initialize the models were all taken
from the Eumeli 5 cruise of December 23, 1992 (Figure 17). Phytoplankton, zooplankton, bacteria
and nitrate concentrations were also taken from Eumeli 5. Detritus and DOM were, however
taken from Eumeli 3. Small zooplankton were given a constant value of 0.0001 mmol N m,3 , and
very small detritus 0.3 mmol N m,3 . Small detritus were 0.3 mmol N m,3 down to 100 m, and
decreased linearly to 0.06 mmol N m,3 at 300 m. Large detritus were 0.1 mmol N m,3 down to 100
m, and decreased linearly to 0.02 mmol N m,3 at 300 m. DOM was given a constant value of 0.7
mmol C m,3 , and bacteria decreased from 0.15 mmol N m,3 at the surface to 0.04 mmol N m,3
at 300 m. For ammonium, a low value of 0.01 mmol N m,3 was chosen. Total CO2 and total
alkalinity were those of the TTO/TAS cruise (station 82).
Data used for parameter estimation All the data from Eumeli when fully assembled will
be made available at a www site indicated on
http://ads.smr.uib.no/jgofs/inventory/Toulouse/index.htm
7.3.3 NABE
Initial proles At NABE, the Discovery cruise 182 of May 8, 1989 was chosen to initialize the
models. Those data included temperature, salinity, oxygen, total CO2 , total alkalinity, nitrate,
ammonium and phytoplankton. Tom Anderson gave the zooplankton (0.12 mmol N m,3 ), DOM
(labile: 0.5 mmol C m,3 , refractory: 42 mmol C m,3 , same fraction as for Eumeli) and bacteria
(0.06 mmol N m,3 ) data (Figure 18). Small and large detritus were given a small value of 0.0001
mmol N m,3 . For the other variables, no initial proles were prepared for the workshop.
Data used for parameter estimation There are two main sources of information about the
observations. The British Oceanographic Data Centre has assembled Discovery observations on
CD-ROM (Lowry et al. 1994) and also holds diskettes with observations from Meteor and Tyro.
Atlantis observations have been made available by G. Heimerdinger and G. Flierl on the www site
http://www1.whoi.edu/jgofs.html. Additional information can be found in the jgofs special
volume of Deep-Sea Research (volume 40 number 1/2 1993).
48
Salinity
-50
-50
-100
-100
-150
-150
Depth (m)
Depth (m)
Temperature
-200
-250
-200
-250
17
18
19
20
21
22
23
24
36.4
36.6
36.8
Oxygen
37.2
Total carbon dixoide
-50
-50
-100
-100
-150
-150
Depth (m)
Depth (m)
37.0
PSU
Degrees Celsius
-200
-200
-250
-250
-300
160
170
180
190
200
210
2100
2105
O2 mmol/m3
Total alkalinity
Nitrate
-50
-50
-100
-100
-150
Depth (m)
Depth (m)
2110
TCO2 mmol/m3
-200
-250
-150
-200
-250
-300
2370
2380
2390
2400
2410
2420
2430
0
5
Zooplankton
-50
-50
-100
-100
-150
-150
Depth (m)
Depth (m)
Phytoplankton
-200
-250
-300
0.00
10
NO3 mmolN/m3
TALK meq/m3
-200
-250
-300
0.05
0.10
0.15
0.20
0.25
0.30
0.010
0.015
mmolN/m3
0.020
0.025
mmolN/m3
Figure 17: Initial conditions at Eumeli.
49
0.030
0.035
37.4
Salinity
-50
-50
-100
-100
-150
-150
Depth (m)
Depth (m)
Temperature
-200
-250
-200
-250
11.5
12.0
12.5
35.560
35.570
35.580
35.590
35.610
35.620
Total carbon dioxide
-50
-50
-100
-100
-150
-150
Depth (m)
Depth (m)
Oxygen
-200
-250
-200
-250
260
265
270
275
280
2070
2080
2090
2100
2110
2120
2130
Nitrate
Total alkalinity
-50
-100
-100
-150
-150
Depth (m)
-50
-200
-250
-200
-250
2315
2320
2325
2330
2335
2340
2
3
4
5
6
7
NO3 mmolN/m3
TALK meq/m3
Phytoplankton
Ammonium
-50
-50
-100
Depth (m)
-100
Depth (m)
2140
TCO2 mmol/m3
O2 mmol/m3
Depth (m)
35.600
PSU
Degrees Celsius
-150
-200
-150
-200
-250
-250
0.4
0.6
0.8
1.0
0.1
1.2
0.2
0.3
mmolN/m3
NH4 mmolN/m3
Figure 18: Initial conditions at NABE.
50
0.4
Before
Phyto NO3
Tom Anderson 0.496 7.54
Ken Denman 10.225 8.824
0.19 2.14
Helge Drange
Scott Doney
0.163 4.181
0.841 6.987
Uli Wolf
Pascal Prunet 0.128 2.477
0.129 3.307
Geo Evans
After
Phyto NO3
0.154 2.102
0.156 6.818
0.17 2.74
0.117 1.952
0.222 1.654
0.115 2.114
0.124 2.362
Table 4: RMS between between data and model outputs before and after iteration at Station P.
7.3.4 BATS
Initial proles For BATS, US jgofs data from December 19, 1988 were chosen to initialize
the models, except for total alkalinity, interpolated measurements from GEOSECS { TTO/NAS
(Drange 1994), Figure 5.5 (Figure 19). Zooplankton were given a constant value of 0.14 mmol N m,3
from the surface down to 50 m, and a constant value of 0.0001 mmol N m,3 from that depth down
to 300 m. For DOM (labile: 1.67 mmol C m,3 , refractory: 70 mmol C m,3 , same fraction as for
Eumeli). Detritus was given a small value of 0.0001 mmol N m,3 for all the size classes.
Data used for parameter estimation Data from BATS are available at the following address:
http://www.bbsr.edu/bats/bats.html.
7.4 Preliminary results
7.4.1 Parameter estimation
We attempted to use the method of Prunet et al. (1996a) described in Chapter 6, with each
model run at Station P and using surface data of nitrate and phytoplankton from 1975 and 1976.
As it turned out, we still had things to learn about the method, and we had persistent problems
with the optimization terminating prematurely. The root-mean-square dierence between data
and model output before and after the iterations for the dierent models (as far as they went)
are shown in Table 4. All the estimation runs were performed with the three years of real forcing,
and without the NO3 resetting discussed in Chapter 4. Some preliminary results are shown in
Figures 20 and 21. Please note that these results are not nal.
For four models (indicated by *) the optimization ran to convergence. Geo Evans's and Pascal
Prunet's (1996b) models started with model parameters which were already optimized. For each
of them the parameters were further adjusted: in Prunet's case because a dierent number of
parameters and a slightly dierent data set were used; in Evans's case because of small changes
in the mist function and the prior values of the parameters. Uli Wolf's model was taken to
convergence before the workshop, and Helge Drange's during the workshop; this model was only
run for the rst two years. Note that Scott Doney's model, though not converged, has smaller
`after' RMS values than some of the converged models.
Table 5 shows the optimized values of the model parameters, which were common in three or
four of the fully optimized models. The parameters are described in Chapter 8. It is not easy
to draw any conclusions from this table. However, one should mention the rather high value
estimated in Geo Evans's model, which probably occurs because this model is not vertically
resolved. The assimilation technique is increasing the value, given the light conditions and
the phytoplankton at Station P, that is, it increases the phytoplankton growth rate. During the
workshop we experimented with forcing Helge Drange's model to use the same value of , but the
51
Salinity
-50
-50
-100
-100
-150
-150
Depth (m)
Depth (m)
Temperature
-200
-250
-200
-250
18
19
20
21
22
36.50
36.55
Total carbon dioxide
-50
-100
-100
-150
-150
Depth (m)
-50
-200
-250
-200
-250
175
180
185
190
195
200
205
2030
2040
2050
Total alkalinity
-100
-100
Depth (m)
-50
-150
-150
-200
-200
-250
-250
2360
2370
2380
1
TALK meq/m3
-50
-100
-150
-200
-250
0.02
0.04
0.06
2
NO3 mmolN/m3
Phytoplankton
-300
0.00
2070
Nitrate
-50
2350
2060
TCO2 mmol/m3
O2 mmol/m3
Depth (m)
Depth (m)
Oxygen
Depth (m)
36.60
PSU
Degrees Celsius
0.08
0.10
0.12
mmolN/m3
Figure 19: Initial conditions at BATS.
52
3
4
Figure 20: Preliminary results of the iteration. Data used for the comparison are plotted as
diamonds.
53
Figure 21: Preliminary results of the iteration. Data used for the comparison are plotted as
diamonds.
54
Parameter Helge Drange Pascal Prunet Geo Evans
Uli Wolf
Before After Before After Before After Before After
1.5
1.84
1.5
1.39 0.68 0.62
1.5
1.94
0.025 0.02
0.23 0.24 0.025 0.008
1.0
1.2
1.0 1.042 1.09 1.56
Kfood
Pphy
0.5
0.5
0.5
0.58 0.59 0.33
Vdet
3.0
3.58
3.0
3.18 4.85 4.04
1.0
1.01
Table 5: Common assimilated parameters.
results of this experiment was that the phytoplankton concentration increased notably, followed
by very high seasonal variations in nitrate.
It was never intended to stop with Station P results, but the diculties encountered with the
parameter estimation software prevented exploration of other sites. This remains an urgent need
for future jgofs work.
