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 and JGOFS International Project Office Department of Earth and Planetary Sciences Centre for Studies of Environment and Resources The Johns Hopkins University University of Bergen Baltimore, MD 21218 5020 Bergen USA 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 Tel: (+47) 55 58 42 46 JGOFS International Project Office Fax: (+47) 55 58 96 87 Centre for Studies of Environment and Resources E-mail: jgofs@uib.no University of Bergen High-Technology Centre N-5020 Bergen, NORWAY or, from our website: http://ads.smr.uib.no/jgofs/jgofs.htm

Table of contents

1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1

2 Biogeochemical processes : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4

3 Biogeochemical models : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13

4 A common physical arena : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 18

5 Surface forcing : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 22

6 Running models, comparing with observations, interpreting : : : : : : : 27

7 Comparative behaviour of 1-D physical and ecological models:

preliminary results : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 33

8 Equations and parameters : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 57

References : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 76

Participants : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 84

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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 e�ort 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 a�ects 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 di�erent

locations, e�cient, and sensible (degrading gracefully when pushed to extremes). jgofs, the

International Geosphere-Biosphere Programme, and the U.S. O�ce 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 e�ectsof 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 e�ects of their particular

modi�cation. (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 di�erent models suggest about ecosys-

tem 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 mod-

els? Do the data give us enough information to choose among candidate models? These questions

1

relate not only to di�erent bgc models but also to di�erent 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 for-

mulate and explore models and how to formulate comparisons between models. Among fascinating

discussions and some frustrating failures, one can discern some tangible achievements. We pro-

duced 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 wereassembled in a systematic way ready for use by other researchers. We produced a preliminary

comparison of how well di�erent models can represent a single data set (although problems with

parameter estimation software prevented more than a preliminary comparison). We identi�ed

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 un�nished state. The workshop generated enthusi-

asm 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 di�erent

models have in common; the original papers can be consulted for the counterbalancing view ofhow 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 di�erent

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 windand 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 e�ciently.

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 Scienti�c 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 di�erent 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 di�erent 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 di�erent subprocess formulations (for example ways to represent the

interactions of nutrients and light, or nitrate and ammonium, or di�erent kinds of zooplanktonfood) 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 di�erent 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 di�erent stopgaps|perhaps concentrating on di�erentparts of what a reputable solution would contain|and evaluate the di�erence 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 a�ect 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-Pyren�ees, the UMR5566 laboratory and Jean-Fran�cois 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 scienti�c

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, theissues involved, and the choices that di�erent workshop models made. Although carbon is theelement of most interest to jgofs, the uptake of carbon by organisms is limited by some othernutrient or by energy. All models therefore use nitrogen as a currency for matter ow amongorganisms, 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 ratiocan change. Consumption appears immediately as population growth: internal pools are ignoredor parameterized. This is appropriate to a study of seasonal to interannual changes.

Models generally represent a community, whose species composition changes with season, bya 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. Tem-perature in uences many physiological rates, and some of the models include terms that take thisinto account.

2.2 Light: nature, propagation and absorption

Before considering in detail the individual biogeochemical processes, we describe the energy drivingthe 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 theearth. One can try for as accurate as possible based on real measurements: for example the modelof Gregg and Carder (1990) that uses properties of atmospheric transmission, either for an averagesolar elevation or integrated over the path of the sun through the sky, and perhaps including theEarth's orbital eccentricity. At the other extreme, perhaps just getting the integrated light over aday roughly right, say with the �rst 3 terms of a Fourier series �tted to the solstices and equinox, isappropriate remembering the much larger inaccuracies there will be in representing the ecologicalinteractions. Models that do not try to predict the dynamics of phytoplankton chlorophyll, but useit to compute primary production, may have a need for a more detailed and accurate treatmentof light.

2.2.2 Transmission

The main issue here is spectral dependence of transmission. The light in a spectral band decreasesexponentially with depth according to an attenuation coe�cient for that band, and the attenu-ated spectral bands at a given depth are added to give total light, perhaps weighted by the usephytoplankton can make of it. The only di�erence among models is whether they use one spectralband, (Evans), or two (Denman), or 19 (Wolf), or 61 (Antoine). The attenuation coe�cient isin uenced by chlorophyll. A further issue is the di�erence between downwelling irradiance (thequantity that is attenuated with depth) and scalar irradiance, which arrives from all directionsincluding upward scatter from below, and is the quantity that is used for photosynthesis.

David Antoine and Andr�e Morel Light propagation is modeled following Morel (1988):

par(z) =

Z �=700

�=400E(�; 0) g(�;chl) exp�

Z z

0

�Kw(�) + �(�)Chl(z)e(�)

�dz d�

4

The factor �(�) and the exponent e(�) are from Morel (1988). g is a geometrical factor to convertdownwelling irradiance to scalar irradiance. Garcon, Ruiz-Pino and Prunet adapted Antoine andMorel's approach for their models.

Ken Denman

par(z) = 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 higherattenuation coe�cient. Phytoplankton concentration does not a�ect the attenuation coe�cients.

Scott Doney

par(z) = 0:45E(0) exp��0:121 chl 0:428 z

�

(Morel, 1988). chl is the mean chlorophyll concentration within the euphotic zone.

Geo� Evans

par(z) = par(0) exp (�Kw + kc chl)

Bannister (1974). Hurtt and Armstrong, Sharada, McGillicuddy compute par(z) in the sameway.

Olaf Haupt and Uli Wolf

par(z) = par(0)n=19Xn=1

Vn exp

��Z z=ze

z=0(Kw;n + kc chl(z)) dz

�

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 whichit cannot readily exchange with the atmosphere, is a main route by which biological processesin uence ocean geochemistry. The processes and factors controlling it are better understood thanfor, say, zooplankton grazing. It is therefore both possible and perhaps desirable that models bemore 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 isnot 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. Thefraction of cell biomass that is chlorophyll can vary; some models take it to be constant, whileothers model phytoplankton nitrogen (phy) and chlorophyll (chl) as coupled dynamical vari-ables, obeying either separate di�erential equations or some algebraic relation that may changewith 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 pri-mary production per unit chlorophyll as a function of photons in terms of the maximum rate ofphotosynthesis PB

max, traditionally measured in units of gC gChl�1 h�1 and the initial slope �B

in gC gChl�1 h�1 (�Em�2 s�1)�1 where E is an einstein, a mole of photons. If we are modellingphy alone, then we want the population growth rate as a function of light (often expressed asenergy rather than photons) in terms of the maximum speci�c growth rate � in d�1 and the initialslope � in d�1 (W m�2)�1. There are of course no constant conversions between the di�erent setsof parameters, but the following values are not atypical:

5

1 gChl = 0:5mol N

1molN = 12 � 106 = 16 = 79:5 gC

1Wm�2 = 2:5 1018 Qm�2 s�1 = 106 � 2:5 �1018 = 6:022 �1023 = 4:15�E m�2 s�1

PBmax = 0:5 � 79:5=24 = 1:656�

�B = 0:5 � 79:5=4:15=24 = 0:4�

Photosynthesis-light curve The wavelength of light a�ects how e�ective it is in photosynthe-sis. Many models treat light as a scalar quantity, but it is more accurate to take account of itsspectral character, either in detail (Sathyendranath et al. 1989, Morel 1991) or in a computation-ally e�cient approximation of an e�ective light, E (Anderson 1993). The function describing howphytoplankton use E is typically described in terms of its initial slope, �, and maximum value,�. Candidates include

��E

�+ �EMichaelis-Menten

��Ep�2 + �2E2

Smith (1936)

��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 longerthe maximum growth rate; growth attains a maximum value which is hard to interpret as afunction of the parameters, at a �nite value of E which is equally hard to interpret. � is stillthe initial slope. The di�erences between the Smith and Webb curves with the same � and � arenot large, and would be even smaller if, instead of using the same parameters, one were to useparameters 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) combinedSmith's equation with an assumed triangular daily light function with day length D and totallight L during the day. If light is so high that photosynthesis is saturated whenever there is anydaylight then the growth in a day is GD = �D; if light is so low that photosynthesis is alwaysin the linear range then growth in a day is GL = �L. The concepts GD and GL are meaningfulfor all equations that are described by an initial slope and a maximum value, not just the Smithequation. If the light attenuation coe�cient k is constant over a layer of thickness M , then theaverage over a numerical layer of the total growth during the day is

G =GD

kM

��

�2GL

GD

�� �

�2GL

GDe�kM

��(1)

where

�(u) = ln�u+

p1 + u2

��p1 + u2 � 1

u: (2)

In the limit as u ! 0, �(u) ! u=2 so that G ! GL(1 � e�kM )=kM , which in turn ! GL askM ! 0. As u!1, �(u)! ln(2u) � 1 so that G ! GD. A useful approximation for �(u) is

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 of0.01 between u = 0 and u = 20. It also degrades slowly when pushed beyond the range for whichit 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 determinedby its initial slope and maximum value, and E decreases with depth at a constant exponentialrate, then, whatever the functional forms of G and of daily light variation, G is given by (1) forsome 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�2a#GLGD

�where

a#, a dimensionless function of depth and chlorophyll concentration, accounts for the change inspectrum.

2.3.2 Nutrients

Growth as a function of nutrients is most often expressed as a Michaelis-Menten (Monod) functionparameterized by its maximum value � and half-saturation abscissa K:

�no3

K + no3:

Dissolved inorganic nitrogen comes in two forms. Nitrate is generally associated with waternewly brought into the well-lit surface layer whereas ammonium is produced in situ by processesof regeneration. There is interest within jgofs in how much production is due to each (newand regenerated production), and therefore many models include expressions for computing theuptake of no3 and nh4 when both are present. One form for the uptake of nitrate and ammoniumrespectively (the ow into phytoplankton is the sum of the two):

�no3e� nh4

KN + no3;

�nh4

KA + nh4

was proposed by Wroblewski (1977) and used in FDM. Its main drawbacks are that the totalgrowth can be greater than the supposed maximum �, and for some values of no3 and nh4 thetotal uptake can be a decreasing function of nh4. Hurtt and Armstrong take nh4 uptake to be afunction of nh4, and total uptake to be a function of no3+nh4, to obtain the forms

�K no3

(K + nh4) (K + nh4+ no3);

�nh4

K + nh4:

Here the single parameter K means many di�erent things. In these formulas nh4 uptake isuna�ected by no3 concentrations whereas no3 uptake is inhibited by the presence of nh4. Thereare also formulas that allow phytoplankton to take up nh4 preferentially but also allow somereduction 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 Chapter8 for details). Evans and Fasham (1993) take a mechanistic, queuing theory approach in whichthe use of no3 requires an extra, reduction step whereas nh4 is already reduced. Although simpleenough in its own terms, this ends up looking complicated in �;K terms. For one thing, there isnot a single �: the maximum growth rate is less on no3 alone than on nh4 alone because of thetime 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 mightexpress 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 ofseparate resources as limiting factors reducing some theoretical maximum growth rate|factorsthat can be determined separately and then combined in one of a small number of ways. Forexample we might take the product of light and nutrient limitation terms, as in FDM, or theirminimum. But in principle it is just as easy to imagine that nutrient limitation reduces theparameter � in the P -I curve (or GD) but does not a�ect � (GL), or vice versa. This wouldprovide a form of interaction intermediate between product and minimum. We might have tothink, at least temporarily, about internal storage pools. Nutrient limitation of the instantaneousphotosynthetic rate might be less relevant if the nutrients can be obtained also at night whenthere is no photosynthesis to limit. Hurtt and Armstrong (1996) use the minimum of two separategrowth functions, each with its own maximum value, instead of two separate limiting factors fora single maximum growth rate.

We have dealt so far only with nitrogen as a limiting nutrient. None of the models consideredat the workshop considers carbon or iron as a limiting nutrient. Ruiz-Pino does consider silicatelimitation.

2.4 Bacteria

Bacteria contain both nitrogen and carbon, and we assume that they contain them in a constantratio �BNC (abbreviated, for this section only, as �). The following description of the issues isconceptually simple, and none of the models described in Chapter 8 treats bacteria in exactly thissimple way. A di�erent account, paying more careful attention to physiological issues, is givenin Anderson (1992). Consider �rst the mass balances implied in producing bacteria. Carbon isavailable 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 ofa single substance so that the ratio of the amounts processed is the same as the ratio of theamounts present. (That is, a dissolved organic molecule is completely broken into its constituentsif 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 thisassumption 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 dissolvedorganic 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 innh4 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 becomesCO2.

When we turn from the amount of product to the rate of production, we make a convenientand plausible, though by no means logically necessary, assumption: nitrogen and carbon limitproduction rate in the same ratio that they limit product. Thus the rate of growth of bac is

� min

��doncar

KN + �doncar;

don+ nh4

KN + don+ nh4

�bac:

The �rst term in the minimum corresponds to the carbon-limited ranges 1 and 2. What arethe rates of use of the constituents (suppressing the common factor �bac which multiplies all ofthem)? 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 ofuse of don is don=(KN + �doncar). When nitrogen is limiting, we can assume that there isno 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 bacminus the use of don. This works out to

min

��doncar� don

KN + �doncar;

nh4

KN + don+ nh4

�

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 di�erent 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 theirabundance and `wasting' the excess don as nh4.

Anderson makes the additional point that bacteria use organic carbon as an energy source aswell as a structural material, so that the amount of doncar that appears as new bacteria is lessthan the amount used. In range 3, bacteria respond separately to don and nh4 rather than totheir sum. That is, uptake of one form can be saturated while uptake of the other is still in thelinear range.

