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Joseph P. Pandolfo

Abstract

The spectral dependence and numerically estimated values of Kraichnan's numerically determined effective eddy viscosity in a test field model of two- and three- dimensional isotropic flow are compared to those of a strain-dependent eddy viscosity formula suggested by Smagorinsky (1963) and frequently used in spatially differenced primitive equation models of the atmosphere. The effective eddy viscosities are in general agreement in the three-dimensional case.

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Joseph P. Pandolfo

Abstract

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Joseph P. Pandolfo

Abstract

A set of wind and temperature profile formulas are derived for the constant-flux atmospheric boundary layer in lapse stratification. These formulas imply a relationship between the eddy transfer coefficient ratio, KH/KM, and the stability parameter, s/L, as well as relationships between various empirical constants appearing in previously suggested profile forms.

The derivation follows from the hypothesis that the gradient Richardson number, Ri, is equal to the Monin-Obukhov number, z/L. Empirical evidence is presented which supports the hypothesis when observational uncertainties in measured vertical wind and temperature differences are taken into account. The relationships between the empirical constants are consistent with previously reported values of these constants. The newly-derived free-convection wind profile agrees well with observed profiles reported by Swinbank (1964).

The derived free-convection wind profile is found to be noticeably, if slightly, more consistent with observed wind profiles than is either Taylor's (1960) free-convection wind profile or Swinbank's (1964) exponential wind profile. The observed ratio of wind gradients for different layers is apparently constant with L in free-convection conditions. This is found to be consistent with the newly derived profile law and inconsistent with the KEYPS function profile law with constant KH/KM (Panofsky, 1963). However, the variation of the KEYPS function profile ratio lies within the observational uncertainty.

It is concluded that the assumptions listed above provide a realistic description of the constant-flux surface boundary layer in lapse conditions within the accuracy of reported observations. The probable validity of the formulas for the eddy coefficient ratio is inferred from these results. Some practical aspects of the use of the profile laws are discussed.

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Joseph P. Pandolfo

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No abstract available.

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Joseph P. Pandolfo

A method for forecasting precipitation type during the winter months at New York City is developed. Surface temperature, freezing level, and horizontal temperature advection at 850 mb are the forecast parameters used. Results of a test of the method indicate that the assumptions applied in the development are valid.

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Philip S. Brown Jr. and Joseph P. Pandolfo

Abstract

A procedure is given here that allows two finite-difference schemes having dissimilar time-differencing operators (say, a horizontal advection-diffusion scheme and a vertical diffusion scheme) to be merged into a single equation at the cost of increasing storage requirements through the introduction of an additional time level. lie accuracy and stability of the combined scheme are investigated.

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Philip S. Brown Jr. and Joseph P. Pandolfo

Abstract

The advection-diffusion equation is often solved by implicit finite-difference schemes that are unconditionally stable when the grid interval is uniform. When such schemes are generalized to account for nonuniform grid spacing, instability can result. The cause of this difficulty is identified and a procedure given to reclaim stability. An example is provided to show that similar computational problems can be encountered in the use of explicit differencing schemes.

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Philip S. Brown Jr. and Joseph P. Pandolfo

Abstract

A numerical analysis of the nonlinear heat diffusion equation has been carted out to bring to light a heretofore little-understood type of instability that can be encountered in many numerical modeling applications. The nature of the instability is such that the error remains bounded but becomes large enough to prevent proper assessment of model results. For the sample problem under investigation, the nonlinearity is introduced through a diffusion coefficient that depends on the Richardson number which, in turn, is a function of the dependent variable. Our analysis shows that the interaction of short-wavelength and inter-mediate-wavelength solution components can induce nonlinear instability if the amplitude of either component is sufficiently large. Since the unstable solution may not wander far from the true solution, the error can be difficult to detect. A criterion, given in terms of a restriction on the Richardson number, guarantees local (short-term) stability of the numerical scheme whenever the criterion is satisfied. Numerical results obtained using a boundary-layer model with GATE Phase III data are presented to support the theoretical conclusions.

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Anthony R. Hansen, Joseph P. Pandolfo, and Alfonso Sutera

Abstract

The effects on surface-layer temperature, pressure, and circulation of flow regimes defined from parameters related to the midtropospheric flow are examined for Northern Hemisphere (NH) winter. Interregime contrasts identified from modes in the probability density distribution of midlalitude planetary-scale wave amplitude are compared and contrasted with those associated with conventionally defined blocking patterns and those associated with the Pacific/North American (PNA) teleconnection index.

The wave amplitude regimes lead to surface pressure contrasts of up to 16 mb, which accompany enhanced meridional surface flow. This meridional flow appears linked to significant low-layer (100 and and 850 mb) temperature contrasts of 4°C to 10°C. Comparison of them results to similar results for blocking and the PNA teleconnection index indicates that all three lead to effects of comparable magnitude in the NH winter low-layer temperature field. These effects are comparable to or greater than the local climatological temperature variability. The amplitude and phase of the interregime temperature and pressure differences implies correspondence between Pacific blocking events and the amplified planetary-wave regime. Conversely, the PNA temperature effects are phase shifted relative to those of both the wave amplitude regimes and the blocking regime.

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Philip S. Brown Jr., Joseph P. Pandolfo, and Anthony R. Hansen

Abstract

Average statistics for periods of large positive 500 mb height anomalies are compared to statistics for all other situations using NMC data for the 15 Januaries from 1963 to 1977. The 500 mb heights and geostrophic streamfunctions are represented as surface spherical harmonics, and energy and enstrophy spectra along with nonlinear wave-wave interaction statistics are computed.

Differences in 500 mb geopotential height variance, kinetic energy and enstrophy spectra occur between large positive anomaly events and other days in the two-dimensional spectral index band from roughly n=6 to n=9, where n is the degree of the associated Legendre function. The same index band experiences a reversal of both the usual kinetic energy and enstrophy cascades during large positive anomaly events. That is, the 6≤n≤9 band gains energy and enstrophy from wave-wave interactions during the anomaly events and loses energy and enstrophy by the same process at other times. The source of this energy and enstrophy is higher index (smaller two-dimensional scale) waves. The indication is that the Atlantic cases are more Subject to this cascade reversal than are Pacific events.

Our results suggest that the smaller scale, transient eddies may play a regime-dependent role in interactions with atmospheric circulation modes on the scale of the persistent anomalies. When interacting with larger-scale features, the role of smaller-scale transients may not always be dissipative.

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