Notes on a Catastrophe: A Feedback Analysis of Snowball Earth

Abstract

The language of feedbacks is ubiquitous in contemporary earth sciences, and the framework of feedback analysis is a powerful tool for diagnosing the relative strengths of the myriad mutual interactions that occur in complex dynamical systems. The ice albedo feedback is widely taught as the classic example of a climate feedback. Moreover, its potential to initiate a collapse to a completely glaciated snowball earth is widely taught as the classic example of a climate ''tipping point.'' A feedback analysis of the snowball earth phenomenon in simple, zonal mean energy balance models clearly reveals the physics of the snowball instability and its dependence on climate parameters. The analysis can also be used to illustrate some fundamental properties of climate feedbacks: how feedback strength changes as a function of mean climate state; how small changes in individual feedbacks can cause large changes in the system sensitivity; and last, how the strength and even the sign of the feedback is dependent on the climate variable in question.

Climate Instability on Tidally Locked Exoplanets

“…Setting Λ = 1 would shut down the instability. We conclude that the CO 2 SDF is unlikely to be important for planets in synchronous rotation and is important in fewer cases than is the icealbedo feedback (Roe & Baker 2010;). …”

“…Climate stability can be undermined by several previously studied climate instabilities. These include atmospheric collapses (Haberle et al 1994;Read & Lewis 2004), photochemical collapses (Zahnle et al 2008;Lorenz et al 1997), greenhouse runaways (Kasting 1988;Lorenz et al 1999;Sugiyama et al 2002), ice-albedo feedback (Roe & Baker 2010), and ocean thermohaline circulation bistability (Stommel 1961;EPICA Community Members 2006). Climate stability can also be undermined if the sign of the dependence of mean surface weathering rate on mean surface temperature is reversed.…”

No Snowball on Habitable Tidally Locked Planets

“…For more information see Abbot et al (2011) and Roe & Baker (2010). This type of modeling is useful because it allows analytical solutions with clear interpretations.…”

“…Physically, we can understand the snowball bifurcation as a competition between solar forcing and heat transport (Roe & Baker 2010;Rose 2015). Both the insolation (warming) and the divergence of the heat flux (cooling) increase as the equator is approached.…”

“…Both an ice-covered (snowball) and a mostly ice-free state like the modern climate can exist, even for the same external forcing (CO 2 , stellar flux, etc.). If the stellar flux is decreased in a climate model of modern Earth, eventually the replacement of surface water with highlyreflective ice (the ice-albedo feedback) overwhelms stabilizing feedbacks in the system (Roe & Baker 2010). At this point the modern climate state ceases to exist and the climate plunges into a snowball state (Budyko 1969;Sellers 1969).…”