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

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.

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