Marine Biogeochemical and Ecosystem Modeling

Michael Schulz

MARUM -- Center for Marine Environmental Sciences

and

Faculty of Geosciences, University of Bremen

9:15 - 9:45

1. Introduction (Lecture)- The global carbon cycle, CO2 in seawater

- “Biological pumps”

- Reservoir or box models

2. Modeling Marine Nutrient and Carbon Cycles (Box-Model Exercise)- Global oceanic phosphate distribution

- Nutrient – productivity interactions

- Oceanic carbon budget and large-scale ocean circulation

10:45 - 11:00 break

11:00 – 12:30

2. cont'd- Circulation-productivity feedback in the global

ocean

3. State-of-the-art Biogeochemical Models (Lecture)- 2D and 3D Models- Included tracers and processes

4. Marine Ecosystem Models (Lecture)

- Why ecosystem models?

- Ecosystem models in paleoceanography

Course Material

www.geo.uni-bremen.de/geomod/

staff/mschulz/lehre/ECOLMAS_Modeling/

This presentation

Box-model exercises

Basic LiteratureNajjar, R. G., Marine biogeochemistry. in Climate system modeling, edited

by Trenberth, K. E., pp. 241-280, Cambridge University Press, Cambridge, 1992.

Rodhe, H., Modeling biogeochemical cycles. in Global biogeochemical cycles, edited by Butcher, S. S., R. J. Charlson, G. H. Orians and G. V. Wolfe, pp. 55-72, Academic Press, London, 1992.

Sarmiento, J. L., and N. Gruber, Ocean biogeochemical dynamics, pp. 503, Princeton University Press, Princeton, 2006.

Walker, J. C. G., Numerical adventures with geochemical cycles, 192 pp., Oxford University Press, New York, 1991.

Ruddiman (2001)

For a climatologist biogeochemical cycles usually translates into carbon cycle.

Sundquist (1993, Science)

Reservoir Sizes in [Gt C]Fluxes in [Gt C / yr]

Carbon-Cycle – Characteristic Timescales

Thurman & Trujillo (2002)

Average surface-Water composition

CO2 0.5 %HCO3

- 89.0 %CO3

2- 10.5 %

- -

- -

23 3

22 3 3

TA [HCO ] + 2[CO ]

CO [HCO ] + [CO ]

Biological Productivity in the Ocean

Ruddiman (2001)

Nutrients:P, N, (Si, Fe)

Atmosphere

Ocean

Primary Production

Inorgan. C Organ. C

Particle-Flux

RemineralisationOrgan. C CO2

CO2

CO2

The Biological Pump

Fig. courtesy of A. Körtzinger

Sediments

Photic Zone

Aphotic Zone

Sediments

Biogenic Calcium Carbonate Production Raises Dissolved CO2 Concentration

2- -2 2 3 3CO + H O + CO 2HCO

pH Reaction:

(1) Biogenic carbonate uptake

(2) More bicarbonatedissociates

(3) More CO2 is formed

Atmosphere

Ocean

CO2

The Calcium Carbonate Pump

CaCO3 Dissolution

Lysocline

Biogenic CaCO3

Formation3

CO32-

CO2

Fig. courtesy of A. Körtzinger

Reservoir or Box Models

• Reservoir = an amount of material defined by

certain physical, chemical or biological

characteristics that, under the particular

consideration, can be regarded as homogeneous.

(Examples: CO2 in the atmosphere, Carbon in living organic matter in

the oceanic surface layer)

• Flux = the amount of material transferred from one

reservoir to another per unit time

Single Reservoir Case

Reservoir (mass M)

Flux In Flux Out

Basic Math of Box Models

(Rate of change of mass in reservoir) =

(Flux in) – (Flux out) + Sources – Sinks

Or, for concentration (C [mol/m3]) and water flux (Q

[m3/s]):

i o

dMF F SMS

dt

i i o

dCV QC Q C SMSdt

Numerical Solution of Box-Model Equations

1 0

1 0 0 0 0

2 1 1 1 1

1

1 0

, ,

, ,

, ,

( )

( )

( )n n n n n

t ti o

t t i t o t t

t t i t o t t

t t i t o t t

M MdM MF F SMS

dt t t t

M M t F F SMS

M M t F F SMS

M M t F F SMS

Solution by finite-difference method (approximation!)

