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## Abstract

The *U.S.N.S*. *Vanguard* provided a set of high quality upper-air wind data during GATE which should he uniquely valuable to researchers. The figures in this note are intended to illustrate the excellent vertical resolution and apparent accuracy of these observations, which were obtained by a high precision tracking radar. The examples have been chosen from Phase I when the ship was positioned at the center of the B army (8.5°N, 23.5°W). The natural evolution of some jet and “wave” features is portrayed in detail as a function of height over periods of a few hours and a few days, respectively. In addition to possible stratosphere “waves” identified in previous studies, the data show that features with 1 km vertical wavelengths are present which may be associated with planetary inertia-gravity waves.

## Abstract

The *U.S.N.S*. *Vanguard* provided a set of high quality upper-air wind data during GATE which should he uniquely valuable to researchers. The figures in this note are intended to illustrate the excellent vertical resolution and apparent accuracy of these observations, which were obtained by a high precision tracking radar. The examples have been chosen from Phase I when the ship was positioned at the center of the B army (8.5°N, 23.5°W). The natural evolution of some jet and “wave” features is portrayed in detail as a function of height over periods of a few hours and a few days, respectively. In addition to possible stratosphere “waves” identified in previous studies, the data show that features with 1 km vertical wavelengths are present which may be associated with planetary inertia-gravity waves.

## Abstract

The concept of the isallobaric wind is extended to include frictional boundary layer effects by use of a simple quasi-balanced analysis which filters out inertia-diffusion oscillations. It is found that transient modifications to Ekman-like flow also possess a spiral hodograph structure. In contrast to Ekman-like flows, the divergence of the isallobaric flow component increases to the top of the boundary layer while the vorticity reaches a maximum within the boundary layer; both quantities are proportional to the Laplacian of local rate of pressure change rather than the Laplacian of pressure. Applications to idealized intensifying and moving systems are given. It is found that the isallobaric correction provides enhanced low-level upward motion in advance of a moving low pressure center and subsidence to its rear.

## Abstract

The concept of the isallobaric wind is extended to include frictional boundary layer effects by use of a simple quasi-balanced analysis which filters out inertia-diffusion oscillations. It is found that transient modifications to Ekman-like flow also possess a spiral hodograph structure. In contrast to Ekman-like flows, the divergence of the isallobaric flow component increases to the top of the boundary layer while the vorticity reaches a maximum within the boundary layer; both quantities are proportional to the Laplacian of local rate of pressure change rather than the Laplacian of pressure. Applications to idealized intensifying and moving systems are given. It is found that the isallobaric correction provides enhanced low-level upward motion in advance of a moving low pressure center and subsidence to its rear.

## Abstract

The properties of 13 computational methods for the integration of first-order differential equations in time are studied. Special attention is given to the representation of periodic fluctuations in a simple spectral baroclinic model of the atmosphere. Errors in the energy, three dimensional scale, and frequency for linear and nonlinear oscillations are evaluated.

Comparisons of both one-step and two-step methods are made. It is found that the two-step schemes compare favorably with one-step methods only when given the advantage of a smaller time increment. Even then, it is concluded that certain one-step procedures incorporating two or more extrapolations over each constant increment of time produce errors which grow most slowly. With small time increments, these errors are generally made smallest by increasing the number of time extrapolations at each step rather than by decreasing the time increment.

## Abstract

The properties of 13 computational methods for the integration of first-order differential equations in time are studied. Special attention is given to the representation of periodic fluctuations in a simple spectral baroclinic model of the atmosphere. Errors in the energy, three dimensional scale, and frequency for linear and nonlinear oscillations are evaluated.

Comparisons of both one-step and two-step methods are made. It is found that the two-step schemes compare favorably with one-step methods only when given the advantage of a smaller time increment. Even then, it is concluded that certain one-step procedures incorporating two or more extrapolations over each constant increment of time produce errors which grow most slowly. With small time increments, these errors are generally made smallest by increasing the number of time extrapolations at each step rather than by decreasing the time increment.

