### Abstract

After removing annual variability, power spectral analyses of local atmospheric temperature from hundreds of stations and ice core records have been carried out from time scales of 10^{-2} to 10^{6} yr. A clear sequence of power-law behaviors is found as follows: 1) from 40 ka to 1 Ma a flat spectrum is observed; 2) from 2 ka to 40 ka the spectrum is proportional to f^{-2} where f is the frequency; and 3) below time scales of 2 ka the power spectrum is proportional to f^{-1/2}. At time scales less than 1 month we observe that the power spectra of continental stations become proportional to f^{-3/2} while maritime stations continue to have power spectra proportional to f^{-1/2} down to time scales of 1 day. To explain these observations, we model the vertical transport of heat in the atmosphere as a stochastic diffusion process. The power spectrum of temperature fluctuations at the earth's surface expected from this model equation in a two-layer geometry with thermal and eddy diffusion properties appropriate to the atmosphere and the ocean and a radiation condition at the top of the atmosphere agrees with the observed spectrum. The difference in power spectra between continental and marine stations can be understood with this approach as a consequence of the air mass above a maritime station exchanging heat with both the atmosphere above and the ocean below while a continental station exchanges heat mostly with the atmosphere above.

Original language | English (US) |
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Pages (from-to) | 157-164 |

Number of pages | 8 |

Journal | Earth and Planetary Science Letters |

Volume | 158 |

Issue number | 3-4 |

DOIs | |

State | Published - May 30 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics

### Cite this

**The power spectral density of atmospheric temperature from time scales of 10 ^{-2} to 10^{6} yr.** / Pelletier, Jon.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The power spectral density of atmospheric temperature from time scales of 10-2 to 106 yr

AU - Pelletier, Jon

PY - 1998/5/30

Y1 - 1998/5/30

N2 - After removing annual variability, power spectral analyses of local atmospheric temperature from hundreds of stations and ice core records have been carried out from time scales of 10-2 to 106 yr. A clear sequence of power-law behaviors is found as follows: 1) from 40 ka to 1 Ma a flat spectrum is observed; 2) from 2 ka to 40 ka the spectrum is proportional to f-2 where f is the frequency; and 3) below time scales of 2 ka the power spectrum is proportional to f-1/2. At time scales less than 1 month we observe that the power spectra of continental stations become proportional to f-3/2 while maritime stations continue to have power spectra proportional to f-1/2 down to time scales of 1 day. To explain these observations, we model the vertical transport of heat in the atmosphere as a stochastic diffusion process. The power spectrum of temperature fluctuations at the earth's surface expected from this model equation in a two-layer geometry with thermal and eddy diffusion properties appropriate to the atmosphere and the ocean and a radiation condition at the top of the atmosphere agrees with the observed spectrum. The difference in power spectra between continental and marine stations can be understood with this approach as a consequence of the air mass above a maritime station exchanging heat with both the atmosphere above and the ocean below while a continental station exchanges heat mostly with the atmosphere above.

AB - After removing annual variability, power spectral analyses of local atmospheric temperature from hundreds of stations and ice core records have been carried out from time scales of 10-2 to 106 yr. A clear sequence of power-law behaviors is found as follows: 1) from 40 ka to 1 Ma a flat spectrum is observed; 2) from 2 ka to 40 ka the spectrum is proportional to f-2 where f is the frequency; and 3) below time scales of 2 ka the power spectrum is proportional to f-1/2. At time scales less than 1 month we observe that the power spectra of continental stations become proportional to f-3/2 while maritime stations continue to have power spectra proportional to f-1/2 down to time scales of 1 day. To explain these observations, we model the vertical transport of heat in the atmosphere as a stochastic diffusion process. The power spectrum of temperature fluctuations at the earth's surface expected from this model equation in a two-layer geometry with thermal and eddy diffusion properties appropriate to the atmosphere and the ocean and a radiation condition at the top of the atmosphere agrees with the observed spectrum. The difference in power spectra between continental and marine stations can be understood with this approach as a consequence of the air mass above a maritime station exchanging heat with both the atmosphere above and the ocean below while a continental station exchanges heat mostly with the atmosphere above.

UR - http://www.scopus.com/inward/record.url?scp=0032580661&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032580661&partnerID=8YFLogxK

U2 - 10.1016/S0012-821X(98)00051-X

DO - 10.1016/S0012-821X(98)00051-X

M3 - Article

AN - SCOPUS:0032580661

VL - 158

SP - 157

EP - 164

JO - Earth and Planetary Sciences Letters

JF - Earth and Planetary Sciences Letters

SN - 0012-821X

IS - 3-4

ER -