2.5 Zooplankton

Within these models, each type of zooplankton is modelled as a single variable following a di�er-ential equation. This is believed to be appropriate for protozoa, which are the zooplankton mostactive 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 di�erent possible functional forms,it is important that, to the extent possible, parameters are chosen to have the same meaning forthe di�erent forms. This will not always be possible, and even when it is the choice will not beunique. Do two di�erent Holling Type I curves have \the same" parameters if they have the sameinitial slope and maximum value, or if they have the same maximum value and half-saturationconcentration? If there are two di�erent functional forms possible, then the parameters shouldideally have the same meaning for each. For example, Michaelis-Menten and Ivlev forms of graz-ing are both linear for small food concentrations and constant for large ones. They might beparameterized by their initial slope, �, and maximum value, �, (as photosynthesis-light curvestraditionally are):

��x

�+ �xand �

�1� e��x=�

�

or by their maximum value and half-saturation abscissa, K, (as nutrient uptake curves tradition-ally are):

�x

K + xand �

�1� 0:5x=K

�:

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 identicallyzero. The half-saturation form is more useful here, for example a form that is quadratic for smallconcentrations and constant for large ones:

�x2

K2 + x2:

There are other classes of function, characterized most easily by behaviour at small and largefood concentrations: for example the rational and Mayzaud-Poulet forms that are quadratic forsmall concentrations and linear for large:

�x2

x+ �=cand �x

�1� e�cx=�

�

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 combinationof individual concentrations: for example FDM use the formula

� food

K + food

where

food =pphyphy

2 + pbacbac2 + pdetdet

2

pphyphy + pbacbac+ pdetdet

Notice that this food is not a monotone increasing function of its components: increasing a scarceprey type decreases the total amount of grazing. The formula was devised to achieve switching ofgrazing to the most abundant food type, in the interest of stability. Evans (unpublished) proposed

food = phy (1 + phy c=K) + bac (1 + bac c=K) + det (1 + det c=K)

grazing =� food

K(1 + c) + food

which accomplishes switching if c > 0 while at the same time making grazing a monotone functionof food density. If there is just one type of prey, then K is the half-saturation concentration. Theformula reduces to Michaelis-Menten when c = 0; when 1 + c is the golden ratio (� 1:62) thecurvature 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 examplenatural mortality, cell lysis and virus production, consumption of zooplankton by higher trophiclevels. Although they are generally poorly understood, not directly measured in the �eld andparameterized only crudely in current ecosystem models, the treatment of losses to non-livingpools can profoundly a�ect 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 simplestcase the rate of contribution is proportional to the ow (dimensionless allocation fraction boundedabove by 1) or compartment (dimensions of inverse time) but more complicated, non-proportionalfunctions have been considered, especially for losses from the zooplankton compartment thatmight either saturate or increase faster than linearly at high concentrations. There is no reasonin 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 bestconveyed by a table with transfers (the arrow indicating what it is transferred to) or compartmentsas rows, destinations of losses as columns, and functional forms that have been used in some modelas entries.

don det nh4 no3

!phy Lphy L, Q, QL, LE L!bac

bac L L L!zoo L L Lzoo 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 forsmall values and quadratic for large like ax+ bx2, and QL a loss that is quadratic for small valuesand linear for large, like ax2= (1 + bx). The loss from phytoplankton to detritus can take almostany form: LE describes the a(ebx�1) form of Hurtt and Armstrong (1996) that is linear for smallvalues and exponential for large. In the model of Anderson the fraction of primary production ofcarbon lost to dissolved organic carbon increases when inorganic nitrogen concentration is low.Losses from the zooplankton compartment generally represent the e�ect of carnivore populationsrather than physiological losses. The quadratic loss term that is common in describing zooplanktonmortality is often justi�ed on the grounds that a large zooplankton population engenders a largepopulation of carnivores to graze on it, although it omits the time lag that might be expected withreal population dynamics of carnivores. Also, in a vertically resolved model, it is not immediatelyclear whether the quadratic dependence should be on the zooplankton at a given level or on thevertically integrated zooplankton (if the carnivores are capable of changing their depth at will).

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 decayin the same ways; the only di�erence is that detritus can have a sinking velocity and is more likelyto be used by zooplankton as food. Decay of detritus to smaller classes is modelled; aggregationof non-living particles to larger classes is not a feature of any of the models considered at theworkshop.

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 dissolvesoon enough and once more be available for exchange with the atmosphere. Sinking particles areremoved 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, followinga spring diatom bloom when there are many small particles ready to collide and aggregate intolarger, rapidly sinking particles. In models with more than one size class of detritus, the relativeabundance 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 thatcomponent.

A model of the whole water column should include the nitri�cation of ammonium into nitrate.This happens mainly at depth, and in Uli Wolf's model the rate is explicitly inversely proportionalto par.

2.8 Inorganic carbon chemistry

Di�erent formulations of the equilibrium among bicarbonate, carbonate and dissolved CO2 (An-toine 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 therole 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 res-piration (the rest is respired at depth and re-enters the surface layer with the water movement).The production and loss terms are speci�ed in the individual dynamical models (those that havean explicit carbon component). The most common assumption is that transfers between organicand dissolved inorganic carbon are the same as between organic and dissolved inorganic nitrogen,multiplied by a constant Red�eld ratio. For the change in alk we need to take account of theformation 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

fCaCO3 =exp[0:6 (T � 10)]

1 + 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 temperaturesclose to 10�C, the biogenic formation of CaCO3 is 10% of the organic material that sinks out ofthe euphotic zone.

The total biologically-induced change in alkalinity is then

dalk

dt=�dno3dt

+dnh4

dt� 2

dCaCO3

dt:

Not all models consider the e�ect 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 describeeach model precisely (the original papers can be read for that) but to make it easy to compare

the structure of di�erent 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 ZOOQC

Q

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 modelis 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 in�nite sinking rate.

3.2 Scott Doney

NO3 PHY

DET

ZOOQL

Q

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 a�ecting 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 e�ects 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

NO3

NH4

PHY ZOO

LQ

LC

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 primar-ily controlled by local forcing (McGillicuddy et al. 1995). The in uence 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 Wrob-

lewski 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. Phyto-

plankton 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

NO3

NH4

PHY

DET

LE

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 di�erent 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-to-

nitrogen ratio adjusts, in response to light and nutrient availabilities, to make the two functions

equal when possible. Day-night di�erences 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 e�ects 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 zooplanktonmaking 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-di�erential equations).

3.5 Olaf Haupt and Uli Wolf

NO3

NH4

PHY

DET �2

ZOOLC

QL

Q

The detritus box in this diagram represents two similar but separate state variables in themodel: 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 nitri�cation

term and the zooplankton quadratic mortality term are modelled as light dependent functions.

3.6 V�eronique Gar�con, Isabelle Dadou and Fran�cois Lamy

NO3

DON �2

PHY

DET �2

ZOOL

LC

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 e�ect 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 di�erences as

indicated by the footnotes.

NO3

NH4

DON

BAC

PHY (2)

DET (2)

ZOO (2)LC

(1)

(5)(4)

(5)

(1)

(3)

(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 othermodels considered at the workshop, it has two di�erent 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 di�ers 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 Red�eld ratios. The models of Anderson and Drange consider

non-living forms of carbon and nitrogen as separate state variables. They are produced by di�erent

organisms in di�erent 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 (Pon-

daven et al. in press) computes the nitrogen (and implicitly carbon) content of 5 living com-

partments 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 statevariables. 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 concentra-

tions 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 theEppley 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 di�cult if each is driven by its own one-dimensional mixed layer model. Participants decided to develop a common physical arena, inwhich each ecosystem model in turn would be embedded. This section starts with a brief accountof current 1-dimensional models of vertical mixing, and then describes conceptual and practicalprogress 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 throughphysical 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 importantand are often condensed into a single measure of the vertical mixing pro�le, the turbulent eddydi�usivity Kz(z). The time evolution of the mean pro�le of a species X(z) is then given by:

@X

@t= �r~u �X +

@

@zKz

@X

@z+ Source

with terms for mean advection, vertical turbulent mixing, and sources such as in situ biologicaltransformations. The classic depth pro�le forKz includes a surface mixed layer with large (O(500)cm2 s�1) di�usivities above a strati�ed interior with small (O(0.1) cm2 s�1) di�usivities generatedby internal wave breaking and double di�usion (Gregg, 1987; Ledwell et al., 1993, Large et al.,1994). Most models capture the basic seasonal mixed layer structure, though they can di�er greatlyon speci�c details. The two regimes are separated by a transition region where the entrainmentinto the mixed layer actually occurs, and it is in this transition region where the behavior of thephysical models tends to diverge. The choice of model depends in part on the application andlevel of desired sophistication of the physics. More in-depth discussions are presented in a recentseries 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 ahomogeneous \mixed layer", the equivalent of setting Kz to a very large value; this class of modelsthen 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 andmay be well mixed for some species, for example temperature, but not others depending on therelative timescales of turbulence and the local source/sink terms; this may be particularly relevantfor biological species that undergo signi�cant diurnal cycles (Stramska and Dickey, 1994; Doney et

al., 1996). Turbulence closure (Mellor and Yamada 1982; Gaspar et al. 1990; Kantha and Clayson1994) and K-Pro�le (Large et al. 1994) approaches, in contrast, compute large �nite mixing ratesnear 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 trivialtask, involving the collection of the appropriate forcing and veri�cation data sets as well as theactual model simulations (Doney, 1996). One alternative that has been suggested is to use histor-ical temperature and salinity pro�les to diagnose a mixed layer depth, and then use that depthas one would in a bulk mixed layer model (e.g. Bisset et al., 1994).

In a further simpli�cation, several models at the workshop (Evans, Hurtt & Armstrong, Ander-son) ran the biogeochemical model in a so-called 0-D or bulk mixed layer arena. Here the mixedlayer depth changes with time, and one must account for entrainment and detrainment across thebottom boundary. The physical exchange is speci�ed from the rate of change of the boundary layer

18

depth hml, the background upwelling/downwelling velocity w, a turbulent exchange velocity wtacross the base of the mixed layer, typically taken as order a few tenths of md�1, and the speciesconcentration X0 below the mixed layer. Vertical advection is often treated as an asymmetricalprocess 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 averageconcentration over the mixed layer is then given by:

dX

dt=wt +max(w + dhml=dt; 0)

hml(X0 �X) (1)

An exception is generally proposed for zooplankton, which are assumed to concentrate in shoalingmixed 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 period1975-77 at Ocean Station P in the subarctic North Paci�c Ocean, with the aim of choosing singlemixed 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 optionof exploring a dynamically incorrect model, for didactic purposes. Also the dynamics requires ashorter 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 asfunctions of time and depth. We turn o� one feedback: the e�ect of phytoplankton concentrationon the penetration of radiant heat from the surface and thence on vertical mixing. This wasa deliberate choice that enabled us to compare all biogeochemical models in the same physicalframework.

4.3 Activities During the Workshop

It was obvious from the collected behaviour of the bgc models that modelled vertical di�usionbelow the mixed layer is too small to supply nutrients to the euphotic layer at Station P. An extraphysical mechanism, such as Ekman upwelling, is needed to supply nutrients to the surface toreplenish those lost to exported production.

One complication was that the models do not use a common bottom boundary condition. The0-D models could probably easily implement a common bottom boundary condition, but it wouldbe 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 boundarycondition 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 accept-able, in order to achieve a larger upward di�usive ux of nitrate from the bottom boundary.

(ii) Specify isopycnal (essentially horizontal) di�usion by estimating the isopycnal nitrate gra-dient (at scales greater than the mesoscale) and the isopycnal (or horizontal) turbulent di�usioncoe�cient Kh along isopycnals.

(iii) Specify Ekman upwelling at the base of the model. This option would be appropriatefor Station P, but might not su�ce at Bermuda where part of the year the surface ocean ow isconvergent with presumably a downwelling transport.

The simplest implementation is to specify a nitrate concentration immediately below the modeland a vertical upwelling current speed decreasing linearly from some value w = w

�h at the baseof the model z = z

�h, to w = 0 at the ocean surface z = 0. Such a recipe is divergent everywherewithin 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), forthe nutrient N can be written as:

@N

@t+r(u �N) = 0: (2)

If we assume incompressibility and horizontal homogeneity, this reduces to vertical advection:

@N

@t= �w

@N

@z(3)

If we specify the state variable n at the gridpoint at the centre of each layer k and the upwardadvection at each interface, as in the diagram, then we can use an upstream �nite di�erenceequation 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, forthe bottom layer m, eq. (5) becomes

�Nm = ��t w�h(Nm �Nd)=�z: (5)

mid-layer

interface

wk+1, (log10Kz)k+1

wk, (log10Kz)k

Nk

Nk+1

After the workshop, Ken Denman implemented this algorithm in his NPZ model coupled to anon-di�usive 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 e�ective 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 physicalprocesses, allowed the recharging of nitrate in the surface layer during autumn and winter as themixed layer deepens to its maximum winter penetration. This raises the issue of whether it makessense to use a climatological mean vertical pro�le of nitrate without also using climatologicalforcing and mixed layer depth. For example, the 1976 nitrate observations had large variationsbelow the mixed layer (eddies?) which showed little resemblance to the climatological annualnitrate cycle from Matear (1995). Do we use a mean annual pro�le or an annual climatologicalcycle, although Matear's plot did not show a clear annual cycle? Resetting rather than restoring(relaxing to climatology according to some speci�ed timescale) is easy to implement but maycause problems with ordinary di�erential equation solvers and the optimisation scheme. Duringthe workshop, we eventually settled on resetting the nitrates below the mixed layer to a meanvertical pro�le estimated from Matear (1995).

4.4 Implementing a Common Physical Arena

During the workshop, we discussed in detail several speci�c aspects of implementation of a commonphysical arena; the results of these discussions are summarized below.

20

(i) Atmospheric forcing. For surface solar radiation, winds, heat uxes, the options (for stationP) are (a) the 3-year time series (1975-77), (b) a mean annual cycle derived from the three years1975-77, 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 becalculated from the Ruiz-Pino model output (see Chapter 7). The climatological annual cycle inmixed layer depth could be taken from Matear (1995), but his summer mixed layer depth seemedtoo spikey, without an expected level or gradually deepening plateau as summer progressed. Thediagnosed climatological mixed layer depth provided by Howard Freeland (Institute of OceanSciences, Sidney, B.C.) seemed too deep in spring and summer because it tracked that maximumgradient 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.TheKz(z; t) �eld was used to choose which physical model to use to drive the ecosystem models. Ifwe were to use a climatological annual cycle of mixed layer thickness, and say there is one constantKz 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 couldbe speci�ed as follows:

logKz(z)� logKz(zM )

logKz(zD)� logKz(zM )= �2(3� 2�) where � =

z � zMzD � zM

:

The cubic function of scaled depth � ensures a smooth, spline-like join to the assumed constantmixing rates above and below; the logarithmic transformation is appropriate because the mixingrates above and below di�er by several orders of magnitude.

(iv) Restoring or resetting nitrate below the mixed layer. Restoring rather than resettingnitrate below the mixed layer reduces the possibility of introducing problems with the integra-tor/solver method used. We thought that a restoring time scale of 1 day would be appropriate witha restoring coe�cient of 1 in deep water and 0 in the upper mixed layer, with a cubic polynomialtransition in between.

21

5 Surface forcing

Surface forcing in uences marine ecosystems both directly (e.g. solar radiation, nutrient inputs)and indirectly through modi�cations of the physical environment and upper ocean boundary layer.This chapter discusses the air-sea uxes of momentum, heat, fresh water and dissolved gases air-sea uxes of heat and solar radiation; although, de�ned more broadly, forcing could include thevertical turbulent mixing �eld as well as any ux (e.g. momentum, energy, or material) acrossthe top, sides and bottom of the model domain. From a biogeochemical perspective, the mostimportant outputs from the physical model solutions are the �elds of temperature T and verticaldi�usivity K (m2 s�1) as functions of time and depth (see Chapter 4). Moreover, compared to adynamical model of mixing, a bgc model needs to know these quantities at relatively infrequentintervals, which is more e�cient.