## Abstract

The purpose of this study is to improve understanding of shallow cumuli in the planetary boundary layer (PBL) by quantitatively analysing subcloud turbulence variables. Aircraft turbulence data for three flights from the 1986 Hydrologic–Atmospheric Pilot Experiment project over southwest France is extensively analyzed in terms of both cumulus regime and eddy dimensions. The turbulent part of any variable has been divided into three spatial frequency bands to estimate the scale-dependent effects of cumuli on the total turbulent fluxes and energy at several levels within the subcloud layer.

Case 1 (21 May) had strong active (positively buoyant) cumuli that were deep and large in diameter; additionally, there were weak active cumuli that were shallow and small in diameter. Case 2 (9 May) had weak active cumuli with a smaller vertical depth, and case 3 (13 June) had only forced (negatively buoyant) cumuli. The National Center of Atmospheric Research King Air aircraft made gust probe measurements along several horizontal flight legs at different times and altitudes within the subcloud layer, and a few vertical sounding legs provided continuous vertical profiles within the entire boundary layer.

The results show that water vapor fluxes, buoyancy fluxes, and vertical motion near cloud base were enhanced by active cumuli influence on larger turbulence scales. In contrast, results for weak active and forced cumulus cases show subcloud turbulence characteristics very similar to those observed in a dry convective boundary layer. By enhancing the larger-scale turbulence and fluxes near cloud base, the active cumuli contribute to cooling and drying of the upper portion of the subcloud layer. These large cumuli were associated with more vigorous convective plumes of medium scale but otherwise did not seem to influence the average surface turbulence of smaller scales.

## Abstract

The purpose of this study is to improve understanding of shallow cumuli in the planetary boundary layer (PBL) by quantitatively analysing subcloud turbulence variables. Aircraft turbulence data for three flights from the 1986 Hydrologic–Atmospheric Pilot Experiment project over southwest France is extensively analyzed in terms of both cumulus regime and eddy dimensions. The turbulent part of any variable has been divided into three spatial frequency bands to estimate the scale-dependent effects of cumuli on the total turbulent fluxes and energy at several levels within the subcloud layer.

Case 1 (21 May) had strong active (positively buoyant) cumuli that were deep and large in diameter; additionally, there were weak active cumuli that were shallow and small in diameter. Case 2 (9 May) had weak active cumuli with a smaller vertical depth, and case 3 (13 June) had only forced (negatively buoyant) cumuli. The National Center of Atmospheric Research King Air aircraft made gust probe measurements along several horizontal flight legs at different times and altitudes within the subcloud layer, and a few vertical sounding legs provided continuous vertical profiles within the entire boundary layer.

The results show that water vapor fluxes, buoyancy fluxes, and vertical motion near cloud base were enhanced by active cumuli influence on larger turbulence scales. In contrast, results for weak active and forced cumulus cases show subcloud turbulence characteristics very similar to those observed in a dry convective boundary layer. By enhancing the larger-scale turbulence and fluxes near cloud base, the active cumuli contribute to cooling and drying of the upper portion of the subcloud layer. These large cumuli were associated with more vigorous convective plumes of medium scale but otherwise did not seem to influence the average surface turbulence of smaller scales.

## Abstract

The dynamics of low-level summer monsoon flow near 900 mb is studied using daily MONEX (1979) satellite wind data to estimate mechanisms influencing the horizontal momentum. We present an improved estimate of the large-scale monsoon geopotential field near the level of maximum wind, and a more approximate field of friction as well. Average fields for the premonsoon and established monsoon periods of 1.5 months are shown. The evolution of forces and accelerations along different trajectories crossing the western Indian Ocean are compared.