7.4.2 NO3-resetting
Resetting of NO3 was included in Helge Drange's model during the workshop and we performed
the parameter estimation with this option. The results are shown in Figure 22. The standard run
denotes the nominal run without any data assimilation. It is clear that the model has a tendency
to follow the nitrate data better with NO3 -resetting, but it is dicult to draw any conclusions
from the phytoplankton data.
55
Figure 22: Results of the NO3 -resetting in Helge Drange's model.
56
8 Equations and parameters
Participants in the workshop generously made available work in progress. Equations and parameter
values presented here probably do not reect the latest thinking of their authors, and may omit
subtleties that are needed for running the models. It would be prudent as well as courteous to
consult with the authors before making any use of material presented in this chapter.
This chapter presents explicit equations for the in situ biogeochemical transformations of the
workshop models. The equations are presented in a common notation that makes it possible to
observe the occurrence of the same parameter in dierent models, and compare its value. There
is some doubt among workshop participants that this is a good thing in all circumstances; but it
was one thing we did, and we report the progress here. To enable a timely release of the whole
report, we have chosen to present the interim, imperfect version we have been able to devise so
far.
8.1 Notation
An ideal common notation would be concise, informative out of context, and consistent across
dierent models. These requirements often work at cross purposes. Consider a parameter name
long enough to be informative: 0phy;det could stand for the linear term in the expansion around
the origin of the curve describing losses from phytoplankton to detritus. This has the advantage
of automatic cross-referencing, so that when we see this parameter as part of a loss term in the
phytoplankton equation, we know without having to seek it out that there should be a balancing
gain in the detritus equation. However, it is unwieldy compared to the corresponding FDM
parameter name 1 . Losses due to sloppy feeding are even more unwieldy because there are three
terms to consider: the source, the target and the agent. In papers that describe a single model, the
context is clearer, and so the merits of conciseness would be given a higher weight than here. Also
parameters whose meanings are easy to compare across models are not always the most natural
for the expression of a particular model. The formulation of the phytoplankton loss term in the
Hurtt & Armstrong model is a case in point.
For the state variables whose evolution the models describe, we use 3-letter abbreviations
in small capitals, such as phy. When a model has more than one class of some variable, we
substitute a number, e.g. de1 and de3 for two size classes of detritus. When the state variable
is not computed in nitrogen units, we add a 3-letter sux to indicate its element: thus doncar
is the carbon asociated with dissolved organic nitrogen. The table of parameter denitions shows
our decisions about how long and complicated to make the names.
8.2 Common parameters
It is a tricky problem to assign `the same' parameters to expressions with dierent functional forms.
Consider the functional response of grazers to food concentrations. The rst 3 (constant, linear,
quadratic) terms in the polynomial expansion about the origin, and about 1, and the abscissa
at which the function attains half of its maximum value, might all be considered quantities of
interest or ecological importance. For Michaelis and Ivlev curves, the constant term at the origin
and the linear and quadratic terms about 1 are identically zero, leaving 4 parameters any two of
which suce to describe either 2-parameter curve. Do the curves
x
1+x
and
57
1 , e,x
have the same parameter values or not? They have the same slope at zero and constant value at
1, but they have half-saturation abscissas 1 and 0.693 respectively, and second derivatives at the
origin -2 and -1 respectively. Should a table of parameters contain all 7 of the above parameter
values, or at least those that are not already xed by the denition of the curve, or just the two
that are necessary for dening the curve? The choice of what to use as parameters will also aect
sensitivity analyses. The partial derivative of some model output with respect to maximum rate,
holding initial slope constant, is not the same as the partial derivative with respect to maximum
rate holding half-saturation concentration constant.
A neutral possibility might be to report, as `parameters', the values of the function at the
appropriate number of representative (in the context of a given data set) values of its argument,
though it would then be dicult to work out other values given these. And would the most
representative values of the argument change if we switched to a function with more or fewer
parameters?
For want of time, we have left one area in an incomplete state. The photosynthesis-light
relations that are reported in this chapter are the instantaneous ones, with no reference to dierent
methods for integrating over variations with time of day and with depth. One might argue that
such integrations are an issue in numerical analysis and do not belong in a chapter on the equations
representing the scientic concepts. However, one might also argue that, because phytoplankton
can take up nutrients also at night, the interaction between nutrients and light is best seen in terms
of the daily integrated response to light, not the instantaneous response. Not enough thinking
has been done on this question.
8.3 Tables of parameter values
These are only tentative. As we reported in Chapter 7, it has not been possible to tune all
the models to a common data set (or at least we are not totally condent about the tuning).
Although a lot of work has been done in developing the common notation, the payos have not
yet arrived. The tables do at least indicate where there are parameter values|where comparisons
will be meaningful once models are tuned to the same set of data. A key question is how much
people learn from the unied notation and tables as far as we have been able to develop them,
and therefore how much eort it is worth to develop them further.
58
State variables
The unit, unless otherwise stated, is mmol Nm,3 .
Symbol
Denition
Nitrate
Ammonium
Phytoplankton
Nanophytoplankton
Microphytoplankton
Zooplankton
Microzooplankton
Mesozooplankton
Bacteria
Dissolved organic nitrogen
Labile DON
Refractory DON
Detritus
Small detritus
Medium or large detritus
Large detritus
chl
xxxcar
sil
xxxsil
Phytoplankton chlorophyll in mg m,3
Carbon content of xxx in mmol Cm,3
Silicate in mmol Sim,3
Silicon content of xxx in mmol Sim,3
Total dissolved inorganic carbon in mmol Cm,3
Total alkalinity in meqm,3
no3
nh4
phy
ph1
ph2
zoo
zo1
zo2
bac
don
do1
do2
det
de1
de2
de3
CO2
alk
59
Parameters
Symbol
Denition
Phytoplankton growth
kw
Light attenuation coecient of water
kc
Light attenuation coecient of chlorophyll
phy
Maximum phytoplankton growth rate
Initial slope of P{I curve
Light inhibition of photosynthesis
Kno3
Half-saturation concentration for no3 uptake
Knh4
Half-saturation concentration for nh4 uptake
Ksil
Half-saturation concentration for sil uptake
nh4 inhibition of no3 uptake
Diana Ruiz-Pino's parameters for dividing
1;
2
nutrient uptake between nitrate and ammonium
term in nutrient-dependent mortality
1
PH
Phytoplankton N:chl ratio at innite light
0PH
Phytoplankton N:chl ratio at zero light
EK
Light level where 0PH starts
PNC
Phytoplankton N:C ratio
Zooplankton growth
zoo
Maximum zooplankton growth rate
Kfood
Half-saturation food concentration for zoo grazing
zoo
Slope of zooplankton grazing curve
c
Quadratic part of zooplankton grazing curve
pphy ; pbac; pdet
Preference of zooplankton for food types
ZNC
Zooplankton N:C ratio
Bacterial growth
bac
Maximum bacterial growth rate
KNbac
Half-saturation for bacterial uptake of nutrients
Excess carbon content of don over what bac needs
BNC
Bacterial N:C ratio
Loss terms
xxx;yyy
constant loss from xxx to yyy
xxx;yyy
linear loss from xxx to yyy
xxx;yyy
quadratic loss from xxx to yyy
"xxx;yyy
fraction of the uptake by xxx that goes to yyy
xxx
fraction of a loss allocated to xxx
60
Unit
m,1
m,1 (mmol N m,3 ),1
d,1
(W m,2 ),1 d,1
(W m,2 ),1 d,1
mmol Nm,3
mmol Nm,3
mmol Nm,3
(mmol Nm,3 ),1
|,|
d,1 mmol Nm,3
mol N(g chl),1
mol N(g chl),1
W m,2
mol N(mol C),1
d,1
mmol Nm,3
d,1 (mmol Nm,3 ),1
d,1 (mmol Nm,3 ),2
|
mol N(mol C),1
d,1
mmol Nm,3
|
mol N(mol C),1
mmol Nm,3 d,1
d,1
d,1 (mmol Nm,3 ),1
|
|
Ken Denman
d phy = min par ; no3 phy , phy2
zoo
phy
phy;no3 phy , zoo
2
dt
phy + par no3 + Kno3
phy2 + Kfood
d zoo = (1 , "
phy2
zoo , zoo;no3 zoo2
zoo;no3 )zoo
2
dt
phy2 + Kfood
d no3 = , min par ; no3 phy
phy
dt
phy + par no3 + Kno3
+"zoo;no3 zoo phy2phy
+ K2
2
food
zoo + phy;no3 phy + zoo;no3 zoo2
Scott Doney
d phy = phy 1 , e, 1HN par=phy chl
dt
1
HN
,zoo phy (1 , e,c phy=zoo ) zoo , phy;no3 phy , phy;det phy2
d zoo = (1 , "
,c phy=zoo )zoo , zoo;no3 zoo2 , zoo;no3 zoo
zoo;det )zoo phy(1 , e
dt
d no3 = , phy 1 , e, 1HN par=phy chl + phy;no3 phy
dt
1
HN
+zoo;no3 zoo + zoo;no3 zoo2
d det = 2
,c phy=zoo )zoo , det;nul det
phy;det phy + "zoo;det zoo phy(1 , e
dt
d (chl=phy) = phy chl 1 , e, 1HN par=phy dt
1
HN
phyno3 par chl P
P
1
no3 + K HN , (HN , HN ) min E ; 1 , phy
no3
K
61
Dennis McGillicuddy
d phy = 1 , e, par=phy e, par=phy
phy
dt
,zoo (1 , 0:5phy=Kfood ) zoo
nh4
nh4 + Knh4
+
no3 e, nh4
no3 + Kno3
!
phy
d zoo = (1 , "
phy=Kfood
) zoo , (zoo;nh4 + zoo;nul) zoo
zoo;nh4 ) zoo (1 , 0:5
dt
,(zoo;nh4 + zoo;nul) zoo2
d no3 = , 1 , e, par=phy e, par=phy no3 e, nh4 phy
phy
dt
no3 + Kno3
d nh4 = , 1 , e, par=phy e, par=phy nh4 phy
phy
dt
nh4 + Knh4
+"zoo;nh4 zoo (1 , 0:5phy=Kfood ) zoo + zoo;nh4 zoo + zoo;nh4 zoo2
George Hurtt and Rob Armstrong
E phy , 1
UE = Ephy e E phy
N phy , 1
UN = Nphy e par
(Ephy )2 + ( par)2
q
no3 + nh4
N phy Knh4 + no3 + nh4
!
d phy = min(U chl; U phy) , 2phy;det
2phy;det phy , 1
exp
E
N
dt
2phy;det phy
phy;det
!
