# Search Results

## You are looking at 1 - 10 of 36 items for

- Author or Editor: J. S. Marshall x

- Refine by Access: All Content x

## Abstract

A new PPI map is made up of 600 radial lines, each of 100 dots. Each dot is in one of six shades of grey, thus indicating target intensity, and dot size varies somewhat with shade. Each dot combines *k* independent data, where 7 < *k* < 75, and the data were combined by taking (electronically) the peak reading among the *k* data. The data from these maps were processed further by counting the fraction of a group of about 20 dots that had a given shade, i.e., that fell in a given echo-intensity interval. This procedure yields improved intensity resolution, on a scale of intensity level that is practically continuous (surprisingly, since only a few spaced thresholds are used) at the expense of spatial resolution.

## Abstract

A new PPI map is made up of 600 radial lines, each of 100 dots. Each dot is in one of six shades of grey, thus indicating target intensity, and dot size varies somewhat with shade. Each dot combines *k* independent data, where 7 < *k* < 75, and the data were combined by taking (electronically) the peak reading among the *k* data. The data from these maps were processed further by counting the fraction of a group of about 20 dots that had a given shade, i.e., that fell in a given echo-intensity interval. This procedure yields improved intensity resolution, on a scale of intensity level that is practically continuous (surprisingly, since only a few spaced thresholds are used) at the expense of spatial resolution.

## Abstract

A characteristic “mares' tail” pattern of falling snow (observed in vertical section by radar) suggests that the snow is generated continuously, in compact generating elements; the pattern results from the snow's falling at constant velocity through the wind shear. For constant wind shear, the snow trails are parabolic, and before reaching the ground become almost horizontal. The velocity of the pattern is that of the generating elements, and can be compared with wind strengths aloft to locate the height of the generating elements when these elements are not detected by the radar.

## Abstract

A characteristic “mares' tail” pattern of falling snow (observed in vertical section by radar) suggests that the snow is generated continuously, in compact generating elements; the pattern results from the snow's falling at constant velocity through the wind shear. For constant wind shear, the snow trails are parabolic, and before reaching the ground become almost horizontal. The velocity of the pattern is that of the generating elements, and can be compared with wind strengths aloft to locate the height of the generating elements when these elements are not detected by the radar.

## Abstract

^{−1}) represent thunderstorms, some single-celled and some multi-celled. These were found to be the sources of lightning observed (as “sferics”) by a radio direction finder, frequency 100±50 kHz, located at the radar. The sferics rates of the storms were related closely to other storm parameters by

*L*

*A*

^{1.64}

*r*

^{−1.62}

*L*is the number of sferics observed per minute,

*r*the distance of the storm (km), and

*A*the area (km

^{2}) of the storm region as specified above. This study supports the findings of Larsen and Stansbury for an earlier day (

*J. Atmos. Terr. Phys.,*1974, 36, 1547–1553) and adds the algebraic relation.

## Abstract

^{−1}) represent thunderstorms, some single-celled and some multi-celled. These were found to be the sources of lightning observed (as “sferics”) by a radio direction finder, frequency 100±50 kHz, located at the radar. The sferics rates of the storms were related closely to other storm parameters by

*L*

*A*

^{1.64}

*r*

^{−1.62}

*L*is the number of sferics observed per minute,

*r*the distance of the storm (km), and

*A*the area (km

^{2}) of the storm region as specified above. This study supports the findings of Larsen and Stansbury for an earlier day (

*J. Atmos. Terr. Phys.,*1974, 36, 1547–1553) and adds the algebraic relation.

## Abstract

Using a CPS-9 radar (wavelength 3.2 cm, beamwidth 1°) in dry snow, radar returns from a layer at an average height of 5000 ft were converted to snowfall rates (taking *Z*∝*R*
^{2.0}) and summed over 36 hr to obtain a map of snowfall amount. This has been compared with a “climat” map based on depth measurements of new fallen snow at 140 climatological stations within 100 mi of the radar, said amounts ranging from under 2 to over 10 inches. For the 5550 mi^{2} area within 42 mi of the radar, the average amount by radar was set equal to the average climat amount. The radar/climat ratio was mapped, with the distribution being log normal. For ranges <42 mi, 68% of the data fell between values of 0.76 and 1.32. For ranges between 42 and 100 mi, 68% fell between 0.63 and 1.60. This scatter is about the same as other workers have found for rain. In the relation *Z* = *aR ^{b}
*, a value for

*b*of 2.0 proved appropriate to this particular storm, with some evidence that a slightly higher value might have been a little better.

