I have a few ideas about how to solve this problem. First, notice that the line representing the past event is subject to a lot of uncertainty. We will have collected data about the past climate episode over a particular set of durations, likely rather high durations. As the best fit line gets extrapolated further and further away from the data we’ve actually collected, the line becomes less tightly constrained, i.e., the uncertainties increase. At some point—I’m not sure exactly where—the degree of uncertainty will become unacceptable to the scientists working on this. The amount of acceptable uncertainty can be used to set an upper and lower bound on the range of acceptable durations to use.
Second, the duration of an event itself can be used to set an upper bound on the range of acceptable durations. For example, the PETM didn’t last forever (about 100,000 years), so it doesn’t make sense to extrapolate to longer durations than the PETM actually lasted. Likewise, the contemporary climate episode won’t last forever either—most probably, much less long than the PETM—so it doesn’t make sense to extrapolate that horizontal line out to the right forever, either. The durations over which we compare these rates must be durations that make sense given how long the relevant events themselves lasted.
Third, I think it’s possible that researchers may be able to further constrain the range of acceptable durations by considering the purposes for which we want to use the paleoclimate analogue. For instance, if we want to use the paleoclimate analogue to make predictions over 100-500 year timescales, we better be comparing past and present rates over durations of 100-500 years. In case anyone is interested, PETM rates are the same as contemporary rates over a duration of about 178 years, according to the data Gingerich used.
Applying these three constraints on the range of acceptable durations might either yield inconsistent upper and lower bounds (an empty set of acceptable durations) or tell us that a past climate episode has very different (higher or lower!) rates than contemporary climate change, in which case maybe we are no longer interested in using that past episode as an analogue. But it might also tell us that past and present climate change episodes weren’t so different after all, with respect to rates. If so, we might be able to use the past climate episode to inform our predictions about contemporary climate change, even for rate-dependent processes like biotic response. However, it is important to also make predictions over the same durations we used to establish analogy between the past and present climate episode—if we make predictions over different durations than that, we’ll be making predictions over durations for which we know that the past and present climate episode occurred at different rates, exactly what we’ve been trying to avoid.
We’ve now seen that comparing rates of climate change in the deep past to those today is really complicated, and we are left without a definitive answer about whether contemporary rates of climate change are unprecedented, because what these rates are depends on how we choose to measure them. Interestingly, whether we take past rates to be higher, lower, or the same as contemporary rates depends in part on what our research purposes are, since these inform which durations we use to compare the rates.
I want to close with two other, philosophically relevant points about rates. Here’s the first: What are the “real” rates of processes like climate change, if the measured rate depends on the duration we use? I think there are a few ways to go here. First, one might specify a specific, salient duration over which to measure the rates, and claim that all rates of that kind of process should be scaled to that duration, over which we will find the “real” rate of that process. (Gingerich argued we could do this for evolutionary rates, which he thought should all be scaled to a duration of one generation.) The problem with this view is that it’s unclear what this salient duration would be for many processes, like climate change. Second, we might say that more precise measurements are always better, and that we should look at what the rate would be as the duration approaches one that is infinitesimally small. The problem here is that all rates that had this inverse relationship with durations—rates of sedimentation, precipitation, evolution, climate change—would then be “really” infinitely high. Recall that in the context of measuring perimeters of coastlines, noticing that the perimeters approach infinity as we use shorter and shorter measuring sticks is what generates the coastline paradox.
A third way to go is to say that there aren’t “real” rates of change for these processes. This view accords with what fractal geometer Benoit Mandelbrot (namesake of the Mandelbrot set fractal) thought about perimeters. He said that the length of a coastline “turns out to be an elusive notion that slips between the fingers of one who wants to grasp it” (Mandelbrot 1982, 25). The idea here is that maybe there isn’t a true perimeter of Great Britain; the perimeter just depends on how we choose to measure it. Similarly, maybe there isn’t one true rate for processes that have this fractal quality; the rate just depends on how we decide to measure (or scale) it. And that might, in turn, depend on our research purposes.
Here is the second point: I’ve been taking for granted that we can carve up the history of Earth’s climate into specific events, like the PETM or contemporary climate change. However, there is some dispute among historical scientists about how, exactly, to demarcate events. The problem is that sometimes events are demarcated by (what seem to be) notable rates. But, again, rates depend on the durations over which they are measured, so it isn’t straightforward to say what rate these processes “really” happened at during the relevant periods of time. Take the case of mass extinctions for example. It isn’t clear what makes an extinction event count as a mass extinction (Bocchi et al. 2022), but one view is that mass extinctions are distinguishable by particularly high rates of extinction. We can now see that this isn’t going to work—biodiversity has these up and down fluctuations that indicate the need to adjust rates by durations, but it isn’t necessarily clear what durations to use in scaling extinction/origination rates, and so it is difficult to tell what the “real” rate of extinction is in any given period of time. We may have other ways of demarcating mass extinction events (e.g., based on magnitude or cause of the extinctions), but it would be ill-advised to rely on rates to do so.
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Gingerich, P.D. 2019. Temporal scaling of carbon emission and accumulation rates: modern Anthropogenic emissions compared to estimates of PETM onset accumulation. Paleoceanography and Paleoclimatology 34:329–335. https://doi.org/10.1029/2018PA003379
Kemp, D.B., Eichenseer, K., Kiessling, W. 2015. Maximum rates of climate change are systematically underestimated in the geological record. Nature Communications 6:8890. https://doi.org/10.1038/ncomms9890
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