r Reprinted [rom ]OURNAL o .. ApPLlElJ 1v1cTEùROLOGY, VoI. 51, No.6, December, 1970, pp. 903-91ù

American Meteorologica1 Society Printed iD U. S. A.

Measurements of Local Density in Artificial and Natural Hailstones

F RANCO PRODIl

National Cellter lor Atmosplzeric Researclt,' Boulder, Colo.

(Manuscript received 12 May 1970, in revised form 25 August 1970)

ABSTRACT

Local density measurements were performed in the internaI structure of bailstones by means of photo­metric observations on x-ray micrographs of th in slices. Comparison with the results of measuremen ts per­formed by the same technique on ice artificially grown by accretion shows that dry growth near the net limit or dry growth wetted in a fina l stage is probably the most common condition of growtb in natural hai lstones. The technique is also suggested as a method for obtaining accurate quantitative data on air bubble size and concentrations which are needed in relating structure to growtb conditions. As a cross check, measurements of the total density by tbc usual im mersion tecbnique were also performed on hailstones from tbe same hai/­fa ll as those examined by the x-ray absorption tecbnique.

1. Introduction

Hailstone density, which depends on the content of trapped air, 1S generally determined from measure­ments of weight and external volume (List, 1958; Vittori and di Caporiacco, 1959; Mossop and Kidder, 1961; Macklin, 1962). The mean value of tbe density tbus obtained does not account for the internallayered structure of the hai lstone and tbe possible corresponding fluctuations in local density. Moreover, wben tbe volume is determined by indirect measurements of bail­stone buoyancy in certain liquids, difficulties arise because of sudace cavities and channels which allow the liquid to penetrate in to tbe interior. It was suggested (Prodi, 1969) tbat measurements of local density of ice by densitometric scanning of x-ray micrograpbs of bail­stone slices sbould produce areaI picture of tbe inner density distribution.

Tbis paper gives results of measurements of ice den­sity in natural bailstones and of tbose grown in a hai! tunnel (Prodi el al., 1970) .

2. Experimental technique

The absorption of a parallel monocbromatic x-ray by a bomogeneous material of density p and thickness x is described by Lambert's law as

(1)

where lo and I denote the intensity of incident and

1 On leave from the Istituto di Fisica dell' Atmosfera del CNR, Sezione di Bologna, Italy.

2 Tbe National Center far Atmospheric Research is sponsored hy the National Science FOllndation .

transmitted radiation, respectively, and }.l / p denotes tbe mass absorption coefficient of the materia!.

In a sample of thickness XA, a void will reduce the total thickness to XB (see Fig. 1). Calling PT the density of the region A corresponding to dear ice (sample free of voids) and PH the density of the region B containing the void (air bubbles in our case), the ratio of the two densities is equal to the ratio of the thicknesses of the sample in the two regions, i.e.,

PH X e

PJ XA

(2)

Thus, from Eq. (1) we have

X B In (Io/In) -=----, X A In (Io/ lA)

(3)

where the absorption coefficient disappears. Eq. (1) applies only to individuaI monochromatic components of a polychromatic beam. I n our experiment, a contin­uous x-ray spectrum was used because of the high inten­sities required by fine-grain photographic emulsions, so that an integrai fonn of Eq. (1) should be tbeoretically required. However, within tbe conditions of our mea-

- SAMPLE

==::===::.:====:::::;:=======.- PLATE 00 D. 08

FIG. 1. X-ray absorption through a sample of bomogeneo,:,s materia/. The photographic plate, which was covered by a thm plastic sheet , was in direct contact wilh the sample .

904 ]OURNAL OF APPLIED METEOROLOGY VOLUME 9

surements the direct application of Eq . (1) is adequate. In addi tion, the use of a region of clear ice as a reference system overcomes the disadvantage of the dependence of the photographic response on the wavelength.