## Abstract

Using a CPS-9 radar (wavelength 3.2 cm, beamwidth 1°) in dry snow, radar returns from a layer at an average height of 5000 ft were converted to snowfall rates (taking *Z*∝*R*
^{2.0}) and summed over 36 hr to obtain a map of snowfall amount. This has been compared with a “climat” map based on depth measurements of new fallen snow at 140 climatological stations within 100 mi of the radar, said amounts ranging from under 2 to over 10 inches. For the 5550 mi^{2} area within 42 mi of the radar, the average amount by radar was set equal to the average climat amount. The radar/climat ratio was mapped, with the distribution being log normal. For ranges <42 mi, 68% of the data fell between values of 0.76 and 1.32. For ranges between 42 and 100 mi, 68% fell between 0.63 and 1.60. This scatter is about the same as other workers have found for rain. In the relation *Z* = *aR ^{b}
*, a value for

*b*of 2.0 proved appropriate to this particular storm, with some evidence that a slightly higher value might have been a little better.

## Abstract

Strong evidence, available from the experiments of Nakaya and his co-workers and bolstered by an analogue experiment, supports the argument that type of snow-crystal growth is determined principally by the excess of the ambient vapor density over that at equilibrium with the ice crystal at its own temperature. Changes in crystal habit occur when this vapor-density excess is sufficient to overcome the inhibitions, first to edge growth and secondly to corner growth, that must exist if the edges and corners have higher surface vapor-densities than the flat faces of the crystal. Equilibrium vapor density for liquid water exceeds that for ice by the order of 10 per cent; slight supersaturation, such as can exist in water cloud, will increase this excess considerably.

Ventilation has been neglected in analyzing the Nakaya experiments. Its effect was probably slight, since the ventilation was due to natural convection. The effect should be much greater in the atmosphere, where the ice crystal is falling freely. Some such factor must surely be introduced in the case of the natural atmosphere as compared with the laboratory experiments, for with decreasing air pressure the psychrometric values change, and the available vapor-density excess drops off, varying roughly as the cube root of the pressure.

The presence of water cloud modifies the diffusion field surrounding an ice crystal, the effect increasing with the size of the crystal. Thus cloud can make a significant contribution to the rate of growth of ice crystals by sublimation. Better spectra of cloud-droplet sizes are needed to evaluate this more fully.

## Abstract

Strong evidence, available from the experiments of Nakaya and his co-workers and bolstered by an analogue experiment, supports the argument that type of snow-crystal growth is determined principally by the excess of the ambient vapor density over that at equilibrium with the ice crystal at its own temperature. Changes in crystal habit occur when this vapor-density excess is sufficient to overcome the inhibitions, first to edge growth and secondly to corner growth, that must exist if the edges and corners have higher surface vapor-densities than the flat faces of the crystal. Equilibrium vapor density for liquid water exceeds that for ice by the order of 10 per cent; slight supersaturation, such as can exist in water cloud, will increase this excess considerably.

Ventilation has been neglected in analyzing the Nakaya experiments. Its effect was probably slight, since the ventilation was due to natural convection. The effect should be much greater in the atmosphere, where the ice crystal is falling freely. Some such factor must surely be introduced in the case of the natural atmosphere as compared with the laboratory experiments, for with decreasing air pressure the psychrometric values change, and the available vapor-density excess drops off, varying roughly as the cube root of the pressure.

The presence of water cloud modifies the diffusion field surrounding an ice crystal, the effect increasing with the size of the crystal. Thus cloud can make a significant contribution to the rate of growth of ice crystals by sublimation. Better spectra of cloud-droplet sizes are needed to evaluate this more fully.

## Abstract

For the summer of 1964, precipitation intensity in the vicinity of Montreal, observed by CPS-9 radar, was recorded on constant-altitude maps at six heights. To allow for attenuation (at λ = 3.2 cm) and other radar uncertainties, the distribution with rainfall rate *R* at 5,000 ft was matched to that for one rain gage at the surface. The extent (area × time) in excess of a given *R* decreased rapidly with increasing *R* and with increasing height: a factor 1000 from 0.4 to 100 mm hr^{–1}, a factor 10 per 15,000 ft. The pattern in plan at any height (with resolution limited to about 2 mi in the recorded maps) can be described in terms of cells with intensity decreasing outward approximately exponentially. A logarithmic function of intensity was used: *T* = 1.66 log (*R/R _{0}
*) where

*R*= 0.25 mm hr

_{0}^{–1}. The value of

*T*for a contour bounding a central area

*A*is given by

*T = T*, where

_{c}−x*T*is the maximum and

_{c}*x*= (A/17.5 n.mi.

