Mathematical Model of Cryospheric Response to Climate Changes

Abstract

This paper focuses on the development of simplified mathematical models of the cryosphere which may be useful in further understanding possible global climate change impacts and in further assessing future impacts captured by global circulation models (GCMs). The mathematical models developed by leveraging the dominating effects of freezing and thawing within the cryosphere to simplify the relevant heat transport equations are tractable to direct solution or numerical modeling. In this paper, the heat forcing function is assumed to be a linear transformation of temperature (assumed to be represented by proxy realizations). The output from the governing mathematical model is total ice volume of the cryosphere. The basic mathematical model provides information as a systems modeling approach that includes sufficient detail to explain ice volume given the estimation of the heat forcing function. A comparison between modeling results in the estimation of ice volume versus ice volume estimates developed from use of proxy data are shown in the demonstration problems presented.