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- Author or Editor: Ralph Shapiro x
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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.
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.
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.
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.
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.
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.
Abstract
A test of an apparent association between solar corpuscular radiation (measured by planetary-scale geomagnetic disturbance) and the subsequent behavior of the sea-level pressure distribution is carried out with completely new and independent data. The new results corroborate the earlier findings which indicated increased persistence in the pressure distribution during the first week and decreased persistence during the second to third week following large geomagnetic disturbances.
Abstract
A test of an apparent association between solar corpuscular radiation (measured by planetary-scale geomagnetic disturbance) and the subsequent behavior of the sea-level pressure distribution is carried out with completely new and independent data. The new results corroborate the earlier findings which indicated increased persistence in the pressure distribution during the first week and decreased persistence during the second to third week following large geomagnetic disturbances.
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 K∇2. For four-grid-length waves, the effect of the filter is nearly the same as that of K∇2, 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.
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 K∇2. For four-grid-length waves, the effect of the filter is nearly the same as that of K∇2, 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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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.
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.
