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Gerald R. North
,
Fanthune J. Moeng
,
Thomas L. Bell
, and
Robert F. Cahalan

Abstract

Zonally averaged meteorological fields can have large variances in polar regions due to purely geometrical effects, because fewer statistically independent areas contribute to zonal means near the poles than near the equator. A model of a stochastic field with homogeneous statistics on the sphere is presented as an idealized example of the phenomenon. We suggest a quantitative method for isolating the geometrical effect and use it in examining the variance of the zonally averaged 500 mb geopotential height field.

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Gerald R. North
,
Thomas L. Bell
,
Robert F. Cahalan
, and
Fanthune J. Moeng

Abstract

Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is “close” to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets.

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Kyung-Sup Shin
,
Gerald R. North
,
Yoo-Shin Ahn
, and
Phillip A. Arkin

Abstract

A statistical analysis of time series of area-averaged rainfall over the oceans has been conducted around the diurnal time scale. The results of our analysis can be applied directly to the problem of establishing the magnitude of expected errors to be incurred in the estimation of monthly area-averaged rain rates from low orbiting satellites. Such statistics as the mean, standard deviation, integral time scale of background red noise and spectral analyses were performed oil time series of the GOES Precipitation Index (GPI) taken at 3-hour intervals during the period spanning 19 December 1987 to 31 March 1988 over the central and eastern tropical Pacific. The analyses have been conducted on 2.5°×2.5° and 5°×5° grid boxes, separately.

The ratio of standard deviation to mean for area-averaged rain rate in the Pacific ITCZ is very regular and similar to that in GATE. Analysis of the area-averaged rainfall in the SPCZ shows a longer autocorrelation time scale than that in the ITCZ. The SPCZ exhibits significant power at the diurnal and semidiurnal frequencies, but the ITCZ shows only a marginally significant diurnal cycle in our data. The rainfall characteristics in the Pacific ITCZ appear to be similar to those in the Atlantic ITCZ in both autocorrelation time scale and diurnal variation. The mechanism driving convection in the ITCZ is suggested to be different from that in the SPCZ. The study shows that rainfall measurements by a sun-synchroneous satellite visiting a spot twice per day will include a bias due to the existence of the semidiurnal cycle in the SPCZ ranging from 5 to 10 percentage points. The bias in the ITCZ may be of the order of 5 percentage points.

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