Derivation of delay equation climate models using the Mori-Zwanzig formalism

Area of Science:

• Climate science
• Dynamical systems theory
• Statistical mechanics

Background:

• Delay models are crucial for understanding climate variability.
• Existing delay models often lack rigorous physical justification.
• The Mori-Zwanzig formalism offers a systematic approach to derive such models.

Purpose of the Study:

• To introduce and apply the Mori-Zwanzig formalism for deriving delay models.
• To provide a rigorous foundation for delay-type models in climate science.
• To improve the accuracy of El Niño Southern Oscillation (ENSO) models.

Main Methods:

• Systematic derivation of delay models using the Mori-Zwanzig formalism.
• Projection onto resolved variables to create a memory term.
• Solving orthogonal dynamics equations for nonlinear systems.
• Application to a two-strip ENSO model.

Main Results:

• A nonlinear delay model for ENSO was derived.
• The derived model includes an additional term compared to ad hoc models.
• The new term resulted in a more accurate ENSO period.

Conclusions:

• The Mori-Zwanzig formalism provides a robust method for deriving climate delay models.
• This approach enhances the physical justification of delay models.
• The improved ENSO model better reflects observed climate variability.