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- Author or Editor: Alexis B. Long x

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## Abstract

Probabilistic and statistical concepts are used to examine how the number of hail observing sites within a region affects the accuracy of estimates of 1) the mean point frequency of hail within the region, 2) the overall regional frequency of hail, and 3) the area covered by individual hailfalls. A practically useful relationship *Nā*/*A*
*N*, to the mean area *ā* of the individual hailfalls and to the area *A* of the region. The error in estimating the mean frequency *n*
^{−1/2}, where *n* is the number of sites placed within a region. If within a region there are proportionally more large hailstorms or if most of the area covered by hail is commonly due to a few large hailstorms, then fewer sites will be needed to estimate the mean point hail frequency. Of the 16 hailfalls detected by the 660 km^{2} 1976 National Hail Research Experiment (NHRE) network of 603 hailpad sites, it is found, using a simple probabilistic expression, that 12 of the hailfalls still would have been detected using only 50 sites. The smaller hailfalls would have been the first to go undetected. There are diminishing returns in fielding sufficient instruments to detect all, or almost all, of the hailfalls in a region. For hailfalls with the lognormal distribution of areas observed by NHRE, the number of instruments needed increases exponentially with the number of hailfalls to be detected. A formula is derived for a correction to be made to the observed regional frequency of hailfalls of a given size so as to obtain the true frequency. For random networks the coefficient of variation of an estimate of the area of a hailfall is proportional to *n*
^{−1/2}. For a hailfall less than one-fifth as large as the instrumented region in which it lies, the coefficient of variation of an estimate of its area approximately equals *n _{h}
*

^{−1/2}, where

*n*is the expected number of sites within the hailfall.

_{h}## Abstract

Probabilistic and statistical concepts are used to examine how the number of hail observing sites within a region affects the accuracy of estimates of 1) the mean point frequency of hail within the region, 2) the overall regional frequency of hail, and 3) the area covered by individual hailfalls. A practically useful relationship *Nā*/*A*
*N*, to the mean area *ā* of the individual hailfalls and to the area *A* of the region. The error in estimating the mean frequency *n*
^{−1/2}, where *n* is the number of sites placed within a region. If within a region there are proportionally more large hailstorms or if most of the area covered by hail is commonly due to a few large hailstorms, then fewer sites will be needed to estimate the mean point hail frequency. Of the 16 hailfalls detected by the 660 km^{2} 1976 National Hail Research Experiment (NHRE) network of 603 hailpad sites, it is found, using a simple probabilistic expression, that 12 of the hailfalls still would have been detected using only 50 sites. The smaller hailfalls would have been the first to go undetected. There are diminishing returns in fielding sufficient instruments to detect all, or almost all, of the hailfalls in a region. For hailfalls with the lognormal distribution of areas observed by NHRE, the number of instruments needed increases exponentially with the number of hailfalls to be detected. A formula is derived for a correction to be made to the observed regional frequency of hailfalls of a given size so as to obtain the true frequency. For random networks the coefficient of variation of an estimate of the area of a hailfall is proportional to *n*
^{−1/2}. For a hailfall less than one-fifth as large as the instrumented region in which it lies, the coefficient of variation of an estimate of its area approximately equals *n _{h}
*

^{−1/2}, where

*n*is the expected number of sites within the hailfall.

_{h}## Abstract

Some results of the first (1988) Australian Winter Storms Experiment are described. The results shed light on precipitation-enhancement opportunities in winter cyclonic storms interacting with the Great Dividing Range of southeast Australia. The results come from analysis of supercooled liquid water amounts provided by a dual-wavelength microwave radiometer, atmospheric structure from Omegasondes, and precipitation amounts from a large number of tipping-bucket gauges. With these data it is possible to calculate and compare two of the terms in a condensed-phase water budget over a cloud-seeding target area in the Great Dividing Range. The two terms are the horizontal flux of supercooled liquid cloud water entering the budget volume and the vertical precipitation flux at ground level out of the volume. The budget terms have implications for the amount of extra precipitation that may result from seeding. It is found that the amount depends on the frontal or postfrontal stage of activity in the target area and on the wind direction with respect to the mountainous terrain.

## Abstract

Some results of the first (1988) Australian Winter Storms Experiment are described. The results shed light on precipitation-enhancement opportunities in winter cyclonic storms interacting with the Great Dividing Range of southeast Australia. The results come from analysis of supercooled liquid water amounts provided by a dual-wavelength microwave radiometer, atmospheric structure from Omegasondes, and precipitation amounts from a large number of tipping-bucket gauges. With these data it is possible to calculate and compare two of the terms in a condensed-phase water budget over a cloud-seeding target area in the Great Dividing Range. The two terms are the horizontal flux of supercooled liquid cloud water entering the budget volume and the vertical precipitation flux at ground level out of the volume. The budget terms have implications for the amount of extra precipitation that may result from seeding. It is found that the amount depends on the frontal or postfrontal stage of activity in the target area and on the wind direction with respect to the mountainous terrain.

