The Global Carbon Cycle Gerrit Lohmann 31. October 2005, 11.15 o‘clock Biogeochemical cycles.
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Transcript of 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
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
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
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
Degassing Dissolution
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:
What controls the pCO2 ?
What controls the pCO2 ?
Sensitivity of pCO2 to changes in DIC and Alk
What controls the pCO2 ?
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).
What controls the pCO2 ?
Sensitivity of pCO2 to changes in DIC and Alk
ca. 10
ca. -10
pCO2 increase by 10% when DIC is increased by 1%
pCO2 decrease by 10% when Alk is increased by 1%
What controls the pCO2 ?
Sensitivity of pCO2 to changes in DIC and Alk
ca. 10
ca. -10
pCO2 = c DIC10
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
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
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