The photographic density D is a fun ction of the photographic exposure E which can be expressed as

E = It, (4)

where t is the exposure time. For a certain photographic emulsion

D D -Y =--=---,

logE 10g(Il) (5)

where -y defines the response characteristic of the film. For the plates (Kodak High Resolulion) -y is constant in the range of densities encountered. Thus, Eq. (3) may be expressed in terrns of photographic deosity, i.e.,

(6)

where Do, DA, Do are the measured values of photo­graphic densi ty in regions ou tside the samçle, in the clear ice reference region, aod in the hailstone sample region, respectively.

The local densitv of the hailstone slice in each area inspected by the d~nsitometer is given by

(7)

The value 0.917 gm cm- 3 was used for Pr, the deosity of clear bu\k ice.

The values of photographic density Dii, correspond­ing to the region free of voids, were taken at the poly­crystalline bu\k ice embryo in the artificial slices, or at small regions of appareotly transparent ice io the hai l­stone slices.

The experimental procedure was basically similar to that used io previous work (Prodi, 1969) . The hailstone sample to be aoalyzed was sawed and slices wereobtained which were then worked on a microtome. The thickness of the slices varied from 1-3 nm1 from sample to sample. The prepared slice was placed in a refrigerated chamber and a microradiograph of the slice was taken. The x-ray equipment used was the Raditluor 360 (Torr X-ray Corp.) with 0.35-nm1 focal spot size. Excitation poten­tials varied from 40-90 kV depending on the thickness of the sample, the exposure time, and the source-to­sample distance. The cathode current was 3 mA. The photographic density of the absorption image obtained 00 the radiograph was measured using a photomultiplier type microdensitometer of high sensit ivity (Aminco Photomultiplier Microphotometer Assembly). The mi­croradiograph slide was placed on the micrometric sup­port of a microscope on which the sensor of the densi-

tometer had been previously mounted. The visible a:·ea of the micrograph with the objective lenses uscd was a circle 0.4 mm in diameter. Observin g at each 0.5 11m1 cf microscopic in crement, almost the entire region was ex­amined and its topography was defined in tenns of point-by-poin t density. The density results are given in mean values of individuai la .l'ers to better correlate them with the internai features and with the geometry of the hailstone. However, each densitometric observa­tion of an arbitrary small area gives a local value of the density from Eq. (7).

The main experimental errors include tbe nonhomo­geneity in intensity of the x-ray's originai beam, the granularity of the photographic emulsion, the errors inherent in the photometric measurements, and the variations of the thickness in both the sample and the plastic sheet covering the photographic emulsion.

The nonhomogeoeity in intensity of the originai x-ray beam was tested by photometric measurement of the photographic density on the plate in the area surround­ing the sample. These measurements, which incidentally give the value of Do to be introduced in Eq . (7), diù not differ more than the read in g error of the instrull1ent in most of the examined p·at :s. When a dilTerence was ob­served, the values in the sample area were corrected accordingly.

The graoularity of the photographic emulsion is a source of m'nor error for the plates that were used and for the magoification at which the readings were taken.

The error in individuai reaùing of photographic den­sity can be attributed to the reading error of the instru­ment. Since dilTerences in photographic density as low as 0.005 are easily detected, the error due to the photo­metri c procedure is less than 1%.

D uring any operation of sawing and shaving down a· pIane surface, melting and refreezing which couU alter the local density of the ice were avoidecl. A microtome was used in working the slices to obtain extremely pIane surfaces; but this procedure does not insure an exact parallelism betweeo the two piane Sllliaces, and some compensation is needed for error due to the variations in sample thickness.