The net horizontal force, equal to the pressure gradient plus friction force, is obtained for the two periods by directly estimating the mean Coriolis and relative acceleration vectors. The contribution to mean acceleration by synoptic-scale transient eddies is significant only south of 30°S. Inertial acceleration by the mean flow produces a Rossby number in excess of 0.25 in an equatorial belt which expands to 10°N in the Somali Jet entrance.

A method is devised to split the observed net force field into its pressure gradient and friction force components; the method corresponds to solving the vorticity and divergence equations, respectively, and uses the property that pressure gradient is exactly irrotational and the assumption that friction force is mostly non-divergent. It is found that the diagnosed friction force tends to oppose the wind and is distinctly weaker than the pressure gradient force. The calculated geopotential field shows the development of a distinctive “reversed S” contour connecting the hemispheres and supporting strong cross-equatorial flow. The corresponding trajectories show that the degree of imbalance is greater in the Northern Hemisphere as the air adjusts to the changing Coriolis influence and monsoonal pressure gradient forces which increase and rotate. Northward moving air slows by friction as it approaches the equator, but increases speed in the Northern Hemisphere by flowing toward lower pressure. The assumptions involving frictional estimates for boundary conditions are evaluated using theory and wind data.

## Abstract

The dynamics of low-level summer monsoon flow near 900 mb is studied using daily MONEX (1979) satellite wind data to estimate mechanisms influencing the horizontal momentum. We present an improved estimate of the large-scale monsoon geopotential field near the level of maximum wind, and a more approximate field of friction as well. Average fields for the premonsoon and established monsoon periods of 1.5 months are shown. The evolution of forces and accelerations along different trajectories crossing the western Indian Ocean are compared.

The net horizontal force, equal to the pressure gradient plus friction force, is obtained for the two periods by directly estimating the mean Coriolis and relative acceleration vectors. The contribution to mean acceleration by synoptic-scale transient eddies is significant only south of 30°S. Inertial acceleration by the mean flow produces a Rossby number in excess of 0.25 in an equatorial belt which expands to 10°N in the Somali Jet entrance.

A method is devised to split the observed net force field into its pressure gradient and friction force components; the method corresponds to solving the vorticity and divergence equations, respectively, and uses the property that pressure gradient is exactly irrotational and the assumption that friction force is mostly non-divergent. It is found that the diagnosed friction force tends to oppose the wind and is distinctly weaker than the pressure gradient force. The calculated geopotential field shows the development of a distinctive “reversed S” contour connecting the hemispheres and supporting strong cross-equatorial flow. The corresponding trajectories show that the degree of imbalance is greater in the Northern Hemisphere as the air adjusts to the changing Coriolis influence and monsoonal pressure gradient forces which increase and rotate. Northward moving air slows by friction as it approaches the equator, but increases speed in the Northern Hemisphere by flowing toward lower pressure. The assumptions involving frictional estimates for boundary conditions are evaluated using theory and wind data.

## Abstract

The effects of horizontal shear of the mean zonal wind on the lateral propagation of disturbances through the Tropics is studied by the use of a one-layer model. The governing equations are reduced to a second-order differential equation for *v*, the northward component of velocity. The equation is analyzed as an eigenvalue problem and solved numerically for the free modes of the Tropics for the case with zero mean flow. These solutions are compared with solutions that are forced at a boundary situated in mid-latitudes, for cases with and without a mean zonal flow.

At “critical latitudes,” the basic equation has a singularity (where the phase speed of a wave forced at the boundary is equal to the mean flow). The case for forced motions is investigated in more detail by numerically studying the evolution of disturbances as an initial value problem for the case of nondivergent flow.

The horizontal shear is shown to significantly alter the types of mid-latitude motions that can affect tropical motions. In particular, disturbances with large eastward phase propagation are shown to have negligible effect. Disturbances that have phase speeds that are somewhere equal to the mean flow are shown to be absorbed at the critical latitude. Disturbances with phase speeds more westward than the mean flow may be free to propagate into the Tropics, providing their wavelengths are not too short.