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 di�cult to measure directly,and the spatial and temporal variability of atmosphere-ocean exchanges are one of the more poorlyknown aspects of the climate system (e.g. Weller and Taylor, 1993). More often surface forcing isspeci�ed using an empirical formula, calibrated at a few locations, and surface atmospheric datataken 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 basicframework for how air-sea uxes are computed for physical models is presented below, followedby a limited outline of available surface forcing and upper ocean data sets.

Perhaps the most straightforward forcing method is to restore the model surface temperatureTs and salinity Ss �elds to observed values (T0, S0) with a relaxation timescale :

Qnet =zscp�

(T0 � Ts) Fnet =

zs�

Ss(S0 � Ss)

where zs is the thickness of the surface layer and cp and � are the heat capacity and density ofseawater, respectively. Surface restoring accounts for both air-sea uxes and ocean advection, andremains a common, stable method for forcing 3-D ocean circulation models. A major drawbackwith restoring, however, is that the uxes are identically zero when the model �elds match theobservations, leading to weak seasonal cycles that lag those in the data. Numerous improvementsto the restoring method have been proposed (Haney, 1971), but the use of surface restoring iscurrently not widespread for 1-D upper ocean models.

A more common approach is to compute the air-sea uxes of momentum, heat and freshwaterusing traditional, bulk surface formulas. The bulk formulas require estimates of wind speed, airtemperature, air humidity, cloud cover and sea surface temperature. The air-sea uxes can becomputed 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 speci�ed from atmospheric climate or weathermodels (e.g. Dadou and Garcon, 1993); it should be noted, however, that the turbulent uxes fromthe 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 withany subsurface horizontal and/or vertical uxes balance to near zero.

The general bulk form for the ux FX of property X is:

FX / CXW10(Xa �Xs)

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where CX is a property-speci�c empirical drag coe�cient, W10 is the 10m wind speed, and Xa andXs are the air and surface values of X. The drag coe�cients vary both with wind speed and loweratmospheric stability, and appropriate corrections can be applied based on the air-sea temperatureand humidity di�erences (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 theatmospheric boundary layer can ensue, and the e�ective transfer rates increase for the same windspeed and atmosphere-ocean gradient. Conversely, stable conditions damp atmospheric boundarylayer turbulence, reducing air-sea exchange.

5.1 Momentum

The downward transfer of momentum from the atmosphere to the ocean plays an importantrole in mixing the surface ocean through the production of near-surface turbulence and shearinstability mixing. The winds also generate the surface wave �eld, which may play a role inLangmuir circulation (Weller and Price, 1988), and contribute to the exchange of trace gases (e.g.Wanninkhof, 1992). The zonal and meridional wind stress components �x and �y can be computedfrom bulk formulas (Large and Pond, 1981):

�x = �aCDU10W10

�y = �aCDV10W10

where U10 and V10 are the 10m zonal and meridional wind components, �a is the air density andCD is an empirical drag coe�cient. One form of the neutral, 10m drag coe�cient is given by:

CND =

�2:70

W10

+ 0:142 + 0:0764W10

�� 10�3:

The drag coe�cient CD is then increased (decreased) when the atmospheric surface layer is un-stable (stable) based on similarity theory (Large and Pond, 1981; Arya, 1988).

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:

Qnet = Qsen +Qlat +Qnet

lw +Qnet

sw :

The turbulent heat uxes, Qsen and Qlat, are typically computed from empirical air-sea transferrelationships (Large and Pond, 1982):

Qsen = �acapCHW10(Ta � Ts)

Qlat = �aLCEW10(qa � qs)

where cap and L are the speci�c heat of air and latent heat of water, and Ts and qs are the seasurface temperature and saturated speci�c humidity. CH and CE are the transfer coe�cients forheat and water, and one set of neutral forms is given by:

CH = 32:7C1=2D � 10�3 when the lower atmosphere is unstable

CH = 18:0C1=2D � 10�3 when it is stable

CE = 34:6C1=2D � 10�3:

Drag coe�cients for the bulk formulae are traditionally computed for a reference height of 10m,and atmospheric data from other levels should be adjusted to 10m height using Monin{Obukovsimilarity theory with appropriate stability corrections (Large and Pond, 1982; Arya, 1988).

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The net longwave radiation Qnet

lwis the di�erence between large upward and downward infrared

uxes and depends upon the atmospheric water vapor pro�le and vertical cloud distribution. Oneapproach is to compute the net longwave ux from a full column 1-D atmospheric radiative transfermodel (e.g. Fung et al., 1984). Several empirical formulas based solely on surface properties havealso been proposed (Fung et al., 1984; Br�eon et al., 1991), an example of which is that of Berliandand Berliand:

Qnet

lw = ����T 4

a [0:39 � 0:05(ea)0:5]F (C) + 4T 3

a (Ts � Ta)�

where Ta and Ts are in Kelvin, ea (mbars) is the surface water vapor pressure, � is the surfaceemissivity taken as 1.0, and � is the Stefan-Boltzmann coe�cient equal to 567�10�10W m�2 K�4.F (C) is a cloud correction factor following Budyko (1974):

F (C) = 1� acC2

where the cloud fraction C varies from 0 to 1, and ac is a latitude-dependent empirical coe�cientadapted by Fung et al. (1984) from Bunker (1976). As estimators for the instantaneous net long-wave ux, the empirical formulas generally fare poorly; but they may be adequate for monthlymean values, especially when the cloud height data required for the radiative-transfer models isnot often known (e.g. Breon et al., 1991). Under limited circumstances, direct measurements ofthe 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 transmissionand 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 fullspectral distribution if needed (see Chapter 2). With the advent of the International SatelliteCloud Climatology Project (Rossow and Schi�er, 1991), the spatial and temporal coverage forcloud cover is su�cient to fully use the power of the radiative transfer model approach. Thepresence of clouds has an opposite and partially compensating e�ect on longwave (warming)and shortwave (cooling) forcing of the ocean surface, and it is important, therefore, to have aconsistent treatment of clouds for both radiative components. In addition, direct measurementsof the downward shortwave ux are available in some locations from research ships, meteorologicalbuoys, and more recently surface drifters (e.g. Weller, 1990).

The ocean surface albedo �:Qnet

sw = (1� �)Qdown

sw

can vary from 3% up to 45% for low zenith angles and calm conditions; however, the albedo fordi�use radiation under overcast skies is only about 6%, which is also a typical value for generaluse (Payne, 1972). Shortwave radiation penetrates into the water column producing subsurfaceheating. Many models have speci�ed the heating rate pro�le using a two-band approximation(a red and infrared band absorbed within the upper meter and a deeper penetrating blue-greenband) (e.g. Paulson and Simpson, 1977; Simpson and Dickey, 1981), though more sophisticatedapproaches are available (e.g. Kantha and Clayson 1994; Morel and Antoine, 1994).

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 oftemperature. Ocean precipitation rates are not well known in general, and climatological estimateshave been created by combining precipitation frequency ship observations with coastal and islandrain-gauge data (e.g. Dorman and Bourke, 1979; 1981; Schmitt et al., 1989; Montgomery andSchmitt, 1994). Satellite precipitation algorithms (e.g. Spencer, 1993) o�er the prospect ofknowing 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.

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Despite several decades of research, the uncertainties in present air-sea heat and freshwater ux estimates generally remain signi�cantly above those required for ocean boundary layer andclimate models (total heat ux 10-15 W m�2, net freshwater ux 0.15 m y�1 (e.g. Weller andTaylor, 1993; OODSP, 1995), though signi�cant advances have been made for limited duration,intensively sampled �eld campaigns such as TOGA-COARE. In part, this problem arises from afundamental mismatch in the space and time scales of satellite data versus direct measurementsfrom ships and buoys. Future gains may depend heavily on the assimilation of these diversemeasurement techniques into numerical weather prediction models.

5.4 Gas exchange

Depending on their complexity, biogeochemical models may require a number of additional sur-face forcings beyond the standard set used by physical models. The discussion of the surface andsubsurface photosynthetically active radiation (par) was presented in the context of the biogeo-chemical processes that use it (Chapter 2.) Other important biogeochemical uxes include air-seagas exchange (e.g. DMS, CO2, O2), wet and dry nutrient deposition (e.g. Knap et al., 1986), andaerosol input of trace metals. The details of air-sea gas exchange are still under debate|relatedto the surface wave, ocean turbulence, surface �lms, and bubble �elds|but for many situationsempirical wind-speed dependent parameterizations (e.g. Liss and Merlivat, 1986; Wanninkhof,1992) will su�ce. The current scatter in the empirical wind speed{gas exchange relationshipsis approximately a factor of two, though this may in part re ect di�erent methods for scalingbetween gas species and for averaging wind speed over time (Wanninkhof, 1992). The processescontrolling nutrient input and aerosol deposition depend more on terrestrial source patterns andlarge-scale atmospheric transport and are thus more di�cult to estimate from local data alone.

5.5 Data sets

Adequate atmospheric and water column observational data are crucial for 1-D numerical modelsboth to drive the physical simulations and to verify the physical/biogeochemical solutions. Evenwith the recent intensive jgofs �eld programs, the number of sites with su�cient meteorologicaland water column observations for detailed upper ocean modeling remains limited.

Not surprisingly, much of the 1-D modeling e�ort to date has focused on the ocean weather-ship data sets, in particular Station P in the subpolar North Paci�c (145�W, 50�N) (e.g. Denman,1973; Denman and Miyake, 1973; Martin, 1985; Gaspar et al., 1990; Large et al., 1994). Availablemeteorological and oceanographic data for Station P include all of the standard surface measure-ments (e.g. SST, air temperature) on 3 hour time scale (Martin, 1985; Tabata, 1965) from whichthe 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, manyof the empirical air-sea relationships discussed above were developed and calibrated using StationP data (e.g. Dobson and Smith, 1988). A variety of long-term biogeochemical datasets were alsocollected at Station P including chlorophyll, nutrients, primary production, surface pCO2, andoxygen (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; meteorolog-ical data 1946-1974, hydrographic data 1964-1973) (Smith and Dobson, 1984), OWS November inthe subtropical Paci�c (30�N 140�W) (Martin, 1985), and OWS India in subpolar Atlantic (59�N19�W, biogeochemical data, 1971-1975) (Williams and Robinson, 1973).

The weathership data are unique because of their continuous coverage over extended timeperiods. Several other local time-series sites exist, though of more limited temporal duration andin 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 ofthe Southern Ocean (Pondaven et al., in press; Jeandel et al., 1996), and the Canary Islands. Thejgofs 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 resourcefor seasonal timescale modelling, though it is usually di�cult to reconstruct more than one- ortwo-year records.

Surface meteorological moorings o�er continuous coverage with temporal resolution of approx-imately 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-Dmodels. Examples of biogeochemical mooring data sets of seasonal to multi-year duration includethe LOTUS and BIOWATT experiments in the subtropical North Atlantic and the MLML ex-periment in the subpolar North Atlantic south of Iceland (Dickey, 1991). As mooring technologyprogresses, they are also becoming a more common component of jgofs process studies. Anextension of the mooring concept, the deployment of the operational TOGA-TAO array in theEquatorial Paci�c has opened up a new era in ocean monitoring, greatly expanding the quantityand character of surface atmosphere and ocean data available for ocean modeling.

In many instances, however, detailed local measurements are not available, and one mustrely 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 volunteermerchant ship reports (e.g. Bunker, 1976), with the COADS data representing the most up todate and extensive archive (Woodru� et al., 1987). The data is concentrated in regions of heavyship tra�c such as the North Atlantic and North Paci�c, and there is, for example, generallyonly poor coverage in the South Paci�c 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-seaheat and freshwater uxes are available generally with monthly resolution. Several wind stressclimatologies 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 (Gloverand Brewer, 1988) climatologies.

The archived analysis data and forecasts from several operational meteorological models areavailable (e.g. National Meteorological Center; European Center for Mid-range Weather Fore-casting ECMWF; Fleet Numerical Oceanographic Center). Two products are available from theoperational centers, an analysis data product which combines previous model forecast �elds andobservations through 4-d data assimilation and the actual model forecast �elds, which includeair-sea ux estimates as well as surface properties. The analysis data is typically provided at 6hour 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 shipobservations, particularly for the more remote, data-poor regions of the global ocean. The algo-rithms used to derive surface data from satellite measurements are generally empirical and maydepend heavily upon atmospheric transmission corrections; further, satellite measurements in thevisible and infrared bands may be often obscured by clouds. Nevertheless, satellites provide apowerful tool for exploring ocean behaviour on spatial and temporal scales that are simply notobservable from local platforms. Satellites are currently providing estimates for a wide range ofsurface 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 andSchi�er, 1991), surface insolation (Bishop and Rossow, 1991), and precipitation (Spencer, 1993).In terms of biogeochemical models, ocean color measurements are invaluable as large-scale observ-able quantities for model veri�cation, and with the imminent launch of both SeaWifs and OCTS,the historical CZCS database (Feldman et al., 1989) will soon be greatly augmented.

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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 partlyby the model structure, but also by the parameter set, driving variables, initial conditions, andalgorithm for numerically approximating the solution of the model equations. There is a furtherquestion of whether the observations play any explicit role in the model realization. In the modelof David Antoine, for example, chlorophyll concentration is determined from observations, andthe model is used not to compute the changes in chl but instead to compute one componentof the bgc uxes associated with the variable, namely primary production. We might say thatchl 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 theforces on the tether: given the rate of change implied by the primary production calculations, howlarge must the loss terms be in total to produce the observed trajectory of chl? A more exibleoption is to let the model run freely in between observations but then make adjustments to thestate variables to bring them back towards available observations. Activities at the workshop wereconcentrated on model runs that were not explicitly a�ected 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 philo-sophical question. The ocean does not repeat itself exactly year after year; do we wish to usereal forcing that varies between years? There are advantages to this approach. That's the waythe ocean was, why pretend otherwise? It is the real ocean with its between-year di�erences thatgenerated the variables that were observed, with which we want to compare model results. Year-to-year variations exercise the model in a wider range of conditions and thereby provide morestringent tests of its performance.

