Frequency–Wavenumber Spectrum for GATF, Phase I Rainfields

Shoichiro Nakamoto Climate System Research Program. College of Geosciences, Texas A&M University. College Station, Texas

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Juan B. Valdés Climate System Research Program. College of Geosciences, Texas A&M University. College Station, Texas

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Gerald R. North Climate System Research Program. College of Geosciences, Texas A&M University. College Station, Texas

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Abstract

The oceanic rainfall frequency-wavenumber spectrum and its associated space-time correlation have been evaluated from subsets of GATE Phase 1 data. The records, of a duration of 4 days, were sampled at 15 minute intervals in 4 × 4 km grid boxes ova a 400 km diameter hexagon.

In the low frequencies-low wavenumber region the results coincide with those obtained by using the stochastic model proposed by North and Nakamoto. From the derived spectrum the inherent time and space scales of the stochastic model were determined to be approximately 13 hours and 36 km. The space-time correlation function evaluated from the function-wavenumber spectrum and that obtained directly from GATE Phase I records agreed.

The formalism proposed by North and Nakamoto was taken together with the derived spectrum to compute the mean square sampling error due to intermittent visits of a spaceborne sensor. The sampling error was estimated to be on the order of 10%, for monthly mean rainfall averaged over 500 × 500 km boxes which meets the scientific requirements of the TRMM mission. This result is consistent with those previously reported in the literature.

Abstract

The oceanic rainfall frequency-wavenumber spectrum and its associated space-time correlation have been evaluated from subsets of GATE Phase 1 data. The records, of a duration of 4 days, were sampled at 15 minute intervals in 4 × 4 km grid boxes ova a 400 km diameter hexagon.

In the low frequencies-low wavenumber region the results coincide with those obtained by using the stochastic model proposed by North and Nakamoto. From the derived spectrum the inherent time and space scales of the stochastic model were determined to be approximately 13 hours and 36 km. The space-time correlation function evaluated from the function-wavenumber spectrum and that obtained directly from GATE Phase I records agreed.

The formalism proposed by North and Nakamoto was taken together with the derived spectrum to compute the mean square sampling error due to intermittent visits of a spaceborne sensor. The sampling error was estimated to be on the order of 10%, for monthly mean rainfall averaged over 500 × 500 km boxes which meets the scientific requirements of the TRMM mission. This result is consistent with those previously reported in the literature.

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