The Global Carbon Cycle Gerrit Lohmann 31. October 2005, 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 Mcontent if a substance in the reservoir Stotal flux out of the reservoir M S=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 water Dissolved inorg. 700 Dissolved org. 25 (Annual increase ~ 0,3) Surface biota 3 Intermediate and Deep water Dissolved inorg. 36,700 Dissolved org. 975 (Annual increase ~ 2,5) Short-lived biota ~110 Long-lived biota ~450 (Annual decrease ~1) Litter ~60 Soil (Annual decrease ~1) Peat (Torf) ~160 Fossil fuels oil, coal, gas 5, ,000 Respiration & decomposition ~36 Primary production ~40 Detritus ~4 Detritus decomposition ~40 ~ ~15 ~40 ~120~60~90~93 Deforestation ~1 ‹1 ~15 ~1 Fig. 4-3 principal reservoirs and fluxes in the carbon cycle. Units are 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 F ij from reservoir i to reservoir j is given by The rate of change of the amount M i i n reservoir i is thus where n is the total number of reservoirs in the system. This system of differential equations can be written in matrix form as where the vector M is equal to (M 1, M 2,... M n ) and the elements of matrix k are linear combinations of the coefficients k ij Master Equation, Statistical Physics

response time turnover times of the two reservoirs

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Simplified model of the carbon cycle. M s represents the sum of all forms of dissolved carbon,, and Atmosphere M A Terrestrial System M T Ocean surface Diss C= CO 2,HCO 3,H 2 CO 3 M S Deep layers of ocean M D F TA F AT F SA F AS F SD F 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 proton Bicarbonatecarbonate Basic concepts, non-linearity in the oceanic carbon system Carbonate acid hydrated

Equilibrium relationships between these species: pCO 2 :Partial pressure atm. [ ]:Concentrations/activities

Ocean: inorganic Carbon Cycle

Simplified model of the carbon cycle. M s represents the sum of all forms of dissolved carbon,, and Atmosphere M A Terrestrial System M T Ocean surface Diss C= CO 2,HCO 3,H 2 CO 3 M S Deep layers of ocean M D F TA F AT F SA F AS F SD F DS The buffer factor results from the equilibrium between CO 2 (g) and the more prevalent forms of dissolved carbon. As a consequence of this strong dependence of F SA on M S, a substantial increase in CO 2 in the atmosphere is balanced by a small increase of M S. Exponent  = 10 Buffer factor Revelle factor DegassingDissolution

Simplified model of the carbon cycle. M s represents the sum of all forms of dissolved carbon,, and Atmosphere M A Terrestrial System M T Ocean surface Diss C= CO 2,HCO 3,H 2 CO 3 M S Deep layers of ocean M D F TA F AT F SA F AS F SD F DS DegassingDissolution Atmosphere to the terrestial system

Equilibrium relationships between these species: pCO 2 :Partial pressure atm. [ ]:Concentrations/activities 3 Equations and 5 unknowns! Specify 2 of the unknowns pH= - log 10 [H + ]

pCO 2 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

What controls the pCO 2 ?

Global mean seawater properties Approximations:

What controls the pCO 2 ?

Sensitivity of pCO2 to changes in DIC and Alk

What controls the pCO 2 ? Sensitivity of pCO2 to changes in DIC ans Alk ca. 10 ca. -10

Fig : 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 pCO 2 ? 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 pCO 2 ? Sensitivity of pCO2 to changes in DIC and Alk ca. 10 ca. -10 pCO2 = c DIC 10

Simplified model of the carbon cycle. M s represents the sum of all forms of dissolved carbon,, and Atmosphere M A Terrestrial System M T Ocean surface Diss C= CO 2,HCO 3,H 2 CO 3 M S Deep layers of ocean M D F TA F AT F SA F AS F SD F DS The buffer factor results from the equilibrium between CO 2 (g) and the more prevalent forms of dissolved carbon. As a consequence of this strong dependence of F SA on M S, a substantial increase in CO 2 in the atmosphere is balanced by a small increase of M S. Exponent  = 10 Buffer factor Revelle factor DegassingDissolution F=k (pCO 2 atm – pCO 2 sol) = k (pCO 2 atm – c DIC 10 )

EQUATIONS FOR MODEL OF SIMPLE OCEAN - ATMOSPHERE CARBON CYCLE –Reservoirs: INIT Atmosphere = 600 {Gt C} INIT Surface_Ocean = {Gt C} INIT Deep_Ocean = {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 = *(T_surf-278) {following Walker, 1993} KCO2 = *(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))

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}

Fig : Map of the annual mean air-sea difference of the partial pressure of CO 2. 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 water Dissolved inorg. 700 Dissolved org. 25 (Annual increase ~ 0,3) Surface biota 3 Intermediate and Deep water Dissolved inorg. 36,700 Dissolved org. 975 (Annual increase ~ 2,5) Short-lived biota ~110 Long-lived biota ~450 (Annual decrease ~1) Litter ~60 Soil (Annual decrease ~1) Peat (Torf) ~160 Fossil fuels oil, coal, gas 5, ,000 Respiration & decomposition ~36 Primary production ~40 Detritus ~4 Detritus decomposition ~40 ~ ~15 ~40 ~120~60~90~93 Deforestation ~1 ‹1 ~15 ~1 Fig. 4-3 principal reservoirs and fluxes in the carbon cycle. Units are g(Pg) C (burdens) and PgC/yr (fluxes). (From Bolin (1986) with permission from John Wiley and Sons.)

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