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Abstract
If distributions of precipitation in the atmosphere could be understood in terms of their associated three-dimensional winds, then radar, radiosonde, and surface observations might be utilized in new ways as sources of information about the winds. In this paper, continuity equations for precipitation content of horizontally uniform updrafts, or to the cores of simple cells such as represented by showers formed in the absence of vertical wind shear. A parabolic profile of updrafts is assumed. When the precipitation profile is steady-state and the fall speed of precipitation is constant, the amount of precipitation per unit volume of air increases rapidly downward in mid-atmosphere. Near the surface, changes in the vertical are very small. Maxima of precipitation content occur aloft before steady conditions obtain throughout the updraft layer; in the steady case, maxima aloft may occur when the terminal fall speed of precipitation increases only slightly faster than the updrafts and with little increase of fall speed during their growth, as is often the case with snow. An explanation is offered for the difference between the vertical distributions of precipitation associated with widespread systems and with showers, and means for practical utilization of the results are suggested.
Abstract
If distributions of precipitation in the atmosphere could be understood in terms of their associated three-dimensional winds, then radar, radiosonde, and surface observations might be utilized in new ways as sources of information about the winds. In this paper, continuity equations for precipitation content of horizontally uniform updrafts, or to the cores of simple cells such as represented by showers formed in the absence of vertical wind shear. A parabolic profile of updrafts is assumed. When the precipitation profile is steady-state and the fall speed of precipitation is constant, the amount of precipitation per unit volume of air increases rapidly downward in mid-atmosphere. Near the surface, changes in the vertical are very small. Maxima of precipitation content occur aloft before steady conditions obtain throughout the updraft layer; in the steady case, maxima aloft may occur when the terminal fall speed of precipitation increases only slightly faster than the updrafts and with little increase of fall speed during their growth, as is often the case with snow. An explanation is offered for the difference between the vertical distributions of precipitation associated with widespread systems and with showers, and means for practical utilization of the results are suggested.
Abstract
The eye region of Hurricane Edna (1954) is studied with the principal aid of radar and dropsonde data. Vertical sections show that over the eye there was a thick layer derived from the wall cloud which bounded the eye on the northeast. Precipitation fell from this upper layer into drier air beneath. A reasonable mechanism is thereby suggested by which large moisture values can become associated with air in the eye without producing the wet bulb potential temperatures or high winds characteristic of the rain-filled masses outside the eye.
Radar data giving the height of the “bright band” or melting level show that the warm core structure of Edna was most pronounced within the radius if maximum surface winds. The result is qualitatively confirmed by soundings and by comparison of surface winds and the speeds of radar weather elements in various portions of the storm. The radar photographs also show that heavy precipitation near the eye of Edna was bounded sharply in the western semicircle along an east-west line through the center of the storm. This boundary must be associated with a rather large change of vertical air speeds and therefore has special dynamic significance.
Abstract
The eye region of Hurricane Edna (1954) is studied with the principal aid of radar and dropsonde data. Vertical sections show that over the eye there was a thick layer derived from the wall cloud which bounded the eye on the northeast. Precipitation fell from this upper layer into drier air beneath. A reasonable mechanism is thereby suggested by which large moisture values can become associated with air in the eye without producing the wet bulb potential temperatures or high winds characteristic of the rain-filled masses outside the eye.
Radar data giving the height of the “bright band” or melting level show that the warm core structure of Edna was most pronounced within the radius if maximum surface winds. The result is qualitatively confirmed by soundings and by comparison of surface winds and the speeds of radar weather elements in various portions of the storm. The radar photographs also show that heavy precipitation near the eye of Edna was bounded sharply in the western semicircle along an east-west line through the center of the storm. This boundary must be associated with a rather large change of vertical air speeds and therefore has special dynamic significance.
Abstract
In order to extend our understanding of the relationships between the atmospheric distributions of water substance and the wind, a two-dimensional continuity equation for water substance is studied in terms of model wind fields. Water-budget parameters are defined, and digital methods are used to develop time-dependent solutions of the continuity equation with the assumptions that the fall speed of condensate with respect to air is uniform, that condensation in rising saturated air and evaporation in subsaturated air occur instantaneously, and that the assumed wind field does not vary with time. It is shown that, for given distributions of the wind and condensation rate, the shape of the developing water distribution is determined only by the ratio of the updrafts to the fall speed of condensate.