^{2})

^{1/3}. (With this relation, one can estimate peak intensity from the area bounded by any given intensity.) The number of cells having

*T*greater than a given value of

_{c}*T*, per 10

^{8}n.mi.

^{2}of map area (as for hourly maps of area 20,000 n.mi.

^{2}throughout a 5,000-hr summer) is

*N*, where log

_{0}*N*and

_{0}= 8.8−T−H*H*= height/15,000 ft. As to shape, the maximum and minimum extents were always within a factor 6 of each other. Usually, the area in the horizontal section of a cell decreased with height. Occasionally it increased to a maximum, at about 20,000 ft, as much as four times greater than the area at 5,000 ft. These maxima aloft were generally identifiable with storms reaching 40,000 ft, which is tall for Montreal.

## Abstract

For the summer of 1964, precipitation intensity in the vicinity of Montreal, observed by CPS-9 radar, was recorded on constant-altitude maps at six heights. To allow for attenuation (at λ = 3.2 cm) and other radar uncertainties, the distribution with rainfall rate *R* at 5,000 ft was matched to that for one rain gage at the surface. The extent (area × time) in excess of a given *R* decreased rapidly with increasing *R* and with increasing height: a factor 1000 from 0.4 to 100 mm hr^{–1}, a factor 10 per 15,000 ft. The pattern in plan at any height (with resolution limited to about 2 mi in the recorded maps) can be described in terms of cells with intensity decreasing outward approximately exponentially. A logarithmic function of intensity was used: *T* = 1.66 log (*R/R _{0}
*) where

*R*= 0.25 mm hr

_{0}^{–1}. The value of

*T*for a contour bounding a central area

*A*is given by

*T = T*, where

_{c}−x*T*is the maximum and

_{c}*x*= (A/17.5 n.mi.

^{2})

^{1/3}. (With this relation, one can estimate peak intensity from the area bounded by any given intensity.) The number of cells having

*T*greater than a given value of

_{c}*T*, per 10

^{8}n.mi.

^{2}of map area (as for hourly maps of area 20,000 n.mi.

^{2}throughout a 5,000-hr summer) is

*N*, where log

_{0}*N*and

_{0}= 8.8−T−H*H*= height/15,000 ft. As to shape, the maximum and minimum extents were always within a factor 6 of each other. Usually, the area in the horizontal section of a cell decreased with height. Occasionally it increased to a maximum, at about 20,000 ft, as much as four times greater than the area at 5,000 ft. These maxima aloft were generally identifiable with storms reaching 40,000 ft, which is tall for Montreal.

## Abstract

Average-size distributions for aggregate snowflakes are well represented above D = 1 mm by *N*
_{D} = *N*
_{oe}
^{−AD
} where *D* is the diameter of the water drop to which the aggregate would melt. This is the same equation that Marshall and Palmer (1948) reported for rain, but for rain *N*
_{o} = 8.0 × 10^{3} m^{−3} mm^{−1} and A = 41 *R*
^{−0.21} while for snow *N*
_{o} = 3.8 × 10^{3} R^{−0.87} m^{−3} mm^{−1} and A = 25.5 *R*
^{−0.48} where *R* is in millimeters of water per hour.

The sum of the sixth powers of the (melted) particle diameters in unit volume (*Z*), the mass of snow in unit volume (*M*), and the precipitation rate (*R*) are found to be related by *Z* = 2000 *R*
^{−2.0} and *M* = 250 *R*
^{−0.90}; combining these two gives *Z* = 9.57 × 10^{−3}
*M*
^{−2.2}, with *Z* in mm^{6} m^{−3}, M in mgm m^{−3} and *R* in mm hr^{−1} of water.

The relation *Z* = 2000 R^{−2.0} is in good agreement with *Z* = 2150 R^{−1.8}, an average locus through recently reported Japanese data for aggregate flakes. The relation *Z* = 200 R^{−1.6} for snow, published earlier by the present authors, is thought to be in error due to the method of sampling used at that time. Comparing standard rain and melted-snow distributions of the same R requires that there be considerable break-up of the larger particles when snow turns to rain at the melting level. Further, to explain the observed radar-signal increase from the rain over that from the snow, a considerable increase in *R* at or below the melting level is required.

