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The Suess Effect: 13Carbon-14Carbon Interrelations

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The Suess Effect: 13Carbon-14Carbon Interrelations Environment International Vol. 2, pp. 229-300 Pergamon Press Ltd. 1979. Printed in Great Britain The Suess Effect: 13Carbon-14Carbon Interrelations Charles D. Keeling Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093, U.S.A. The Suess Effect is a term which has come to signify the decrease in 14C in atmospheric CO2 owing to ad- mixture of CO 2 produced by the combustion of fossil fuels. This term is here extended, as a concept, to the shifts in isotopic ratio of both 13C and 14C in any reservoir of the carbon cycle owing to anthropo- genic activities. To explain this generalized Suess Effect a four reservoir global model of the natural car- bon cycle is developed in which isotopic fractionation and radioactive decay are fully taken into account. The model includes the cases in which the deep ocean is treated either as a single undifferentiated box model reservoir or is vertically differentiated with eddy diffusion governing the transport of carbon. Also, the governing equations are expressed with sufficient generality to apply simultaneously to both rare isotopes. In so far as possible, the model is expressed without approximation of the isotopic processes even though this leads to non-linear differential equations to describe the rates of change of rare isotopic carbon within carbon reservoirs. Linear approximations are also developed and solved using the method of Laplace transforms. The sensitivity of the predicted Suess Effects to uncertainties in the assigned values of the model parameters is investigated in detail, including estimates of some of the effects of linearizing the governing equations. The approximation of Stuiver, in which the atmospheric Suess Effect is assumed to be 0.018 times the corresponding effect for 24C, is examined in detail and shown to arise when both isotopic fractionation and radioactive decay are left out of the model. This approximation, although correct as to order of magnitude, is found to be too imprecise to .be recommended in modeling studies. As found in previous work, the predicted atmospheric Suess Effect for 13C for a given airborne fraction of industrial CO2 is of similar magnitude whether the land biosphere has been a net source or sink of carbon during recent times. On the other hand, the corresponding effect for a surface ocean water is considerably smaller than otherwise if the land biosphere has been a source of CO2 instead of a sink. The model is thus useful in indicating the need to consider isotopes in several reservoirs simultaneously. Although the emphasis is on formulating models rather than surveying and interpreting data, obser- vational data are summarized and compared with model predictions. The oceanic data are seen to be too meager as yet to help settle the question of biospheric responses to man's activities. List of symbols d, operator for differentiation (2.4) d, subscript for subsurface ("deep") The numbers in parentheses refer to the first equation ocean reservoir (8.1) in which the symbol appears. Symbols in parentheses e, natural logarithm base (2.10) denote steady state values. Symbols for chemical ele- F, (F0), flux of carbon-total emerging from ments (e.g. C or Ca) are not listed. an unspecified reservoir (4.1) The following algebraic symbols are used: Fij, (Fio, flux of carbon-total from reservoir Ai, average area of oceanic reservoir i (8.50) Fij0), i toj (3.2) A(z), area of oceans at depth z (8.49) Fcij, same for calcium from oceanic a, subscript for atmospheric reservoir (1.2) reservoir i to j (10.15) aca, aco3, chemical activity of subscripted *Fij, (*Fio, same for laC or 14C (3.4) etc., chemical species (10.49) *rw), b, subscript for land biospheric reser- Fg, (F~), oceanic gravitational flux of voir or for an unspecified reservoir carbon-total (8.1) in contact with the atmosphere (2.4) Fcg, (FcgO), oceanic gravitational flux of Ci, (Cio) abundance of calcium, or calcium carbon-total in the form of and magnesium, in reservoir i (10.3) carbonate (lO. 15) c, subscript for calcium or biogenic Fpg, :Pp~o), same for carbon-total in the form carbonate (10.15) of particulate organic carbon (10.33) 229 230 Charles D. Keeling f, general function with derivations, *n/0, same for laC or 14C (2.30) f',f", ... (4.1) o, subscript for preindustrial g, subscript for oceanic gravitational steady state (1.7) flux (8.1) PC%, partial pressure of CO2 (7.13) g, special column vector (9.21) Pi, (P~) partial