Knh4 no3
d no3 = , min(U chl; U phy)
E
N
dt
(Knh4 + nh4)(nh4 + no3)
d nh4 = , min(U chl; U phy) nh4(Knh4 + nh4 + no3) + E
N
dt
(Knh4 + nh4)(nh4 + no3) det;nh4 det
!
!
2phy;det
2 phy;det phy , 1 , d det =
exp
det;nh4 det
dt
2 phy;det phy
phy;det
chl
= min(UN =UE ; PHN )phy
62
Olaf Haupt and Uli Wolf
d phy = q par
phy
dt
2phy + ( par)2
nh4
nh4 + Knh4
, min phy;de1 phy ; phy;de1 phy
+
!
no3 e, nh4
phy , Gphy
no3 + Kno3
2
d zoo = (1 , "phy ) G + (1 , "de1 ) G + (1 , "de2 ) G , phy
de1
de2
zoo;nh4 zoo
zoo;de2
zoo;de2
zoo;de2
dt
,zoo;de1 zoo2 par
where
X2
food
GX = zoo (p phy2 + p pX de1
zoo
2 +p
2
phy
de1
de2 de2 ) Kfood + food
X = phy; de1; de2
p phy2 + pde1 de12 + pde2 de22
food = phy
pphy phy + pde1 de1 + pde2 de2
d no3 = , q par
phy
dt
2phy + ( par)2
no3 e, nh4
nh4
phy + nh4;no3
no3 + Kno3
par
d nh4 = , q par
phy
dt
2phy + ( par)2
nh4
nh4
phy , nh4;no3
nh4 + Knh4
par
+de1;nh4 de1 + de2;nh4 de2 + zoo;nh4 zoo
d de1 = min 2
phy;de1 phy ; phy;de1 phy
dt
+zoo;de1 zoo2 par , Gde1 , de1;nh4 de1
d de2 = "phy G + "de1 G + ("de2 , 1) G , de2
de2;nh4 de2
zoo;de2 phy
zoo;de2 de1
zoo;de2
dt
63
Veronique Garcon, Isabelle Dadou and Francois Lamy
d phy = 1 , e, par=phy e, par=phy no3 phy
phy
dt
no3 + Kno3
pphy phy2
,zoo p phy
+ pde1 de1 zoo
phy
d zoo = (1 , "
zoo;de1 , "zoo;de2 ) zoo food zoo , (zoo;de1 + zoo;no3 ) zoo
dt
where
food
2
+ pde1 de12
= ppphy phy
phy + p de1
phy
de1
d no3 = , 1 , e, par=phy e, par=phy no3 phy + phy
zoo;no3 zoo
dt
no3 + Kno3
+do2;no3 do2 + do1;no3 do1
d do1 = det;do1 det;do1 de2 + det;do1det;do1 de1 , dt
det;do1 + det;do1 de2 det;do1 + det;do1 de1 do1;no3 do1
d do2 = det;do2 det;do2 de2 + det;do2det;do2 de1 , dt
det;do2 + det;do2 de2 det;do2 + det;do2 de1 do2;no3 do2
pde1 de12
d de1 = zoo;de1 zoo + "zoo;de1 zoo food zoo , zoo
dt
pphy phy + pde1 de1 zoo
;do1 de1 , det;do2 det;do2 de1
, det;do1+det
det;do1 de1 det;do2 + det;do2 de1
det;do1
d de2 = zoo;de2 zoo + "zoo;de2 zoo food zoo
dt
;do1 de2 , det;do2 det;do2 de2
, det;do1+det
det;do1 de2 det;do2 + det;do2 de2
det;do1
64
FDM; M. K. Sharada
d phy = (1 , "
par
phy;don )phy p 2
dt
phy + ( par)2
,Gphy , phy;det phy
nh4
nh4 + Knh4
!
no3 e, nh4
+ no3
+ Kno3 phy
d zoo = (1 , "phy )G + (1 , "bac )G + (1 , "det )G
phy
bac
det
zoo;det
zoo;det
zoo;det
dt
,(zoo;nh4 + zoo;don + zoo;nul)zoo
where
X2
food
GX = zoo (p phy2 + p pX bac
zoo
2 +p
2) K
det
phy
bac
det
food + food
X = phy; bac; det
8
phy + pbac bac + pdet det
>
< pphy
FDM
= > pphy phy + pbac bac + pdet det
: pphy phy + pbac bac + pdet det
Sharada
2
food
2
2
d bac = bac min(nh4; don) + don , bac
dt
KNbac + min(nh4; don) + don bac;nh4 bac , Gbac
no3 e, tnh4
d no3 = , p par
phy
phy
dt
2phy + ( par)2 no3 + Kno3
d nh4 = , p par
nh4
min(nh4; don)
phy , bac bac bac
phy
2
2
dt
KN + min(nh4; don) + don
phy + ( par) nh4 + Knh4
+bac;nh4 bac + zoo;nh4 zoo
d don = "
par
phy;don phy p 2
dt
phy + ( par)2
nh4
nh4 + Knh4
+
!
no3 e, nh4
phy
no3 + Kno3
don
+zoo;don zoo + det;don det , bac bac K bac + min(nh4
; don) + don
N
d det = "phy G + "bac G + ("det , 1) G
det
zoo;det phy
zoo;det bac
zoo;det
dt
+phy;det phy , det;don det
65
Helge Drange
d phy = (1 , "
par
phy;don ) phy p 2
dt
phy + ( par)2
;det phy2
, phy;det+phy
phy;det phy
phy;det
nh4
nh4 + Knh4
!
no3 e, nh4
+ no3
+ Kno3 phy , Gphy
d zoo = min U ; U Z , zoo zoo zoo2 ( + + )
N C NC
dt
zoo + zoo zoo nh4 don nul
where
X2
food
GX = zoo (p phy2 + p pXbac
zoo
2 +p
2
phy
bac
det det ) Kfood + food
X = phy; bac; det
p phy2 + pbacbac2 + pdetdet2
food = phy
pphy phy + pbacbac + pdet det
bac
det
UN = (1 , "phy
zoo;det ) Gphy + (1 , "zoo;det ) Gbac + (1 , "zoo;det ) Gdet
P
bac
B
det
UC = (1 , "phy
zoo;det ) Gphy =NC + (1 , "zoo;det ) Gbac =NC + (1 , "zoo;det ) Gdetcar
d bac = min
BNC doncar ; nh4 + don
bac
dt
KNbac + BNC doncar KNbac + nh4 + don
!
bac , bac;nh4 bac , Gbac
no3 e, nh4
d no3 = , p par
phy
phy
dt
2phy + ( par)2 no3 + Kno3
d nh4 = , p par
nh4
phy + bac;nh4 bac
phy
2
2
dt
phy + ( par) nh4 + Knh4
nh4; max(0; B
NC doncar , don)) bac + nh4 zoo zoo zoo
,bac min(
bac
B
+ zoo
K + min( doncar; don + nh4)
2
N
NC
zoo
!
zoo
d don = "
nh4
par
no3 e, nh4
+
phy + det;don det
phy;don phy p 2
dt
phy + ( par)2 nh4 + Knh4 no3 + Kno3
zoo2
min(BNC doncar; don)
+don zoo+zoo
,
bac bac
zoo zoo
KN + min(BNC doncar; don + nh4) bac
zoo
d det = "phy G + "bac G + ("det , 1)G
det
zoo;det phy
zoo;det bac
zoo;det
dt
;det phy2 , + phy;det+phy
det;don det
phy
phy;det
phy;det
66
nh4
d doncar = "
par
no3 e, nh4
+
phy;don phy p 2
dt
phy + ( par)2 nh4 + Knh4 no3 + Kno3
2
+ zoo;don zoo;don zoo B + det;don detcar
(zoo;don + zoo;don )zoo NC
!
phy=PNC
,bac K bac + min(Bdoncar
bac
doncar; don + nh4)
N
NC
d detcar = "phy G =P + "bac G =B + ("det , 1)G
detcar
zoo;det phy NC
zoo;det bac NC
zoo;det
dt
;det phy2 =P , + phy;det+phy
phy;det phy NC det;don detcar
phy;det
Tom Anderson
, par=phy d phy = (1 , "
phy;don ) phy 1 , e
dt
;det phy2
,Gphy , phy;det+phy
phy;det phy
phy;det
nh4
nh4 + Knh4
+
!
no3e, nh4
phy
no3 + Kno3
d zoo = (1 , "
zoo;don , "zoo;nh4 , "zoo;det , "zoo;nul )(Gphy + Gbac + Gdet )
dt
zoo2
, zoo+zoo
zoo zoo (nh4 + nul)
zoo
where
food
X2
zoo
GX = zoo (p phy2 + p pXbac
2 +p
2
phy
bac
det det ) Kfood + food
X = phy; bac; det
p phy2 + pbacbac2 + pdet det2
food = phy
pphy phy + pbacbac + pdetdet
d bac = min BNC (1 , "bac;nul) doncar ; don + nh4
bac
N + don
N + don Kbac
N + nh4
dt
Kbac
Kbac
,bac;don bac , bac;nul bac , Gbac
d no3 = , 1 , e, par=phy no3 e, nh4 phy
phy
dt
no3 + Kno3
67
!
bac
d nh4 = , 1 , e, par=phy nh4 phy + phy
bac;nh4 bac
dt
nh4 + Knh4
zoo2
+ zoo+zoo
zoo zoo nh4 + "zoo;nh4(Gphy + Gbac + Gdet )
zoo
!