“Euler Method”

Initial Condition

Tim

e (

in s

tep

s of

t)

Numerical Solution of Box-Model Equations

1 0

1 0 0 0 0

2 1 1 1 1

1

1 0

, ,

, ,

, ,

( )

( )

( )n n n n n

t ti o

t t i t o t t

t t i t o t t

t t i t o t t

M MdM MF F SMS

dt t t t

M M t F F SMS

M M t F F SMS

M M t F F SMS

Solution by finite-difference method (approximation!)

Initial Condition

Numerical Solution of Box-Model Equations

1 0

1 0 0 0 0

2 1 1 1 1

1

1 0

, ,

, ,

, ,

( )

( )

( )n n n n n

t ti o

t t i t o t t

t t i t o t t

t t i t o t t

M MdM MF F SMS

dt t t t

M M t F F SMS

M M t F F SMS

M M t F F SMS

Solution by finite-difference method (approximation!)

“Euler Method”

Initial Condition

Tim

e (

in s

tep

s of

t)

M(tn)

t

tn+1 tn t

M

“Prediction”

True Value

Error Slope = Fi(tn) - Fo(tn) + SMS(tn)

M(tn+1)

Euler Method

Assumption: Slope at time tn remains constant throughout time interval t

Coupled Reservoirs

Reservoir 1 (mass M1)

F12

Reservoir 2 (mass M2)

F21

Principle of mass-conservation requires M1 + M2 = const.

Large-Scale Ocean Circulation

(after Broecker, 1991)

Box-Model ofOceanic PO4 Distribution

AABW_A(4 Sv)

AABW_P(20 Sv)

NADW(10 Sv)

Indo-Pacific Southern Ocean Atlantic

Surface(0-100 m)

Deep(> 100 m)

20 Sv 10 Sv20 Sv

www.geo.uni-bremen.de/geomod/staff/mschulz/lehre/ECOLMAS_Modeling/bm1_po4_only.gsp

Box-Model Experiment 1

• Vary the water transports and initial PO4

concentration and observe the final PO4

concentration and evolution (time series).

• Q1: How does the final PO4 distribution depend

on these settings?

• Q2: How do these settings affect the time it

takes to reach a steady state? (What

characterizes the steady state?)

Inducing PO4 Gradients – Biological Productivity

• Assume an average export production of

12 g C/m2/yr

• With a “Redfield ratio” of C:P = 117:1

(molar ratio) and 1 mol C = 12 g C

Corresponding biological PO4 fixation is

1/117 mol P/m2/yr

Box-Model of Oceanic PO4 Distribution with Productivity

AABW_A(4 Sv)

AABW_P(20 Sv)

NADW(10 Sv)

Indo-Pacific Southern Ocean Atlantic

Surface(0-100 m)

Deep(> 100 m)

Assumption: Biologically fixed PO4 sinks from the surface layer to the underlying deep layer, where the organic material is completely remineralized.

www.geo.uni-bremen.de/geomod/staff/mschulz/lehre/ECOLMAS_Modeling/bm1_po4_fix_prod.gsp

Box-Model Experiment 2

• Q: How does the inclusion of biological productivity affect

the PO4-concentration difference between Atlantic and Indo-

Pacific Oceans in the standard case?

10 m water depth

1750 m water depth

Box-Model Experiment 2

• Vary the water transports (try max. and small values)

and observe how the PO4 distribution changes. Explain

the changes.

