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Charles E. Graves
,
Juan B. Valdés
,
Samuel S. P. Shen
, and
Gerald R. North

Abstract

The spatial and temporal characteristics of rainfall over Oklahoma and Kansas are analyzed in this paper using the raingage data collected during the Preliminary Regional Experiment for STORM-Central (PRESTORM). The autocorrelation function and the spectrum are obtained directly from both processing the raingage data and using a theoretical stochastic model of space–time precipitation. This theoretical model serves as an intermediate step to obtain more information from the raingage records. The spectra obtained are then compared with those obtained from oceanic precipitation in the GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment (GATE) and with that obtained from analyzing raingage records in east Texas. Finally, the spectra are used to evaluate the sampling errors that are due to the spatial gaps in measurements. The sampling error is expressed as an integral over the product of the spectral density of the stochastic rain field and a filter function. This filter function solely depends on the space–time configuration of the measurement instruments. The values of the analytical and numerical results on the sampling error are obtained for ground, spaceborne, and combined sensors of precipitation for several aggregation levels in space and time and alternative spacing and visiting times. It was found that sampling errors of land precipitation are higher than those reported for ocean precipitation.

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Adam H. Monahan
,
John C. Fyfe
,
Maarten H. P. Ambaum
,
David B. Stephenson
, and
Gerald R. North

Abstract

Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.

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