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Ralph Shapiro

Abstract

An improved amplitude restoring interpolation operator is specialized into a form that corrects the phase error as well as the amplitude damping introduced by two-point linear interpolation. The efficiency and accuracy of the operator is demonstrated by a series of test comparisons with amplitude restoring interpolation and cubic spline interpolation.

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Ralph Shapiro

Abstract

The brightness of the planet Jupiter is found to be related to mean annual and monthly relative sunspot numbers which are used to indicate the general level of solar activity. The evidence for the relationship is presented and is examined for possible meteorological implications.

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Ralph Shapiro

Abstract

The solar magnetic sector structure has recently been reported to be related to the atmospheric absolute vorticity (Wilcox et al., 1973, 1974). An examination of some of the statistics of this association shows that it may not be as highly significant as had been postulated, and raises serious question of its physical reality. A comparable analysis of the atmospheric relative vorticity shows that it responds in a more consistent fashion to the solar sector structure. The implication of this analysis is that if a physically real association exists, the solar sector structure is more likely to he related to the relative vorticity rather than the absolute vorticity.

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Ralph Shapiro

Abstract

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Ralph Shapiro

Abstract

A simple linear filter is adapted for use in numerical models of the large-scale circulation to act in place of an explicit horizontal diffusion term in the equations. The filter can be shown to be ideally suited for this purpose in the sense that it can be made increasingly scale-dependent as the order of the filter is increased. The one-dimensional filter of order n is constructed from n three-point symmetrical operators and involves 2n/1 grid points. It is capable of eliminating two-grid-interval waves completely, yet allowing little or no damping of longer waves.

In one space dimension, the use of the n = 1 order filter can be shown to be equivalent to the incorporation of a one-dimensional Fickian diffusion term in the differential equation. For any order n, the use of the one-dimensional filter is equivalent to the incorporation of a one-dimensional linear diffusion of order 2n. It is therefore apparent that as n increases, the ability of the filter to discriminate in its response to short- and long-wavelength components becomes increasingly sensitive.

The damping properties of linear diffusion are examined by means of the two-dimensional, horizontal Fickian equation and compared with the response of the order n = 8 filter in two dimensions. With typical values for the space and time increments and with K=4×109 cm2 sec−1, K −2> reduces two-grid-length waves by a factor e in 15 hr, four-grid-length waves in 30 hr, and ten-grid-length waves in 147 hr (6.1 days). The filter, applied each time step, removes the two-grid-length waves immediately and reduces three-grid-length waves by a factor e in 0.8 hr. This compares with ∼20 hr for K2. For four-grid-length waves, the effect of the filter is nearly the same as that of K2, but for longer waves the damping effect is drastically reduced. The filter requires 5 × 105 days to damp 10-grid-interval waves by a factor e and 3 × 1010 days for 20-grid-interval waves.

Thus, waves shorter than four grid lengths are effectively eliminated, while longer waves are essentially unaffected, except in so far as nonlinear interactions among the longer waves produce a cascade to shorter wavelengths. If the grid length is properly chosen for the physical system being studied and the equations adequately model the large-scale dynamics, the filter will automatically handle the cascade to smaller scale and should represent the effect of viscous damping that takes place in the atmosphere.

Some desirable properties of the filter are demonstrated by a one-dimensional example with no dynamics in which the order n = 8 filter is applied successively ten thousand times to grid-point data of the sea level pressure field.

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Ralph Shapiro

Abstract

Observations of the persistence of the surface pressure distribution are compared for two regions of the northern hemisphere. One region covers most of North America ; the other region is comparable in size and is centered on the Greenwich meridian. The linear correlation coefficient is used as a quantitative measure of persistence. The European pressure distribution is found to have considerably greater persistence up to periods of three days.

Comparison of the monthly means of the persistence observations and crude measures of the vertical wind shear indicate that the atmosphere behaves in a manner which is consistent with the conclusions of theoretical studies on the growth of atmospheric disturbances.

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Ralph Shapiro

Abstract

No abstract available.

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Ralph Shapiro

Abstract

A critical examination is given of two recent claims of association between solar and meteorological variability. One of these claims (Markson, 1971, 1978a) was chosen for examination because it invokes a possible physical mechanism, the other (Wilcox et al., 1974, 1976) because it has received widespread attention and acceptance. The evidence offered here, while not addressed to any physical mechanism, clearly indicates that the claims of association are unsubstantiated and most likely have arisen from statistical sampling fluctuations.

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Ralph Shapiro

Abstract

An analysis of the sea-level pressure distribution over North America for 47 years (1899–1945) provides what appears to be firm evidence of a solar-weather effect and tends to confirm an earlier pilot study. A pronounced decrease in a persistence correlation is found to occur about two weeks after large increases in geomagnetic activity.

A qualitative interpretation of the observed effect is advanced in the light of some recent experimental and theoretical work.

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Ralph Shapiro

Abstract

The persistence of the three-day mean surface pressure distribution in a mid-latitude region centered on the Greenwich meridian is examined in connection with large increases in geomagnetic activity and is compared with an earlier study concerned with the same parameters over a different region. The reactions of certain individual features of the pressure distributions of the two regions are also investigated.

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