,
nh4
don , B
(1
,
"
bac;nul ) doncar
NC
; K N + nh4 bac
+bac max
N + don
Kbac
bac
!
, par=phy d don = "
nh4
no3e, nh4
1
,
e
+
phy
phy;don phy
dt
nh4 + Knh4 no3 + Kno3
+det;don det + "zoo;don (Gphy + Gbac + Gdet ) , bac K N don
+ don bac
bac
phy;det phy;det phy2 , d det = ,G + "
det
zoo;det (Gphy + Gbac + Gdet ) +
dt
phy;det + phy;det phy det;don det
"
d doncar = 1 , e, par=phy "phy;don
phy
dt
PNC
nh4
nh4 + Knh4
+
!#
no3 e, nh4
no3 + Kno3
!
no3e, nh4
+"phy;doncar 1 , nh4nh4
,
+ Knh4 no3 + Kno3 phy
zoo2
Z
B
+ zoo+zoo
zoo zoo don =NC + det;don detcar + bac;don bac=NC
zoo
don
!
doncar
1
nh4
,bac min K N + don ; B (1 , "
+ K N + nh4 bac
N
bac;nul ) Kbac + don
bac
bac
NC
!
Gphy + Gbac + G detcar
d detcar = ,G detcar + "
det
zoo;det
det
dt
det
det
PNC BNC
;det phy2 1 + zoo zoo zoo2 =Z , + phy;det+phy
phy;det phy PNC zoo + zoo zoo det NC det;don detcar
phy;det
68
Diana Ruiz-Pino
no3
d ph1 = (1 , "
nh4
ph1;don )ph1 f1 (par)
dt
Kno3 + no3 (1 , )+ Knh4 + nh4 ph1 , ph1;de1ph1 , Gph1
where
f1 (par) = 1 , e,1 par=ph1 e,1 par=ph1
=
no3
1
no3 + nh4
+ (1 , 1 )
no3
no3 + nh4
2
d ph2 = (1 , "
S
1
ph2 , Gph2
ph2;don )Uph2 , min ph2;de1 ; ph2;de1 +
dt
sil
where
nh4
sil
Lph2 = 1 , e,2 par=ph2 e,2 par=ph2 min K no3
(1
,
)
+
;
Knh4 + nh4 Ksil + sil
no3 + no3
Uph2 = ph2 Lph2 ph2
1 + d zo1 = (1 , "
1
)(
G
+
G
)
,
min
;
+
zo1;de1
ph1
bac
zo1;de1 zo1;de1
zo1;nh4 zo1 , Gzo1
dt
food1
where
2
GX = zo1 (p ph1p2X+Xp bac2 ) K food1
zo1; X = ph1; bac
ph1
bac
food1 + food1
p ph12 + pbacbac2
food1 = ph1
pph1ph1 + pbacbac
2 + d zo2 = (1 , "
1
)(
G
+
G
)
,
min
;
+
zo2;de2
ph2
zo1
zo2;de2 zo2;de2
zo2;nh4 zo2
dt
food2
where
2
GY = zo2 (p ph2p2Y+Y p zo22 ) K food2
zo2; Y = ph2; zo1
ph2
zo1
food2 + food2
p ph22 + pzo1zo12
food2 = ph2
pph2ph2 + pzo1zo1
d bac = (1 , "
min(nh4; don) + don
bac;don )bac bac
dt
K + min(nh4; don) + don bac , bac;nh4 bac , Gbac
N
d no3 = , f (par) no3 (1 , ) ph1 ,
ph1 1
dt
Kno3 + no3
69
Uph2 Kno3no3
(1 , )
+no3
no3
nh4
Kno3+no3 (1 , ) + Knh4+nh4
+ nh4;no3 nh4
nh4
d nh4 = zo1;nh4 zo1 + zo2;nh4 zo2 + bac;nh4 bac , ph2 f1 (par)
dt
Knh4 + nh4 ph1
nh4
U
nh4; don)
, no3 ph2 Knh4+nh4 nh4 , bac K bac +min(
min(nh4; don) + don bac
Kno3+no3 (1 , ) + Knh4+nh4
N
,nh4;no3 nh4
no3
d don = "
nh4
f
(
par
)
(1
,
)
+
ph1;don ph1 1
dt
Kno3 + no3
Knh4 + nh4 ph1
+zo1;don zo1 + zo2;don zo2 + de1;don de1 + de2;don de2 + "ph2;don Uph2
nh4; don) + don
bac
+"bac;don bac K bacmin(
+
min(
nh4; don) + don
N
don
,bac K bac + min(nh4
; don) + don bac
N
d de1 = S ph2
1
ph1
+
min
;
+
ph1;de1
ph2;de1 ph2;de1
dt
sil
1 ) zo1
+"zo1;de1 (Gph1 + Gbac) + min(zo1;de1 ; 1
zo1;de1 +
food1
,de1;don de1
d de2 = "
1 ) zo2 , 1
zo2;de2 (Gph2 + Gzo1 ) + min(zo2;de2 ; zo2;de2 +
de2;don de2
dt
food2
S ph2sil , G ph2sil
d ph2sil = 1
L
ph2sil
,
min
;
+
ph2sil ph2
ph2;de1 ph2;de1
ph2
dt
sil
ph2
d de1sil = , min S
1
ph2sil , det;sil de1sil
ph2;de1 ; ph2;de1 +
dt
sil
d de2sil = G ph2sil , ph2
det;sil de2sil
dt
ph2
d sil = ph2sil
det;sil (de1sil + de2sil) , Uph2
dt
ph2
70
Pascal Prunet
This model is derived from that of Diana Ruiz-Pino but diers in the following ways. The
Wroblewski (1977) interaction of no3 and nh4 is used. Large phytoplankton, ph2, and all silicate
variables are omitted. Large zooplankton, zo2, eat ph1 instead. (To avoid duplication the
amount of grazing is still denoted by Gph2.) Phytoplankton mortality is less at high nutrient
concentrations:
N min ph1;de1 ; 1
+
ph1;de1
no3 + nh4
There are three classes of detritus, whose equations are
d de1 = ph1;de1 ph1 + zo1;de1 zo1 , de1;don de1
dt
d de2 = ph1;de2 ph1 + zo1;de2 zo1 + "zo1;de2 (Gph1 + Gbac ) , de2;don de2
dt
d de3 = "
zo2;de2 (Gph2 + Gzo1 ) , de3;don de3
dt
Parameter values
Some parameters are omitted from the following table because they occur in only one model:
[A] Scott Doney: 1
HN = 1:0; EK = 90: The remineralization of detritus goes to the single
combined dissolved inorganic nitrogen component, which we call no3 here.
[B] George Hurtt: = ,3:26; the sinking rate of detritus is V (eV P , 1)=V P where
V = :0024; V = :3456. Thus the value in the table is the limit as P ! 0.
[C] Scott Doney, Helge Drange: The parameters are temperature-dependent: the values given
are for 20 C. In general multiply by eQ(T ,20) where Q = 1:88.
[D] Diana Ruiz-Pino: 1 = ,0:21; 2 = 0:2; ph2sil = 1:04 if ph2sil < 3:47 ph2; else =0.
1
Ksil = 8; 1 = 2 = 0:024; S = 0:035; 1
zo1;de1 = zo2;de3 = 0:03.
[E] Uli Wolf: The rate of remineralization of nh4 to no3 increases as light decreases. The
quadratic zooplankton mortality rate increases with light. Sinking rate increases with depth
according to the thickness of the numerical layer: the value given is for the surface.
[F] Veronique Garcon: The constant losses from det to don at high det concentrations are
det;don = 3:9; 1:3 for small and large detritus respectively.
[G] Tom Anderson: The zooplankton mortality parameters like : zoo ! nul stand for
zoo nul in the list of his equations.