Nevertheless, there are arguments for exploring the response to periodic forcing inde�nitelyprolonged. The questions that jgofs poses are more about the behaviour of an average oceanthan about the accidents of a particular year: how does the ocean work, in general; not howexactly did it work in 19XX? Long-term persistence is as much an observation as the results ofa 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 runthe model for a few years with real forcing, we must establish initial conditions; for a verticallyresolved model this means initial pro�les for all the state variables. Typically there are notenough observations to enable one to do this, and if they are initialized wrongly the period ofadjustment can easily be 30 years: longer than the time series we aim to match. Estimating, asmodel parameters, all the numbers that would be required to specify the starting pro�les createsproblems. If we run the model with eternally repeating forcing, then the long-term behaviour isusually independent of initial conditions and so there is no need to know or estimate them. Butwe do not know the climatological cycle to use for driving: we can only hope that the average ofthe few years we do have is close to the long term average cycle. Because of non-linear e�ects, itis probably best to make the average as late as possible, and construct a climatology of mixingrates, not of surface forcing, if we can. It is probably best to try both approaches { real andaverage forcing { and acknowledge the weaknesses of each. When it makes a big di�erence togoodness-of-�t or parameter estimates, we have an indication of where the whole of jgofs needsto do more work.

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Similar issues arise over the question of how smooth we make the driving variables. Do wewant to take account of day-night di�erences? storms? Again, we are pulled in the direction ofmore detail by the data sets we want to compare with, which have been a�ected by all the detailthere is. We are pulled in the direction of less detail by the nature of jgofs and the questionsit wishes to address. jgofs contains the assumption that we know enough about the ocean at acoarse, smoothed scale to be able to make statements about global carbon ow abstracted fromall the details. So models abstracted from all the details are in a sense more true to the natureof jgofs than detailed data sets are. We want to capture the essential variability for addressingjgofs questions, rather than all the variability there is. This requires some experimenting todetermine which variability should be explicitly represented, which parameterized, and which leftunresolved. If we do choose to represent day-night di�erences in light, consistency would suggesttaking account also of di�erences in mixing caused by nighttime cooling and convection (Wolf andWoods 1992).

6.1.2 Algorithms for solving the model equations

One di�erence among common algorithms is whether they use a �xed time step or let the algorithmadjust the time step to be as great as possible consistent with desired accuracy and times of output.Aside from gains in e�ciency, automatic time step adjustment can also provide more accuracywhen 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, whena model is run with two slightly di�erent parameter sets it will probably choose slightly di�erentseries 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 toconfuse other software, for numerical optimization, that thinks it is dealing with a smooth functionof its parameters. Another di�erence is between forward- and backward-di�erence (explicit andimplicit) methods. Vertically resolved models are typically sti�: mixing in the upper mixed layerequilibrates more quickly than the ecological processes of interest. Backwards di�erence methodscan often get away with much large time steps.

There is another advantage to dealing with smoothed driving variables: the state variableswe wish to predict will as a consequence vary more gradually and routines that approximatesolutions of systems of di�erential equations can reach their answers with less computing e�ort|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 di�erent parameter sets seeking a bestset, then the time a single model run takes can determine whether the research can be carried outpractically or not. This is an advantage one should be careful of invoking, because of the dangerthat the scienti�c questions we wish to address will be steered by considerations of what we cancompute easily rather than what we believe to be true. On the other hand, if the distance betweena quick-to-compute model and a slow-to-compute model is small compared with the distance ofeither from the full complexity they seek to represent, then it may make sense to explore the cheapmodel �rst and more fully.

6.2 Comparing with data

We are approaching the key question: How do we combine models and data to address thequestions 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 mis�t between modeland data, how do we use the data to help select model parameter values, and how do we use thedata to help select among di�erent models?

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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 ofFDM? What in the model corresponds to particulate organic nitrogen measurements? Whatfraction of dissolved organic nitrogen takes part in the reactions that the models are concernedwith? What is the correspondence between detrital ux and collections in sediment traps atdi�erent depths? (We have in mind here both the performance of traps at shallow depths andthe wide potential collection area of traps at deep depths.) Sediment trap measurements haveintegrating properties that make them especially appropriate to jgofs time and space scales; sothat e�orts to understand their properties and uncertainties would be rewarded.

How seriously should we take the depth of the observations, when there are internal wavesthat a�ect the observations but not the models? Again, if the model predicts that observationbut at a slightly di�erent depth, is that pretty good? Although most globally available data willbe at the surface, we expect that the few places where there are vertically resolved observationswill have a lot of ability to constrain.

The issues of how to compare data with model results are su�ciently complicated and variedto 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 mis�t

There is an underlying `right' way to measure mis�t, which we don't know enough to implement.It entails making a statistical model where every observation has an associated error, and thencomputing 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 dataset: intrinsic measurement variances, intrinsic small-scale variation in space of the process beingmeasured, covariances among measurements (e.g. chlorophyll and primary production), serialcorrelation of variables (if an unmodelled process creates a perturbation in the system that lastslong enough to a�ect successive observations). When we have such a model of the errors in thedata, then a simulation model run can be judged by its likelihood: the probability (density) ofobtaining the observed data had the model been true.

Intuition says that for nutrient measurements the intrinsic spatial variation is the largest partof 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 wecan convey to the jgofs community how the conclusions we can draw change drastically as onechanges measures of likelihood, models of error, etc., it may be possible to induce jgofs (or anysuccessor project) to put more e�ort into understanding its variances.

Comparing real data with an average model may produce phase problems: a real peak thatappears at a di�erent time in di�erent years will appear in the averaged data as a qualitativelydi�erent low, broad rise. Do we compare strictly model predictions and observations at the sametime? Or times at which the model prediction and observation give the same value? This leadsinto some of the issues in errors-in-variables regression. For predictions, jgofs can only useaverages (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 ofreal observations.

There are important issues of mis�t that the workshop did not address except in passing. Isa `good' model �t one that does a number of di�erent things adequately, so that the mis�t ismore appropriately a minimax than sum of squares? What about requirements that the modelbehave `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 speci�cobservation program? How do we weight explicit and anecdotal observations? The workshop alsodid not address issues of goodness-of-�t and model rejection, although the Hurtt & Armstrongmodel 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 localstudies to con�rm that we know them and they are the same globally. We can run models withthe parameters that the authors suggest, and compare their outputs, for example compare valuesof the mis�t function for a particular set of data. But a large mis�t need not indicate a poormodel; it might indicate a poor choice of undetermined parameters. It therefore makes sense tocompare models when each uses the parameter values that gives the best �t we can �nd to thedata. In a sense the question is how much we are prepared to learn from a particular measurementprogram, and if we think this program tells us all we will ever know or if we have learned thingsin the past that we will not reject without good reason. This is a question for the whole jgofscommunity: what do they think they know already (e.g. parameter priors) and what new thingswas the study designed to learn?

There are di�erent techniques, with di�erent strengths and weaknesses, for �nding the param-eter set that produces minimum mis�t. The mis�t function of the parameters may have localminima, so that a routine like simulated annealing (used by Matear 1995 and Hurtt & Armstrong1996), which tries to explore wide areas of parameter space before concentrating on the mostpromising areas, may be indicated. Or the function may not be smooth (if for example it is de-rived from numerical approximations to solutions of di�erential equations) so that gradient-basedmethods can fail. Press et al. (1992) discuss many approaches brie y, 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 knowledgeof ranges and likely values, from years of experimenting, that the results of a particular set ofdata should not be able to totally override. Especially when the data set may not be very infor-mative about some of the parameters. It therefore makes sense to start with a prior distributionfor parameters, and minimize the sum of a model-data mis�t and a parameter-prior mis�t? Ata pragmatic level, a numerical optimization routine that knows no science can try meaninglessparameter values even when it is going to converge on sensible ones: a prior distribution incorpo-rating bounds on possible values can avoid this. And a structure than allows for prior distributionsallows also for making them non-informative over a huge range if that is desired. The prior orpenalty function approach has been used by Fasham and Evans (1995). Another way to makeparameter estimates more de�nitive is to use models with a small number of parameters. Here thevery model structure contains decisions that are more rigid than decisions about prior parameterdistributions. This is the approach of Hurtt and Armstrong (1996).

The important issue of how much information the data contain about which parameters wasaddressed in many ways during the workshop, both in discussions and in working models. Theparameter estimation technique of Prunet et al. (1996a) also assesses which linear combinationsof parameters can be estimated. Assume that the parameter and observation vectors have beenscaled so that the components have equal prior error estimates. If we have a current estimate pkof the parameter vector p, and if the predictions c(p) of the model are linearized around pk:

c(pk + �p) � c(pk) +A�p

where A is the jacobian matrix of partial derivatives @c=@p, and if the cost function we wish tominimize 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

�p =�ATA

��1

AT (o� c(pk)):

That is, the linear approximation to the model, combined with the quadratic form of the penaltyfunction, produces a paraboloid in parameter space whose minimum we can compute in a singlestep. However, the paraboloid may be so at in certain directions, and the step in those directionstherefore so large, that the linear approximation on which it was based becomes useless and themis�t value at the predicted point can even become larger than at pk. Conventional minimizationpractice when this happens is to take a smaller step in the same direction (which is initially adescent direction) to remain in the neighbourhood where the linear approximation is valid. Inthe initial stages of seeking the minimum this is still the recommended technique. However, nearthe minimum, Prunet et al. attempt to extract more information concerning the nature of theproblem and how much of a solution can be expected. Singular value decomposition allows oneto identify directions along which the quadratic surface has a very shallow curve that leads tolarge and meaningless steps, and then �nd a `nearby' surface that is exactly at and horizontalin these directions, so that no step at all is taken. Deciding which directions should be retainedand 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 theeigenvectors of successively smaller eigenvalues, produces a succession of estimates of �p for whichthe model is run and the mis�t computed. As long as the mis�t is a decreasing function of thenumber of eigenvectors, they judge that the approximation is reasonable. When increasing thenumber of eigenvectors leads to an increase in the mis�t, they judge that the linear approximationis 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 e�ect of the singular vectors on the mis�t.

It is useful to express the imposition of prior parameter distributions in the same notation. Itamounts 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 di�erent parameters. The solution to the newminimization problem is then

�p = (ATA+ I)�1�AT (o� c(pk)�A�p) + S�

1

2 (p0 � pk)�

and the replacement of (ATA)�1 by (ATA+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 thedata have enabled us to constrain parameter values? Do we really believe that we have determinedparameters that can be carried con�dently to other parts of the ocean? This at least can be tested:estimate parameters for one data set and then use them in di�erent physical surroundings andcompare the model's predictions with what is observed there. A less ambitious plan is to estimatethe parameters that enable the best �t to two di�erent data sets in di�erent places. [Or atdi�erent times in the same place if, as in McGillicuddy et al. (1995), we determine that a shiphas drifted from one eddy to another and therefore in some sense the model should be restartedwith new initial conditions.] But note that this is less ambitious: what we want of jgofs is thatit converge|that the next major measurement program would not vastly change the estimates ofparameters|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 �tsome 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 wellit is predicted by the best �t to the rest of the data. A poor �t, and a need to adjust parametervalues substantially to obtain a good �t, would indicate that the model investigation process hasnot converged and we should be unwilling to trust the answers obtained so far. It often happensthat simple models extrapolate better than complicated ones. Think of polynomial �tting to aset of slightly noisy data: a su�ciently high-order polynomial can �t all of the data exactly, bywrithing in between the observations in a way that has absolutely no predictive power; whereas alow order polynomial (an average or a linear regression) will probably �t new observations muchbetter.

At a second level of comparison, how do we compare the model-data mis�t of two di�erentmodels that have di�erent numbers of parameters? Akaike's information criterion and likelihoodratio are possibilities. We might use a null model (Fourier series with the same number of param-eters?) to assess skill of models. It makes sense to develop new models with a level of complexitythat is quantitatively justi�ed by the available data, if this can be determined.

Although the workshop did not get this far, one of the purposes of jgofs modelling (forsuccessor programmes if not for jgofs itself) is to determine the e�ects of di�erent samplingfrequencies, depths, di�erent types of variables, etc. on the ability of a data set to constrainparameter values. An example of the sort of question that only modelling studies can answer:Is it worth spending a lot of e�ort on (or devoting scarce shipboard resources to) measurementsthat are intrinsically low precision (think of microzooplankton grazing rates)? Do the merits ofconstraining from a di�erent direction outweigh the merits of high accuracy that extra nutrientmeasurements 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 di�erent models at di�erent sites inthe 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 StationP and partly for Eumeli; the second, for all the models at Station P; and the last was partlyaccomplished at Station P. All the data that were assembled and processed in the course ofpreparing the results of this chapter will be made available to the general community through ajgofs 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 valuesof incoming solar radiation, non-solar heat uxes, two-dimensional wind stress, wind speed andsea 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-timeobservations with a 6-hour model forecast from the previous state. The analysis surface �eldsinclude the components of the air-sea ux estimates, of the zonal and meridional 10m winds, thesea surface temperature, and the surface (2m) air and dew point temperatures. Some of the modelsneed forcing data every three hours, and the ecmwf data was therefore interpolated linearly togive the required frequency. The time and e�ort spent by Christophe Herbaud, LODYC, in theextraction of the ecmwf �elds are very much appreciated. The ecmwf has performed a reanalysisback to 1979 in order to ensure a consistent data set, with the same parameterization for all themodel years; this will avoid bias corrections such as those we report here for Eumeli.

1Nansen Environmental and Remote Sensing Center, Edvard Griegsvei 3a, 5037 Solheimsviken, Norway

33

Year Solar Infrared Sensible Latent Total

1986 130.72 -65.98 -16.59 -87.55 -39.401987 141.94 -72.31 -18.29 -87.16 -35.821988 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 from3-hourly records of sea surface temperature, air temperature, wind speed at 10m height, sea-level barometric pressure and total cloudiness index (Antoine and Morel 1995). The average heatbudget over the three years is -0.5 Wm�2, which is su�ciently 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- andy-components of the wind stress. During the workshop an average atmospheric forcing for the 3years 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 from1986 to 1990 were extracted, but only data from 1990 to 1992 were used in this study). Datafrom the four ecmwf grid points closest to the site were interpolated to give the atmosphericforcing at the study site. Incoming solar radiation, infrared, latent and sensible heat uxes, seasurface temperature, wind velocity vector, and wind stress vector were extracted. Gleckler andTaylor (1993) found, by comparing with existing climatologies, that the ecmwf model short waveradiation 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) di�erence between the modeled ecmwf and observed short waveradiation is 50 Wm�2; the Eumeli oligotrophic site is a�ected by this error. Correcting the ecmwf1990 incoming solar radiation made the SST computed from a 1-D upper ocean model (Gaspar etal. 1990) comparable with the SST �eld from ecmwf 1990 (Dadou and Gar�con 1993). However,applying this correction in 1990 resulted in mixed layer depths far too deep in January/February1991. After some experimenting, the best �t between model and observations was found withcorrections of -42 Wm�2 in 1990 (giving a net budget for that year of -6 Wm�2), -10 Wm�2 in1991 (net budget +3 Wm�2), and no correction in 1992 (net budget 0). Siefriedt (1994) comparedecmwf output with existing climatologies and suggested a similar correction for 1990. The heatimbalance averaged over the 3 years is close enough to zero (-1 Wm�2). Figure 3 gives the monthlymeans 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. Datafrom 1986 to 1988 indicated a large heat imbalance (Table 1). It was not feasible to use 1989ecmwf data (the year of the NABE program) because the model algorithm was changed in themiddle of the year. The heat imbalance indicated a large horizontal contribution, but this wasnot incorporated in our 1-D models due to lack of time, and therefore precluded further analysisat NABE. The atmospheric uxes of the three years, 1986 { 1988 are plotted in Figure 4.

