Cumulative Departure Model of the Cryosphere During the Pleistocene

Abstract

A mathematical model is developed to describe changes in ice volume in the cryosphere. Modeling the cryosphere may be useful in assessing future climate impacts currently captured by global circulation models (GCMs) by providing an opportunity to validate GCMs. Leveraging the dominating effects of freezing and thawing in the cryosphere to simplify relevant heat transport equations allows for the derivation of a mathematical model that can be solved exactly. Such exact solutions are useful in investigating other climatic components that may be similarly analyzed for possible GCM validation. The current trend in GCM advancement is to increase the complexity and sophistication of the various heat transport effects that are represented in the governing mathematical model in cumulative form as the heat forcing function. In this paper, simplified models are developed whose solution can be directly compared with available data forms representing temperature and ice volume during the Pleistocene. With careful integration of the Pleistocene temperature term in the mathematical solution, the well-known cumulative departure method can be resolved from the mathematical solution using a two-term expansion of the corresponding Taylor series. This simplification is shown to be a good approximation of the Pleistocene ice volume for given Pleistocene temperatures.