Comparison of Two Analytic Energy Balance Models Shows Stable Partial Ice Cover Possible for Any Obliquity

Abstract: In this study, we compare two analytic energy balance models with explicit dependence on obliquity to study the likelihood of different stable ice configurations. We compare the results of models with different methods of heat transport and different insolation distributions. We show that stable partial ice cover is possible for any obliquity, provided the insolation distribution is sufficiently accurate. Additionally, we quantify the severity of the transition to the Snowball state as different model parameters are varied. In accordance with an earlier study, transitions to the Snowball state are more severe for higher values of the albedo contrast and energy transport across latitudes in both model; however, we find that the Snowball transition is not equally likely across both models. This work is general enough to apply to any rapidly rotating planet and could be used to study the likelihood of Snowball transitions on planets within the habitable region of other stars.