The distributions of water substance derived from the continuity equations show features analogous to radar observations of water substance in the real atmosphere. For example, when the falling speed of condensate is larger than the maximum speed of updrafts, relatively small amounts of condensed water exist aloft, and vertical profiles of condensed water content correspond to those observed by radar in widespread precipitation. When the maximum updrafts are larger, condensate occurs aloft in large amounts: in these cases, the vertical protiles display upper-level maxima similar to radar observations of thunderstorms and early stages of shower development.
When fall speeds are large, nearly all the water condensed is also precipitated. However, the amount of precipitation decreases to about 35 per cent of the condensed water when fall speeds are comparatively quite small; in these cases, condensate aloft is so distributed that much of it evaporates in the downdraft part of the assumed wind field.
The methods used in this study can readily be adapted to study a variety of wind fields and to incorporate less restrictive postulates regarding the physical processes of precipitation.
Abstract
In order to extend our understanding of the relationships between the atmospheric distributions of water substance and the wind, a two-dimensional continuity equation for water substance is studied in terms of model wind fields. Water-budget parameters are defined, and digital methods are used to develop time-dependent solutions of the continuity equation with the assumptions that the fall speed of condensate with respect to air is uniform, that condensation in rising saturated air and evaporation in subsaturated air occur instantaneously, and that the assumed wind field does not vary with time. It is shown that, for given distributions of the wind and condensation rate, the shape of the developing water distribution is determined only by the ratio of the updrafts to the fall speed of condensate.
The distributions of water substance derived from the continuity equations show features analogous to radar observations of water substance in the real atmosphere. For example, when the falling speed of condensate is larger than the maximum speed of updrafts, relatively small amounts of condensed water exist aloft, and vertical profiles of condensed water content correspond to those observed by radar in widespread precipitation. When the maximum updrafts are larger, condensate occurs aloft in large amounts: in these cases, the vertical protiles display upper-level maxima similar to radar observations of thunderstorms and early stages of shower development.
When fall speeds are large, nearly all the water condensed is also precipitated. However, the amount of precipitation decreases to about 35 per cent of the condensed water when fall speeds are comparatively quite small; in these cases, condensate aloft is so distributed that much of it evaporates in the downdraft part of the assumed wind field.
The methods used in this study can readily be adapted to study a variety of wind fields and to incorporate less restrictive postulates regarding the physical processes of precipitation.
Hurricanes Edna, 1954, and Ione, 1955 were observed by radar at South Truro, Massachusetts. Both storms are associated with convective shower bands near the northern extremities of their circulations. Shower characteristics in the two cases are virtually identical in most respects, but the bands which they comprise propagate in grossly dissimilar ways. The differences are attributed to the presence of a convergence line or zone (cold front) at the boundary between two large scale air streams in the case of Ione, and the absence of a corresponding feature in the case of Edna.
The Ione observations are in general accord with the Bjerknes cold frontal model, as recently modified by Sanders, in which warm air is entrained into the frontal zone and converges and rises there and above it. While the showers thereby formed move with the warm air in which they are embedded, the convergence zone moves with the winds northwest of the wind shift line. The Edna showers develop in an almost horizontally homogeneous wind field, and there is some question as to the persistence of the small scale lines of convergence which produce them.
This note also contains some brief discussion of banded structures associated with altostratus clouds and rain which occur in the outskirts of both Edna and Ione.
Hurricanes Edna, 1954, and Ione, 1955 were observed by radar at South Truro, Massachusetts. Both storms are associated with convective shower bands near the northern extremities of their circulations. Shower characteristics in the two cases are virtually identical in most respects, but the bands which they comprise propagate in grossly dissimilar ways. The differences are attributed to the presence of a convergence line or zone (cold front) at the boundary between two large scale air streams in the case of Ione, and the absence of a corresponding feature in the case of Edna.
The Ione observations are in general accord with the Bjerknes cold frontal model, as recently modified by Sanders, in which warm air is entrained into the frontal zone and converges and rises there and above it. While the showers thereby formed move with the warm air in which they are embedded, the convergence zone moves with the winds northwest of the wind shift line. The Edna showers develop in an almost horizontally homogeneous wind field, and there is some question as to the persistence of the small scale lines of convergence which produce them.
This note also contains some brief discussion of banded structures associated with altostratus clouds and rain which occur in the outskirts of both Edna and Ione.
Abstract
Continuity equations are used to clarify relationships between air motions and distributions of accompanying precipitation. The equations embody simple modeling of condensation and evaporation with the following assumptions: (1) water vapor shares the motion of the air in all respects; (2) condensate shares horizontal air motion, but falls relative to air at a speed that is the same for all the particles comprising precipitation at a particular time and height; (3) the cloud phase is omitted.
