The Power Spectrum of Climate Change

TL;DR

This paper introduces a spherical harmonics-based framework to analyze climate change across all spatial scales, revealing a universal pattern and increased volatility driven by longitudes from planetary to local levels.

Contribution

It presents a novel unified diagnostic tool using spherical harmonics to analyze climate change across multiple spatial scales simultaneously.

Findings

Temperature anomalies decompose accurately within 0.05 K

Universal shape of scale dependence across seasons and decades

Climate change induces increased volatility on all scales from 2,000 to 50 km

Abstract

Both global, intermediate and local scales of Climate Change have been studied extensively, but a unified diagnostic framework for examining all spatial scales concurrently has remained elusive. Here we present a new tool-set using spherical harmonics to examine climate change through surface temperature anomalies from 1850 to 2021 on spatial scales ranging from planetary to $50$ km scales. We show that the observed temperature anomalies are accurately decomposed in spherical harmonics typically within 0.05 K. This decomposition displays a remarkably simple dependence on spatial scale with a universal shape across seasons and decades. The decomposition separates two distinct regimes by a characteristic turnover-length of approximately $3000$ km. The largest scales confirm established trends, while local fluctuations are consistent with 2-dimensional turbulence. We observe a downward cascade, from which it follows that climate change feeds increasing volatility on all spatial scales from $2.000$ to $50$ km. This increase is primarily driven by growing volatility along longitudes.