On the representation of multiplicative noise in modeling Dansgaard–Oeschger events

Abstract

The interpretation of multiplicative noise in a stochastic differential equation in the context of data-driven inverse modeling is discussed. Application to the well-known paleoclimate phenomenon of Dansgaard–Oeschger events leads to qualitatively different ‘climate potentials’ in the case of the Itô or the Stratonovich interpretation of the stochastic integral. While a physical model is endowed with an interpretation from construction, whether implicitly or explicitly, inverse models derived from data do not afford such a luxury. In this case, a physical model must accompany the mathematical model equation in order to be able to choose a stochastic interpretation. This case study illustrates the differences between the two representations of stochastic noise and demonstrates the need for input from physical constraints when constructing conceptual stochastic models of the observed climate records.