the global carbon cycle gerrit lohmann 31. october 2005, 11.15 o‘clock biogeochemical cycles

The Global Carbon Cycle

Gerrit Lohmann31. October 2005, 11.15 o‘clock

• Biogeochemical cycles

How much CO2 is dangerous?

• Present levels in the atmosphere are approaching 300 ppm having risen from 150 ppm pre the industrial revolution.

• Levels beyond a few percent are dangerous and at over 30% can cause the human nervous system to shut down in seconds.

• Even levels of a few percent can cause problems.Rooms are not meant to reach 0.5%

Turnover Time, renewal time

M content if a substance in the reservoir

S total flux out of the reservoir

MS=kMQ

single reservoir with source flux Q, sink flux S, and content M

The equation describing the rate of change of the content of a reservoir can be written as

Atmosphere 725(Annual increase ~3)

Surface waterDissolved inorg. 700

Dissolved org. 25(Annual increase ~ 0,3)

Surface biota3

Intermediate andDeep water

Dissolved inorg. 36,700Dissolved org. 975

(Annual increase ~ 2,5)

Short-lived biota~110

Long-lived biota ~450(Annual decrease ~1)

Litter~60

Soil 1300 - 1400(Annual decrease ~1)

Peat (Torf)~160

Fossil fuelsoil, coal, gas

5,000 - 10,000

Respiration &decomposition

~36

Primaryproduction

~40

Detritus~4

Detritus decomposition

54-50

~40 ~38

5

2 - 5

2 - 5

~15~40

~120~60~90~93Deforestation

~1

‹1

‹1

~15~1

Fig. 4-3 principal reservoirs and fluxes in the carbon cycle. Units are 1015 g(Pg) C (burdens)and PgC/yr (fluxes). (From Bolin (1986) with permission from John Wiley and Sons.)

The adjustment process is

e-folding time

The flux Fij from reservoir i to reservoir j is given by

The rate of change of the amount Mi in reservoir i is thus

where n is the total number of reservoirs in the system. This system of differential equationscan be written in matrix form as

where the vector M is equal to (M1, M2,... Mn) and the elements of matrix k are linear combinationsof the coefficients kij

Master Equation,

Statistical Physics

response time

cycle 1k12 k21

turnover times of the two reservoirs

cycle

1

01

1

02

1

Simplified model of the carbon cycle. Ms represents the sum of all forms ofdissolved carbon , , and

CO2

H 2 HCO3

HCO3

,

CO 22

Atmosphere

M A

Terrestrial System

M T

Ocean surfaceDiss C= CO2,HCO3,H2CO3

M S

Deep layers of ocean

M D

F TA

F AT

F SA F AS

F SDF DS

Non-linear System: Simplified model of the biogeochemical carbon cycle. (Adapted from Rodhe and Björkström (1979) with the permission of the Swedish Geophysical Society.)

Inorganic Carbon Cycle

Free protonBicarbonate carbonate

Basic concepts, non-linearity in the oceanic carbon system

Carbonate acid

hydrated

Equilibrium relationships between these species:

pCO2:Partial pressure atm.

[ ]:Concentrations/activities

Ocean: inorganic Carbon Cycle


CO2

H 2 HCO3

HCO3

,

CO 22

Atmosphere

M A

Terrestrial System

M T


M S


M D

F TA

F AT

F SA F AS

F SDF DS

The buffer factor results from the equilibrium between CO2(g)

and the more prevalent forms of dissolved carbon.

As a consequence of this strong dependence of FSA on MS,

a substantial increase in CO2 in the atmosphere is balanced by a small increase of MS.

FSA kSAM S

SA

Exponent = 10

Buffer factor

Revelle factor

Degassing Dissolution


CO2

H 2 HCO3

HCO3

,

CO 22

Atmosphere

M A

Terrestrial System

M T


M S


M D

F TA

F AT

F SA F AS

F SDF DS


FAT K AT M AAT

Atmosphere to the terrestial system

Equilibrium relationships between these species:

pCO2:Partial pressure atm.