Two ways for reduciog this source of error have been followed. The th ickness of the slice was measured with high accuracy alI along the periphery and the photo­metric values corrected for the measured difiercnces in thickoess. A 20 J1. variation in thicknesss on a 2 nun thick slice produces a further error of 1%, which can largely be reduced if more reference regions are available in the slice. When circular symmetry WitS noticeable (as in artificia l and occasionally in natural ha ilstones), mea­surements were performed along different radiaI paths and the mean values calculated for each la yer. A drastic, although more complex, method of overcoming the thickness varia tion error was to introduce a full ring of a ir-free bulk ice ali around the sample slice as a contin­uous reference system. The whole hailstone was wrapped into an extremely thin plastic sheet and placed in a

OECEMDER 1970 FRANCO PRODI 905

'" ' E u "­q>

r " t- .

'(/J

Z w o

FIG. 2. Density diagram, reUected light picture, and x-ray micro);raph of ice accreted in dry cOlldilions on a polycrystalline bulk ice cylinder.

plas tic cylinder a few millimeters larger in diameter than the hailstone. Supercooled air-free water was poured into the cylinder and completely frozen around the hail­stone. The resulting ice cylinder was sawed and micro­tomed wi th the embedded bailstone inside; tbe external ring of clear ice in tbe final sIi ce had tbe same tb ickness as the sample. An example of this procedure is given in Fig. 4. The regions between clear ice ring and the bail­stone indicated by the stars are air inclusions trapped in wrapping the hailstone.

The use of thick slices reduces the rela tive error and is thus p refe rable. However, an upper limi t to the thick­ness is prescribed by the intensilies required in the originai x- ray be:tm a·nd by the resolution obtained in exposing the internai features of tbe bailstone.

3. Results and discussion

In the areas examined, mean values of density were plotted vs distances measured on a straight line which startcd from or passed throllgh the hailstone embryo, or th rollgh the axis of cylindcrs of artificial growth. The areas on which the average density was calculated were frequenti)' chosen in correspondcnce with morphological variations of the sample or with peculiar air bubble con-

figurations visible on the micrograph. The irregular boundary between layers sometimes obstructed tbis correspondence.

Pictures of tbe sample and/or micrographs were combined witb density diagrams for direct comparison of average values with the corresponding areas. Tbe results on ice accreted in the tunnel are given first (Figs. 2-3). The conditions of growth were sirnilar to those reported in a previous work (Prodi et al., 1970).

The density of ice accreted in dry conditions (Fig. 2) was measured, taking the ai l'-free bu\k ice embryo as a reference system and assigning it the density of pure ice. The mean values of tbe density in tbis case were mucb lower than that of bulk ice and decreased with tbe radiaI distance.

It was cxpected that density would decrease as tbe distance from the axis increased, following the findings of Macklin (1962) wbo expressed the density of accreted ice as a fun ction of (n'o)IT ., r being tbe median drop volume radius, 1'0 the impact speed, and T, the mean temperature (0C) of the accreting surface. Tbe impact velocity Vo decreased with the increasing diameter of the deposi t, a lthough the air speed in tbe tunnel and the size distribution of droplets were unchanged during accretion. Macklin interpreted tbe different densities

906 JOURNAL 01' APPLIED METEOROLOGY

VOLUME 9

FIG. 3. Radiai density diagram, reflected light picture, and x-ray micrograpb or ice accreted in wet con­ditions (layer a-bl, dry wetted conditions (layer b-c) and wet conditions (layers c-d and d-e) on a poly­crystalline bulk ice cylinder.

as an effect of the distortion, spreading, and varying arrangement of the spherical droplets at different im­pact velocities. A distortion and deformation effect of droplets was confirmed by the density value of accreted ice near the embryo (0,854 gm cm-a), a value which is much higher than the 0.69 gm cm-a computed for a dose packed structure of perfect spheres. Other significant

FIG. 4. Density diagram, reflected light picture, and x-ray micrograpb 01 a hailstone slice [rom Cbadron, Neb., 7 June 1967. Tbe ring of clear reference ice is visible around tbe hailstone. Examples of t,,"o individuai readings (in areas 1 aod 2) are given witb tbe corresponding values 01 tbe locaJ density.

effects on density appear to be the formation of pro­tuberances and lobes which have a capture efficiency higher than the adjacent regions, leading to fonnation of long channels. It is a lso possible that in the existing layers an increase of density Occurs during growth of the next layer. The micrographic technique makes possible a separate evaluation of these effects by giving a point­by-point density value, thus aV;Jiding tbe need to define the total value of each accretion.