34

20

40

60

80

100

120

140

160

180

6 12 18 24 30 36

W/m

^2

Months

Incoming solar radiation

-180

-160

-140

-120

-100

-80

-60

-40

-20

6 12 18 24 30 36

W/m

^2

Months

Nonsolar flux

-65

-60

-55

-50

-45

-40

-35

-30

6 12 18 24 30 36

W/m

^2

Months

Infrared heat flux

-40

-35

-30

-25

-20

-15

-10

-5

0

5

6 12 18 24 30 36W

/m^2

Months

Sensible heat flux

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

6 12 18 24 30 36

W/m

^2

Months

Latent heat flux

-150

-100

-50

0

50

100

150

6 12 18 24 30 36

W/m

^2

Months

Surface net heat flux

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

6 12 18 24 30 36

N/m

^2

Month

Wind stress, u-component

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

6 12 18 24 30 36

N/m

^2

Month

Wind stress, v-component

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

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12

W/m

^2

Months

Incoming solar radiation

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

1 2 3 4 5 6 7 8 9 10 11 12

W/m

^2

Months

Nonsolar flux

-65

-60

-55

-50

-45

-40

-35

1 2 3 4 5 6 7 8 9 10 11 12

W/m

^2

Months

Infrared heat flux

-80

-70

-60

-50

-40

-30

-20

-10

1 2 3 4 5 6 7 8 9 10 11 12

W/m

^2

Month

Sensible heat flux

-25

-20

-15

-10

-5

0

5

1 2 3 4 5 6 7 8 9 10 11 12

W/m

^2

Months

Latent heat flux

-150

-100

-50

0

50

100

150

1 2 3 4 5 6 7 8 9 10 11 12

W/m

^2

Months

Surface net heat flux

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

1 2 3 4 5 6 7 8 9 10 11 12

N/m

^2

Month

Wind stress, u-component

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

1 2 3 4 5 6 7 8 9 10 11 12

N/m

^2

Month

Wind stress, v-component

Figure 2: Monthly means of the components of the average forcing at Station P during 1975{77.

36

120

140

160

180

200

220

240

260

280

300

6 12 18 24 30 36

W/m

^2

Months

Incoming solar radiation

-400

-350

-300

-250

-200

-150

-100

6 12 18 24 30 36

W/m

^2

Months

Nonsolar flux

-90

-85

-80

-75

-70

-65

-60

-55

-50

-45

6 12 18 24 30 36

W/m

^2

Months

Infrared heat flux

-30

-25

-20

-15

-10

-5

0

6 12 18 24 30 36W

/m^2

Months

Sensible heat flux

-260

-240

-220

-200

-180

-160

-140

-120

-100

-80

-60

6 12 18 24 30 36

W/m

^2

Months

Latent heat flux

-200

-150

-100

-50

0

50

100

150

6 12 18 24 30 36

W/m

^2

Month

Surface net heat flux

-0.13

-0.12

-0.11

-0.1

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

6 12 18 24 30 36

N/m

^2

Month

Wind stress, u-component

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

6 12 18 24 30 36

N/m

^2

Month

Wind stress, v-component

Figure 3: Monthly means of the components of the total energy ux and wind stress at theocean-atmosphere interface from ecmwf at Eumeli for the years 1990{1992, correction applied.

37

0

50

100

150

200

250

0 6 12 18 24 30 36

W/m

^2

Month

Incoming solar radiation

-260

-240

-220

-200

-180

-160

-140

-120

-100

-80

-60

-40

0 6 12 18 24 30 36

W/m

^2

Month

Nonsolar flux

-90

-85

-80

-75

-70

-65

-60

-55

-50

-45

0 6 12 18 24 30 36

W/m

^2

Month

Infrared heat flux

-40

-35

-30

-25

-20

-15

-10

-5

0

5

0 6 12 18 24 30 36

W/m

^2

Month

Sensible heat flux

-160

-140

-120

-100

-80

-60

-40

-20

0

0 6 12 18 24 30 36

W/m

^2

Month

Latent heat flux

-250

-200

-150

-100

-50

0

50

100

150

0 6 12 18 24 30 36

W/m

^2

Month

Surface net heat flux

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 6 12 18 24 30 36

N/m

^2

Month

Wind stress, u-component

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 6 12 18 24 30 36

N/m

^2

Month

Wind stress, v-component

Figure 4: Monthly means of the components of the total energy ux and wind stress at theocean-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) from1987 to 1994 was calculated by Doney (1996) using ecmwf and ISCPP (International SatelliteCloud 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 interactivelywith the model SST). The forcing data are based primarily on the uninitialized, 6-hourly TOGAglobal surface analysis from ecmwf. The �elds are supplemented by daily cloud fraction andsurface insolation estimates from ISCPP and monthly satellite precipitation estimates from theMicrowave Sounding Unit (MSU). The uxes are shown in Figure 5. The average heat budgetover 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 acommon physical framework. The 1-D models in which the physics were explicitly computed wererun with the same physical forcing, to see which gave the best results according to observed mixedlayer depth and temperature. The 1-D models that were run were those of Scott Doney, DennisMcGillicuddy, David Antoine, Diana Ruiz-Pino, V�eronique Gar�con and Pascal Prunet. The fourlatter are all based on the physical model of Gaspar et al. (1990), with a minimum turbulentkinetic energy imposed below the upper mixed layer. Some of the 0-D models needed a smoothmixed 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 �lterof 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 meanof the nearest 25 points. Other smoothing procedures (e.g. cubic spline interpolation) failed toreproduce the original structure .

7.2.1 Station P

The workshop concentrated its attention on Station P. One reason for picking this site is thatmost of the physical mixing models have been studied there, so it was a good location where tocompare physical models and to get diverse bgc models to run in the same physical arena. It isnot a perfect choice. Iron limitation is quite likely an important factor there, and it is absentfrom the models considered at the workshop. In addition, only nutrient and chlorophyll data wereavailable for validating or constraining parameter sets.

All the model output plots at Station P were sent to the physical oceanographers participatingat 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 modelsmatched the data best, and so the root-mean-square di�erences in SST were computed for thesetwo models (Table 2).

Of the two models compared, Scott Doney's reproduces the SST cycle better for the three years(see Table 2). The di�erence was not overwhelming, however, and we decided to proceed withDiana Ruiz-Pino's model on the practical ground that people in Toulouse who would be involved inpreliminary work were more familiar with it. Temperature, salinity, MLD and turbulent di�usioncoe�cient 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 TomAnderson) that assume a steady cyclic forcing and are run to a steady cyclic solution were drivenby the 3-year average MLD cycle given in Figure 9. During the workshop we also produced a1975 { 1977 average radiation forcing for the 0-D models (Figure 2).

39

50

100

150

200

250

300

350

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

W/m

^2

Months

Incoming solar radiation

-450

-400

-350

-300

-250

-200

-150

-100

-50

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

W/m

^2

Months

Nonsolar flux

-300

-250

-200

-150

-100

-50

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

W/m

^2

Months

Infrared heat flux

-80

-70

-60

-50

-40

-30

-20

-10

0

10

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

W/m

^2

Months

Sensible heat flux

-80

-75

-70

-65

-60

-55

-50

-45

-40

-35

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

W/m

^2

Months

Latent heat flux

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

W/m

^2

Month

Surface net heat flux

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

N/m

^2

Month

Wind stress, u-component

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

N/m

^2

Month

Wind stress, v-component

Figure 5: Monthly means of the components of the total energy ux and wind stress at theocean-atmosphere interface from ecmwf and ISCPP at BATS for the years 1987 { 1994.

40

4

44

4

4

4

4

4

4

4

4

4

4

4

4

44

4

5

5

55

555

5

5

5

5

5

55

55

55

5

5

5

5

5

5

5

5

5

5

5

5

5

55

55

5

5

5

5

5

5

5

5

6 66

6

6

6

6

6 6

6

6

6

6

6

67 7

77

7

7

7

7

7 7

7

8

8

8

8

8

8

8

8

8

9 9

9

9

9

910

10

10

10

10 1011

11 11

12

12

0

50

100

150

200

250

300

dept

h (m

)

3 6 9 12 15 18 21 24 27 30 33 36Month

STATION P : Contour plot of temperature (Bathythermographic records)

(1975 to 1977)

Figu

re6:

Bath

ytherm

ographicrecord

s,for

comparison

with

themodeloutputs

oftem

peratu

re.

41

Diana Ruiz-Pino Scott Doney

1975 0.55 0.531976 1.24 0.721977 1.34 0.57Global 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 theresults 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 condi-tions 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 parameterestimation. Total CO2 and total alkalinity are presented as well, although the carbon systems ofthe models where this is included were not run during the workshop.

7.3.1 Station P

Initial pro�les At Station P, the temperature were bathythermographic records, salinity fromLevitus and oxygen data were taken from in situ measurements, see Figure 14 (Antoine & Morel1995). For the biology, di�erent sources were also involved. The phytoplankton data were theequilibrium of the NPZD-model of Prunet et al. (1996a) (see Table 3), the nanophytoplanktonvariable in Ruiz-Pino's model was set to zero. The zooplankton, detritus, labile DOM and bacteriawere in situ measurements provided by Diana Ruiz-Pino (Table 3). For the refractory DOM pool,a value of 70 mmolC�m�3 was assumed, giving the same fraction between the labile and refractoryDOM 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 homogeneousvalue of 22 mmol Si�m�3 was chosen. The ammonium data was that of Wheeler & Kokkinakis(1990). For total CO2 and total alkalinity, a pro�le after one year of spin-up of David Antoine'smodel was used.

Data used for parameter estimation The surface phytoplankton and nitrate data, used forthe parameter estimation were in situ measurements from 1975 and 1976 (Figures 15 and 16), asreported in Prunet et al. (1996b).

42

Figure 7: Station P, 1975 { 1977. Diana Ruiz-Pino's model. The coe�cient of turbulent di�usionand the depth of the mixed layer have been averaged over a week. Thereafter a boxcar-�lter of 3is applied twice. For temperature and salinity, only the boxcar-�lter has been used.

Figure 8: Station P, 1975 { 1977. Scott Doney's model. The coe�cient of turbulent di�usion hasbeen averaged over a week. Thereafter a boxcar-�lter of 3 is applied twice. For temperature, onlythe boxcar-�lter has been used.

43

Figure 9: \Climatology" of the mixed layer history.

Figure 10: Eumeli, 1990 { 1992. V�eronique Gar�con's model. The coe�cient of turbulent di�usionand the depth of the mixed layer have been averaged over a week. Thereafter a boxcar-�lter of 3is 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

-300

-250

-200

-150

-100

-50

0

4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2

Dep

th (

m)

Degrees Celsius

Temperature

-300

-250

-200

-150

-100

-50

0

32.8 33 33.2 33.4 33.6 33.8 34

Dep

th (

m)

PSU

Salinity

-300

-250

-200

-150

-100

-50

0

100 150 200 250 300 350

Dep

th (

m)

O2 mmol/m3

Oxygen

-300

-250

-200

-150

-100

-50

0

2090 2100 2110 2120 2130 2140 2150 2160

Dep

th (

m)

TCO2 mmol/m3

Total carbon dioxide

-300

-250

-200

-150

-100

-50

0

2270 2280 2290 2300 2310 2320 2330

Dep

th (

m)

meq/m3

Total alkalinity

-300

-250

-200

-150

-100

-50

0

10 15 20 25 30 35 40

Dep

th (

m)

mmolN/m3

Nitrate

Figure 14: Initial conditions at Station P.

46

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 Initial Value { surface Initial Value { bottom

Phytoplankton 0.18 mmolN�m�3 0.18 mmolN�m�3

Zooplankton 0.14 mmolN�m�3 0.0001 mmolN�m�3

Microzooplankton 0.14 mmolN�m�3 0.0001 mmolN�m�3

Bacteria 0.14 mmolN�m�3 0.0001 mmolN�m�3

Very small detritus 0.14 mmolN�m�3 0.0001 mmolN�m�3

Small detritus 0.0001 mmolN�m�3 0.0001 mmolN�m�3

Large detritus 0.0001 mmolN�m�3 0.0001 mmolN�m�3

Labile DOM 1.67 mmolC�m�3 1.67 mmolC�m�3

Refractory DOM 70 mmolC�m�3 1.67 mmolC�m�3

Nitrate 14.50 mmolN�m�3 38.9 mmolN�m�3

Ammonium 0.15 mmolN�m�3 0.15 mmolN�m�3

Silicate 22 mmol Si�m�3 22 mmol Si�m�3

Table 3: Initial values for the di�erent variables at Station P.

7.3.2 Eumeli

Initial pro�les The temperature, salinity and oxygen data to initialize the models were all takenfrom the Eumeli 5 cruise of December 23, 1992 (Figure 17). Phytoplankton, zooplankton, bacteriaand nitrate concentrations were also taken from Eumeli 5. Detritus and DOM were, howevertaken from Eumeli 3. Small zooplankton were given a constant value of 0.0001 mmolN�m�3, andvery small detritus 0.3 mmolN�m�3. Small detritus were 0.3 mmolN�m�3 down to 100 m, anddecreased linearly to 0.06 mmolN�m�3 at 300 m. Large detritus were 0.1 mmolN�m�3 down to 100m, and decreased linearly to 0.02 mmolN�m�3 at 300 m. DOM was given a constant value of 0.7mmolC�m�3, and bacteria decreased from 0.15 mmolN�m�3 at the surface to 0.04 mmolN�m�3

at 300 m. For ammonium, a low value of 0.01 mmolN�m�3 was chosen. Total CO2 and totalalkalinity were those of the TTO/TAS cruise (station 82).

Data used for parameter estimation All the data from Eumeli when fully assembled willbe made available at a www site indicated onhttp://ads.smr.uib.no/jgofs/inventory/Toulouse/index.htm

7.3.3 NABE

Initial pro�les At NABE, the Discovery cruise 182 of May 8, 1989 was chosen to initialize themodels. Those data included temperature, salinity, oxygen, total CO2, total alkalinity, nitrate,ammonium and phytoplankton. Tom Anderson gave the zooplankton (0.12 mmolN�m�3), DOM(labile: 0.5 mmolC�m�3, refractory: 42 mmolC�m�3, same fraction as for Eumeli) and bacteria(0.06 mmolN�m�3) data (Figure 18). Small and large detritus were given a small value of 0.0001mmolN�m�3. For the other variables, no initial pro�les were prepared for the workshop.