71
72
Growth terms Denman Doney McGill. Hurtt Wolf Garcon Sharada Evans Drange Anderson Prunet
Ruiz
Phytoplankton
phy
2.0
2.1
0.66 1.2, 2.8 0.8
2.0
2.9
0.68
2.15
2.9
2.0
2.46, 1.07
0.1
0.04
0.04
0.72 .025
0.1
0.04
0.23 0.026
0.025 0.23, 0.18 0.23, 0.18
.0002
0.01
.002, .002 .002, .002
Kno3 0.25
0.2
0.2
0.01
1.5
0.5
0.5
0.44
0.5
0.5
0.5
0.42, 1.62
Knh4
0.05
1.0
0.5
0.6
0.5
0.5
0.5
0.1, 0.4
27.2
1.5
1.5
0.68
1.5
1.5
1.5
PHN
2.5
6.7
.151
.151
PNC
Bacteria
bac
2.0
2.0
2.0
2.0
KN bac
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.6
0.6
BNC
.196
.196
Zooplankton
zoo 0.35
0.69
0.3
1.0
0.74
1.0
1.0
0.48
1.0
1.0
1.09
1.0
1.0
1.0, 1.38 1.1, 1.38
Kfood 0.75
zoo
4.0
5.28
c
2.0
pphy
0.7
0.5
0.33
0.59
0.5
0.333
0.8, 0.5
0.8, 0.5
pbac
0.33
0.20
0.25
0.333
0.2
0.2
pdet
.1, .2 0.5
0.33
0.21
0.25
0.333
ZCN
0.182
Extras
[A,C]
[B]
[E]
[C]
[D]
73
Extras
phy
det
Sinking
phy ! don
zoo ! det
zoo ! no3
zoo ! nh4
zoo ! don
zoo ! nul
bac ! nul
": uptake
phy ! det
zoo ! no3
zoo ! nh4
zoo ! det
zoo ! nul
: quadratic
zoo ! det
zoo ! don
zoo ! nul
bac ! don
bac ! nh4
det ! nh4
det ! don
don ! no3
nh4 ! no3
0.3
0.2
10
[A]
0.3
0.1
0.18
0.1
0.5
0.25
0.13
0.39
0.02
.0024
[B]
-0.52
0.4
Loss terms Denman Doney McGill. Hurtt
: linear
phy ! det
0.5
phy ! no3
0.05
0.075
0.03
zoo ! no3
zoo ! nh4
0.09
.051, .004
.033, .0033
0.3, 0.1
0.15
Garcon
2, 4
[E]
1, 10
[F]
0.3, 0.4 .225, .075
0.1
0.1
0.25
.05
0.05
0.1
Wolf
1
0.25
0.25
0.05
0.15
0.045
0.34
0.36
0.36
0.04
0.05
.014
0.04
.021
0.018
5.
0.25
0.25
0.05
0.21
0.06
0.05
10
[G]
0.304
0.1
0.1
0.5
0.05
0.192
0.333
0.667
0.25
0.05
0.067
0.1
0.133
0.05
Sharada Evans Drange Anderson
0.1
Ruiz
1, 3, 10
0.3
0.3, 0.6
0.1,.09,.08
0.2
0.02
5, 88
[D]
0.1, .05
0.3, 0.6
0.1, 0.08
0.2
0.2
.075, .0165 .25, .075
.045
.045
.083, .025 .083, .025
0.015
Prunet
Inorganic carbon chemistry
Among the various models only ve described the chemistry of the carbonic acid system in seawater and its coupling with the ecosystem. The intention here is not to provide the reader with a
full description of the carbon chemistry routine the authors used, and whenever possible we will
simply give the appropriate bibliographic reference. We will try to emphasize the links between
the dissolved inorganic carbon and total alkalinity pools and the dierent biological compartments
playing a role in their evolution.
David Antoine and Andre Morel Sources and sinks of CO are ,PP + R, where PP
2
is the net primary production computed with the formulas of Chapter 2 in the tethered model
framework described in Chapter 3, and R = L(1 , f ) where
L = C : Chl(|PPdaily {z Chl : C} , | Chl
{z obs})
2
1
is the daily carbon loss, the dierence between the theoretical (term 1) and observed (term 2)
increase in chl; and f is the f-ratio either prescribed or computed from the annual value of PP
(Eppley and Peterson 1979). The export of organic carbon is X = L f (this quantity is assumed
to exit the model domain).
Sources and sinks of alkalinity are
(,PP RCO )[2RCA , PNC RCO ]
where RCO is the ratio of C xation via soft tissues formation to the total (soft plus carbonates)
C xation, and RCA is the ratio of C xation via calcium carbonates formation to the total (soft
tissues plus carbonates) C xation.
Tom Anderson The evolution equations for CO and alk are as in Bacastow (1981).
2
74
Helge Drange
0
1
kez
@ detcar + X
zoozoo zoo2 A phy
d CaCO3;k = f
k + zook ZNC
Z
@
P
V
CaCO3
dt
@z ez l=1 nul NC zoo + zoo zoo
l (phyl + zool )
where the rst and second terms in the main parenthesis are the particulate organic carbon and
the amount of zooplankton that falls out of the euphotic zone, respectively.
d CO2 = , p par
phy
dt
2phy + ( par)2
"
nh4
nh4 + Knh4
, nh4
3 e
+ NO
NO3 + KNO3
#
phy PNC , dCaCO3 =dt
zoo
P
+bac;nh4 bac BNC + zoo+zoo
zoo nh4 NC
2
zoo
zoo
d alk = ,dno3=dt + dnh4=dt , 2 dCaCO =dt :
3
dt
Pascal Prunet, Diana Ruiz-Pino
We will show here the modications of the dissolved inorganic carbon and total alkalinity
contents due to trophic activity in the simplest case of Pascal Prunet's model. The reader will
easily adapt them for Diana Ruiz-Pino's model.
"
d CO2 = "
min(nh4; don) + don
NC bac;don bac K bac + min(nh4; don) + don bac + bac;nh4 bac
dt
N
nh4
(1
,
)
+
+zo1;nh4 zo1 + zo2;nh4 zo2 ,phy f (par) K no3
Knh4 + nh4
no3 + no3
"
phy
no3
CaCO
nh4
3
, NC C
(1 , "phy;don ) phy f (par) K + no3 (1 , ) + K + nh4 phy
org
no3
nh4
+ min ; 1
+ 1 zo1 + min ; 1
+ 2 zo2
zo1;de1
zo1;de1
zo2;de2
food1
zo2;de2
food2
"
no3
d alk = ,2 CaCO3 (1,"
nh4
NC C
phy;don )phy f (par)
dt
Kno3 + no3 (1 , ) + Knh4 + nh4 phy
org
1
+ min zo1;de1 ; 1
zo1;de1 +
food1
2
zo1 + min zo2;de2; 1zo2;de2 + food
2
75
zo2
References
Anderson, T. R. 1992. Modelling the inuence of food C:N ratio and respiration on growth and
nitrogen excretion in marine zooplankton and bacteria. J. Plankton Res. 14: 1645-1671.
Anderson, T. R. 1993. A spectrally averaged model of light penetration and photosynthesis.
Limnol. Oceanogr. 38: 1403{1419.
Antoine, D. and A. Morel. 1995. Modelling the seasonal course of the upper ocean pCO2
(I) Development of a one-dimensional model. Tellus. 47B: 103-121.
Antoine, D. and A. Morel, 1995b. Modelling the seasonal course of the upper ocean pCO2
(II) Validation of the model and sensitivity studies. Tellus., 47B: 122{144.
Archer, D., 1995. Upper ocean physics as relevant to ecosystem dynamics: a tutorial. Ecolog.
Applic., 5: 724{739.
Archer, D., S. Emerson, T. Powell, and C. S. Wong, 1993. Numerical hindcasting of sea surface
pCO2 at Weathership Station Papa. Prog. Oceanog., 32: 319{351.
Arya, S. P. 1988. Introduction to Micrometeorology. Academic Press, New York, 307pp.
Bacastow, R., 1981. Numerical evaluation of the evasion factor, in : Carbon Cycle Modelling
(B. Bolin ed.), John Wiley. 95-101.
Bannister, T. T. 1974. Production equations in terms of chlorophyll concentration, quantum
yield, and upper limit to production. Limnol. Oceanogr. 19: 1{12.
Barnier, B., L. Siefriedt, and P. Marchesiello, 1995. Thermal forcing for a global ocean circulation
model using a three-year climatology of ECMWF analyses. J. Mar. Sys., 6: 363{380.
Bishop, J. K. B., and W. B. Rossow, 1991. Spatial and temporal variability of global surface solar
irradiance. J. Geophys. Res., 96: 16839{16858.
Bishop, J. K. B., J. McLaren, Z. Garrao, and W. B. Rossow, 1995. Documnetation and description of surface solar irradiance data sets produced for SeaWiFS. unpubl. man.
Bissett, W. P., M. B. Meyers, J. J. Walsh, and F. E. Muller-Karger, 1994. The eects of temporal
variability of mixed layer depth on primary productivity around Bermuda. J. Geophys. Res.,
99: 7539{7553.
Breon, F.-M., R. Frouin, and C. Gautier, 1991. Downwelling longwave irradiance at the ocean
surface: an assessment of in situ measurements and parameterizations. J. Appl. Meteor.,
30: 17{31.
Broecker, W. S. and T. H. Peng, 1982. Tracers in the Sea, Eldigeo Press, Lamont-Doherty Geological Observatory, Palisades, NY, 690 pp.
Budyko, M.I., 1974: Climate and Life. International Geophysics Series, 18, Academic Press.
Bunker, A. F., 1976. Computation of surface energy ux and annual air-sea cycle of the North
Atlantic Ocean. Mon. Weather. Rev., 104: 1122{1140.
Dadou, I. and F. Lamy, 1996, Modele unidimensionnel integre en mode force: Application au
site oligotrophe d'EUMELI, Rapport JGOFS-France No 22, 34 pp.
76
Dadou, I. C. and V. G. Garcon, 1993. EUMELI oligotrophic site: response of an upper ocean
model to climatological and ECMWF atmospheric forcing. J. Mar. Systems. 4: 371{390.
Denman, K. L., 1973. A time-dependent model of the upper ocean. J. Phys. Oceanogr., 3: 173184.
Denman, K. L. and A. E. Gargett, 1995. Biological-physical interactions in the upper ocean: the
role of vertical and small scale transport processes, Ann. Rev. Fluid Mech., 27: 225-255.
Denman, K. L., and M. Miyake, 1973. Upper layer modication at ocean station PAPA: observations and simulation. J. Phys. Oceanogr., 3: 185{196.
Dennis, J. E. and R. B. Schnabel. 1983. Numerical Methods for Unconstrained Optimization and
Nonlinear Equations. Prentice-Hall. 378p.
