Ambient temperature fluctuations exhibit inverse-cubic spectral behavior over time scales from a minute to a day

TL;DR

This study reveals that ambient temperature fluctuations follow an inverse-cubic spectral pattern over short to medium time scales, transitioning to an inverse-square pattern over longer periods, consistent with weather station data.

Contribution

The paper demonstrates a consistent $1/f^3$ spectral behavior in temperature fluctuations over minutes to hours, and a transition to $1/f^2$ over days, supported by extensive laboratory data.

Findings

Temperature fluctuations follow $1/f^3$ spectral behavior from 40 seconds to 1.2 days.

A transition to $1/f^2$ spectral behavior occurs over periods longer than 1.2 days.

Laboratory results align with European weather station data.

Abstract

Ambient temperature fluctuations are of importance in a wide variety of scientific and technological arenas. In a series of experiments carried out in our laboratory over an 18-month period, we discovered that these fluctuations exhibit $1/f^3$ spectral behavior over the frequency range $1.0 \times 10^{-5} \le f \le 2.5 \times 10^{-2}$ Hz, corresponding to $40$ s $ \le T_f \le 1.2$ d, where $T_f = 1/f$. This result emerges over a broad range of conditions. For longer time periods, $1.2 < T_f \le 11.6$ d, corresponding to the frequency range $1.0 \times 10^{-6} \le f < 1.0 \times 10^{-5}$ Hz, we observed $1/f^2$ spectral behavior. This latter result is in agreement with that observed in data collected at European weather stations. Scalograms computed from our data are consistent with the periodograms.