## Abstract

Two Australian winter mountain storm field research projects were conducted by the Commonwealth Scientific and Industrial Research Organisation Division of Atmospheric Research and the Desert Research Institute Atmospheric Sciences Center in the austral winters of 1988 and 1990. These projects gained information about winter storms in support of the ongoing Melbourne Water randomized cloud seeding experiment aimed at increasing runoff into Melbourne's main water supply, the Thomson Reservoir. This paper discusses some of the 1988 instrumentation data. One variable of interest is the precipitation augmentation potential π. It is the difference between (a) the horizontal supercooled liquid water flux in the clouds crossing the mountains and (b) the vertical precipitation flux at the surface from the clouds. These fluxes are based on calculations of supercooled liquid water depth in clouds with a microwave radiometer, Omegasonde wind velocity, and rates of precipitation from gauges. It was found that π varies systematically during a winter storm. The greatest potential occurs in the post-cold-frontal stage of a storm when the cloud-top temperature is warm and about −12°C and the wind direction of 240° is approximately orthogonal to the main southwest face of the predominant orographic feature, Baw Baw Plateau, of the study area. The potential is significantly less during the prefrontal and frontal stages, with cloud-top temperatures of about −35°C and a wind direction of about 3O0° parallel to the Baw Baw Plateau. The results show that cloud seeding would have the greatest benefit in the postfrontal stage.

## Abstract

Two Australian winter mountain storm field research projects were conducted by the Commonwealth Scientific and Industrial Research Organisation Division of Atmospheric Research and the Desert Research Institute Atmospheric Sciences Center in the austral winters of 1988 and 1990. These projects gained information about winter storms in support of the ongoing Melbourne Water randomized cloud seeding experiment aimed at increasing runoff into Melbourne's main water supply, the Thomson Reservoir. This paper discusses some of the 1988 instrumentation data. One variable of interest is the precipitation augmentation potential π. It is the difference between (a) the horizontal supercooled liquid water flux in the clouds crossing the mountains and (b) the vertical precipitation flux at the surface from the clouds. These fluxes are based on calculations of supercooled liquid water depth in clouds with a microwave radiometer, Omegasonde wind velocity, and rates of precipitation from gauges. It was found that π varies systematically during a winter storm. The greatest potential occurs in the post-cold-frontal stage of a storm when the cloud-top temperature is warm and about −12°C and the wind direction of 240° is approximately orthogonal to the main southwest face of the predominant orographic feature, Baw Baw Plateau, of the study area. The potential is significantly less during the prefrontal and frontal stages, with cloud-top temperatures of about −35°C and a wind direction of about 3O0° parallel to the Baw Baw Plateau. The results show that cloud seeding would have the greatest benefit in the postfrontal stage.

## Abstract

This paper reports on work carried out in the National Hail Research Experiment (NHRE) on hailpad materials, on procedures for reducing hailpad data, and on hailpad calibration. A recommendation is made for a pad constructed of 2.5 cm thick type-SI Styrofoam (manufactured by Dow Chemical USA) and sprayed with a 25–50 *μ*m coating of white latex paint for protection from the deteriorating effects of sun-light. Calibration of the hailpad provides a relation between the minor axis of a dent in the pad and the dimensions of the stone producing the dent. It is recommended that measurements of the minor axis be categorized in size intervals no wider than 4 mm.

The NHRE laboratory technique for calibrating hailpads involves simulating a hailstone impact by dropping a steel sphere onto a pad from a height such that the impact kinetic energy achieved by the sphere equals that of a hailstone of equal diameter falling onto the pad in an environment with known horizontal wind. The pad is tilted to preserve the stone impact angle found in nature. A second-degree polynomial in sphere diameter *D* satisfactorily describes the calibration relation between *D* and the dent minor axis. Application of the calibration relation developed for the particular case of no wind to hailpads which have been hit by hail falling in a wind leads to an overestimate of hailstone diameter of approximately 0.5–1% per meter per second of wind speed. This effect of the wind is about twice as large as that found by others.

A theoretical expression is developed that explicitly relates the minor axis of a dent produced by a sphere to the diameter of the sphere. Two controlling parameters in this expression are the impact kinetic energy of the sphere and a factor *p*, with dimensions of pressure, which quantitatively embodies the response of a pad to a sphere impact. The effect of variations in *p* on the sphere diameter derived from dent minor axis and information supplied by Dow Chemical USA on possible variability in the compressive modulus of Styrofoam between manufacturing batches together suggest that the user of hailpads obtains a one time all the foam he may need for his work.

## Abstract

This paper reports on work carried out in the National Hail Research Experiment (NHRE) on hailpad materials, on procedures for reducing hailpad data, and on hailpad calibration. A recommendation is made for a pad constructed of 2.5 cm thick type-SI Styrofoam (manufactured by Dow Chemical USA) and sprayed with a 25–50 *μ*m coating of white latex paint for protection from the deteriorating effects of sun-light. Calibration of the hailpad provides a relation between the minor axis of a dent in the pad and the dimensions of the stone producing the dent. It is recommended that measurements of the minor axis be categorized in size intervals no wider than 4 mm.

