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  • Author or Editor: Gerald R. North x
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Gerald R. North
,
Juan B. Valdés
,
Eunho Ha
, and
Samuel S. P. Shen

Abstract

In this paper a scheme is proposed to use a point raingage to compare contemporaneous measurements of rain rate from a single-field-of-view estimate based on a satellite remote sensor such as a microwave radiometer. Even in the ideal case the measurements are different because one is at a point and the other is an area average over the field of view. Also the point gauge will be located randomly inside the field of view on different overpasses. A space-time spectral formalism is combined with a simple stochastic rain field to find the mean-square deviations between the two systems. It is found that by combining about 60 visits of the satellite to the ground-truth site, the expected error can be reduced to about 10% of the standard deviation of the fluctuations of the systems alone. This seems to be a useful level of tolerance in terms of isolating and evaluating typical biases that might be contaminating retrieval algorithms.

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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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