14-5 If Your Age is too Old – a New Dating App

Session: Lake Sedimentary Records of Past Climate and Environment

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Abstract:

Most ¹⁴C ages from lake C_org or carbonate precipitates are too old, labeled as ‘apparent ages’. Poor DIC equilibration with atmospheric ¹⁴C is one principal reason for these apparent ages. The point of ingress of ¹⁴CO₂^air into a water body is CO₂^aq, with rapid chemical and isotopic equilibration. Full DIC isotopic equilibration depends on the concentration and motility of the CO₂^aq species, and the HCO₃^- and CO₃⁼ concentrations. The equilibration rate between CO₂^aq and carbonate/bicarbonate equals tau = (DIC/CO₂^aq) (z/k_w), where tau is the e-folding time of equilibration, z thickness of the mixed layer, and k_w is the piston velocity of dissolved CO₂ gas. The first ratio is pH dependent, and z/K_w depends largely on physical lake processes. The air-water ¹⁴C equilibration can be counteracted by lake inflows of ¹⁴C-poor carbonate-rich fluids, and then the DIC concentration becomes the dominant rate factor. We use the mismatch between real and apparent ages as a tool to retrodict either lake water pH (dilute lakes with minor/no inputs of carbonate-rich liquids) or approximate paleo-DIC for lakes with substantial ¹⁴C-free carbonate inputs. The ¹⁴C dating equation is t = -8033 ln F_m, where F_m equals N_t/N_o and t is the ¹⁴C age; N_t is the remaining ¹⁴C in the sample after t years, and N_o is the original ¹⁴C contents during plant growth or carbonate precipitation, traditionally taken as the 1950 ¹⁴C standard value. The difference between apparent and real ages at time t^x in the past is normalized on the same age difference in modern (t^m) lake DIC. We introduce a new variable N_o*, which represents N_o corrected for the poor isotopic ¹⁴C equilibration of the lake water.  After a lengthy derivation, the obtained master equation ^xN_o*/^mN_o*= e^-DDt/8033 relates the difference between the differences between apparent and real ages at times t^x and t^m to the ratio of the N_o* values at these two times. We re-phrase the N_o* factors in terms of N_o and tau, the latter linked to water pH. We estimate the paleo-DIC if fluid mixing is the dominant process for the ¹⁴C air-water disequilibrium by converting N_o into N_o* with a 1/DIC scaling parameter.  We apply this approach to ¹⁴C data from two volcanic lakes at Newberry Volcano (OR).

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