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A. A. White

Abstract

The behavior of two quasi-geostrophic, β-plane formulations under two translation operations is considered. The translation operations are zonal coordinate translation, in which the coordinate frame is translated zonally with uniform velocity U 0 relative to the β-plane, and zonal flow translation, in which U 0 is added to the flow at all points at some initial time. The quasi-geostrophic β-plane formulations are the Type 1 set (QG 1: valid when N 2 Hg) and the non-Doppler set (NDQ: valid when N 2 Hg, where N is the buoyancy frequency, g the acceleration due to gravity and H the vertical scale of the motion). Both formulations are here defined with geometric height as vertical coordinate. QG1 motion is invariant to zonal coordinate translation, and the only effect of zonal flow translation is a Doppler shift whereby U 0 is added to the flow at all points at all subsequent times. NDQ motion is invariant to zonal coordinate translation if the accompanying change in apparent vertical is allowed for, but the effect of zonal flow translation is not a simple Doppler shift. This non-Doppler property is evident in various published stability analyses, and it also appears in certain stability criteria (some of which are derived here for the first time). Zonal coordinate translation invariance is used to re-express some established stability criteria for both QG1 and NDQ flows.

The zonal coordinate translation properties of thc, β-plane formulations are substantiated by considering the corresponding zonal coordinate rotation properties of the meridional component of the hydrostatic Navier-Stokes equation on the sphere. It is shown that the usual form of this component equation exhibits the required invariance only if the accompanying change in apparent vertical is allowed for. The parameter N 2 H/g is interpreted for the case of certain zonal flows in thermal wind balance on the sphere. It represents the ratio of Δα (the angular range of apparent verticals seen by observers moving with the flow at heights differing by H) and α1 (the slope of the isentropes).

Examination of the behavior of the whole NDQ set under zonal coordinate translation reveals that the horizontally non-divergent flow depends strictly on the adopted coordinate frame. Further investigation of the consequences of this effect is advocated.

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A. A. White

Abstract

Attention is given to the extra term appearing in the quasi-geostrophic horizontal boundary condition when it is required that the vertical velocity (ω), rather than the material derivative of pressure (ω), be zero on a constant pressure surface. This extra term (here called the stratification term) has been retained in recent baroclinic instability studies by Geisler and Dickinson (1975) and Geisler and Garcia (1977). Their linearized problems, which used log pressure as vertical coordinate, are shown to be isomorphic with problems formulated in the altitude coordinate set put forward by White (1977). Examination of the small-amplitude free modes on a uniform barotropic zonal flow shows that the effects of the stratification term are: 1) in the absence of an upper lid, to allow the existence of progressive modes if the flow is easterly, and to disallow the Rossby mode if the easterly flow exceeds a certain value depending on the wavelength; 2) in the presence of an upper lid, to allow the existence of progressive modes in easterly or westerly flow; and 3) whether or not an upper lid is present, to reduce significantly the retrogression phase speeds of the largest scale Rossby modes, at least for flows of an intensity comparable with observed average zonal flows in the earth's atmosphere.

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A. A. White

Abstract

Several published models of the zonal average circulation on a sphere have not defined geostrophic equilibrium of the zonal flow in an energetically consistent way. The effect of the inconsistency is expected to be small, at least for realistic models of the atmospheric zonal average circulation.

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A. A. White

Abstract

In Newtonian particle dynamics the covariance of the kinetic energy equation to transformation between different inertial frames may he demonstrated only if the correct momentum equation is applied. A similar relation exists between the angular momentum equation and covariance of the kinetic energy equation to transformation between frames rotating with different angular velocities. Lagrangian and global versions hold for fluid motion. Analogous relations are implied by the hydrostatic primitive equations on a sphere (for the class of coaxial transformations, at least) when changes of the apparent vertical are properly allowed for. Repercussions for numerical forecasting and climate simulation models are discussed, the suggestion being that the importance of finite analogues of angular momentum conservation principles has been underestimated.

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M. J. Bell and A. A. White

Abstract

Eady's and Green's baroclinic instability problems are examined in N-level models with 2 ⩽ N ⩽ 180. As N is increased, both the maximum growth rate and the wavelength at which it occurs converge monotonically, without the irregular oscillatory behavior reported by Staley in a study of the instability of more complicated mean flows. Secondary and higher order maxima of growth rate occur amongst the short waves in the N-level Green problem, as noted by Arakawa and as found by Staley in the problems he studied. Each such spurious subsidiary maximum is associated with the occurrence of a critical level close to a model grid level. Regions of spurious stability may be associated with critical levels falling between model grid levels. A simple analytical model of these phenomena is proposed. It represents the potential vorticity gradient only at the grid level nearest to the critical level, and is quantitatively successful in reproducing the isolated subsidiary maxima found in the N-level Green problem.

