HR: 09:30h
AN: B11B-07    [PDF]
TI: Deconvolving the Carbon Isotope Record
AU: * Cramer, B S
EM: benjamin@dges.tohoku.ac.jp
AF: Institute of Geology and Paleontology, Tohoku University, Aoba, Aramaki, Sendai, 980-8578 Japan
AB: The evolution of the whole-ocean $\delta^{13}$C value, under an assumption of steady state with respect to mass, can be modeled as: \[ {d \over dt}\delta_\Sigma(t)+{\delta_\Sigma(t) \over \tau_C}={1 \over \tau_C}\delta_F(t) \] where $\delta_\Sigma$ is the whole-ocean $\delta^{13}$C value, $\tau_C$ is the residence time of carbon and a net instantaneous $\delta^{13}$C forcing function is defined: \[ \delta_F=\delta_i-f_{carb}\Delta_{carb}-\left(1-f_{carb}\right)\Delta_{org} \] where $\delta_i$ is the $\delta^{13}$C value of carbon input (e.g. weathering and volcanism), $f_{carb}$ is the fraction of carbon removed through burial of carbonates as opposed to organic carbon, and $\Delta_{carb}$ and $\Delta_{org}$ are the differences between $\delta_\Sigma$ and $\delta^{13}$C values for buried carbonate and organic carbon. The solution to this differential equation is: \[ \delta_\Sigma\left(t\right)={1 \over \tau_C}\int_0^t{{\delta_F\left(t^\prime\right)}e^{\left(-{t-t^\prime \over \tau_C}\right)}dt^\prime} \] which can be expressed as a convolution \[ \delta_\Sigma\left(t\right)={1 \over \tau_C} {{\delta_F\left(t^\prime\right)} \otimes e^{\left(-{t-t^\prime \over \tau_C}\right)}} \] revealing that the evolution of the whole ocean $\delta^{13}$C value is determined by the instantaneous $\delta^{13}$C forcing ($\delta_F$) subjected to a causal (i.e. phase-shifting) low-pass filter whose frequency response is dependent only on the carbon residence time. One consequence of this observation is that variance in $\delta^{13}$C records should be concentrated at wavelengths $>$0.1 m.y., thereby explaining the persistent appearance of cyclicity dependent on orbital eccentricity ($\sim$0.1~and $\sim$0.4 m.y.~periods) in $\delta^{13}$C records. I demonstrate that an assumption of non-linear forcing of $f_{carb}$ by orbitally-forced variations in insolation can explain most of the structure of high-resolution $\delta^{13}$C records throughout the Cenozoic. A second consequence is that $\tau_C$ and $\delta_F$ should be separable by numerical manipulation of $\delta^{13}$C records. Two applications are 1) estimation of the residence time of carbon at various times in the past and 2) investigation of changes in the instantaneous forcing through time.
DE: 4215 Climate and interannual variability (3309)
DE: 4267 Paleoceanography
DE: 4806 Carbon cycling
DE: 4870 Stable isotopes
SC: Biogeosciences [B]
MN: 2003 Fall Meeting