Fig. 3 shows the results corresponding to an alternate growth in wet-dry-wet conditions. Wet growth layers (a-b and c-e) have an average density value (0.909 gm cm-a) dose to that of the bulk ice of the polycrystal­line embryo; a minor decrease of density (0.904 gm cm-a) is noticeable in the outer layer (d-e) correspond­ing to a series of concentric cirdes of released bubbles (distance between cirdes, }.""'0.3 rom). The density of the former dry growth layer (b-c in Fig. 2), after the final freezing of the superimposed wet one, increased from 0.720 (mean value corresponding to that radiaI distance in the pure dry growth) to 0.823 gm cm-a (mean value in the layer b-c in Fig. 2); these values were similar to those observed in natural hailstones. Introducing the concept of spongy growth, List (l961a) attributed the process to two mechanisms: spongy growth may Occur initialiy, or water may seep into a previously formed porous structure. Both mechanisms are demonstrated in Fig. 3 where results show a com­plete difference in density and bubble distribution of the resulting ice. ~

Density measures on adjacent regions of slices from natural hailstones are shown in Figs. 4-6.

DECEMBER 1970 FRANCO PRODI

FIG. 5. Density diagram, reflected light picture, and x-ray micrograph of a hailstone slice Lrom New Raymer, Colo., 10 June 1969.

907

H ailstones were collected and analyzed from different precipi tatioos to observe the widest range of growth condi tioos. A concise list of results on each hailstone is given subsequently.

A slice was taken from a hailstone collected at Chadron, Neb., on 7 June 1967. Values of density corre­sponding to concentri c la yers of the rnicrograph are shown in Fig. 4. They continuously decrease from the

FIG. 6. Density diagram and reflected light picture of a hails tone slice from Kansas City, Kans., 21 June 1969.

908 ]O URNAL OF APPLIED METE O R O L O G Y VOLUME 9

TADLE 1. Total density values or hai lstone samples from tbe western Crea t rlains area.

Analysis of bailstone by the immersion technique T otal density

T otal density \Veight correcte<.l for by immersion alter tbc elfect of

techn ique Weight im mersion penetra l ion

Totul density eSlimaLed by

x-ra)' al>sorplion Lechniquc· (gm cm-') Hailfall (gm cm-') (gm) (gm) (gm cm- ' )

Chadron, !\eb. 7 Ju ne 1967 0.860 21.23 21. 77 0.838 0.828

Boulcler, Colo. 1 July 1967 0.865 16.89 17.43 0.839 0.845**

Niwot, Colo. 10 June 1969 0.864 21.02 21.75 0.834 0.857**

0.8iO 8.27 8.38 0.856 Chadron, Neb.

12 Aprii 1967 0.838*'

New Raymer, Colo. lO J une 1969

Kansas City, Kans. 29 June 1969

0.849

0.867

* The samples llsed to obtain these values are not the same hailstones used by the immersion technique. ** PicLures and IDeai deusity va lues are not reported in the text. .

external layer (0.848 gm cm-3) to the embryo (0.803 gm on-3) . T wo diverging values of local density corresp:md­ing to DA mm diameter regions are also shown.

A slice taken from a hailstone of 29 mm diameter, collected a t N ew Raymer, Colo., on 10 J une 1969, showed :I low density embryo (0.708 gm Cln-3) due to large air bubbles. Ncvertheless, this value rose to 0.829 gm Cln - 3 when the surrounding area was measured together with tbe embryo. There was also a general decrease of density from the periphery toward the center (Fig. 5)_

A slice taken from a large hailstone collected a t Kansas City, K ans. , on 21 .lune 1969 showed asequence of op~que and transparent layers. No strong varia tion in density was observable in the morphologically differ­ent layers. D ue to a few large bubbles in the transparent layer (b-a) , it showed a lower density. The embryo region had a higher density (0.881 gm cm-3) , while a generai decrease occurred from the periphery toward the center of.the slice. I n the reBected light picture it was possible to observe a peculiar array of jpterrupted layers suggesting that they may have resulted in the final freezing stage.