Data used for parameter estimation There are two main sources of information about theobservations. The British Oceanographic Data Centre has assembled Discovery observations onCD-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 sitehttp://www1.whoi.edu/jgofs.html. Additional information can be found in the jgofs specialvolume of Deep-Sea Research (volume 40 number 1/2 1993).

48

17 18 19 20 21 22 23 24

-250

-200

-150

-100

-50

Temperature

Degrees Celsius

Dep

th (

m)

36.4 36.6 36.8 37.0 37.2 37.4

-250

-200

-150

-100

-50

Salinity

PSU

Dep

th (

m)

160 170 180 190 200 210

-250

-200

-150

-100

-50

Oxygen

O2 mmol/m3

Dep

th (

m)

2100 2105 2110-300

-250

-200

-150

-100

-50

Total carbon dixoide

TCO2 mmol/m3

Dep

th (

m)

2370 2380 2390 2400 2410 2420 2430-300

-250

-200

-150

-100

-50

Total alkalinity

TALK meq/m3

Dep

th (

m)

0 5 10

-250

-200

-150

-100

-50

Nitrate

NO3 mmolN/m3

Dep

th (

m)

0.00 0.05 0.10 0.15 0.20 0.25 0.30-300

-250

-200

-150

-100

-50

Phytoplankton

mmolN/m3

Dep

th (

m)

0.010 0.015 0.020 0.025 0.030 0.035-300

-250

-200

-150

-100

-50

Zooplankton

mmolN/m3

Dep

th (

m)

Figure 17: Initial conditions at Eumeli.

49

11.5 12.0 12.5

-250

-200

-150

-100

-50

Temperature

Degrees Celsius

Dep

th (

m)

35.560 35.570 35.580 35.590 35.600 35.610 35.620

-250

-200

-150

-100

-50

Salinity

PSU

Dep

th (

m)

260 265 270 275 280

-250

-200

-150

-100

-50

Oxygen

O2 mmol/m3

Dep

th (

m)

2070 2080 2090 2100 2110 2120 2130 2140

-250

-200

-150

-100

-50

Total carbon dioxide

TCO2 mmol/m3

Dep

th (

m)

2315 2320 2325 2330 2335 2340

-250

-200

-150

-100

-50

Total alkalinity

TALK meq/m3

Dep

th (

m)

2 3 4 5 6 7

-250

-200

-150

-100

-50

Nitrate

NO3 mmolN/m3

Dep

th (

m)

0.4 0.6 0.8 1.0 1.2

-250

-200

-150

-100

-50

Ammonium

NH4 mmolN/m3

Dep

th (

m)

0.1 0.2 0.3 0.4

-250

-200

-150

-100

-50

Phytoplankton

mmolN/m3

Dep

th (

m)

Figure 18: Initial conditions at NABE.

50

Before AfterPhyto NO3 Phyto NO3

Tom Anderson 0.496 7.54 0.154 2.102Ken Denman 10.225 8.824 0.156 6.818

� Helge Drange 0.19 2.14 0.17 2.74Scott Doney 0.163 4.181 0.117 1.952

� Uli Wolf 0.841 6.987 0.222 1.654� Pascal Prunet 0.128 2.477 0.115 2.114� Geo� Evans 0.129 3.307 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 pro�les For BATS, US jgofs data from December 19, 1988 were chosen to initializethe 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 mmolN�m�3

from the surface down to 50 m, and a constant value of 0.0001 mmolN�m�3 from that depth downto 300 m. For DOM (labile: 1.67 mmolC�m�3, refractory: 70 mmolC�m�3, same fraction as forEumeli). Detritus was given a small value of 0.0001 mmolN�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 eachmodel 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 problemswith the optimization terminating prematurely. The root-mean-square di�erence between dataand model output before and after the iterations for the di�erent 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 inFigures 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 PascalPrunet's (1996b) models started with model parameters which were already optimized. For eachof them the parameters were further adjusted: in Prunet's case because a di�erent number ofparameters and a slightly di�erent data set were used; in Evans's case because of small changesin the mis�t function and the prior values of the parameters. Uli Wolf's model was taken toconvergence before the workshop, and Helge Drange's during the workshop; this model was onlyrun 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 orfour of the fully optimized models. The parameters are described in Chapter 8. It is not easyto draw any conclusions from this table. However, one should mention the rather high � valueestimated in Geo� Evans's model, which probably occurs because this model is not verticallyresolved. The assimilation technique is increasing the � value, given the light conditions andthe phytoplankton at Station P, that is, it increases the phytoplankton growth rate. During theworkshop we experimented with forcing Helge Drange's model to use the same value of �, but the

51

18 19 20 21 22

-250

-200

-150

-100

-50

Temperature

Degrees Celsius

Dep

th (

m)

36.50 36.55 36.60

-250

-200

-150

-100

-50

Salinity

PSU

Dep

th (

m)

175 180 185 190 195 200 205

-250

-200

-150

-100

-50

Oxygen

O2 mmol/m3

Dep

th (

m)

2030 2040 2050 2060 2070

-250

-200

-150

-100

-50

Total carbon dioxide

TCO2 mmol/m3

Dep

th (

m)

2350 2360 2370 2380

-250

-200

-150

-100

-50

Total alkalinity

TALK meq/m3

Dep

th (

m)

1 2 3 4

-250

-200

-150

-100

-50

Nitrate

NO3 mmolN/m3

Dep

th (

m)

0.00 0.02 0.04 0.06 0.08 0.10 0.12-300

-250

-200

-150

-100

-50

Phytoplankton

mmolN/m3

Dep

th (

m)

Figure 19: Initial conditions at BATS.

52

Figure 20: Preliminary results of the iteration. Data used for the comparison are plotted asdiamonds.

53

Figure 21: Preliminary results of the iteration. Data used for the comparison are plotted asdiamonds.

54

Parameter Helge Drange Pascal Prunet Geo� Evans Uli WolfBefore 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 0.008Kfood 1.0 1.2 1.0 1.042 1.09 1.56Pphy 0.5 0.5 0.5 0.58 0.59 0.33Vdet 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, followedby very high seasonal variations in nitrate.

It was never intended to stop with Station P results, but the di�culties encountered with theparameter estimation software prevented exploration of other sites. This remains an urgent needfor future jgofs work.

7.4.2 NO3-resetting

Resetting of NO3 was included in Helge Drange's model during the workshop and we performedthe parameter estimation with this option. The results are shown in Figure 22. The standard rundenotes the nominal run without any data assimilation. It is clear that the model has a tendencyto follow the nitrate data better with NO3-resetting, but it is di�cult to draw any conclusionsfrom 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 re ect 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 theworkshop models. The equations are presented in a common notation that makes it possible toobserve the occurrence of the same parameter in di�erent models, and compare its value. Thereis some doubt among workshop participants that this is a good thing in all circumstances; but itwas one thing we did, and we report the progress here. To enable a timely release of the wholereport, we have chosen to present the interim, imperfect version we have been able to devise sofar.

8.1 Notation

An ideal common notation would be concise, informative out of context, and consistent acrossdi�erent models. These requirements often work at cross purposes. Consider a parameter namelong enough to be informative: �0phy;det could stand for the linear term in the expansion aroundthe origin of the curve describing losses from phytoplankton to detritus. This has the advantageof automatic cross-referencing, so that when we see this parameter as part of a loss term in thephytoplankton equation, we know without having to seek it out that there should be a balancinggain in the detritus equation. However, it is unwieldy compared to the corresponding FDMparameter name �1. Losses due to sloppy feeding are even more unwieldy because there are threeterms to consider: the source, the target and the agent. In papers that describe a single model, thecontext is clearer, and so the merits of conciseness would be given a higher weight than here. Alsoparameters whose meanings are easy to compare across models are not always the most naturalfor the expression of a particular model. The formulation of the phytoplankton loss term in theHurtt & Armstrong model is a case in point.

For the state variables whose evolution the models describe, we use 3-letter abbreviationsin small capitals, such as phy. When a model has more than one class of some variable, wesubstitute a number, e.g. de1 and de3 for two size classes of detritus. When the state variableis not computed in nitrogen units, we add a 3-letter su�x to indicate its element: thus doncaris the carbon asociated with dissolved organic nitrogen. The table of parameter de�nitions showsour 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 di�erent 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 abscissaat which the function attains half of its maximum value, might all be considered quantities ofinterest or ecological importance. For Michaelis and Ivlev curves, the constant term at the originand the linear and quadratic terms about 1 are identically zero, leaving 4 parameters any two ofwhich su�ce to describe either 2-parameter curve. Do the curves

x

1 + xand 1� e�x

57

have the same parameter values or not? They have the same slope at zero and constant value at1, but they have half-saturation abscissas 1 and 0.693 respectively, and second derivatives at theorigin -2 and -1 respectively. Should a table of parameters contain all 7 of the above parametervalues, or at least those that are not already �xed by the de�nition of the curve, or just the twothat are necessary for de�ning the curve? The choice of what to use as parameters will also a�ectsensitivity 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 maximumrate holding half-saturation concentration constant.

A neutral possibility might be to report, as `parameters', the values of the function at theappropriate number of representative (in the context of a given data set) values of its argument,though it would then be di�cult to work out other values given these. And would the mostrepresentative values of the argument change if we switched to a function with more or fewerparameters?

For want of time, we have left one area in an incomplete state. The photosynthesis-lightrelations that are reported in this chapter are the instantaneous ones, with no reference to di�erentmethods for integrating over variations with time of day and with depth. One might argue thatsuch integrations are an issue in numerical analysis and do not belong in a chapter on the equationsrepresenting the scienti�c concepts. However, one might also argue that, because phytoplanktoncan take up nutrients also at night, the interaction between nutrients and light is best seen in termsof the daily integrated response to light, not the instantaneous response. Not enough thinkinghas 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 allthe models to a common data set (or at least we are not totally con�dent about the tuning).Although a lot of work has been done in developing the common notation, the payo�s have notyet arrived. The tables do at least indicate where there are parameter values|where comparisonswill be meaningful once models are tuned to the same set of data. A key question is how muchpeople learn from the uni�ed notation and tables as far as we have been able to develop them,and therefore how much e�ort it is worth to develop them further.

58

State variables

The unit, unless otherwise stated, is mmolN�m�3.

Symbol De�nition

no3 Nitratenh4 Ammoniumphy Phytoplanktonph1 Nanophytoplanktonph2 Microphytoplanktonzoo Zooplanktonzo1 Microzooplanktonzo2 Mesozooplanktonbac Bacteriadon Dissolved organic nitrogendo1 Labile DONdo2 Refractory DONdet Detritusde1 Small detritusde2 Medium or large detritusde3 Large detritus

chl Phytoplankton chlorophyll in mg� m�3

xxxcar Carbon content of xxx in mmolC�m�3

sil Silicate in mmol Si�m�3

xxxsil Silicon content of xxx in mmol Si�m�3

�CO2 Total dissolved inorganic carbon in mmolC�m�3

alk Total alkalinity in meq�m�3

59

Parameters

Symbol De�nition Unit

Phytoplankton growthkw Light attenuation coe�cient of water m�1

kc Light attenuation coe�cient of chlorophyll m�1(mmolN� m�3)�1

�phy Maximum phytoplankton growth rate d�1

� Initial slope of P{I curve (Wm�2)�1 d�1

� Light inhibition of photosynthesis (Wm�2)�1 d�1

Kno3 Half-saturation concentration for no3 uptake mmolN�m�3

Knh4 Half-saturation concentration for nh4 uptake mmolN�m�3

Ksil Half-saturation concentration for sil uptake mmolN�m�3

nh4 inhibition of no3 uptake (mmolN�m�3)�1

1; 2 Diana Ruiz-Pino's parameters for dividing |,|nutrient uptake between nitrate and ammonium

� term in nutrient-dependent mortality d�1mmolN�m�3

�1PH Phytoplankton N:chl ratio at in�nite light molN�(g chl)�1

�0PH Phytoplankton N:chl ratio at zero light molN�(g chl)�1

EK Light level where �0PH starts W m�2

�PNC Phytoplankton N:C ratio molN(molC)�1

Zooplankton growth�zoo Maximum zooplankton growth rate d�1

Kfood Half-saturation food concentration for zoo grazing mmolN�m�3

�zoo Slope of zooplankton grazing curve d�1 (mmolN�m�3)�1

c Quadratic part of zooplankton grazing curve d�1 (mmolN�m�3)�2

pphy; pbac; pdet Preference of zooplankton for food types |�ZNC Zooplankton N:C ratio molN(molC)�1

Bacterial growth�bac Maximum bacterial growth rate d�1

Kbac

N Half-saturation for bacterial uptake of nutrients mmolN�m�3

� Excess carbon content of don over what bac needs |�BNC Bacterial N:C ratio molN(molC)�1

Loss terms�xxx;yyy constant loss from xxx to yyy mmolN�m�3 d�1

�xxx;yyy linear loss from xxx to yyy d�1

�xxx;yyy quadratic loss from xxx to yyy d�1 (mmolN�m�3)�1

"xxx;yyy fraction of the uptake by xxx that goes to yyy |�xxx fraction of a loss allocated to xxx |

60

Ken Denman

dphy

dt= �phymin

�� par

�phy + � par;

no3

no3+Kno3

�phy� �phy;no3 phy� �zoo

phy2

phy2 +K2food

zoo

d zoo

dt= (1� "zoo;no3)�zoo

phy2

phy2 +K2food

zoo� �zoo;no3 zoo2

dno3

dt= ��phy min

�� par

�phy + � par;

no3

no3+Kno3

�phy

+"zoo;no3 �zoophy

2

phy2 +K2food

zoo+ �phy;no3 phy+ �zoo;no3 zoo2

Scott Doney

dphy

dt=

�phy�1HN

�1� e�� �

1

HNpar=�phy

�chl

��zoo phy (1� e�c phy=�zoo) zoo� �phy;no3 phy� �phy;det phy

2

d zoo

dt= (1� "zoo;det)�zoo phy(1� e

�c phy=�zoo)zoo� �zoo;no3 zoo2� �zoo;no3 zoo

dno3

dt= �

�phy�1HN

�1� e���

1

HNpar=�phy

�chl+ �phy;no3 phy

+�zoo;no3 zoo+ �zoo;no3 zoo2

ddet

dt= �phy;det phy

2 + "zoo;det�zoo phy(1� e�cphy=�zoo)zoo� �det;nul det

d (chl=phy)

dt=

�phy�1HN

chl

phy

�1� e�� �

1

HNpar=�phy

��

�no3

no3+Kno3

��PHN � (�PHN � �

1

HN )min

�par

EK; 1

���

chl

phy

�

61

Dennis McGillicuddy

dphy

dt= �phy

�1� e�� par=�phy

�e�� par=�phy

nh4

nh4+Knh4

+no3 e� nh4

no3+Kno3

!phy

��zoo (1� 0:5phy=Kfood) zoo

d zoo

dt= (1� "zoo;nh4)�zoo (1� 0:5phy=Kfood) zoo� (�zoo;nh4 + �zoo;nul) zoo

�(�zoo;nh4 + �zoo;nul) zoo2

dno3

dt= ��phy

�1� e�� par=�phy

�e�� par=�phy

no3 e� nh4

no3+Kno3

phy

dnh4

dt= ��phy

�1� e�� par=�phy

�e�� par=�phy

nh4

nh4+Knh4

phy

+"zoo;nh4 �zoo (1� 0:5phy=Kfood) zoo+ �zoo;nh4 zoo+ �zoo;nh4 zoo2

George Hurtt and Rob Armstrong

UE = �Ephye�E phy

� 1

�E phy

�parq(�Ephy)