## Abstract

Average-size distributions for aggregate snowflakes are well represented above D = 1 mm by *N*
_{D} = *N*
_{oe}
^{−AD
} where *D* is the diameter of the water drop to which the aggregate would melt. This is the same equation that Marshall and Palmer (1948) reported for rain, but for rain *N*
_{o} = 8.0 × 10^{3} m^{−3} mm^{−1} and A = 41 *R*
^{−0.21} while for snow *N*
_{o} = 3.8 × 10^{3} R^{−0.87} m^{−3} mm^{−1} and A = 25.5 *R*
^{−0.48} where *R* is in millimeters of water per hour.

The sum of the sixth powers of the (melted) particle diameters in unit volume (*Z*), the mass of snow in unit volume (*M*), and the precipitation rate (*R*) are found to be related by *Z* = 2000 *R*
^{−2.0} and *M* = 250 *R*
^{−0.90}; combining these two gives *Z* = 9.57 × 10^{−3}
*M*
^{−2.2}, with *Z* in mm^{6} m^{−3}, M in mgm m^{−3} and *R* in mm hr^{−1} of water.

The relation *Z* = 2000 R^{−2.0} is in good agreement with *Z* = 2150 R^{−1.8}, an average locus through recently reported Japanese data for aggregate flakes. The relation *Z* = 200 R^{−1.6} for snow, published earlier by the present authors, is thought to be in error due to the method of sampling used at that time. Comparing standard rain and melted-snow distributions of the same R requires that there be considerable break-up of the larger particles when snow turns to rain at the melting level. Further, to explain the observed radar-signal increase from the rain over that from the snow, a considerable increase in *R* at or below the melting level is required.

## Abstract

Precipitation particles which fall from a source aloft through a wind shear are sorted as to size, the largest particles reaching the ground closest to the generating source, the smaller particles further from it. If precipitation is assumed to form continuously in cloud, with a fixed size distribution, this sorting affects significantly the size distributions to be observed below the cloud, and so the relationship between the precipitation rate *R* and the radar scattering-parameter *Z* (which is ∑*D*
^{6}, where *D* is the diameter of a raindrop or the water drop to which a snowflake would melt, and the summation is over unit volume).

As an approximation to a small isolated shower, a horizontal generating element has been taken, of linear extent 1.6 kilometers in the direction of the wind shear. The quantities *R* and *Z* tend to be less at the ground than in the generating region, the size distributions remaining the same except for upper and lower limits of size imposed by the sorting. Several values of *R* and *Z* in the generating region have been considered, all obeying *Z* = *aR ^{b}
*. The

*Z/R*data below the showers have been found to be widely scattered about a locus

*Z*=

*a′Rb′,*where a′ >

*a*and

*b*′ <

*b*. If a given

*R*is obtained at the ground on many occasions involving widely varying values of

*R*aloft, the corresponding values of

*Z*are found to differ by as much as a factor of twelve. Findings regarding an isolated shower agree with the observations of Atlas and Plank (1953).

As an approximation to “continuous” snow and rain, a regular array of snow-generating elements was considered. In this, there was one element of linear extent one mile every five miles. A size sample taken at the ground over a time interval less than a minute would then yield a discontinuous distribution, with a small range of sizes contributed by each cell. The distribution of a sample collected over several minutes would be fairly smooth and resemble that aloft except as to scale. In any case, *Z* and *R* at the ground would be reduced by a factor of approximately five, compared with the values in the generating elements. This introduces a scatter in the *Z/R* data at the ground, and a shift in the *Z/R* locus, similar to those noted for the case of an isolated shower.

## Abstract

Precipitation particles which fall from a source aloft through a wind shear are sorted as to size, the largest particles reaching the ground closest to the generating source, the smaller particles further from it. If precipitation is assumed to form continuously in cloud, with a fixed size distribution, this sorting affects significantly the size distributions to be observed below the cloud, and so the relationship between the precipitation rate *R* and the radar scattering-parameter *Z* (which is ∑*D*
^{6}, where *D* is the diameter of a raindrop or the water drop to which a snowflake would melt, and the summation is over unit volume).