Dickey, T., 1991. The emergence of concurrent high-resolution physical and bio-optical measurements in the upper ocean and their applications. Reviews Geophys., 29: 383{413
Dickey, T., T. C. Granata, and I. Taupier-Letage, 1992 . Automated in situ observations of upper
ocean biogeochemistry, bio-optics, and physics and their potential use for global studies.
Proceedings of the ocean Climate Data Workshop, February 18-21, Goddard Space Flight
Center, Greenbelt, Maryland, US NOAA and NASA publ., 317-353.
Dobson, F. W. and S. D. Smith, 1988. Bulk models of solar radiation at sea. Q. J. R. Meteorol.
Soc., 114: 165{182.
Doney, S. C., 1996. A synoptic atmospheric surface forcing data set and physical upper ocean
model for the U.S. JGOFS Bermuda Atlantic Time-Series Study site. J. Geophys. Res.,
Oceans, 101: 25615{25634.
Doney, S. C., D. M. Glover, and R. G. Najjar, 1996. A new coupled, one-dimensional biological{
physical model for the upper ocean: applications to the JGOFS Bermuda Atlantic Time
Series (BATS) site. Deep-Sea Res. II, 43: 591{624.
Dorman, C. E., and R. H. Bourke, 1979, Precipitation over the Pacic ocean, 30 S to 60 N, Mon.
Wea. Rev., 107: 896{910.
Dorman, C. E., and R. H. Bourke, 1981. Precipitation over the Atlantic Ocean, 30 S to 70 N.
Mon. Wea. Rev., 109: 554{563.
Drange, H. 1994. An isopycnic coordinate carbon cycle model for the North Atlantic. Tech.
Rept. 93, Nansen Environmental and Remote Sensing Center, Bergen, Norway.
Ducklow, H. W. and R. P. Harris, 1993. Introduction to the JGOFS North Atlantic Bloom
Experiment. Deep-Sea Res., Part II, 40: 1{8.
Eppley, R. W. and B. J. Peterson, 1979. Particulate organic matter ux and planktonic new
production in the deep ocean. Nature, 282: 677-680.
Esbensen, S. K. and Y. Kushnir, 1981. The heat budget of the global ocean: atlas based on
estimates from surface marine observations. Climatol. Res. Inst., Rep. 29, Oregon State
Univ., Corvallis, USA.
Etcheto, J., and L. Merlivat, 1988. Satellite determination of the carbon dioxide exchange
coecient at the ocean-atmosphere interface: a rst step. J. Geophys. Res., 93: 15669-15678.
77
Evans, G. T. and M. J. R. Fasham. 1993. Themes in modelling ocean biogeochemical processes.
In G. T. Evans and M. J. R. Fasham, eds. Towards a Model of Ocean Biogeochemical Proceses. Springer. 1-19.
Evans, G. T. and J. S. Parslow. 1985. A model of annual plankton cycles. Biol. Oceanogr.
3: 327{347.
Fasham, M. J. R., H. W. Ducklow, and S. M. McKelvie. 1990. A nitrogen-based model of plankton
dynamics in the oceanic mixed layer. J. Mar. Res. 48: 591{639.
Fasham, M. J. R. and G. T. Evans. 1995. The use of optimization techniques to model marine ecosystem dynamics at the JGOFS station at 47 N 20 W. Phil. Trans. R. Soc. Lond.
B348: 203-209.
Feldman, G., N. Kuring, C. Ng, W. Esaias, C. McClain, J. Elrod, N. Maynard, D. Endres, R.
Evans, J. Brown, S. Walsh, M. Carle and G. Podestra, 1989. Ocean color, availability of the
global data set. EOS Trans. Am. Geophys. Union, 70: 634{641.
Fung, I. Y., D. E. Harrison, and A. A. Lacis, 1984. On the variability of the net longwave radiation
at the ocean surface. Rev. Geophys. Space Phys., 22: 177{193.
Gargett, A.E., 1991. Physical processes and the maintenance of nutrient-rich euphotic zones.
Limnol. Oceanogr., 36: 1527{1545.
Gaspar, P., Y. Gregoris, and J.-M. Lefevre, 1990. A simple eddy kinetic energy model for
simulations of the oceanic vertical mixing: tests at Station Papa and long-term upper ocean
study site. J. Geophys. Res., 95: 16179{16193.
Gleckler, P. and K. Taylor. 1992. The eect of horizontal resolution on ocean surface heat uxes
in the ECMWF model. Climate Dynamics, 9, 17-32.
Glover, D.M. and P.G. Brewer, 1988: Estimates of wintertime mixed layer nutrient concentrations
in the North Atlantic. Deep-Sea Res., 35, 1525{1546.
Gregg, M. C., 1987. Diapycnal mixing in the thermocline: a review. J. Geophys. Res., 92: 5249{
5286.
Gregg, W. W. and K. L. Carder. 1990. A simple spectral solar irradiance model for cloudless
maritime atmospheres. Limnol. Oceanogr. 35: 1657{1675
Haney, R. L., 1971. Surface thermal boundary condition for ocean circulation models. J. Phys.
Oceanogr., 1: 145{167.
Heinze, C. E., E. Maier-Reimer and K. Winn, 1990. Glacial pCO2 reduction by the world oceanexperiments with the Hamburg Carbon Cycle Model. Report 57, Max-Planck Institut fur
Meteorologie, Hamburg.
Hellerman, S. and M. Rosenstein, 1983. Normal monthly wind stress over the world ocean with
error estimates. J. Phys. Oceanogr., 13: 1093-1104.
Hurtt, G. C. and R. A. Armstrong. 1996. A pelagic ecosystem model calibrated with BATS data.
Deep-Sea Research 43: 653-684.
Isemer, H. and L. Hasse, 1985a. The Bunker Climate Atlas of the North Atlantic Ocean, vol 1,
Observations, Springer-Verlag, New York, 218 pp.
78
Isemer, H. and L. Hasse, 1985b. The Bunker Climate Atlas of the North Atlantic Ocean, vol 2,
Air-Sea Interactions, Springer-Verlag, New York, 252 pp.
Jaeger, L., 1976. Monthly maps of precipitation for the whole world ocean. Dtsch. Wetterdienst
Ber., 18(139) Oenbach.
Jeandel et al., submitted. KERFIX, a time series in the Southern Ocean : a presentation, J.
Mar. Sys..
Jerlov, N. G., 1978. The optical classication of sea water in the euphotic zone. Report No. 36;
Inst. Fysisk Oceanogr., Copehagen Univ.
Kalnay, E., M. Kanamitsu, R. Kistler, W. Collins, D. Deaven, L. Gandin, M. Iredell, S. Saha,
G. White, J. Woollen, Y. Zhu, M. Chelliah, W. Ebisuzaki, W. Higgins, J. Janowiak, K. C.
Mo, C. Ropelewski, A. Leetmaa, R. Reynolds, and R. Jenne, submitted. The NMC/NCAR
reanalysis project. Bull. Amer. Meteor. Soc..
Kantha, L. H., and C. A. Clayson, 1994. An improved mixed layer model for geophysical applications. J. Geophys. Res., 99: 25235-25266.
Karl, D. M., and R. Lukas, 1996. The Hawaii Ocean Time-series (HOT) program: Background,
rationale and eld implementation. Deep-Sea Res., 43: 129{156.
Kent, E. C., P. K. Taylor, B. S. Truscott, and J. S. Hopkins, 1993. The accuracy of voluntary
observing ships' meteorological observations|results from the VSOP-NA. J. Atmos. Ocean.
Tech., 10: 591{608.
Knap, A., T. Jickells, A. Pszenny and J. Galloway, 1986. Signicance of atmospheric-derived
xed nitrogen on productivity of the Sargasso Sea, Nature, 320: 158{160.
Knox, J. L., 1991. An assessment of the 27-year record of measured precipitation at ocean
weather station \P" in the northeast Pacic Ocean. Clim. Bull. Canadian Met. Ocean Soc.,
25: 65{80.
Kraus, E. B. and J. S. Turner, 1967. A one-dimensional model of the seasonal thermocline, Part
II. Tellus, 19: 98-105.
Lancelot, C., S. Mathot, S. Becquevort, J. M. Dandois and G. Billien, 1993. Carbon and nitrogen
cycling through the microbial network of the marginal ice zone of the Soutehrn Ocean with
particular emphasis on the northwestern Weddell Sea. In S. Caschetto, ed., Belgian scientic
research program on the Antarctic - Scientic results of phase two (10/1988 - 05/1992)
Volume I: Plankton Ecology and Marine Biogeochemistry. 3-103.
Large, W. G., J. C. McWilliams, and S. C. Doney, 1994. Oceanic vertical mixing: A review and
a model with a nonlocal boundary layer parameterization. Rev. Geophys., 32: 363{403.
Large, W. G. and S. Pond, 1981. Open ocean momentum ux measurements in moderate to
strong winds. J. Phys. Oceanogr., 11: 324{336.
Large, W. G. and S. Pond, 1982. Sensible and latent heat ux measurements over the oceans. J.
Phys. Oceanogr., 12: 464{482.
Ledwell, J. R., A. J. Wilson, and C. S. Low, 1993. Evidence for slow mixing across the pycnocline
from an open-ocean tracer release experiment. Nature, 364: 701{703.
LeGates, D. R., and C. J. Wilmott, 1990. Mean seasonal and spatial variability in gaugecorrected, global precipitation. Int. J. Climatol., 10: 111{127.
79
LeGates, D. R., 1995. Global and terrestrial precipitation: a comparative assessment of existing
climatologies. Int. J. Clim., 15: 237{258.