2 + (� par)2

UN = �Nphye�N phy

� 1

�N phy

no3+ nh4

Knh4 + no3+ nh4

dphy

dt= min(UE chl; UN phy)�

�2phy;det2�phy;det phy

exp

2�phy;det phy

�phy;det

!� 1

!

dno3

dt= �min(UE chl; UN phy)

Knh4 no3

(Knh4 + nh4)(nh4+ no3)

dnh4

dt= �min(UE chl; UN phy)

nh4(Knh4 + nh4+ no3)

(Knh4 + nh4)(nh4+ no3)+ �det;nh4 det

ddet

dt=

�2phy;det2�phy;det phy

exp

2�phy;det phy

�phy;det

!� 1

!� �det;nh4 det

chl = min(UN=UE ; �PHN )phy

62

Olaf Haupt and Uli Wolf

dphy

dt= �phy

�parq�2phy

+ (� par)2

nh4

nh4+Knh4

+no3 e� nh4

no3+Kno3

!phy�Gphy

�min��phy;de1 phy

2; �phy;de1 phy�

d zoo

dt= (1� "phyzoo;de2)Gphy + (1� "de1zoo;de2)Gde1 + (1� "de2zoo;de2)Gde2 � �zoo;nh4 zoo

��zoo;de1 zoo2par

where

GX = �zoopX X

2

(pphy phy2 + pde1 de12 + pde2 de22)

food

Kfood + foodzoo

X = phy;de1;de2

food =pphy phy

2 + pde1 de12 + pde2 de2

2

pphy phy+ pde1 de1+ pde2 de2

dno3

dt= ��phy

� parq�2phy + (� par)2

no3 e� nh4

no3+Kno3

phy+ �nh4;no3nh4

par

dnh4

dt= ��phy

� parq�2phy + (� par)2

nh4

nh4+Knh4

phy � �nh4;no3nh4

par

+�de1;nh4 de1+ �de2;nh4 de2+ �zoo;nh4 zoo

dde1

dt= min

��phy;de1 phy

2; �phy;de1phy�

+�zoo;de1 zoo2par�Gde1 � �de1;nh4 de1

dde2

dt= "phyzoo;de2Gphy + "de1zoo;de2Gde1 + ("de2zoo;de2 � 1)Gde2 � �de2;nh4 de2

63

V�eronique Gar�con, Isabelle Dadou and Fran�cois Lamy

dphy

dt= �phy

�1� e�� par=�phy

�e�� par=�phy

no3

no3+Kno3

phy

��zoopphy phy

2

pphy phy+ pde1 de1zoo

d zoo

dt= (1� "zoo;de1 � "zoo;de2)�zoo food � zoo� (�zoo;de1 + �zoo;no3) zoo

where

food =pphy phy

2 + pde1 de12

pphy phy+ pde1 de1

dno3

dt= ��phy

�1� e�� par=�phy

�e�� par=�phy

no3

no3+Kno3

phy+ �zoo;no3 zoo

+�do2;no3 do2+ �do1;no3 do1

ddo1

dt=

�det;do1�det;do1 de2

�det;do1 + �det;do1 de2+

�det;do1�det;do1 de1

�det;do1 + �det;do1 de1� �do1;no3 do1

ddo2

dt=

�det;do2�det;do2 de2

�det;do2 + �det;do2 de2+

�det;do2�det;do2 de1

�det;do2 + �det;do2 de1� �do2;no3 do2

dde1

dt= �zoo;de1zoo+ "zoo;de1�zoo food � zoo� �zoo

pde1 de12

pphy phy+ pde1 de1zoo

�

�det;do1�det;do1 de1

�det;do1 + �det;do1 de1�

�det;do2�det;do2 de1

�det;do2 + �det;do2 de1

dde2

dt= �zoo;de2 zoo+ "zoo;de2 �zoo food � zoo

�

�det;do1�det;do1 de2

�det;do1 + �det;do1 de2�

�det;do2�det;do2 de2

�det;do2 + �det;do2 de2

64

FDM; M. K. Sharada

dphy

dt= (1� "phy;don)�phy

� parp�2phy + (� par)2

nh4

nh4+Knh4

+no3 e� nh4

no3+Kno3

!phy

�Gphy � �phy;det phy

d zoo

dt= (1� "phyzoo;det)Gphy + (1� "baczoo;det)Gbac + (1� "detzoo;det)Gdet

�(�zoo;nh4 + �zoo;don + �zoo;nul)zoo

where

GX = �zoopX X

2

(pphy phy2 + pbac bac2 + pdet det2)

food

Kfood + foodzoo

X = phy;bac;det

food =

8>><>>:

pphy phy2 + pbac bac

2 + pdet det2

pphy phy + pbac bac+ pdet detFDM

pphy phy + pbac bac+ pdet det Sharada

dbac

dt= �bac bac

min(nh4; � don) + don

Kbac

N +min(nh4; � don) + don� �bac;nh4 bac�Gbac

dno3

dt= ��phy

� parp�2phy + (� par)2

no3 e� tnh4

no3+Kno3

phy

dnh4

dt= ��phy

� parp�2phy + (� par)2

nh4

nh4+Knh4

phy� �bac bacmin(nh4; � don)

Kbac

N +min(nh4; � don) + don

+�bac;nh4 bac+ �zoo;nh4 zoo

ddon

dt= "phy;don�phy

�parp�2phy + (� par)2

nh4

nh4+Knh4

+no3 e� nh4

no3+Kno3

!phy

+�zoo;don zoo+ �det;don det� �bac bacdon

Kbac

N +min(nh4; � don) + don

ddet

dt= "phyzoo;detGphy + "baczoo;detGbac + ("detzoo;det � 1)Gdet

+�phy;det phy � �det;don det

65

Helge Drange

dphy

dt= (1� "phy;don)�phy

�parp�2phy + (� par)2

nh4

nh4+Knh4

+no3 e� nh4

no3+Kno3

!phy�Gphy

�

�phy;det �phy;det phy2

�phy;det + �phy;det phy

d zoo

dt= min

�UN ; UC �

ZNC

��

�zoo �zoo zoo2

�zoo + �zoo zoo(�nh4 + �don + �nul)

where

GX = �zoopXX

2

(pphyphy2 + pbacbac2 + pdetdet2)

food

Kfood + foodzoo

X = phy;bac;det

food =pphyphy

2 + pbacbac2 + pdetdet

2

pphyphy + pbacbac+ pdetdet

UN = (1� "phyzoo;det)Gphy + (1� "baczoo;det)Gbac + (1� "detzoo;det)Gdet

UC = (1� "phyzoo;det)Gphy=�PNC + (1� "baczoo;det)Gbac=�

BNC + (1� "detzoo;det)Gdetcar

dbac

dt= �bacmin

�BNC doncar

Kbac

N + �BNC doncar;

nh4+ don

Kbac

N + nh4+ don

!bac� �bac;nh4 bac�Gbac

dno3

dt= ��phy

�parp�2phy + (� par)2

no3 e� nh4

no3+Kno3

phy

dnh4

dt= ��phy

�parp�2phy + (� par)2

nh4

nh4+Knh4

phy + �bac;nh4bac

��bacmin(nh4;max(0; �BNC doncar� don))

Kbac

N +min(�BNC doncar;don+ nh4)bac+ �nh4

�zoo �zoo zoo2

�zoo + �zoo zoo

ddon

dt= "phy;don �phy

� parp�2phy + (� par)2

nh4

nh4+Knh4

+no3 e� nh4

no3+Kno3

!phy+ �det;don det

+�don�zoo �zoo zoo

2

�zoo + �zoo zoo� �bac

min(�BNC doncar;don)

Kbac

N +min(�BNC doncar;don+ nh4)bac

ddet

dt= "phyzoo;detGphy + "baczoo;detGbac + ("detzoo;det � 1)Gdet

+�phy;det �phy;det phy

2

�phy;det + �phy;det phy� �det;dondet

66

ddoncar

dt= "phy;don �phy

� parp�2phy

+ (� par)2

nh4

nh4+Knh4

+no3 e� nh4

no3+Kno3

!phy=�PNC

+�zoo;don �zoo;don zoo

2

(�zoo;don + �zoo;don)zoo�BNC+ �det;dondetcar

��bacdoncar

Kbac

N +min(�BNC doncar;don+ nh4)bac

ddetcar

dt= "phyzoo;detGphy=�

PNC + "baczoo;detGbac=�

BNC + ("detzoo;det � 1)Gdetcar

+�phy;det �phy;det phy

2

�phy;det + �phy;det phy=�PNC � �det;don detcar

Tom Anderson

dphy

dt= (1� "phy;don)�phy

�1� e�� par=�phy

� nh4

nh4+Knh4

+no3e� nh4

no3+Kno3

!phy

�Gphy �

�phy;det �phy;det phy2

�phy;det + �phy;det phy

d zoo

dt= (1� "zoo;don � "zoo;nh4 � "zoo;det � "zoo;nul)(Gphy +Gbac +Gdet)

�

�zoo �zoo zoo2

�zoo + �zoo zoo(�nh4 + �nul)

where

GX = �zoopXX

2

(pphyphy2 + pbacbac2 + pdetdet2)

food

Kfood + foodzoo

X = phy;bac;det

food =pphyphy

2 + pbacbac2 + pdetdet

2

pphyphy+ pbacbac+ pdetdet

dbac

dt= �bacmin

�BNC(1� "bac;nul)doncar

KNbac + don

;don

KNbac + don

+nh4

KNbac + nh4

!bac

��bac;don bac� �bac;nul bac�Gbac

dno3

dt= ��phy

�1� e�� par=�phy

�no3 e� nh4

no3+Kno3

phy

67

dnh4

dt= ��phy

�1� e�� par=�phy

�nh4

nh4+Knh4

phy+ �bac;nh4 bac

+�zoo �zoo zoo

2

�zoo + �zoo zoo�nh4 + "zoo;nh4(Gphy +Gbac +Gdet)

+�bacmax

don� �BNC(1� "bac;nul)doncar

KNbac + don

;�nh4

KNbac + nh4

!bac

ddon

dt= "phy;don �phy

�1� e�� par=�phy

� nh4

nh4+Knh4

+no3e� nh4

no3+Kno3

!phy

+�det;dondet+ "zoo;don(Gphy +Gbac +Gdet)� �bacdon

KNbac

+ donbac

ddet

dt= �Gdet + "zoo;det(Gphy +Gbac +Gdet) +

�phy;det �phy;det phy2

�phy;det + �phy;det phy� �det;don det

ddoncar

dt= �phy

�1� e�� par=�phy

� ""phy;don�PNC

nh4

nh4+Knh4

+no3 e� nh4

no3+Kno3

!

+"phy;doncar

1�

nh4

nh4+Knh4

�

no3e� nh4

no3+Kno3

!#phy

+�zoo �zoo zoo

2

�zoo + �zoo zoo�don=�

ZNC + �det;dondetcar+ �bac;don bac=�

BNC

��bacmin

doncar

KNbac + don

;1

�BNC(1� "bac;nul)

�don

KNbac + don

+nh4

KNbac + nh4

�!bac

ddetcar

dt= �Gdet

detcar

det+ "zoo;det

Gphy

�PNC+Gbac

�BNC+Gdet

detcar

det

!

+�phy;det �phy;det phy

2

�phy;det + �phy;det phy

1

�PNC+

�zoo �zoo zoo2

�zoo + �zoo zoo�det=�

ZNC � �det;don detcar

68

Diana Ruiz-Pino

dph1

dt= (1� "ph1;don)�ph1f1(par)

�no3

Kno3 + no3(1� )+

nh4

Knh4 + nh4

�ph1��ph1;de1ph1�Gph1

where

f1(par) =�1� e��1 par=�ph1

�e��1 par=�ph1

= 1no3

no3+ nh4+ (1� 1)

�no3

no3+ nh4

� 2

dph2

dt= (1� "ph2;don)Uph2 �min

��ph2;de1; �

1

ph2;de1 +�Ssil

�ph2�Gph2

where

Lph2 =�1� e��2 par=�ph2

�e��2 par=�ph2 min

�no3

Kno3 + no3(1� ) +

nh4

Knh4 + nh4 ;

sil

Ksil + sil

�Uph2 = �ph2 Lph2 ph2

d zo1

dt= (1�"zo1;de1)(Gph1 +Gbac)�

�min

��zo1;de1; �

1

zo1;de1 +�1

food1

�+ �zo1;nh4

�zo1�Gzo1

where

GX = �zo1pXX

2

(pph1ph12 + pbacbac2)

food1

Kfood1 + food1zo1; X = ph1;bac

food1 =pph1ph1

2 + pbacbac2

pph1ph1+ pbacbac

d zo2

dt= (1� "zo2;de2)(Gph2 +Gzo1)�

�min

��zo2;de2; �

1

zo2;de2 +�2

food2

�+ �zo2;nh4

�zo2

where

GY = �zo2pY Y

2

(pph2ph22 + pzo1zo22)

food2

Kfood2 + food2zo2; Y = ph2; zo1

food2 =pph2ph2

2 + pzo1zo12

pph2ph2+ pzo1zo1

dbac

dt= (1� "bac;don)�bac

min(nh4; � don) + don

Kbac

N +min(nh4; � don) + donbac� �bac;nh4 bac�Gbac

dno3

dt= ��ph1f1(par)

no3

Kno3 + no3(1� )ph1�

Uph2no3

Kno3+no3(1� )

no3

Kno3+no3(1� ) + nh4

Knh4+nh4 + �nh4;no3 nh4

69

dnh4

dt= �zo1;nh4 zo1+ �zo2;nh4 zo2+ �bac;nh4 bac� �ph2f1(par)

nh4

Knh4 + nh4 ph1

�

Uph2nh4

Knh4+nh4

no3

Kno3+no3(1� ) + nh4

Knh4+nh4 � �bac

min(nh4; � don)

