Modeling the biological
component of the ocean carbon
cycle
Anand Gnanadesikan
Johns Hopkins University
Ocean ecosystems-The simplest picture
Biological activity takes up these nutrients
Shallow sunlit
euphotic zone
Mixing and
upwelling
bring
nutrients to
the surface.
High nutrient
ocean interior
Sinking fluxes export nutrients back to depth
Nutrients include: N,P,Si,Fe
Key question
• How much of the nutrient brought to the
surface is taken up by biological cycling?
• How much is reinjected to depth?
M
M ([ N d ]  [ N s ])  Export
M [ N d ]  Potential Export
Export
Efficiency 
Potential Export
Observed “efficiency”
Key point- in modern ocean efficiency is low in high latitudes.
Different ways of dealing with
“efficiency”
• LOSCAR (last week’s paper), Constant value of 0.8.
– “Volume averaged” value is closer to 50%
– Changes in carbon can only be driven by changes in nutrient
inventory.
• “Diagnostic” models (Marinov et al., 2008) restore
nutrients to a surface value- effectively fit observed
levels of efficiency.
– Captures relationship between volume-averaged efficiency and
circulation…
– But not clear what to do in past.
• “Prognostic” ocean models (try to match nutrients and
some measure of biological activity).
– Will generally fit modern nutrients worse than a diagnostic
model.
– Generally requires more inputs
– Equations can be debated.
What do we need to build a
prognostic model
• Formulation of phytoplankton growth rate
– Macronutrient limitation (nitrogen,
phosphorus, silicon?)
– Micronutrient limitation (iron)
– Light
• Formulation of phytoplankton death rate.
– Explicit treatment of zooplankton
– Implicit treatment of zooplankton
Basic strategy
• In order to get nutrients right, we need to model their
uptake.
• In order to get chlorophyll right we need to model the
biomass accomplishing this uptake.
Uptake=Growth rate*Biomass
Start by looking at growth rate.
Uptake~Loss rate*Biomass
Close the loop by parameterizing mortality.
What are the conceptual tools we
want to use to do this?
• Multiple limitations (temperature, light,
macronutrients, iron). Builds on theory by
Richard Geider.
• Allometric (size-structured) relationship
between ecosystem structure and
function. Builds on theory by Dunne,
Armstrong, Gnanadesikan and Sarmiento.
Representing growth:
1. Temperature limitation
Eppley (1972) showed that
the maximum growth rate of
plankton had a temperaturedependent upper limit.
Note the spread!
Individual species tend to be
adapted for specific
temperature range.
C
PC  Pmax
exp( 0.063T )
Representing growth:
2. Macronutrient limitation
… is balanced by rate at
which free nutrient
encounters open binding
sites= N*(K-B)
Rate at which nutrient
is incorporated from
binding sites to which
it is attached = CB
Solution has form
C
max
P N
P 
KN  N
C
Curve shows uptake rate (v) vs
concentration
Line shows nutrient
concentration/uptake rate vs. nutrient
concentration.
Eppley, Rodgers and McCarthy, 1969
Representing growth:
3.Iron limitation
• Tricky because of luxury uptake (plankton don’t stop
taking up iron at concentrations above repletion).
• Let uptake ratio go as Michaelis-Menten….
• But allow plankton to become replete at lower
concentrations of iron.
Fe
Fe : P  ( Fe : P) 0
K Fe  Fe
( Fe : P) chl  ( Fe : P) 0
( Fe : P)
def _ fe 
*
( Fe : P) chl  ( Fe : P)
( Fe : P) 0
Representing growth:
4.Light limitation
Also saturates at high levels
P P
C
C
max
1  exp(  Irr / Irrk )
Key parameter is the slope of this
curve at low light levels
Tilzer et al., Polar Biology, 1986.
Irrk  P
C
max
/    Slope   
chl
Chlorophyll-normalized photosynthetic efficiency
chl
Chl:C ratio
Geider+ co-limitation theory
Key ideas:
Phytoplankton adjust their ability to harvest light to match
their inherent growth rate. (Geider)

Growth rate
Maximal light processingcapacity
PNC
Irr
 Irrk 

 2
Their ability to do this can be limited/affected by iron.
(Dunne- TOPAZ).
Total growth rate
P P
C
tot
C
max
 exp( 0.063 * T )
N
 min(
, def _ fe)
KN  N
 1  exp(  Irr / Irrk )
Temperature
Macro/micronutrient
Light
Basic formulation common to TOPAZ, CCSM, IBGC….
Key complication, light limitation depends on other variables!
But to get nutrient uptake, we need
an estimate for biomass
Key insight: On time
scales of months, almost
all of the production is
balanced by loss terms.
Accumulation of biomass
is a small residual.
Growth_rate*biomass~
Loss rate*biomass
But loss rate may itself
depend on the biomass
concentration.
Schultz, 2008
Accounting for loss rates
Growth rate  P   * ( Biomass / P )  Loss rate
C
tot
But is there a way of coming up
with , P* and a?
Answer: Calibrate them to
ecosystem structure. (High
productivity regions dominated
by big plankton).
* a
Dunne et al. (2005) theory
Define small (S) and large
(L) phytoplankton
 
  
P 
C
tot
C
tot
P
S
P*
L 1/ 3
P*
(P / )
L

C
2
S  L 1  ( Ptot /  )
C
tot
2
So we are able to diagnose
•
•
•
•
Growth rates
Phytoplankton biomass
Chlorophyll concentration (from )
Ecosystem structure (small vs. large)
How do we now connect this to nutrient
cycling?
Sinking a function of ecosystem
structure
Ecosystems dominated by small
plankton (like blue-green algae at
left) don’t generate a lot of sinking
material
Ecosystems dominated by large
plankton (like diatom at left)
generate a lot of sinking material
det  (s fracS  L fracL )e
0.032T
Parameter list
Taken from
literature
unmodified
(in blue)
Fit to ocean
chlorophyll.
Fit to ocean
nutrients/
DOM/
oxygen
Fit to iron
Additional parameters when
modeling carbon
• PIC:POC export ratio (from modern data)
• PIC remineralization length scale (from
modern alkalinity distribution).
• C:P ratio (fixed from modern nutrients)
• Outputs include
– Export
– Flux to bottom
– pH/calcite saturation parameters
Detritus then sinks and
remineralizes
Schneider et al.,
Biogeosciences 2008
Obs PO4
BLING PO4
BLING-Obs PO4
Iron simulation
BLING Chl
Obs Chl
Productivity
Key question asked in this paper
• What’s the impact of including explicit iron
limitation (spatiotemporally dependent) on
phytoplankton physiology?
C
N
P
Irr
Irrk 

 2
• Does iron affect growth, photosynthetic
efficiency, carbon:chl ratio, or all three?
Adding iron limitation decreases efficiency in
Southern Ocean more than north
Reflected in nutrient concentrations
Biggest impact of iron-light
colimitation on NH seasonal cycle
For applying this to future climate
• Macronutrient inventory.
– Set equal to today’s at first guess…
– But lifetime for PO4 is only 50,000 yr
– Isotope constraints?
• Iron delivery to ocean
– look at distribution of deserts
– Iron delivery from hydrothermal vents?