As an approximation to a small isolated shower, a horizontal generating element has been taken, of linear extent 1.6 kilometers in the direction of the wind shear. The quantities *R* and *Z* tend to be less at the ground than in the generating region, the size distributions remaining the same except for upper and lower limits of size imposed by the sorting. Several values of *R* and *Z* in the generating region have been considered, all obeying *Z* = *aR ^{b}
*. The

*Z/R*data below the showers have been found to be widely scattered about a locus

*Z*=

*a′Rb′,*where a′ >

*a*and

*b*′ <

*b*. If a given

*R*is obtained at the ground on many occasions involving widely varying values of

*R*aloft, the corresponding values of

*Z*are found to differ by as much as a factor of twelve. Findings regarding an isolated shower agree with the observations of Atlas and Plank (1953).

As an approximation to “continuous” snow and rain, a regular array of snow-generating elements was considered. In this, there was one element of linear extent one mile every five miles. A size sample taken at the ground over a time interval less than a minute would then yield a discontinuous distribution, with a small range of sizes contributed by each cell. The distribution of a sample collected over several minutes would be fairly smooth and resemble that aloft except as to scale. In any case, *Z* and *R* at the ground would be reduced by a factor of approximately five, compared with the values in the generating elements. This introduces a scatter in the *Z/R* data at the ground, and a shift in the *Z/R* locus, similar to those noted for the case of an isolated shower.

## Abstract

According to Rayleigh scattering theory for small spheres, back scattering is proportional to |*K*
^{2}
*Z* where *K* is the dielectric factor and *Z* is the sum of the sixth powers of the diameter *D*. For small non-spherical particles of uncertain density, a similar quantity can be used: |*K*
_{1}
^{2}
*ZS*, where *K*
_{1} is the dielectric factor for the material when reduced to unit density, and *Z* = ∑*D*
_{1}
^{6}, where *D*
_{1} is the diameter of the particle when reduced to a sphere of unit density; *S* is a shape factor which for snow remains between 1 and 1.5.

An analysis of Langille and Thain's (1951) radar observations on snow shows fairly good correlation between *Z* and the snowfall *R*, particularly when considered one day at a time. An overall *Z* = *Z*(*R*) relation for snow for all days of Langille's observations is found to agree with that previously established for rain (Marshall, Langille and Palmer, 1947). That is, equal precipitation rates *R*, whether rain or snow, give equal values of *Z*.

The transition at the melting level in the case of “continuous” rain is considered in the light of this finding. Rapid aggregation amongst the raindrops and wet snowflakes in the melting region could account for the necessary differences in size distribution between snow and rain of the same precipitation rate.

Marshall and Palmer (1949) have suggested that all size distributions for precipitation are exponential when plotted as number against diameter. Taking as a fair approximation for rain that the distribution curves belong to a single family, one may establish the particular distribution by a measurement of *R*. When this approximation is less valid, as it appears to be for snow, one may still establish the particular exponential distribution by measuring *Z* and *R* simultaneously.

## Abstract

According to Rayleigh scattering theory for small spheres, back scattering is proportional to |*K*
^{2}
*Z* where *K* is the dielectric factor and *Z* is the sum of the sixth powers of the diameter *D*. For small non-spherical particles of uncertain density, a similar quantity can be used: |*K*
_{1}
^{2}
*ZS*, where *K*
_{1} is the dielectric factor for the material when reduced to unit density, and *Z* = ∑*D*
_{1}
^{6}, where *D*
_{1} is the diameter of the particle when reduced to a sphere of unit density; *S* is a shape factor which for snow remains between 1 and 1.5.

An analysis of Langille and Thain's (1951) radar observations on snow shows fairly good correlation between *Z* and the snowfall *R*, particularly when considered one day at a time. An overall *Z* = *Z*(*R*) relation for snow for all days of Langille's observations is found to agree with that previously established for rain (Marshall, Langille and Palmer, 1947). That is, equal precipitation rates *R*, whether rain or snow, give equal values of *Z*.

The transition at the melting level in the case of “continuous” rain is considered in the light of this finding. Rapid aggregation amongst the raindrops and wet snowflakes in the melting region could account for the necessary differences in size distribution between snow and rain of the same precipitation rate.

Marshall and Palmer (1949) have suggested that all size distributions for precipitation are exponential when plotted as number against diameter. Taking as a fair approximation for rain that the distribution curves belong to a single family, one may establish the particular distribution by a measurement of *R*. When this approximation is less valid, as it appears to be for snow, one may still establish the particular exponential distribution by measuring *Z* and *R* simultaneously.