Kbac

N +min(nh4; � don) + donbac

��nh4;no3 nh4

ddon

dt= "ph1;don �ph1 f1(par)

�no3

Kno3 + no3(1� ) +

nh4

Knh4 + nh4

�ph1

+�zo1;don zo1+ �zo2;don zo2+ �de1;don de1+ �de2;don de2+ "ph2;don Uph2

+"bac;don�bacmin(nh4; � don) + don

Kbac

N +min(nh4; � don) + donbac

��bacdon

Kbac

N +min(nh4; � don) + donbac

dde1

dt= �ph1;de1 ph1+min

��ph2;de1; �

1

ph2;de1 +�Ssil

�ph2

+"zo1;de1(Gph1 +Gbac) +min(�zo1;de1; �1

zo1;de1 +�1

food1) zo1

��de1;don de1

dde2

dt= "zo2;de2(Gph2 +Gzo1) + min(�zo2;de2; �

1

zo2;de2 +�1

food2) zo2� �de2;don de2

dph2sil

dt= �ph2sil Lph2 ph2sil�min

��ph2;de1; �

1

ph2;de1 +�Ssil

�ph2sil�Gph2

ph2sil

ph2

dde1sil

dt= �min

��ph2;de1; �

1

ph2;de1 +�Ssil

�ph2sil� �det;sil de1sil

dde2sil

dt= Gph2

ph2sil

ph2� �det;sil de2sil

d sil

dt= �det;sil (de1sil+ de2sil)� Uph2

ph2sil

ph2

70

Pascal Prunet

This model is derived from that of Diana Ruiz-Pino but di�ers in the following ways. TheWroblewski (1977) interaction of no3 and nh4 is used. Large phytoplankton, ph2, and all silicatevariables are omitted. Large zooplankton, zo2, eat ph1 instead. (To avoid duplication theamount of grazing is still denoted by Gph2.) Phytoplankton mortality is less at high nutrientconcentrations:

min

��ph1;de1; �

1

ph1;de1 +�N

no3+ nh4

�There are three classes of detritus, whose equations are

dde1

dt= �ph1;de1 ph1+ �zo1;de1 zo1� �de1;don de1

dde2

dt= �ph1;de2 ph1+ �zo1;de2 zo1+ "zo1;de2(Gph1 +Gbac)� �de2;don de2

dde3

dt= "zo2;de2(Gph2 +Gzo1)� �de3;don de3

Parameter values

Some parameters are omitted from the following table because they occur in only one model:

[A] Scott Doney: �1HN = 1:0; EK = 90: The remineralization of detritus goes to the singlecombined dissolved inorganic nitrogen component, which we call no3 here.

[B] George Hurtt: �� = �3:26; the sinking rate of detritus is V (e�V 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.

Ksil = 8; �1 = �2 = 0:024; �S = 0:035; �1zo1;de1 = �1zo2;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 depthaccording to the thickness of the numerical layer: the value given is for the surface.

[F] V�eronique Gar�con: 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

Growthterms

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

�P HN

2.5

6.7

�P NC

.151

.151

Bacteria

�bac

2.0

2.0

2.0

2.0

KNbac

0.5

0.5

0.5

0.5

�

0.6

0.6

0.6

0.6

0.6

0.6

�B NC

.196

.196

Zooplankton

�zoo

0.35

0.69

0.3

1.0

0.74

1.0

1.0

Kfood

0.75

0.48

1.0

1.0

1.09

1.0

1.0

1.0,1.38

1.1,1.38

�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

�Z CN

0.182

Extras

[A,C]

[B]

[E]

[C]

[D]

72

Lossterms

Denman

Doney

McGill.

Hurtt

Wolf

Garcon

Sharada

Evans

Drange

Anderson

Prunet

Ruiz

�:linear

phy!

det

0.5

0.1

0.045

0.018

0.05

0.05

0.015

0.1

phy!

no3

0.05

0.075

zoo!

no3

0.03

0.15

zoo!

nh4

0.09

0.05

0.15

0.04

0.21

0.133

.075,.0165

.25,.075

zoo!

det

0.3,0.1

.021

0.06

.045

.045

zoo!

don

.083,.025

.083,.025

zoo!

nul

0.02

.014

0.067

bac!

don

0.1

0.2

0.2

bac!

nh4

0.05

0.05

0.05

0.02

0.2

det!

nh4

0.1

0.4

.05

det!

don

.051,.004

0.04

0.05

0.1,.09,.08

0.1,0.08

don!

no3

.033,.0033

nh4!

no3

0.25

�:quadratic

phy!

det

0.1

-0.52

0.1

0.25

zoo!

no3

0.2

0.18

zoo!

nh4

0.39

0.667

zoo!

det

0.1

zoo!

nul

0.13

0.333

":uptake

phy!

don

0.25

0.36

0.25

0.05

0.3

0.1,.05

zoo!

det

0.3

0.3,0.4

.225,.075

0.25

0.36

0.25

0.192

0.3,0.6

0.3,0.6

zoo!

no3

0.3

zoo!

nh4

0.25

0.304

zoo!

don

0.1

zoo!

nul

0.1

bac!

nul

0.5

Sinking

phy

0.5

det

10

.0024

2,4

1,10

1

0.34

5.

10

1,3,10

5,88

Extras

[A]

[B]

[E]

[F]

[G]

[D]

73

Inorganic carbon chemistry

Among the various models only �ve described the chemistry of the carbonic acid system in sea-water and its coupling with the ecosystem. The intention here is not to provide the reader with afull description of the carbon chemistry routine the authors used, and whenever possible we willsimply give the appropriate bibliographic reference. We will try to emphasize the links betweenthe dissolved inorganic carbon and total alkalinity pools and the di�erent biological compartmentsplaying a role in their evolution.

David Antoine and Andre Morel Sources and sinks of �CO2 are �PP + R, where PPis the net primary production computed with the formulas of Chapter 2 in the tethered modelframework described in Chapter 3, and R = L(1� f) where

L = C : Chl(PPdaily � Chl : C| {z }1

��Chlobs| {z }2

)

is the daily carbon loss, the di�erence 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 assumedto 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 (softtissues plus carbonates) C �xation.

Tom Anderson The evolution equations for �CO2 and alk are as in Bacastow (1981).

74

Helge Drange

dCaCO3;k

dt= fCaCO3

0@V @detcar

@z

����ez+

kezXl=1

�nul �ZNC

�zoo�zoozoo2

�zoo + �zoozoo

1A phyk + zook � �

ZNCP

l(phyl + zool)

where the �rst and second terms in the main parenthesis are the particulate organic carbon andthe amount of zooplankton that falls out of the euphotic zone, respectively.

d�CO2

dt= ��phy

� parp�2phy + (� par)2

"nh4

nh4+Knh4

+NO3 � e

� �nh4

NO3 +KNO3

#phy � �PNC � dCaCO3=dt

+�bac;nh4 � bac � �BNC +

�zoo�zoozoo2

�zoo + �zoozoo� �nh4 � �

PNC

dalk

dt= �dno3=dt+ dnh4=dt� 2 dCaCO3=dt :

Pascal Prunet, Diana Ruiz-Pino

We will show here the modi�cations of the dissolved inorganic carbon and total alkalinitycontents due to trophic activity in the simplest case of Pascal Prunet's model. The reader willeasily adapt them for Diana Ruiz-Pino's model.

d�CO2

dt= �NC

""bac;don � �bac

min(nh4; �don) + don

Kbac

N +min(nh4; �don) + donbac + �bac;nh4 � bac

+�zo1;nh4 � zo1+ �zo2;nh4 � zo2 ��phy f(par)

�no3

Kno3 + no3(1� ) +

nh4

Knh4 + nh4

�phy

�

� �NC �CaCO3

Corg

"(1� "phy;don) � �phy � f(par) �

�no3

Kno3 + no3(1� ) +

nh4

Knh4 + nh4

�phy

+min

��zo1;de1; �

1

zo1;de1 +�1

food1

�� zo1 +min

��zo2;de2; �

1

zo2;de2 +�2

food2

�� zo2

�

dalk

dt= �2��NC �

CaCO3

Corg

"(1�"phy;don)��phy�f(par)�

�no3

Kno3 + no3(1� ) +

nh4

Knh4 + nh4

��phy

+min

��zo1;de1; �

1

zo1;de1 +�1

food1

�� zo1 +min

��zo2;de2; �

1

zo2;de2 +�2

food2

�� zo2

�

75

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83

Participants

Tom AndersonSouthampton Oceanography CentreEuropean WaySouthampton SO14 3ZHUnited Kingdomfax: +44 1703 596247tel: +44 1703 596337email: tra@soc.soton.ac.uk

David AntoineLaboratoire de Physique et Chimie MarinesObservatoire OceanologiqueBP 806230 Villefranche sur MerFrancefax: +33 4 93 76 37 39tel: +33 4 93 76 37 23email: david@ccrv.obs-vlfr.fr

Shigeaki AokiNational Institute of Resourcesand Environment Technology16 Onogawa, Tsukuba, Ibaraki 305Japanfax: +81 298 58 8357tel: +81 298 58 8376email: s-aoki@nire.go.jp

Isabelle DadouUMR5566/GRGS18 Avenue Edouard Belin31055 Toulouse CedexFrancefax: +33 5 61 25 32 05tel: +33 5 61 33 29 54email: dadou@pontos.cst.cnes.fr

Ken DenmanInstitute of Ocean SciencesPO Box 6000Sidney, BC V8L 4B2Canadafax: +1 250 363 6746tel: +1 250 363 6346email: denman@ios.bc.ca

Scott DoneyClimate and Global Dynamics DivisionNational Center for Atmospheric ResearchBoulder CO 80307USAfax: +1 303 497 1700tel: +1 303 497 1639email: doney@ncar.ucar.edu

Helge DrangeNansen Environmental andRemote Sensing CenterEdv. Griegsvei 3a5037 SolheimsvikenNorwayfax: +47 55 20 00 50tel: +47 55 29 72 88email: Helge.Drange@nrsc.no

Geo� EvansDepartment of Fisheries and OceansScience BranchPO Box 5667St John's, NF A1C 5X1Canadafax: +1 709 772 3207tel: +1 709 772 4105email: evans@mrspock.nwafc.nf.ca

V�eronique Gar�conUMR556/CNRS/GRGS18 Avenue Edouard Belin31055 Toulouse CedexFrancefax: +33 5 61 25 32 05tel: +33 5 61 33 29 57email: garcon@pontos.cst.cnes.fr

George HurttEcology and Evolutionary BiologyPrinceton UniversityPrinceton NJ 08544USAfax: +1 609 258 1334tel: +1 609 258 3868email: george@eno.princeton.edu

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Dennis McGillicuddyPhysical Oceanography DepartmentWoods Hole Oceanographic InstitutionWoods Hole MA 02543USAfax: +1 508 457 2181tel: +1 508 457 2000 ext 2683email: mcgillic@epl.whoi.edu

Cathrine MyrmehlNansen Environmental andRemote Sensing CenterEdv. Griegsvei 3a5037 SolheimsvikenNorwayfax: +47 55 29 72 88tel: +47 55 20 00 50email: Cathrine.Myrmehl@nrsc.no

Andreas OschliesInstitut f�ur MeereskundeD�usternbrooker Weg 2024105 KielGermanyfax: +49 431 565 876email: aoschlies@ifm.uni-kiel.de

John ParslowCSIRO Division of FisheriesGPO Box 1538, HobartTasmania 7001Australiafax: +61 02 325000tel: +61 02 325202email:parslow@ml.csiro.au

Trevor PlattBedford Institute of OceanographyPO Box 1006Dartmouth, N.S. B2Y 4A2Canadafax: +1 902 426 9388tel: +1 902 426 3793email: tplatt@is.dal.ca

Pascal PrunetGMAP/AADCentre National de Recherches M�et�eorologiques42, avenue G. Coriolis31057 Toulouse CedexFranceTel: +33 5 61 07 84 54Fax: +33 5 61 07 84 53e-mail: prunet@cnrm.meteo.fr

Diana Ruiz-PinoLaboratoire de Physique et Chimie MarinesTour 24-25Universite Paris VI4 Place Jussieu75230 Paris Cedex 05Francefax: +33 1 44 27 49 93tel: +33 1 44 27 48 60email: ruiz@ccr.jussieu.fr

M.K. SharadaCSIR Centre for Mathematical Modellingand Computer SimulationNational Aerospace LaboratoriesBelur CampusBangalore 560037Indiafax: +91 812 526 0392tel: +91 812 527 4649email: sharada@cmmacs.ernet.in

Uli WolfInstitut f�ur OstseeforschungSeestr. 1518119 Warnem�undeGermanyfax: +49 381 5197 440tel: +49 381 5197 260email: uli.wolf@io-warnemuende.de

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The JGOFS Report Series includes the following:

1 Report of the Second Session of the SCOR Committee for JGOFS. The Hague, September 1988 2 Report of the Third Session of the SCOR Committee for JGOFS. Honolulu, September 1989 3 Report of the JGOFS Pacific Planning Workshop. Honolulu, September 1989 4 JGOFS North Atlantic Bloom Experiment: Report of the First Data Workshop. Kiel, March 1990 5 Science Plan. August 1990 6 JGOFS Core Measurement Protocols: Reports of the Core Measurement Working Groups 7 JGOFS North Atlantic Bloom Experiment, International Scientific Symposium Abstracts.

Washington, November 1990 8 Report of the International Workshop on Equatorial Pacific Process Studies. Tokyo, April 1990 9 JGOFS Implementation Plan. (also published as IGBP Report No. 23) September 1992 10 The JGOFS Southern Ocean Study 11 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

12 Report of the Second Meeting of the JGOFS North Atlantic Planning Group 13 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

14 Biogeochemical Ocean-Atmosphere Transfers. A paper for JGOFS and IGAC by Ronald Prinn, Peter Liss and Patrick Buat-Ménard. March 1994

15 Report of the JGOFS/LOICZ Task Team on Continental Margin Studies. April 1994 16 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

17 JGOFS Arabian Sea Process Study. March 1995 18 Joint Global Ocean Flux Study: Publications, 1988-1995. April 1995 19 Protocols for the Joint Global Ocean Flux studies (JGOFS) core measurements (reprint). June,

1996 20 Remote Sensing in the JGOFS programme. September 1996 21 First report of the JGOFS/LOICZ Continental Margins Task Team. October 1996 22 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