Data-driven, non-Markovian modelling of weather in the presence of non-stationary, non-Gaussian, and heteroskedastic climate dynamics

TL;DR

This paper presents a data-driven method to model complex weather dynamics that are non-stationary, non-Gaussian, and heteroskedastic, using a generalized master equation approach to accurately reproduce temperature fluctuations.

Contribution

The authors develop a protocol combining classification, local homoskedasticity, and generalized master equations to model complex weather data beyond traditional Gaussian assumptions.

Findings

Accurately reproduces Boulder temperature fluctuations

Classifies weather data based on seasonal cycles

Addresses non-Gaussian, non-stationary, heteroskedastic dynamics

Abstract

While the generalized Langevin equation (GLE) is a powerful tool to understand the behavior of complex dissipative systems, driving by external fields renders standard GLE construction workflows invalid. Filtering approaches that separate fluctuations from the non-equilibrium response can sometimes circumvent the need for a non-equilibrium formalism when the residual fluctuations are homoskedastic, stationary, and preferably Gaussian. Here, we introduce the temperature time series from Boulder, Colorado, as representative of the more general and complex case where the filtered time series remains non-Gaussian, non-stationary, and heteroskedastic. With this example, we develop a protocol to build an accurate and efficient low-dimensional description of the weather fluctuations. Our protocol classifies the weather data based on the position in the annual cycle, and introduces local homoskedasticity as a metric to identify seasons of likely stationarity. Within these seasons, we build pseudo-equilibrium models. Leveraging state-based generalized master equation modelling as an alternative to the GLE, we resolve difficulties like non-Gaussianity and position dependence of the memory (friction) kernel. Our data-driven approach accurately reproduces the evolving fluctuations of the Boulder temperature time series, illustrating the feasibility of our method as a general tool to describe driven, dissipative systems.