• Q: What happens if NADW = 0 Sv? (Keep the

remaining parameters at their default values.) Does this

result make sense in the real world?

• Q: For which initial PO4 concentration do no negative

concentrations result (with NADW = 0 Sv)? Is this a

reasonable increase for Late Pleistocene glacials?

Avoiding Negative PO4 Concentrations – Nutrient-Dependent Productivity

• Assume that productivity scales with the PO4

availability in the surface layer (variety of relationships are possible: linear, non-linear with saturation…)

• PO4 fixation = [PO4]sfc * Volsfc / [mol/yr],

where is the residence time of PO4 in the

surface due to biological productivity

• Assume ATL = IPAC = 5 yr and SOC = 50 yr (Broecker

and Peng, 1986)

www.geo.uni-bremen.de/geomod/staff/mschulz/lehre/ECOLMAS_Modeling/bm1_po4_dyn_prod.gsp

Box-Model Experiment 3a

• Run the model for NADW of 0 and 10 Sv

and write down the PO4 concentrations for

the Atlantic boxes for each case.

• Calculate the difference between conc. in

deep and surface box. What do you

observe?

Box-Model Experiment 3a – Atlantic

NADW

(Sv)

PO4 Surface

(mol/l)

PO4 Deep

(mol/l)

PO4

(mol/l)

10 0.24 0.69 0.45

0 0.18 0.88 0.70

Shift of PO4 content from surface to deep Atlantic as NADW drops

Box-Model Experiment 3b

• Run the model for NADW = {0, 5, 10, 15,

20} Sv and write down the final PO4

fixation in the Atlantic Ocean.

• Sketch NADW vs. PO4 fixation.

• Q:What is the paleoceanographic

implication of this finding?

NADW and Productivity in the Atlantic Ocean

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

0 5 10 15 20

PO

4 F

ixat

ion

[1011

mol

P /

yr]

NADW Flow [Sv]

Including the Marine Carbon-Cycle

• Tracers: PO4 ( controls productivity)

DIC (dissolved inorganic carbon)

ALK (alkalinity)

• Aqueous CO2 partial pressure = f(DIC, ALK)

• Redfield ratio of organic matter (C:N:P = 117:16:1)

• Ratio between Corg and CaCO3 production (“rain

ratio”) assumed to be temperature dependent (a crude parameterization of ecosystem dynamics)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 5 10 15 20 25 30

Rai

n R

atio

= P

CaC

O3

/ PC

org

Water Temperature [°C]

Rain-Ratio Parameterization

Area-WeightedAverage

AtmosphericpCO2 ≈ Mean Oceanic pCO2

www.geo.uni-bremen.de/geomod/staff/mschulz/lehre/ECOLMAS_Modeling/bm1_c-cycle_fix_prod.gsp

Box-Model Experiment 4C-Cycle with Fixed Productivity

• Run the model for the default setting. Identify the

sources and sinks with respect to atmospheric

CO2.

• Run the model for NADW of 0 and 10 Sv. Write

down the final global mean pCO2 and the

productivity in the Atlantic Ocean. (Neglect the

negative PO4 conc., identified in the previous exp.)

Box-Model Experiment 4C-Cycle with Fixed Productivity

NADW

(Sv)

Prod. ATL

(Pg C/yr)

Prod. Glob.

(Pg C/yr)

Global pCO2

(ppm)

10 0.447 5.03 281

0 0.447 5.03 265

16 ppm Reduction

Box-Model Experiment 5C-Cycle with Dynamic Productivity

• How will the response of the mean pCO2

change if productivity is no longer constant

but a function of PO4?

www.geo.uni-bremen.de/geomod/staff/mschulz/lehre/ECOLMAS_Modeling/bm1_c-cycle_dyn_prod.gsp

Box-Model Experiment 5C-Cycle with Dynamic Productivity

• Run the model for again for NADW of 0

and 10 Sv. Write down the final global

mean pCO2 and the productivity in the

Atlantic Ocean.

