<i>π</i>-theorem generalization of the ice-age theory
<p>Analyzing a dynamical system describing the global climate variations requires, in principle, exploring a large space spanned by the numerous parameters involved in this model. Dimensional analysis is traditionally employed to deal with equations governing physical phenomena to reduce the n...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2020-03-01
|
| Series: | Earth System Dynamics |
| Online Access: | https://www.earth-syst-dynam.net/11/281/2020/esd-11-281-2020.pdf |
| Summary: | <p>Analyzing a dynamical system describing the global climate variations
requires, in principle, exploring a large space spanned by the numerous
parameters involved in this model. Dimensional analysis is traditionally
employed to deal with equations governing physical phenomena to reduce the
number of parameters to be explored, but it does not work well with
dynamical ice-age models, because, as a rule, the number of parameters in
such systems is much larger than the number of independent dimensions.
Physical reasoning may, however, allow us to reduce the number of effective
parameters and apply dimensional analysis in a way that is insightful. We
show this with a specific ice-age model (Verbitsky et al., 2018), which is a
low-order dynamical system based on ice-flow physics coupled with a linear
climate feedback. In this model, the ratio of positive-to-negative feedback
is effectively captured by a dimensionless number called the “<span class="inline-formula"><i>V</i></span> number”,
which aggregates several parameters and, hence, reduces the number of
governing parameters. This allows us to apply the central theorem of the
dimensional analysis, the <span class="inline-formula"><i>π</i></span> theorem, efficiently. Specifically, we show
that the relationship between the amplitude and duration of glacial cycles
is governed by a property of scale invariance that does not depend on the
physical nature of the underlying positive and negative feedbacks
incorporated by the system. This specific example suggests a broader idea;
that is, the scale invariance can be deduced as a general property of ice
age dynamics if the latter are effectively governed by a single ratio
between positive and negative feedbacks.</p> |
|---|---|
| ISSN: | 2190-4979 2190-4987 |