Modelling the sedimentary response to orbital variations.

Carbonate-rich middle Eocene sedimentary sequences are relatively scarce, hampering the reconstruction of paleoclimate dynamics within this high-CO₂ world. Nevertheless, the Newfoundland Ridge (North-Atlantic Ocean) hosts a unique sedimentary archive of middle Eocene paleoceanographic change at astronomical 10⁴-year resolution. International Ocean Discovery Program (IODP) Sites U1408 and U1410 exhibit well-defined lithologic alternations between calcareous ooze and clay-rich intervals, occurring at the obliquity beat and associated with changing intensities of Northern Component Water (NCW) formation (Vahlenkamp et al., 2018). These lithological variations are captured by the calcium-iron ratio (Ca/Fe) proxy as a measure of carbonate content. Yet, the asymmetric shape of the Ca/Fe cycles immediately reflects a strong non-linear response to the sinusoidal obliquity forcing. To explore the causes of this non-linearity, we built a simple physically-motivated and time-dependent model that simulates the sedimentary response at IODP Sites U1408 and U1410 between 46 and 42 million years ago.  

dy/dt = 1/T (b^x – y)

The orbital input x constitutes of an insolation gradient during boreal winter (more specifically at winter solstice), as NCW formation is a high northern latitude winter process that depends on the Atlantic interhemispheric temperature gradient (Karas et al., 2017; Vahlenkamp et al., 2018). The latitudes between which the insolation gradient x is calculated is not user-prescribed but part of the parametrization of the model. Two further parameters define the model. The characteristic time constant T accelerates (T < 1) or slows the response to the forcing (T > 1), whereas the base of the exponential-response term b determines the degree of non-linearity in the system. We explored this four-space first with a coarse and then with a finer mesh, and found that the optimum model lies in the neighbourhood of the following values: latitudinal gradient between 63°N and 31°S, T = 4.94 kyr, b = 2.13. The corresponding system reproduces the asymmetric shape of the Ca/Fe cycles, while also exhibiting precession-obliquity interference patterns that occur in the proxy series. These kind of simple modelling efforts hold the potential to refine our mechanistic understanding of the Earth System response to astronomical forcing in the deep and warmer-than-present geologic past.

Karas et al. (2017) Pliocene oceanic seaways and global climate. Scientific Reports 7: 39842

Vahlenkamp et al. (2018) Astronomically paced changes in deep-water circulation in the western North Atlantic during the middle Eocene. Earth and Planetary Science Letter 484: 329 – 340.