pressure of CO2 in reservoir ha, depth of ocean water containing i (7.3) the same amount of inorganic *Pi, (*Pio) same for 13C or 14C (7.26) carbon-total as the atmosphere in p, subscript for particulate organic preindustrial times (11.3) carbon (10.33) hb depth of oceanic layer i below sea Q, cumulative production of indus- surface (8.49) trial CO2 in units of carbon-total (1.8) i, general subscript (1.1) q (z, t), concentration of carbon-total at J(z, O, rate of regeneration of inorganic depth z in the oceans at time t (8.51) carbonate-total from particulate R, 13C/C or 14C/C ratio of an un- organic carbon and biogenic specified chemical (11.27) carbonate at depth z in subsurface Ri, 13C/C or 14C/C ratio of carbon in ocean water per unit volume at reservoir i (1.1) time t (8.49) Rf, 13C/C or 14C/C ratio of industrial second general subscript (1.6) CO 2 (zero for 14C) (1.12) It, steady state transfer coefficient for R O, standard 13C/C or 14C/C ratio (1.24) carbon-total for the flux emerging R,yi, average 13C/C or 14C/C ratio of from an unspecified reservoir (4.5) the sum of all external sources of k) matrix of perturbation transfer carbon-total to reservoir i (6.18) coefficients (9.12) ri, fraction of industrial CO 2 residing ki, (i = 1 to 6) perturbation transfer in reservoir i (1.8) coefficient for carbon-total for r, column vector of r i and *riRio/Rao (9.24) reservoir i (5.6) *ri, rate of change in abundance of (i = 1 to 6) same for 13Cor 14C (6.19) rare isotopic carbon in reservoir i ki' , (i = 7 to 10) virtual source coeffi- relative to rate of industrial CO 2 cient for reservoir i (6.19) input multiplied by preindustrial k~ steady state transfer coefficient for isotopic ratio of reservoir i (1.14) carbon-total from reservoir itoj (2.4) r, chemical (11.27) *kij, same from IsC or 14C (6.2) rc e, standard 13C/12C or 14C/12C ratio (11.33) K, oceanic vertical eddy diffusion Si, theoretical Suess Effect of reser- coefficient (8.51) voir i (1.7) Ki, (i = 0, 1, or 2) thermodynamic Sij, observed Suess Effect of reservoir i equilibrium quotients of carbonic at time t i (1.6) acid in sea water (7.11 - 13) s, Laplace transform frequency (2.9) KCaCO3, same for solid CaCO 3, respectively s, subscript for ocean as a whole (8.49) KMgCOs, MgCO 3 (10.49,50) t, time (2.4) solubility product for calcium Ksp, subscripts for subsurface oceanic carbonate in sea water (10.2) vu) reservoirs (8.4) Kspc, same for CaC03 in a solid solution Wi" volume of oceanic reservoir i (8.3) of calcium-magnesium carbonate (10. 51) mole fraction of MgCO 3 in magne- same for MgCO 3 in a solid sol- x, KspM, sium carbonate (10.48) ution of calcium~magnesium z, vertical coordinate in the oceans (8.49) carbonate (10.52) isotopic fractionation factor for ¢ isotopic label in reservoir i (1.18) oqj, transfer of carbon from reservoir m, subscript for oceanic surface (or phase) i toj (6.08) ("mixed") layer (7.1) 0~', isotopic fractionation factor for N, (No) abundance of carbon-total in an transfer of CO2 gas from reservoir unspecified reservoir (4.1) i toj (applies only to air-sea ex- N~, (N~) abundance of carbon-total in change, expressed in terms of reservoir i (1.1) partial pressures Pi and their rare *Ni, (*Nio) same for 13C or 14C (1.1) isotopic equivalents) (7.29) n) column vector of n i and *n i (9.12) equilibrium isotopic fractionation no, column vector of n/o and *n/o (9.17) C~eq" factor for surface ocean carbon- ni, departure of Ni from its initial total relative to atmosphere CO 2 (11.73) value N~ (1.9) B, perturbation factor relating a *ni, same for *N i (1.14) change in emerging flux to a nio, value of ni at time t = 0 assuming change in carbon abundance for an an exponential rate of increase in unspecified reservoir (4.4) ni, (not a steady state value) (2.19) The Suess Effect 231 13g, factor for perturbation of the 6"C, relative variation in *C/12C ratio oceanic gravitational flux (8.19) from standard where *C denotes 3~ perturbation factor for the depen- 13C or 14C (11.34) dence of the rate of transfer of 613Ci, (613Cio) same for 13C in reservoir i (11.39) carbon out of reservoir i on the efi, relative variation in 13C/C or 14C/ change in abundance of carbon- C ratio of industrial CO2 from that total in reservoir i (3.1) of preindustrial carbon in reservoir i', same except related to a change in i (2.2) abundance of carbon-total in the g'i, carbonate perturbation factor for reservoir to which carbon is being reservoir i (10.11) transfered (4.9) ~ij, terms in the Taylor's expansion of m, factor for perturbation in flux ~'i(J = 0, 1,2 ...
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