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Roy M. Endlich

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In certain meteorological problems it is desirable to make a grid-point analysis of observed winds. In order to combine a wind analysis with other quantities, or to use the wind analysis in a numerical model, one may wish to know the geostrophic winds (or the heights) that conform to the analyzed winds. Many previous studies have shown that the balance equation accurately describes relationships between winds and the height field. In this paper the balance equation is used to equate geostrophic vorticity at each grid point to a sum of terms evaluated from the wind analysis. Then the geostrophic winds are found by altering an initial guess field of zonal and meridional wind components until the geostrophic vorticity and divergence required at each point are met within a close tolerance. The final wind vectors are a geostrophic field that conforms to the original wind analysis according to the balance equation. Typical examples are shown of geostrophic wind vectors computed by this method in a sloping planetary boundary layer, and in the upper troposphere. In addition, geostrophic departures are compared with irrotational winds calculated for the same cases.

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Roy M. Endlich
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Roy M. Endlich

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ROY M. ENDLICH

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The viewpoint is taken that in large portions of the atmosphere, wind speeds (Vgr), divergence (Dgr), and vorticity (ζgr) obtained under the gradient wind assumption are considerably more accurate representations of true conditions than those one obtains from the geostrophic assumption. Equations are derived for computing Vgr, Dgr, and ζgr. The equation for the vorticity of gradient winds has a considerable resemblance to “balance” equations of Charney [3] and Phillips [17]. Gradient winds and their space derivatives may have advantages over other formulations due to their relative simplicity. The quantities Vgr, Dgr, and ζgr may be computed quite easily from geopotential data at grid points by use of high-speed computers. Possible applications of gradient winds in practical and theoretical meteorology are suggested.

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Roy M. Endlich

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Three-hour average vertical velocity values are computed at the 500-and 300-mb levels under the assumption of adiabatic motion by the “isobaric” technique. The patterns of the isolines of vertical velocity (isanabats) are shown for several upper flow patterns. Vertical velocity values of 10 cm sec−1 are found to be common at both levels, and a maximum value of 25 cm sec−1 is given. Computational errors are felt to be smaller by an order of magnitude. The strong isanabatic centers are shown to lie in or near the jet stream, indicating that the jet is an important vertical transport mechanism. Cloud observations show good qualitative agreement with the computations. Limited evidence, based on a study of the vertical velocity patterns over the Northern Hemisphere for a ten-day period, indicates that the mean circulation around the jet stream is thermally indirect.

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Roy M. Endlich

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Grid-point values of eastward and northward wind components imply that specific fields of divergence, vorticity and deformation exist. For certain purposes, one may wish to change the winds slightly to make them non-divergent, or to make them conform to fields of vorticity or deformation somewhat different than the original values. Control over the kinematic properties of a wind field can be exercised by the procedure given in this paper. The desired wind fields are obtained by a point iterative method applied to the two simultaneous linear partial differential equations that define horizontal divergence and relative vorticity, or stretching and shearing deformation. Some possible applications of this technique in analysis and forecasting are described briefly.

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Roy M. Endlich

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The structure of the atmosphere in regions of clear-air turbulence is investigated by means of aircraft observations of wind and temperature in combination with objective and subjective turbulence records. The nature of the aircraft data and the assumptions inherent in the analyses are described. The detailed fields of vertical and horizontal wind shear, stability and Richardson number are presented for turbulence encountered in three different patterns of flow, viz., a sharp trough, an anticyclonic jet stream, and an intense straight jet. Severe turbulence (equivalent in intensity to that measured by the same aircraft in a mature thunderstorm) was found in certain portions of the trough and ridge, and moderate turbulence existed in the straight jet. Comparison of these cases and of twenty other flights indicates certain similarities and certain differences of the flow conditions in the turbulent regions. The necessary and sufficient conditions for the existence of clear-air turbulence have not been isolated. However, certain mesoscale conditions that appear to be important include large vertical variations of both wind speed and direction, a discontinuity in lapse rate at an upper front or tropopause, sharp trajectory curvature, and appreciable vertical motions. These conditions are believed to favor the development of short, unstable waves that are probably the dominant turbulent mechanism.

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Roy M. Endlich and George McLean

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John M. Livingston and Roy M. Endlich

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Particulate extinction profiles measured by the satellite-borne SAM II and SAGE I sensors have been used to investigate the relationship between stratospheric aerosols (between 15 and 30 km) and the location of the north polar night stratospheric jet stream during selected periods of the winters of 1979–1982. Mean profiles of aerosol extinction mixing ratio (the ratio of particulate to molecule extinction) and temperature across the jet axis have been constructed by determining the location and the distance of individual SAM II profiles relative to the position of the jet axis on the 50-mb isobaric surface, and averaging all profiles located at similar distances on the same side (cyclonic or anticyclonic) of the jet. Variations in aerosol extinction mixing ratio patterns among winters and during major stratospheric warming events within separate winters have been examined. The analyses show a well-defined positive gradient in extinction mixing ratio and temperature across the jet stream from the cyclonic side to the anticyclonic side at altitudes between 20 and 30 km during each winter period. During major stratospheric warming events, this relationship between the distribution of aerosols and the jet stream axis remained intact, even though the dynamic meteorological structure underwent major changes that typically included the breakdown of an elongated, intense polar vortex into two separate, smaller, and less intense vortices. Time-averaged estimates of extinction mixing ratio profiles measured at locations near the center of the polar vortex suggest that a gradual subsidence took place within the polar vortex during at least three of the four winter periods.

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Roy M. Endlich and Daniel E. Wolf

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Improvements to the SRI automatic cloud-tracking system are described that enable it to operate on multilayer clouds associated with severe storms. The improved method has been tested using rapid-scan observations of Hurricane Eloise obtained by the GOES satellite on 22 September 1975. We performed cloud tracking using target selection (clustering) based either on visible or infrared data and tracked the targets using a pattern recognition technique. The technique matches targets with their best likeness (in terms of size, brightness and shape) at successive times in a manner analogous to human pattern recognition, and also rejects vectors in disagreement with the predominant motion in their height (infrared) category. For data of 4 and 8 km resolution, the automatic system gave results very comparable in accuracy and coverage to those obtained by NASA analysts using the Atmospheric and Oceanographic Information Processing System (AOIPS). We also tracked the same targets using a cross-correlation technique, but without internal editing. For targets that were tracked properly by both methods, the rms differences in displacements were only fractions of a pixel.

To learn whether the automatic system can track the motions of water vapor patterns we applied it to METEOSAT 6.7 μm water vapor measurements. For experimentation, typical data for the midlatitudes, subtropics and tropics were chosen from a sequence of METEOSAT pictures for 25 April 1978. In flat (low contrast) water vapor fields, the automatic motion computations were not reliable, but in areas where the water vapor fields contained small-scale structure (i.e., in the vicinity of active weather phenomena) the computations were successful. The tracking results appear to be similar to those obtained by visual analysis of these same data. For the same cases (including tropical convective systems and midlatitude jet stream cirrus) we computed cloud motions using METEOSAT infrared observations and obtained excellent results.

The cloud-motion vectors computed automatically appear to be competitive in accuracy and coverage with motions determined by human analysts working within reasonable time limits.

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