SOES6002 - Toby Tyrrell
Model of Primary Production
and the Phosphorus Cycle
•Description of the P cycle
•Model of how it is regulated
Why is the Earth the way it is?
SOES6002 - Modelling in Environmental and Earth System Science
Regulation, control, homeostasis,
stable equilibria, steady states, feedbacks.
Bernouilli Blower (Science Museum)
What keeps the system in whack?
Control mechanisms operating in
the sea (chapter 6)
Model of Oceanic Phosphorus Cycle
Homeostasis, resistance to perturbations
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SOES6002 - Toby Tyrrell
Phytoplankton Composition
Different forms of P in the sea.
PO4 = phosphate
Phosphorus is required in order to
construct key biomolecules, such as
DNA (left) and ATP.
DIP = dissolved inorganic phosphorus = PO4
DOP = dissolved organic phosphorus
Nitrogen is required to
build proteins, such as
RUBISCO (right).
Redfield ratio, e.g. C:N:P:(-O2) = 106:16:1:(-138)
SRP = soluble reactive phosphorus = DIP (more or
less, but subject to error, some organic phosphates
and other substances are also included inadvertently
in the measurement)
photosynthesis
106CO2 + 16HNO3 + H3PO4 + 122H2O
(CH2O)106(NH3)16H3PO4 + 138 O2
remineralisation
Different forms of P in the sea (2)
-- Typical Concentrations.
PO4 / SRP : (surface) low
(deep) 1 - 3 micro-Moles kg-1
(mean 2.25)
DOP / SNP : (surface) 0.2 - 1.7 micro-Moles kg-1
(deep)
< 0.3 micro-Moles kg-1
(few measurements)
Most P in the oceans exists as PO4 (rather little
DOP compared to DOC and DON).
Model of Oceanic Phosphorus Cycle
Surface Phosphate Concentration
(World Ocean Atlas)
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SOES6002 - Toby Tyrrell
Depth profiles, tropical North
Pacific (13N, 152W)
Typical depth profiles of SRP (= soluble reactive P)
(C.R. Benitez-Nelson, 2000, “The biogeochemical cycling of
phosphorus in marine systems,” Earth-Sci. Rev., 51: 109-135)
Magnitude of P fluxes in the ocean.
Diagenetic redistribution
of organic P in sediments
Schematic of marine P cycle
TDP = Total Dissolved P, SRP = Soluble Reactive P, SNP = Soluble Non-Reactive P.
(C.R. Benitez-Nelson, 2000, “The biogeochemical cycling of phosphorus in
marine systems,” Earth-Sci. Rev., 51: 109-135)
Model of Oceanic Phosphorus Cycle
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SOES6002 - Toby Tyrrell
Regulation of
the Phosphorus Cycle
?
?
?
For ocean phosphate:
(1) where is the equilibrium point?
(2) what process restores equilibrium when it goes too low?
(3) what process restores equilibrium when it goes too high?
Analogy with a Central Heating
Thermostat
A simple model of P cycling.
(1) what is the target room temperature? (or in other words,
what temperature is the dial set to?)
(2) How is equilibrium restored if the room temperature has
become too high? [stop pumping hot water to radiators]
(3) How is equilibrium restored if the room temperature has
become too cold? [pump more hot water to radiators]
Model of Oceanic Phosphorus Cycle
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SOES6002 - Toby Tyrrell
Model ecosystem
Phytoplankton growth rate is reduced if any critical
nutrient is scarce:
The processes affecting phytoplankton are simplified
down to birth and death
Population
=
change
CULTURE EXPERIMENTS
A similar
relationship holds
for phytoplankton
growth and
phosphate
D. Tilman,
“Resource Competition and
Community Structure”
1982, Princeton Univ. Press
-
Model equations
Model Parameter Values.
Symbol
Description
SD
DD
K
SR
depth of surface layer
depth of deep layer
mixing coefficient
fraction of TPP regenerated
above 500m
fraction of TPP regenerated
below 500m (=100-SR-SF)
fraction of TPP permanently
buried
river input of P (total
dissolved)
DR
SF
RP
µ’
M
PH
Model of Oceanic Phosphorus Cycle
Maximum growth rate
mortality (mainly grazing)
half-saturation constant
Units
m
m
m per year
%
Model
Value
Literature
Values
500
3230
3
95
3
92, 97,
%
4.8
-
%
0.2
mMol P per
m2 per
year
0.2
0.1-0.2,
0.16
0.09, 0.19,
0.15, 0.21
Per day
Per day
µMol per
kg
0.25
0.20
0.03
0.1-4.1
0.25-1.2
0.03, 0.05
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SOES6002 - Toby Tyrrell
A simple model of P cycling.
More phosphate
One Run from a NonEquilibrium Initial State
More phytoplankton
More sinking particles
More burial of
organic matter
More remineralisation of organic
matter in deep ocean
Initial Conditions Analysis
Model of Oceanic Phosphorus Cycle
Recovery from Perturbations
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SOES6002 - Toby Tyrrell
Comparison of Standing Stocks
Model
28303930
Literature
Phytoplankton
concentration
1.7
1.6-2.3 g C m-2
Phosphate concentration
(surface ocean)
0.15
0.5 mMol m-3
Phosphate concentration
(deep ocean)
1.75
2.2 mMol m-3
Broecker & Peng: Tracers in the Sea
Why Does the Ocean Have
~2 mMol PO4 at Depth, and
Almost None at the Surface?
What happens when you double the speed of mixing?
1. Any more and the resulting massive burial of
phytoplankton (containing P) would bring levels
back down.
2. Any less and the reduction in burial would allow
rivers to fill up the ocean with phosphate.
Model of Oceanic Phosphorus Cycle
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