• Interpret your results.

Box-Model Experiment 5C-Cycle with Dynamic Productivity

NADW

(Sv)

Prod. ATL

(Pg C/yr)

Prod. Glob.

(Pg C/yr)

Global pCO2

(ppm)

10 0.447 5.03 281

0 0.350 4.83 275

Only 6 ppm Reduction

Box-Model Experiment 5C-Cycle with Dynamic Productivity

NADW = 0 DIC shifted from surface to deep Atlantic pCO2 reduced

BUT: PO4 is shifted to deep ocean too less nutrients in surface productivity decreases biological pump weakens pCO2 increases

Negative Feedback Mechanism

Ruddiman (2001)

From Box-Models to 2D/3D-Models

Structure of a Global Biogeo-chemical Model

Ridgwell (2001, Thesis)

Ridgwell (2001, Thesis)

Modeling Deep-Sea Sediments

Phosphate in the Atlantic Ocean [mol/l]

2D-Model

(Zonal Mean)

3D-Model

(N-S Section)

(Schulz and Paul, 2004)

(Heinze et al., 1999)

0

10

20

30

40

50

60

70

80

90

-80 -60 -40 -20 0 20 40 60 80Latitude

Atlantic Ocean Export Production [gC/(m2 yr)]

(Schulz and Paul, 2004)

Horizontal Resolution in a 2D-Biogeochemical Model

(Heinze et al., 1999)

Horizontal Resolution in a 3D-Biogeochemical Model

A Modeled Sediment Stack in the North Atlantic

Heinze, C. et al., 1999: A global oceanic sediment model for long-term climate studies. Global Biogeochemical Cycles, 13, 221-250.

Modeled and Observed Modern CaCO3 Content of Deep-Sea Sediments

Heinze et al. (1999)

Even the most sophisticated biogeochemical models allow only for a crude approximation of the real world. Discrepancies are largely due to an inadequate resolution (e.g. MOR) and a lack of knowledge of the processes being involved.

Model Observations

Marine Ecosystem Models – Why?

• Productivity may depend on more than a single

nutrient (N, P, Si, Fe)

• Export production controlled by ecosystem

dynamics

• Understanding the preferential growth of

different algae groups (e.g. diatoms vs.

coccolithophores)

• Disentangling the seasonal imprint in biological

proxy records

• 4 Compartments

• Coupled to carbon and

alkalinity

• Nutrients are

transported by ocean

circulation

• Efficient in predicting

seasonal patterns

NPZD-Type Ecosystem Model

(after Fasham et al., 1990)

Marine Ecosystem Model Components (Moore et al., 2002)

Marine Ecosystem Model Forcing

Output from global OGCM

Global Foraminifera Model

Fraile et al. (subm.)

Fraile et al. (subm.)

Brown University Foraminiferal Database (Prell et al., 1999)

Modeled / Observerd Distribution of N. pachyderma (sin.)

Fraile et al. (subm.)

Brown University Foraminiferal Database (Prell et al., 1999)

Modeled / Observerd Distribution of N. pachyderma (dex.)

Fraile et al. (subm.)

Brown University Foraminiferal Database (Prell et al., 1999)

Modeled / Observerd Distribution of G. bulloides

Fraile et al. (subm.)

Brown University Foraminiferal Database (Prell et al., 1999)

Modeled / Observerd Distribution of G. ruber (white)

Fraile et al. (subm.)

Brown University Foraminiferal Database (Prell et al., 1999)

Modeled / Observerd Distribution of G. sacculifer

Fraile et al. (subm.)

Modeled LGM shift in seasonality of G. bulloides

Fraile et al. (subm.)

Benefits of Paleoecosystem Modeling

• To facilitate model-“data“ comparison

• To obtain a mechanistic understanding of

reconstructed shifts in species

• To assess the potential effect of altered plankton

successions on proxy reconstructions based on

organisms