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Douglas A. Miller and Richard A. White

Abstract

Soil information is now widely required by many climate and hydrology models and soil–vegetation–atmosphere transfer schemes. This paper describes the development of a multilayer soil characteristics dataset for the conterminous United States (CONUS-SOIL) that specifically addresses the need for soil physical and hydraulic property information over large areas. The State Soil Geographic Database (STATSGO) developed by the U.S. Department of Agriculture–Natural Resources Conservation Service served as the starting point for CONUS-SOIL. Geographic information system and Perl computer programming language tools were used to create map coverages of soil properties including soil texture and rock fragment classes, depth-to-bedrock, bulk density, porosity, rock fragment volume, particle-size (sand, silt, and clay) fractions, available water capacity, and hydrologic soil group. Interpolation procedures for the continuous and categorical variables describing these soil properties were developed and applied to the original STATSGO data. In addition to any interpolation errors, the CONUS-SOIL dataset reflects the limitations of the procedures used to generate detailed county-level soil survey data to the STATSGO map units. CONUS-SOIL is available in several formats and may be accessed via the World Wide Web.

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M. J. Bell and A. A. White

Abstract

The stability of internal baroclinic jets to quasi-geostrophic, normal mode perturbations is studied. Some important aspects are clarified by considering a jet which consists of a baroclinic layer sandwiched between two barotropic layers of finite depth on an f-plane. Even when the total available potential energy is kept constant (by appropriately changing the velocity difference across the baroclinic layer) the maximum unstable mode growth rate increases as the depth of the baroclinic layer is decreased. Certain primitive equation instability calculations reported by James and Hoskins (1985) show qualitatively different behavior, and hence require reinterpretation; it is suggested that the tendency of a β-effect to stabilize internal baroclinic jets is important in these cases. Examination of continuous sinusoidal internal jets establishes the existence of short-wave cutoffS to instability (SWCs) for such flows. A similar result for a more general class of internal jets is stated. It is found that the parametric location of the SWC is in some cases sensitively dependent on the degree and form of the lateral shear present in the basic flow. Implications for the theoretical interpretation of the upper axisymmetric flow transition in rotating annulus experiments are discussed. Some sinusoidal internal jet stability problems are solved numerically and it is found that, so long as the β-effect is weak, the results are well reproduced analytically by coarsely truncated spectral representations which exploit the internal jet character of the basic flow and the perturbations. Phase diagrams of the f-plane stability properties according to these spectral representations are constructed. Via a three-dimensional anticascade argument, the spectral representations also provide useful interpretations of the location of the SWC in the sinusoidal internal jet flows.

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W. B. WHITE and A. E. WALKER

Abstract

The meridional atmospheric teleconnections over the central North Pacific Ocean during winter are investigated by correlating the year-to-year fluctuations in the convective activity at the Equator, mid-latitude pressure/wind system, and subtropical pressure/wind system from 1950 to 1972. To establish fluctuations in these climatological systems, we consider the 23-yr time sequences of the maximum strength of the subtropical ridge, maximum intensity of the Aleutian Low, and strength of convective activity at the Equator, the latter inferred from the rainfall and sea-surface temperature at Canton Island (2°48′S, 171°43′W) observed by numerous authors to be representative of rainfall and sea-surface temperature over the entire central and eastern equatorial Pacific Ocean.

Upon cross correlation of these time sequences, we find that, throughout the two decades from 1950 to 1972, the intensity of the subtropical ridge and of the Aleutian Low were significantly correlated with one another (−0.50) as were the absolute magnitudes of their associated wind systems, the westerlies and northeast trades (0.83). Only during 1964–72, however, was the intensity of the Aleutian Low correlated (0.62) with fluctuations in the convective activity of the Equator. This indicates that the anomaly activity in the mid-latitude and subtropical pressure/wind systems and in the convective activity at the Equator were closely coupled during this time period. Conversely, during 1950–63, the lack of correlation between the convective activity at the Equator and the mid-latitude pressure/wind system suggests that the anomalies in these two systems were decoupled, at least in a linear way.

Bjerknes has found that fluctuations in the convective activity along the Equator in the Pacific were in association with the global tropical “southern oscillation” from 1955 to 1967. This suggests that, during the period of our study prior to 1964, the fluctuations in the mid-latitude pressure/wind system were independent of the fluctuations of sea-level pressure in the tropical latitudes of the world. However, the results of this paper together with the work of Bjerknes suggest that, after 1963, the mid-latitude pressure/wind system fluctuated in concert with the fluctuations of sea-level pressure over the tropical latitudes of the world. Speculation as to the causes for the approximate decadal variation in the meridional atmospheric teleconnections over the North Pacific is presented in terms of the decadal fluctuations found in the long-term trends of the major atmospheric systems.

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Robert M. White and R. A. Chandler
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Dorothy A. White and James J. Nehez

Abstract

This article describes a procedure used in progressing from the magnetic tape recordings of telemetered Morse coded data to the decoded data values used in subsequent calculations.

The process provides for the elimination of the greater portion of noise present during the initial data recordings, subsequent digitizing of the coded signals, and the decoding method utilized in the digital computer.

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