# Low-dimensional modeling approach promises more efficient climate predictions

*Novel dynamical systems approach may lead to better forecasting using less computational power.*

Predictive accuracy is crucial for climate change science – and civilization. But forecasting conditions never experienced is no small feat. Typically, the task involves building mathematical Earth System Models (ESMs), such as those used to inform assessment reports issued by the UN’s Intergovernmental Panel on Climate Change.

But ESMs are complicated and expensive, and even with high-performance computers, they can take weeks or months to produce a single result.

As a proof of concept, de Melo Viríssimo et al. used a low-dimensional dynamical systems approach to produce more informative outcomes given limited costs and time.

“In contrast to the billions of equations in a discretized ESM, we look at a climate-like system with only five, which allows for systematic studies because it can be run thousands of times at a very low computational cost,” said author Francisco de Melo Viríssimo.

The researchers combined the climate science concept of micro initial condition uncertainty with the mathematical idea of pullback attractors, which account for asymptotic patterns over time, to define a new object in the phase space that they named the “evolution set.”

“This object, although intuitive, represents the evolution of climate and its probability distribution, or climate prediction, constrained to today’s best knowledge – assuming we have this information,” said de Melo Viríssimo.

The team assessed the sensitivity of both the evolution set and its distribution to uncertainty in initial condition and rate of change, specifically examining how this pair is affected by other sources of uncertainty.

“We think the study may shape the design of influential new climate prediction modeling ensembles that support decision-making and the wider society,” said de Melo Viríssimo.

**Source:** “The evolution of a non-autonomous chaotic system under non-periodic forcing: A climate change example,” by F. de Melo Viríssimo, D. A. Stainforth, and J. Bröcker, *Chaos* (2024). The article can be accessed at http://doi.org/10.1063/5.0180870 .