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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

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Published on: December 9, 2015

An applied mathematics perspective on stochastic modelling for climate.

Andrew J Majda¹, Christian Franzke, Boualem Khouider

¹Department of Mathematics and Center for Atmosphere-Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, 10012 NY, USA. majda@cims.nyu.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|May 1, 2008

Summary

Applied mathematics offers systematic strategies for climate stochastic modeling. New models capture mid-latitude variability and tropical convection intermittency, improving climate simulations.

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Area of Science:

Climate Science
Applied Mathematics
Atmospheric Physics

Background:

Stochastic modeling is crucial for understanding climate variability and phenomena not resolved by deterministic models.
Mid-latitude low-frequency variability and tropical convection exhibit complex, intermittent features requiring advanced modeling approaches.

Purpose of the Study:

To review systematic strategies from applied mathematics for stochastic climate modeling.
To develop and test a new low-dimensional stochastic model for mid-latitude variability.
To illustrate a design principle for stochastic column models capturing tropical convection intermittency.

Main Methods:

Review of applied mathematics strategies for stochastic climate modeling.
Development of a low-dimensional stochastic model mimicking atmospheric general circulation models.
Application of a stochastic column modeling design principle to idealized deep tropical convection.

Main Results:

A new stochastic model was developed to test stochastic mode reduction procedures.
The study demonstrates the physical mechanisms behind multiplicative noise in teleconnection patterns.
Stochastic column modeling effectively captures irregular and intermittent features in tropical convection, slowing waves and increasing fluctuations.

Conclusions:

Systematic application of mathematical strategies enhances stochastic climate modeling capabilities.
The developed models provide insights into mid-latitude variability and tropical convection dynamics.
Stochastic modeling is essential for accurately representing complex climate phenomena.