After a review of one-dimensional models, the distributions of condensate in two-dimensional model wind fields are discussed with regard to instantaneous evaporation of condensate in unsaturated air and to no evaporation. The most nearly natural cases must lie between these extremes. The methods for obtaining solutions are instructive of basic interactions between air motion and water transport. The steady-state precipitation rate from a saturated horizontally uniform updraft column is shown to equal the sum of the vertically integrated condensation rate and a term that contains the horizontal divergence of wind. The latter term becomes relatively small as the ratio of precipitation fall speeds to updrafts becomes large. A basis for some studies of precipitation mechanisms, the equation N(V + w) = const., where N is the number of particles comprising precipitation at a particular point in space and time, V is their fall velocity, and w is the updraft, is shown to imply violation of continuity principles unless variations in w are quite small. Continuity equations are applied to radar-observed convective cells (generators) and their precipitation trails, and to radar-observed precipitation pendants (stalactites), and provide bases for estimating the strength, duration, and vertical extent of the associated vertical air currents. The stalactite study also discloses how horizontal variations of precipitation intensity arise during precipitation descent through a saturated turbulent atmosphere.
The continuity equations are powerful tools for illuminating fundamental properties of wind-water relationships. The conclusion discusses attractive paths along which this work should be extended.
Abstract
Continuity equations are used to clarify relationships between air motions and distributions of accompanying precipitation. The equations embody simple modeling of condensation and evaporation with the following assumptions: (1) water vapor shares the motion of the air in all respects; (2) condensate shares horizontal air motion, but falls relative to air at a speed that is the same for all the particles comprising precipitation at a particular time and height; (3) the cloud phase is omitted.
After a review of one-dimensional models, the distributions of condensate in two-dimensional model wind fields are discussed with regard to instantaneous evaporation of condensate in unsaturated air and to no evaporation. The most nearly natural cases must lie between these extremes. The methods for obtaining solutions are instructive of basic interactions between air motion and water transport. The steady-state precipitation rate from a saturated horizontally uniform updraft column is shown to equal the sum of the vertically integrated condensation rate and a term that contains the horizontal divergence of wind. The latter term becomes relatively small as the ratio of precipitation fall speeds to updrafts becomes large. A basis for some studies of precipitation mechanisms, the equation N(V + w) = const., where N is the number of particles comprising precipitation at a particular point in space and time, V is their fall velocity, and w is the updraft, is shown to imply violation of continuity principles unless variations in w are quite small. Continuity equations are applied to radar-observed convective cells (generators) and their precipitation trails, and to radar-observed precipitation pendants (stalactites), and provide bases for estimating the strength, duration, and vertical extent of the associated vertical air currents. The stalactite study also discloses how horizontal variations of precipitation intensity arise during precipitation descent through a saturated turbulent atmosphere.
The continuity equations are powerful tools for illuminating fundamental properties of wind-water relationships. The conclusion discusses attractive paths along which this work should be extended.
Abstract
A study of radar summary maps collected from July to December 1961 shows that the echo areas reported are closely associated with precipitation and that the reported echo intensifies and heights of tops are valuable for assessing the occurrence of thunderstorms and other precipitation types. Use of past-hour motion arrows shown on the maps for prediction by translation gives better 3-, 6-, and 9-hr forecasts of echo areas over St. Louis, Mo., than does persistence. The symbols given to indicate the fractional echo coverage within echo areas are usefully related in summer to the probability that precipitation occurs at any point within the echo area. Such relationships can be combined with the probabilities associated with echo-area forecasts to obtain a probability for the future occurrence of echo at any particular point. Some means for extending such probability designations to route forecasts are briefly indicated.
A principal weakness of the present radar data observing and reporting methods is the coding scheme. The encoded echo observations are very general and the location of echoes within the areas indicated on the radar summary maps is not shown except for particularly noteworthy cases. However, the present data demonstrate both that radar is a valuable aid for terminal and enroute forecasting and that forecasts of useful accuracy and greater precision should be possible when more precise radar data become available.
Abstract
A study of radar summary maps collected from July to December 1961 shows that the echo areas reported are closely associated with precipitation and that the reported echo intensifies and heights of tops are valuable for assessing the occurrence of thunderstorms and other precipitation types. Use of past-hour motion arrows shown on the maps for prediction by translation gives better 3-, 6-, and 9-hr forecasts of echo areas over St. Louis, Mo., than does persistence. The symbols given to indicate the fractional echo coverage within echo areas are usefully related in summer to the probability that precipitation occurs at any point within the echo area. Such relationships can be combined with the probabilities associated with echo-area forecasts to obtain a probability for the future occurrence of echo at any particular point. Some means for extending such probability designations to route forecasts are briefly indicated.