## Abstract

The effects of horizontal shear of the mean zonal wind on the lateral propagation of disturbances through the Tropics is studied by the use of a one-layer model. The governing equations are reduced to a second-order differential equation for *v*, the northward component of velocity. The equation is analyzed as an eigenvalue problem and solved numerically for the free modes of the Tropics for the case with zero mean flow. These solutions are compared with solutions that are forced at a boundary situated in mid-latitudes, for cases with and without a mean zonal flow.

At “critical latitudes,” the basic equation has a singularity (where the phase speed of a wave forced at the boundary is equal to the mean flow). The case for forced motions is investigated in more detail by numerically studying the evolution of disturbances as an initial value problem for the case of nondivergent flow.

The horizontal shear is shown to significantly alter the types of mid-latitude motions that can affect tropical motions. In particular, disturbances with large eastward phase propagation are shown to have negligible effect. Disturbances that have phase speeds that are somewhere equal to the mean flow are shown to be absorbed at the critical latitude. Disturbances with phase speeds more westward than the mean flow may be free to propagate into the Tropics, providing their wavelengths are not too short.

## Abstract

Vertical gradients are usually calculated by a finite-difference approximation, where the level of interest is midway between the levels at which measurements are made. When this approach is used, considerable error may occur if the gradient varies with height, i.e., if the profile is not linear. Near the ground, non-linearity is the rule rather than the exception. The finite-difference approach may still be used, but measurements must be made at heights determined by the form of the profile, and not at heights equally distant from the level of interest.

A set of charts is presented showing the heights at which the sensors must be mounted to give the gradient at the level of interest, and the height to which the gradient as usually measured actually applies. Correction factors are derived so that the gradient at any level may be determined from measurements at any two heights, provided the form of the profile is known. Use of this technique eliminates one source of error in comparison of gradient measurements from different locations, and in determination of parameters in which one or more gradient measurements at a predetermined level are required.

## Abstract

Vertical gradients are usually calculated by a finite-difference approximation, where the level of interest is midway between the levels at which measurements are made. When this approach is used, considerable error may occur if the gradient varies with height, i.e., if the profile is not linear. Near the ground, non-linearity is the rule rather than the exception. The finite-difference approach may still be used, but measurements must be made at heights determined by the form of the profile, and not at heights equally distant from the level of interest.

A set of charts is presented showing the heights at which the sensors must be mounted to give the gradient at the level of interest, and the height to which the gradient as usually measured actually applies. Correction factors are derived so that the gradient at any level may be determined from measurements at any two heights, provided the form of the profile is known. Use of this technique eliminates one source of error in comparison of gradient measurements from different locations, and in determination of parameters in which one or more gradient measurements at a predetermined level are required.

## Abstract

The three-dimensional structure and implied dynamics of a strong tropospheric gravity wave event am studied. It is shown that satellite and continuous surface observations reveal the subsynoptic nature of this “wave of depression” to an extent impossible with conventional data. The observations and theory suggest that the gravity wave originated in the upper troposphere near a jet streak, was quasi-hydrostatic and hence relatively nondispersive and long-lived.

The behavior of the wave at upper-tropospheric levels is revealed by sequences of visible and infrared goesynchronous satellite imagery. Quantitative estimates of cloud top temperatures and winds suggest strong subsidence new 300 mb with an isentropic depression as large as 900 m. The upper-level depression and the surface disturbance propagate coherently with a speed of 32 m s^{−1} indicating that they are part of the same internal gravity wave. The vertical tilt with height is opposite to the propagation direction and thus is consistent with an upper-tropospheric energy source. The negative surface pressure deviation reaches 7 mb and is qualitatively consistent with the field of surface wind divergence.