Levitus, S., R. Burgett and T. P. Boyer, 1994 . World Ocean Atlas 1994 Volume 4 : Temperature,
NOAA Atlas NESDIS 4, 117 pp.
Levitus, S., R. Burgett, and T. R. Boyer , 1994 . World Ocean Atlas 1994 Volume 3 : Salinity,
NOAA Atlas NESDIS 3, 99 pp.
Liu, W. T., 1988. Moisture and latent heat ux variabilities in the tropical Pacic derived from
satellite data. J. Geophys. Res., 93: 6749{6760.
Liss, P. S. and L. Merlivat. 1986. Air-sea gas exchange rates: Introduction and synthesis. in
The Role of Air-Sea Exchange in Geochemical Cycling. ed. P. Buat-Menard. D. Reidel,
Hingham, Mass., USA, 113{129.
Lowry, R. K., Machin, P. and Cramer R. N. (compilers). 1994. BOFS North Atlantic Data Set,
Natural Environment Research Council (UK).
Maier-Reimer, E., 1993. Geochemical cycles in an ocean general circulation model. Preindustrial
tracer distributions. Global Biogeochem. Cycles, 7: 645-677.
Martin, P. J., 1985. Simulation of the ocean mixed layer at OWS November and Papa with
several models. J. Geophys. Res., 90: 903{916.
Matear, R. J. 1995. Parameter optimization and analysis of ecosystem models using simulated
annealing: A case study at Station P. J. Mar. Res. 53: 571-607.
McClain, C. R., K. Arrigo, K.-S. Tai, and D. Turk, 1996. Observations and simulations of
physical and biological processes at ocean weather station P, 1951-1980. J. Geophys. Res.,
101: 3697{3713.
McGillicuddy D.J., J.J. McCarthy and A.R. Robinson, 1995. Coupled physical and biological modelling of the spring bloom in the North Atlantic (I) : Model formulation and onedimensional bloom processes, Deep-Sea Research, 42: 1313-1357.
Mellor, G. L., and T. Yamada, 1982. Development of a turbulence closure model for planetary
boundary layers. J. Atmos. Sci., 31: 1791{1806.
Michaels, A. F., and A. H. Knap, 1996. Overview of the U.S. JGOFS Bermuda Atlantic Timeseries Study and the Hydrostation S program. Deep-Sea Res., Part II, 43: 157{198.
Montgomery, E. T, and R. W. Schmitt, 1994 . The annual cycle of freshwater forcing over the
Atlantic ocean. Ocean Sciences Meeting Abstract, EOS, Trans. Amer. Geophys. Union
75: 172.
Morel, A. 1988. Optical modeling of the upper ocean in relation to its biogenous matter content
(case 1 waters). J. Geophys. Res. 93: 10749{10768
Morel, A. 1991. Light and marine photosynthesis : a spectral model with geochemical and
climatological implications. Prog. Oceanogr. 26: 263{306
Morel, A., 1996: An ocean ux study in eutrophic, mesotrophic and oligotrophic situations : the
EUMELI program. Deep-Sea Res., EUMELI Special issue, in press.
Morel, A., and D. Antoine, 1994. Heating rate within the upper ocean in relation to its bio-optical
state. J. Phys. Oceanogr., 24: 1652{1665.
80
Murray, J. W., E. Johnson, and C. Garside, 1995. A U.S. JGOFS Process Study in the equatorial
Pacic (EqPac): Introduction. Deep-Sea Res., Part II, 42: 275{294.
Neckel, H. and D. Labs. 1984. The solar radiation between 300 and 12500 A. Sol. Phys. 90: 205{
258
Oberhuber, J. M., 1988. An atlas based on the `COADS' data set: the budget of heat, buoyancy and turbulent kinetic energy at the surface of the global ocean. Max-Plank-Institute
Meteorol. Rep., 15, 20 pp.
The Ocean Observing System Development Panel, 1995 . Scientic design for the Common Module of the Global Observing System and the Global Climate Observing System : An Ocean
Observing Sustem for Climate. Department of Oceanography, Texas A and M University,
College Station, Texas, 265 pp.
Paulson, C. A., and J. J. Simpson, 1977. Irradiance measurements in the upper ocean. J. Phys.
Oceanogr. 7: 952{956.
Payne, R. E., 1972. Albedo of the sea surface. J. Atmos. Sci, 29: 959-970.
Peng, T. H., T. Takahashi, W. S. Broecker and J. Olafsson, 1987. Seasonal variability of carbon
dioxide, nutrients and oxygen in the Northern North Atlantic surface water: observations
and a model. Tellus, 39B: 439-458.
Pinker, R. T., R. Frouin, and Z. Li, 1995. A review of satellite methods to derive surface shortwave
irradiance. Remote Sens. Environ., 51: 108-124.
Platt, T., C. L. Gallegos, and W. G. Harrison. 1980. Photoinhibition of photosynthesis in natural
assemblages of marine phytoplankton. J. Mar. Res. 38: 687{701
Platt, T., S. Sathyendranath, and P. Ravindran. 1990. Primary production by phytoplankton
: analytic solutions for daily rates per unit area of water surface. Proc. R. Soc. Lond B.
241: 101{111
Platt, T. and S. Sathyendrenath, 1993. Estimates of primary production for interpretation of
remotely sensed data on ocean color. J. Geophys. Res. Oceans, 98: 14561{14576
Pondaven, P., D. Ruiz-Pino D., C. Fravalo, and P. Treguer, in press. Modeling the biological
seasonal cycle in the permanently open zone of the southern ocean : Comparison of Si and
N cycles, J. Mar. Systems.
Press, W. H., S. A. Teukolsky, W. T. Vetterling and B. P. Flannery. 1992. Numerical Recipes in
C (2nd ed). Cambridge. 994p.
Price, J. F., R. A. Weller, and R. Pinkel, 1986. Diurnal cycling: observations and models of
the upper ocean response to diurnal heating, cooling, and wind mixing. J. Geophys. Res.,
91: 8411{8427.
Prunet, P., J.-F. Minster, D. Ruiz-Pino and I. Dadou. 1996a Assimilation of surface data in
a one-dimensional physical-biogeochemical model of the surface ocean (1). Method and
Preliminary results, Global Biogeochem. Cycles. 10: 111-138.
Prunet, P., J.-F. Minster, V. Echevin and I. Dadou. 1996b. Assimilation of surface data in a
one-dimensional physical-biogeochemical model of the surface ocean (2). Adjusting a simple
trophic model to chlorophyll, temperature, nitrate and pCO2 data. Global Biogeochem.
Cycles. 10: 139-158.
81
Reed, R. K., 1977. On estimating insolation over the ocean. J. Phys. Oceanogr., 7: 482{485.
Rossow, W. B. and R. A. Schier, 1991. ISCCP Cloud Data Products. Bull. Amer. Meteor. Soc.,
72: 2{20.
Sathyendranath, S. and T. Platt. 1993. Computation of aquatic primary production: Extended
formalism to include eect of angular and spectral distribution of light. Limnol. Oceanogr.,
34: 188{198.
Schmitt, R.W., 1994: The ocean freshwater cycle. CCC0{JSC Ocean Observing System Development Panel, Texas A & M University, College Station, TX 77843{3146, 32 pp.
Schmitt, R. W., P. S. Bogden, and C. E. Dorman, 1989. Evaporation minus precipitation and
density uxes for the North Atlantic. J. Phys. Oceanogr., 19: 1208{1221.
SCOR 1992. Joint Global Ocean Flux Study: Implementation Plan. JGOFS Report 9. Scientic
Committee on Oceanic Research.
Shea, D. J., K. E. Trenberth, and R. W. Reynolds, 1990. A global monthly sea surface temperature climatology. NCAR Technical Note NCAR/TN-345. 167pp.
Siefriedt, L. 1994. Validation des donnees de vent ERS-1 et des ux de surface du CEPMMT
dans le contexte de la modelisation des circulations oceaniques a l'echelle d'un bassin. Ph.D.
thesis, L'Universite Joseph Fourier-Grenoble, France. 200p.
Simpson, J. J., and T. D. Dickey, 1981. Alternative parameterizations of downward irradiance
and their dynamical signicance. J. Phys. Oceanogr., 11: 876{882.
Smith, E. L. 1936. Photosynthesis in relation to light and carbon dioxide. Proc. Nat. Acad. Sci.
20: 177{184
Smith, S. D. and F. W. Dobson, 1984. The heat budget at ocean weather station Bravo. AtmosphereOcean, 22: 1-22.
Spencer, R. W., 1993. Global oceanic precipitation from the MSU during 1979{91 and comparisons to other climatologies. J. Climate, 6: 1301{1326.
Stramska, M. and T. D. Dickey, 1994. Modeling phytoplankton dynamics in the northeast Atlantic during the initiation of the spring bloom. J. Geophys. Res., 99: 10,241{10,253.
Tabata, S., 1965. Variability of oceanographic conditions at ocean station P in the northeast
Pacic Ocean. Trans. R. Soc. Canada, Vol. III, Series IV, 367{418.
Thomas, F., V. Garcon, and J.-F. Minster, 1990. Modelling the seasonal cycle of dissolved oxygen
in the upper ocean at Ocean Weather Station P. Deep-Sea Res., 37: 463{491.
Trenberth, K. E., J. G. Olson, and W. G. Large, 1989. A global ocean wind stress climatology
based on ECMWF analyses. NCAR Tech. Note NCAR/TN-338+STR, 93pp.
Tricot, C., 1985. Estimation des ux chaleur en surface a la station meteo-oceanographique
Papa. Sci. Rep. 1985/9, Inst. d'Astron. et de Geophys. G. Lema^itre, Univ. Cath. de
Louvain, Louvain-La-Neuve, Belgium.