The NHRE laboratory technique for calibrating hailpads involves simulating a hailstone impact by dropping a steel sphere onto a pad from a height such that the impact kinetic energy achieved by the sphere equals that of a hailstone of equal diameter falling onto the pad in an environment with known horizontal wind. The pad is tilted to preserve the stone impact angle found in nature. A second-degree polynomial in sphere diameter *D* satisfactorily describes the calibration relation between *D* and the dent minor axis. Application of the calibration relation developed for the particular case of no wind to hailpads which have been hit by hail falling in a wind leads to an overestimate of hailstone diameter of approximately 0.5–1% per meter per second of wind speed. This effect of the wind is about twice as large as that found by others.

A theoretical expression is developed that explicitly relates the minor axis of a dent produced by a sphere to the diameter of the sphere. Two controlling parameters in this expression are the impact kinetic energy of the sphere and a factor *p*, with dimensions of pressure, which quantitatively embodies the response of a pad to a sphere impact. The effect of variations in *p* on the sphere diameter derived from dent minor axis and information supplied by Dow Chemical USA on possible variability in the compressive modulus of Styrofoam between manufacturing batches together suggest that the user of hailpads obtains a one time all the foam he may need for his work.

## Abstract

The hailstone size (diameter) distributions measured by hailpads during the 1972-74 randomized seeding experiment of the National Hail Research Experiment are analyzed statistically for evidence of seeding effects and differences from year to year. Two approaches are taken, one comparing the entire empirical size distributions on seed days and on control days and the other comparing the mean diameters. The latter is based on the consistency with the exponential distribution (truncated at a prescribed minimum diameter), since the exponential distribution can be characterized completely by the difference between the mean diameter and the minimum diameter. Both approaches yield statistically significant results (10% level) only for 1974, when the hailstones were larger on seed days than on control days on the average. This may have resulted from the addition of seeding by rockets in 1974 or from differences in the hailpads used in that year. However, the physical hypothesis for the experiment predicted *smaller* stones on seed days; that tendency did appear in 1973 (though not significantly) and the difference was negligible in 1972.

## Abstract

The hailstone size (diameter) distributions measured by hailpads during the 1972-74 randomized seeding experiment of the National Hail Research Experiment are analyzed statistically for evidence of seeding effects and differences from year to year. Two approaches are taken, one comparing the entire empirical size distributions on seed days and on control days and the other comparing the mean diameters. The latter is based on the consistency with the exponential distribution (truncated at a prescribed minimum diameter), since the exponential distribution can be characterized completely by the difference between the mean diameter and the minimum diameter. Both approaches yield statistically significant results (10% level) only for 1974, when the hailstones were larger on seed days than on control days on the average. This may have resulted from the addition of seeding by rockets in 1974 or from differences in the hailpads used in that year. However, the physical hypothesis for the experiment predicted *smaller* stones on seed days; that tendency did appear in 1973 (though not significantly) and the difference was negligible in 1972.

## Abstract

An extensive statistical analysis is made of the precipitation data collected during the randomized seeding experiment conducted by the National Hail Research Experiment during 1972-74, aimed at testing the feasibility of diminishing hail by seeding with silver iodide. The major conclusion is that no effect of seeding is detected at the 10% significance level. This is true regardless of whether hail or rainfall response variables are considered, which of two methods of obtaining daily values for the response variables over the target area is used, or what distribution, if any, is assumed for the variables. Even though the ratios of hailfall or rainfall on seed days to those on control days are generally greater than 1, the confidence intervals attached to these ratios are so large, because of the large natural variance in each response variable and the small sample sizes, that the true underlying seeding effects could in every case have ranged from substantial decreases to large increases. The large confidence intervals emphasize the necessity of large sample sizes, large experimental areas or effective covariates for obtaining definitive results in precipitation modification experiments.

## Abstract

An extensive statistical analysis is made of the precipitation data collected during the randomized seeding experiment conducted by the National Hail Research Experiment during 1972-74, aimed at testing the feasibility of diminishing hail by seeding with silver iodide. The major conclusion is that no effect of seeding is detected at the 10% significance level. This is true regardless of whether hail or rainfall response variables are considered, which of two methods of obtaining daily values for the response variables over the target area is used, or what distribution, if any, is assumed for the variables. Even though the ratios of hailfall or rainfall on seed days to those on control days are generally greater than 1, the confidence intervals attached to these ratios are so large, because of the large natural variance in each response variable and the small sample sizes, that the true underlying seeding effects could in every case have ranged from substantial decreases to large increases. The large confidence intervals emphasize the necessity of large sample sizes, large experimental areas or effective covariates for obtaining definitive results in precipitation modification experiments.