Regularization of a conceptual model for Dansgaard–Oeschger events

The Dansgaard–Oeschger events are sudden and irregular warmings of the North Atlantic region that occurred during the last glacial period. A key characteristic of these events is a rapid shift to warmer conditions (interstadial), followed by a slower cooling toward a colder climate (stadial), resulting in a saw-tooth pattern in regional proxy temperature records. These events occurred many times during the last 100 000 years and have been hypothesized to result from various mechanisms, including millennial variability of the ocean circulation and/or nonlinear interactions between ocean circulation and other processes. Our starting point is a non-autonomous, conceptual, but process-based, model of Boers et al. Proc. Natl. Acad. Sci. 115, E11005–E11014 (2018) that includes a slowly varying non-autonomous forcing represented by reconstructed global mean temperatures. This model can reproduce Dansgaard–Oeschger events in terms of shape, amplitude, and frequency to a reasonable degree. However, the model of Boers et al. has instantaneous switches between different sea-ice evolution mechanisms on crossing thresholds and, therefore, cannot show early warning signals of the onset or offset of these warming events. In this paper, we regularize this model by adding a fast dynamic variable so that the switching occurs smoothly and in finite time. This means the model has the potential to show early warning signals for sudden changes. However, the additional fast timescale means these early warning signals may have short time horizons. Nonetheless, we find some evidence of early warning for the transition between slow and rapid cooling for the model.