Wanninkhof, R. 1992. Relationship between wind speed and gas exchange over the ocean. J.
Geophys. Res. 97: 7373{7382.
Warren, S. G., C. J. Hahn, J. London, R. M. Chervin, R. L. Jenne, 1988. Global distribution of
total cloud and cloud type over the ocean. NCAR Tech. Note, NCAR-TN-317+STR.
82
Webb, W. L., M. Newton, and D. Starr. 1974. Carbon dioxide exchange of alnus rubra : a
mathematical model. Ecologia. 17: 281{291
Weller, R. A. and J. F. Price, 1988. Langmuir circulation within the oceanic mixed layer. DeepSea Res., 35: 711{747.
Weller, R. A., 1990. High quality meteorological measurements from research ships and buoys,
U.S. WOCE Planning Rep., 15: 13-33.
Weller, R. A., and P. K. Taylor, 1993. Surface conditions and air-sea uxes. CCCO{JSC Ocean
Observing System Development Panel, 131 pp., Texas A&M University, College Station, TX
77843{3146.
Wheeler, P. A. and S. A. Kokkinakis. 1990. Ammonium recycling limits nitrate use in the oceanic
subarctic Pacic. Limnol. Oceanogr. 35: 1267-1278.
Williams R., and G. A. Robinson, 1973. Primary production at Ocean Weather Station India.
(59 00N, 19 00W) in the North Atlantic, Bull. Mar. Ecol., 8: 115-121.
Wolf, K.-U. and J. D. Woods. 1992. Lagrangian simulation of primary production in the physical
environment { the deep chlorophyll maximum and nutricline. In B.J. Rothschild, ed. Toward
a theory on biological-physical interactions in the world ocean. Kluwer. 51-70.
Woodru, S. D., R. J. Slutz, R. L. Jenne, and P. M. Steurer, 1987. A comprehensive oceanatmosphere data set. Bull. Amer. Meteor. Soc., 68: 1239{1250.
Wroblewski, J. C. 1977. A model of phytoplankton plume formation during variable Oregon
upwelling. J. Mar. Res. 35: 357-394.
83
Participants
Tom Anderson
Southampton Oceanography Centre
European Way
Southampton SO14 3ZH
United Kingdom
fax: +44 1703 596247
tel: +44 1703 596337
email: [email protected]
Scott Doney
Climate and Global Dynamics Division
National Center for Atmospheric Research
Boulder CO 80307
USA
fax: +1 303 497 1700
tel: +1 303 497 1639
email: [email protected]
David Antoine
Laboratoire de Physique et Chimie Marines
Observatoire Oceanologique
BP 8
06230 Villefranche sur Mer
France
fax: +33 4 93 76 37 39
tel: +33 4 93 76 37 23
email: [email protected]
Helge Drange
Nansen Environmental and
Remote Sensing Center
Edv. Griegsvei 3a
5037 Solheimsviken
Norway
fax: +47 55 20 00 50
tel: +47 55 29 72 88
email: [email protected]
Shigeaki Aoki
National Institute of Resources
and Environment Technology
16 Onogawa, Tsukuba, Ibaraki 305
Japan
fax: +81 298 58 8357
tel: +81 298 58 8376
email: [email protected]
Geo Evans
Department of Fisheries and Oceans
Science Branch
PO Box 5667
St John's, NF A1C 5X1
Canada
fax: +1 709 772 3207
tel: +1 709 772 4105
email: [email protected]
Isabelle Dadou
UMR5566/GRGS
18 Avenue Edouard Belin
31055 Toulouse Cedex
France
fax: +33 5 61 25 32 05
tel: +33 5 61 33 29 54
email: [email protected]
Veronique Garcon
UMR556/CNRS/GRGS
18 Avenue Edouard Belin
31055 Toulouse Cedex
France
fax: +33 5 61 25 32 05
tel: +33 5 61 33 29 57
email: [email protected]
Ken Denman
Institute of Ocean Sciences
PO Box 6000
Sidney, BC V8L 4B2
Canada
fax: +1 250 363 6746
tel: +1 250 363 6346
email: [email protected]
George Hurtt
Ecology and Evolutionary Biology
Princeton University
Princeton NJ 08544
USA
fax: +1 609 258 1334
tel: +1 609 258 3868
email: [email protected]
84
Dennis McGillicuddy
Physical Oceanography Department
Woods Hole Oceanographic Institution
Woods Hole MA 02543
USA
fax: +1 508 457 2181
tel: +1 508 457 2000 ext 2683
email: [email protected]
Pascal Prunet
GMAP/AAD
Centre National de Recherches Meteorologiques
42, avenue G. Coriolis
31057 Toulouse Cedex
France
Tel: +33 5 61 07 84 54
Fax: +33 5 61 07 84 53
e-mail: [email protected]
Cathrine Myrmehl
Nansen Environmental and
Remote Sensing Center
Edv. Griegsvei 3a
5037 Solheimsviken
Norway
fax: +47 55 29 72 88
tel: +47 55 20 00 50
email: [email protected]
Diana Ruiz-Pino
Laboratoire de Physique et Chimie Marines
Tour 24-25
Universite Paris VI
4 Place Jussieu
75230 Paris Cedex 05
France
fax: +33 1 44 27 49 93
tel: +33 1 44 27 48 60
email: [email protected]
Andreas Oschlies
Institut fur Meereskunde
Dusternbrooker Weg 20
24105 Kiel
Germany
fax: +49 431 565 876
email: [email protected]
M.K. Sharada
CSIR Centre for Mathematical Modelling
and Computer Simulation
National Aerospace Laboratories
Belur Campus
Bangalore 560037
India
fax: +91 812 526 0392
tel: +91 812 527 4649
email: [email protected]
John Parslow
CSIRO Division of Fisheries
GPO Box 1538, Hobart
Tasmania 7001
Australia
fax: +61 02 325000
tel: +61 02 325202
email:[email protected]
Uli Wolf
Institut fur Ostseeforschung
Seestr. 15
18119 Warnemunde
Germany
fax: +49 381 5197 440
tel: +49 381 5197 260
email: [email protected]
Trevor Platt
Bedford Institute of Oceanography
PO Box 1006
Dartmouth, N.S. B2Y 4A2
Canada
fax: +1 902 426 9388
tel: +1 902 426 3793
email: [email protected]
85
The JGOFS Report Series includes the following:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Report of the Second Session of the SCOR Committee for JGOFS. The Hague, September 1988
Report of the Third Session of the SCOR Committee for JGOFS. Honolulu, September 1989
Report of the JGOFS Pacific Planning Workshop. Honolulu, September 1989
JGOFS North Atlantic Bloom Experiment: Report of the First Data Workshop. Kiel, March 1990
Science Plan. August 1990
JGOFS Core Measurement Protocols: Reports of the Core Measurement Working Groups
JGOFS North Atlantic Bloom Experiment, International Scientific Symposium Abstracts.
Washington, November 1990
Report of the International Workshop on Equatorial Pacific Process Studies. Tokyo, April 1990
JGOFS Implementation Plan. (also published as IGBP Report No. 23) September 1992
The JGOFS Southern Ocean Study
The Reports of JGOFS meetings held in Taipei, October 1992: Seventh Meeting of the JGOFS
Scientific Steering Committee; Global Synthesis in JGOFS - A Round Table Discussion; JGOFS
Scientific and Organizational Issues in the Asian Region - Report of a Workshop;
JGOFS/LOICZ Continental Margins Task Team - Report of the First Meeting. March 1993
Report of the Second Meeting of the JGOFS North Atlantic Planning Group
The Reports of JGOFS meetings held in Carqueiranne, France, September 1993: Eighth Meeting
of the JGOFS Scientific Steering Committee; JGOFS Southern Ocean Planning Group - Report
for 1992/93; Measurement of the Parameters of Photosynthesis - A Report from the JGOFS
Photosynthesis Measurement Task Team. March 1994
Biogeochemical Ocean-Atmosphere Transfers. A paper for JGOFS and IGAC by Ronald Prinn,
Peter Liss and Patrick Buat-Ménard. March 1994
Report of the JGOFS/LOICZ Task Team on Continental Margin Studies. April 1994
Report of the Ninth Meeting of the JGOFS Scientific Steering Committee, Victoria, B.C.
Canada, October 1994 and The Report of the JGOFS Southern Ocean Planning Group for
1993/94
JGOFS Arabian Sea Process Study. March 1995
Joint Global Ocean Flux Study: Publications, 1988-1995. April 1995
Protocols for the Joint Global Ocean Flux studies (JGOFS) core measurements (reprint). June,
1996
Remote Sensing in the JGOFS programme. September 1996
First report of the JGOFS/LOICZ Continental Margins Task Team. October 1996
Report on the International Workshop on Continental Shelf Fluxes of Carbon, Nitrogen and
Phosphorus. 1996
The following reports were published by SCOR in 1987 - 1989 prior to the establishment of the
JGOFS Report Series:
• The Joint Global Ocean Flux Study: Background, Goals, Organizations, and Next Steps. Report of the
International Scientific Planning and Coordination Meeting for Global Ocean Flux Studies. Sponsored
by SCOR. Held at ICSU Headquarters, Paris, 17-19 February 1987
• North Atlantic Planning Workshop. Paris, 7-11 September 1987
• SCOR Committee for the Joint Global Ocean Flux Study. Report of the First Session. Miami, January
1988
• Report of the First Meeting of the JGOFS Pilot Study Cruise Coordinating Committee. Plymouth, UK,
April 1988
• Report of the JGOFS Working Group on Data Management. Bedford Institute of Oceanography,
September, 1988