An inverse approach to understanding benthic oxygen isotope records from the last deglaciation

Inferring surface water equilibrium calcite δ18O during the last deglacial period from benthic foraminiferal records: Implications for ocean circulation

“…in the absence of observational uncertainty and illustrates which features of q lie in the null space and cannot be reproduced inq [Wunsch, 2006]. In the benthic tracer inverse problem, unresolvable features in time are due to low-pass filtering by ocean tracer propagation [Rutberg and Peacock, 2006;Amrhein, 2014], and unresolvable features in space are due to the sparsity of deepwater formation regions and mixing in the ocean interior (section 4 and Appendix C).…”

“…To compute objectively mapped values, a statistically stationary estimate of the signal autocovariance, , is necessary for each record, where τ is a time lag, s is the δ 18 O c record signal component, and angle brackets indicate the expected value. Signal autocovariances are calculated by fitting a power law to the structure function, , computed between every two points in each record [ Press et al , ; Rybicki and Press , ; Amrhein , ]; the signal variance, , is approximated from the record variances and σ n . The resulting interpolation (Figure ) has uncertainties determined by σ n , the estimate of R ( τ ), and the data distribution.…”

“…computed between every two points in each record Rybicki and Press, 1992;Amrhein, 2014]; the signal variance, ⟨ s 2 (t) ⟩ , is approximated from the record variances and n . The resulting interpolation ( Figure 2) has uncertainties determined a "N." and "G." stand for Neogloboquadrina and Globigerina; "pachy" stands for pachyderma; and "s." and "d." stand for sinistral and dextral.…”