[ ]:Concentrations/activities

3 Equations and 5 unknowns!

Specify 2 of the unknowns

pH= - log10 [H+]

pCO2 change with temperature etc.; kept as variable

Introduce new variables which are measured:

Dissolved inorganic carbon

Total alkalinity: measure of excess of bases over acids

Borate ion

4 new unknowns, 2 more equations

Additional contrains: 3 Equations & 1 new unknown

The total boron concentration is nearly constant within the ocean:

log log

log log

What controls the pCO2 ?

Global mean seawater properties

Approximations:


Sensitivity of pCO2 to changes in DIC and Alk


Sensitivity of pCO2 to changes in DIC ans Alk

ca. 10

ca. -10

Fig. 8.1.2: Horizontally averaged profiles of salinity normalized DIC and Alk in the global oceans. Based on the gridded climatological data from the GLODAP project (R. M. Key, personal communication).



ca. 10

ca. -10

pCO2 increase by 10% when DIC is increased by 1%

pCO2 decrease by 10% when Alk is increased by 1%



ca. 10

ca. -10

pCO2 = c DIC10


CO2

H 2 HCO3

HCO3

,

CO 22

Atmosphere

M A

Terrestrial System

M T


M S


M D

F TA

F AT

F SA F AS

F SDF DS

The buffer factor results from the equilibrium between CO2(g)

and the more prevalent forms of dissolved carbon.

As a consequence of this strong dependence of FSA on MS,

a substantial increase in CO2 in the atmosphere is balanced by a small increase of MS.

FSA kSAM S

SA

Exponent = 10

Buffer factor

Revelle factor


F=k (pCO2 atm – pCO2 sol) = k (pCO2 atm – c DIC10)

• EQUATIONS FOR MODEL OF SIMPLE OCEAN - ATMOSPHERE CARBON CYCLE– Reservoirs:

• INIT Atmosphere = 600 {Gt C}• INIT Surface_Ocean = 891.62591 {Gt C}• INIT Deep_Ocean = 38000 {Gt C}

– Flows: • external_additions = 0 {volcanic emissions or fossil fuel burning, etc.} • oc--atm_exchange = k_ao*(pCO2_atm-pCO2_Ocean)• bio_pump = 10• ocean_turnover = 100*(Deep_Ocean/INIT(Deep_Ocean))-90.6*(Surface_Ocean/INIT(Surface_Ocean)) {this is upwelling

minus downwelling}• burial = 0.6*(bio_pump/10)• runoff = 0.6

– Converters: • Alk_Surf = 2.22 {slightly modified from Walker, 1993}• CO3 = (Alk_Surf-HCO3)/2 {following Walker, 1993}• HCO3 = (Surf_C_conc-SQRT(Surf_C_conc^2-Alk_Surf*(2*Surf_C_conc-Alk_Surf)*(1-4*Kcarb)))/(1- 4*Kcarb) {following

Walker, 1993}• Kcarb = .000575+.000006*(T_surf-278) {following Walker, 1993}• KCO2 = .035+.0019*(T_surf-278) {following Walker, 1993}• k_ao = .278 {Gt C/yr/ppm -- the observationally-derived rate constant; this is for the entire surface area of the ocean}• pCO2_atm = Atmosphere*(280/600)• pCO2_Ocean = 280*KCO2*(HCO3^2/CO3) {following Walker, 1993}• Surf_C_conc = (Surface_Ocean/12000)/Vol_surf {1e18 moles/m^3}• T_surf = 288 {°K following Walker, 1993}}• Vol_surf = .0363 {units are 1E18 m^3 -- this is the upper 100 m}• del_atm = (Atmosphere-600)-(DELAY(Atmosphere,1)-600)• del_deep_ocean = (Deep_Ocean-INIT(Deep_Ocean))-(DELAY(Deep_Ocean, 1)-INIT(Deep_Ocean))• del_surf_ocean = (Surface_Ocean-INIT(Surface_Ocean))-(DELAY(Surface_Ocean, 1)- INIT(Surface_Ocean))

• http://www.acad.carleton.edu/curricular/GEOL/DaveSTELLA/Carbon/c_cycle_models.htm

• EQUATIONS FOR MODEL OF SIMPLE TERRESTRIAL CARBON CYCLE– RESERVOIRS:

• INIT Atmosphere = 600 {Gt C -- 1 Gt=1e15 g -- from IPCC, 1995}• INIT Land_Biota = 610 { Gt C -- 1 Gt=1e15 g -- from IPCC, 1995}• INIT Soil = 1580 { Gt C -- 1 Gt=1e15 g -- from IPCC, 1995}

– FLOWS: (all in Gt C/yr) • Soil_Respiration = (49.4/INIT(Soil))*Soil*(1+(Tsens_sr*global_temp)) {initial value from Siegenthaler and Sarmiento,

1993}• Plant_Respiration = Photosynthesis*(50/100) {equation modified from Gifford, 1993; initial value from Siegenthaler and

Sarmiento, 1993}• External_addition = 0.6 {volcanic emissions or fossil fuel burning, etc.} }• Photosynthesis = (Pmax*(pCO2_eff/(pCO2_eff+Khs)))*(1+(Tsens_p*global_temp)) {equation modified from Gifford,

initial value from S&S}• Litter_fall = 50*(Land_Biota/610) {modified from Gifford, 1993 initial value from S&S}• Runoff = .6*Soil/INIT(Soil) {value from S&S}

– CONVERTERS: • Khs = 62.5 {ppm CO2; this is the half-saturation value -- the level of atmospheric C at which the rate of photosynthesis is

half of the ultimate saturation value, given that particular temperature; modified from Gifford, 1993}• Pmax = ((Khs+250)*100)/250 {Gt C/yr; this is the maximum rate of photosynthesis possible at the saturation level of CO2,

ignoring the temperature effect -- from Gifford, 1993}• global_temp = (pCO2_atm-280)*.01 {°C relative to today's temp of 15; from K&S, 1994}• pCO2_atm = Atmosphere*(280/600) {ppm}• pCO2_min = 30 {ppm -- no photosynthesis can occur below this level; from Gifford, 1993}• pCO2_eff = pCO2_atm-pCO2_min {ppm; the effective atmospheric CO2 concentration}• Tsens_p = .04 {°C-1; temperature sensitivity factor for photosynthesis; after Gifford}• Tsens_sr = .10 {°C-1; temperature sensitivity factor for soil respiration; after Gifford}• Atmos_Change = Atmosphere-600 { Gt C; change in atmospheric carbon -- used to compare results of various experiments}• Land_Biota_Change = Land_Biota-610 {Gt C}• Soil_Change = Soil-1580 {Gt C}• Total_Change = Atmos_Change+Land_Biota_Change+Soil_Change {Gt C}

• http://www.acad.carleton.edu/curricular/GEOL/DaveSTELLA/Carbon/c_cycle_models.htm#eqns3

Fig. 8.1.1: Map of the annual mean air-sea difference of the partial pressure of CO2. Based on data from Takahashi et al. (2002).

• CO2 atm. const. -> delta is driven by the oceans

• Temp., salinity, DIC, Alk

Atmosphere 725(Annual increase ~3)

Surface waterDissolved inorg. 700

Dissolved org. 25(Annual increase ~ 0,3)

Surface biota3

Intermediate andDeep water

Dissolved inorg. 36,700Dissolved org. 975

(Annual increase ~ 2,5)

Short-lived biota~110

Long-lived biota ~450(Annual decrease ~1)

Litter~60

Soil 1300 - 1400(Annual decrease ~1)

Peat (Torf)~160

Fossil fuelsoil, coal, gas

5,000 - 10,000

Respiration &decomposition

~36

Primaryproduction

~40

Detritus~4

Detritus decomposition

54-50

~40 ~38

5

2 - 5

2 - 5

~15~40

~120~60~90~93Deforestation

~1

‹1

‹1

~15~1

Fig. 4-3 principal reservoirs and fluxes in the carbon cycle. Units are 1015 g(Pg) C (burdens)and PgC/yr (fluxes). (From Bolin (1986) with permission from John Wiley and Sons.)

• http://www.acad.carleton.edu/curricular/GEOL/DaveSTELLA/Carbon/c_cycle_models.htm

• http://cran.r-project.org/src/contrib/Descriptions/longmemo.html

http://www.acad.carleton.edu/curricular/GEOL/DaveSTELLA/Carbon/c_cycle_models.htm



the global carbon cycle gerrit lohmann 31. october 2005, 11.15 o‘clock biogeochemical cycles

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