Theory is applied to estimate and explain gravity wave properties throughout the troposphere: vertical tilt (decreasing upward) as large as 1:9 in the lower troposphere; maximum wave energy at upper levels, with maximum wind deviation ∼ 15 m s^{−1}, horizontal divergence ∼ 4×10^{−4} s^{−1}, vertical parcel displacement ∼ 1 km, local potential temperature deviations of several degrees, pressure perturbations ∼ 7 mb, and the time to completely establish the wave throughout the troposphere ∼ 4 h. Further improvement in the description may demand development of “solitary” wave theory for deep depression waves in shear flow.

## Abstract

The three-dimensional structure and implied dynamics of a strong tropospheric gravity wave event am studied. It is shown that satellite and continuous surface observations reveal the subsynoptic nature of this “wave of depression” to an extent impossible with conventional data. The observations and theory suggest that the gravity wave originated in the upper troposphere near a jet streak, was quasi-hydrostatic and hence relatively nondispersive and long-lived.

The behavior of the wave at upper-tropospheric levels is revealed by sequences of visible and infrared goesynchronous satellite imagery. Quantitative estimates of cloud top temperatures and winds suggest strong subsidence new 300 mb with an isentropic depression as large as 900 m. The upper-level depression and the surface disturbance propagate coherently with a speed of 32 m s^{−1} indicating that they are part of the same internal gravity wave. The vertical tilt with height is opposite to the propagation direction and thus is consistent with an upper-tropospheric energy source. The negative surface pressure deviation reaches 7 mb and is qualitatively consistent with the field of surface wind divergence.

Theory is applied to estimate and explain gravity wave properties throughout the troposphere: vertical tilt (decreasing upward) as large as 1:9 in the lower troposphere; maximum wave energy at upper levels, with maximum wind deviation ∼ 15 m s^{−1}, horizontal divergence ∼ 4×10^{−4} s^{−1}, vertical parcel displacement ∼ 1 km, local potential temperature deviations of several degrees, pressure perturbations ∼ 7 mb, and the time to completely establish the wave throughout the troposphere ∼ 4 h. Further improvement in the description may demand development of “solitary” wave theory for deep depression waves in shear flow.

## Abstract

Patterns of fluctuating cloud amount in the tropical Pacific are decomposed into individual frequency bands and presented in longitude-time and latitude-time sections. The natural variability of propagating “clusters” is identified by considering zonal deviation fields, While patterns closer to planetary scale are studied in the zonal means for this limited domain. Periods of both regular and irregular transient activity are made apparent as a function of location. Regimes of “regular” activity are found to differ in direction of cloud propagation, horizontal scale, and waveform tilts.

## Abstract

Patterns of fluctuating cloud amount in the tropical Pacific are decomposed into individual frequency bands and presented in longitude-time and latitude-time sections. The natural variability of propagating “clusters” is identified by considering zonal deviation fields, While patterns closer to planetary scale are studied in the zonal means for this limited domain. Periods of both regular and irregular transient activity are made apparent as a function of location. Regimes of “regular” activity are found to differ in direction of cloud propagation, horizontal scale, and waveform tilts.

## Abstract

The transient behavior of the simple model of moist convection devised by Asai is studied. It is shown that the initial behavior of convective disturbances depends strongly upon the geometry of the disturbance, its initial buoyancy, and dissipative mechanisms. Final approach to a steady convective cell is dependent upon the relative importance of entrainment of heat and momentum. These conclusions derived mainly from linear analysis are substantiated by a series of numerical experiments exhibiting the full nonlinear behavior of the system from formative stages to the final steady-state cell.

## Abstract

The transient behavior of the simple model of moist convection devised by Asai is studied. It is shown that the initial behavior of convective disturbances depends strongly upon the geometry of the disturbance, its initial buoyancy, and dissipative mechanisms. Final approach to a steady convective cell is dependent upon the relative importance of entrainment of heat and momentum. These conclusions derived mainly from linear analysis are substantiated by a series of numerical experiments exhibiting the full nonlinear behavior of the system from formative stages to the final steady-state cell.