A new technique to derive delay models from systems of partial differential equations, based
on the Mori-Zwanzig formalism, is used to derive a delay difference equation model for the
Atlantic Multidecadal Oscillation. The Mori-Zwanzig formalism gives a rewriting of the original
system of equations which contains a memory term. This ...
A new technique to derive delay models from systems of partial differential equations, based
on the Mori-Zwanzig formalism, is used to derive a delay difference equation model for the
Atlantic Multidecadal Oscillation. The Mori-Zwanzig formalism gives a rewriting of the original
system of equations which contains a memory term. This memory term can be related to a delay
term in a resulting delay equation. Here the technique is applied to an idealized, but spatially
extended, model of the Atlantic Multidecadal Oscillation. The resulting delay difference model
is of a different type than the delay differential model which has been used to describe the El
Ni˜no- Southern Oscillation. In addition to this model, which can also be obtained by integration
along characteristics, error terms for a smoothing approximation of the model have been derived
from the Mori-Zwanzig formalism. Our new method of deriving delay models from spatially
extended models has a large potential to use delay models to study a range of climate variability
phenomena.