A principal weakness of the present radar data observing and reporting methods is the coding scheme. The encoded echo observations are very general and the location of echoes within the areas indicated on the radar summary maps is not shown except for particularly noteworthy cases. However, the present data demonstrate both that radar is a valuable aid for terminal and enroute forecasting and that forecasts of useful accuracy and greater precision should be possible when more precise radar data become available.
Abstract
The great information-processing capacity of modern digital computers is used to assemble radar data in a form suitable for its application to weather analysis and forecasting studies and for investigation of the data's physical and statistical properties. Data are collected by PPI photography at steps of the antenna-elevation angle and radar-system sensitivity and aye reduced manually to digital form. The data are registered on magnetic tape for entry to the digital computer, wherein they are edited, range-normalized, reassembled to produce plan distributions that refer to a constant altitude above the earth, and processed for the distributions of the heights of echo bases and tops. Any of a practically limitless number of processing combinations can be selected to portray the intensity, male, and vertical development characteristic of the echoes for a particular period and location. The outputs of the computer program are printed distributions, for visual inspection and manual processing, and magnetic tapes containing the data in a form suitable for analysis by other computer routines. This program provides practical means for developing knowledge of radar data; realization of the full benefits of radar under operational conditions will require instruments which quantize the data rapidly.
Abstract
The great information-processing capacity of modern digital computers is used to assemble radar data in a form suitable for its application to weather analysis and forecasting studies and for investigation of the data's physical and statistical properties. Data are collected by PPI photography at steps of the antenna-elevation angle and radar-system sensitivity and aye reduced manually to digital form. The data are registered on magnetic tape for entry to the digital computer, wherein they are edited, range-normalized, reassembled to produce plan distributions that refer to a constant altitude above the earth, and processed for the distributions of the heights of echo bases and tops. Any of a practically limitless number of processing combinations can be selected to portray the intensity, male, and vertical development characteristic of the echoes for a particular period and location. The outputs of the computer program are printed distributions, for visual inspection and manual processing, and magnetic tapes containing the data in a form suitable for analysis by other computer routines. This program provides practical means for developing knowledge of radar data; realization of the full benefits of radar under operational conditions will require instruments which quantize the data rapidly.
Observations of a sharp cold front and closely associated squall line in New England are analyzed. A striking feature is a line of convective clouds and heavy precipitation, which does not extend above 10,000 ft. The radar indication of the true plan-position and vertical extent of such disturbances is of special importance to air operations.
Observations of a sharp cold front and closely associated squall line in New England are analyzed. A striking feature is a line of convective clouds and heavy precipitation, which does not extend above 10,000 ft. The radar indication of the true plan-position and vertical extent of such disturbances is of special importance to air operations.
A brief description is given of the preparation of charts depicting vorticity and space-mean flow patterns, in a manner similar to that proposed by Fjørtoft (1952). A comparison of the velocity of pronounced vorticity centers and the velocity of the wind over the centers indicated by the space-mean flow pattern is made from a series of daily charts for the autumn and early winter of 1953. It is found that the directions of motion of the centers and of the winds do not differ by more than ten degrees in slightly more than half the cases. A correlation coefficient of +0.69 is found between the speed of the centers and the speed of the winds. Use of the space-mean wind as a method of forecasting the displacement of the vorticity centers appears to be superior to the use of extrapolation. Application of the Rossby wave formula to all ridges and troughs in the space-mean flow patterns yields forecasts of the displacement of these features which are slightly better than extrapolation forecasts.
A brief description is given of the preparation of charts depicting vorticity and space-mean flow patterns, in a manner similar to that proposed by Fjørtoft (1952). A comparison of the velocity of pronounced vorticity centers and the velocity of the wind over the centers indicated by the space-mean flow pattern is made from a series of daily charts for the autumn and early winter of 1953. It is found that the directions of motion of the centers and of the winds do not differ by more than ten degrees in slightly more than half the cases. A correlation coefficient of +0.69 is found between the speed of the centers and the speed of the winds. Use of the space-mean wind as a method of forecasting the displacement of the vorticity centers appears to be superior to the use of extrapolation. Application of the Rossby wave formula to all ridges and troughs in the space-mean flow patterns yields forecasts of the displacement of these features which are slightly better than extrapolation forecasts.