The total density of hailstones rr,ay be roughly evaluated from the density of the individual layers, considering their contribution to the total volume of the hailstone. T ests were also performed by the usual immersion technique and the results compared. H ow­ever, both techniques canno t be applied on the same hailstone and the comparison is limited to two different hailstones from the same hailfa ll. Measurements of total density were performed by weighing the extra weight created by imm ersing the ha ilstone iDto a chilled liquid. E thylene dichloride was used as a suitable fluid because of its low freezin g point and low viscosity; also, ice is completely insoluble in it. At the experimental

temperature of - loC, the density of this fluid was accurately measured as 1.250 gm cm- 3• E ach hailstone was weighed again after it was removed from the flu id and a reasonable time (5 min) had elapsed for the Sllr­

face layer of the Buid to evaporate. The remarkable in­creasc in weight of all the measured hailstones is sup­porti, e evidence of liquid penetration to the inside structure during immersion, especially in hailstones of relatively low density. T able 1 gives the results of these measurements, tbe values corrected for penetration effect, and the values of total density estima ted by the densitometric technique on hailstones from the same hailfalls. The two techniques give results in t he same range when the proper correction for the penetration eflect is made fo r the immersion technique.

Vittori and di Caporiacco (1959) obtained values between 0.87 and 0.91 gm =-3 for 37 stones from tlle Po Valley (Italy), and 0.80 gm =-3 for three others. For 16 stones from Sou th Africa, Mossop and K idder (1961) found total densities from 0.87-0.90 gm cm-3

with an avcrage value of 0.89 gm on-3. A comparison of these results with those in Table 1, using tlle same uncorrected immersion technique, shows that hailstones from the western Great Plains have sligh tly lower den­sities on the average. If the difference is systematic, measurements of local densi ty inside hailstones from various regions could be useful for investigating even­tual structural differences.

In sununary, the analysis shows that:

1) The values of the mean density of the total hail­stone lie between 0.82 and 0.87 gm Cln-3, and tbe indi­viduai values corresponding to artificial wet growth (0.909 gm Cln - 3) are never reached by these natural hailstones.

2) I n almost all of the hailstones a general decrease of density is noticeable from the periphcry toward the

ÙECElIDER 1970 FRANCO PR OD I 909

center. The embryo region has remarkably differentj.!!fshape and the ou tward-convex Iayered strllcture would densities which may be ei ther higher or lower with re-:~f be determined in this final phase. Tbe ice-air-water con­spect to the surrounding areas. . tr glomerate formed in tbis way would contain more air

3) No strong variation in density was observed from than that accounted for by the SOlllbility of air in water one layer of different morphology to another (for ex- even at low temperatures; depending upon the speed ampIe, from opaque to trans-ice). Tbe presence of large and structure of the bailstone's crystallization front, bubbles seemed to have more effect on tbe density this air would eitber become trapped in tbe ice in tbe values. As transparent layers in natural hailstones are form of small bubbles, or would be releascd into un­often associated with large bubbles (in the inner bound- frozen water and allowed to coalesce into a few large ary or between lobes), we can assume that tbe usual bubbles that then lower the dcnsi ty of the inner layers. association of opaque layers with low density, and of The higher pressures in the hailstone during tbe inward transparent layers with high density, may be disre- final freezing would probably also affect the distribu­garded. Opacity can be due to the presence of micron tion and sbape of air bubbles. size air bubbles whose influence on decreasing dcnsity Goyer et al. (1969) observed a structure of well­may be less than, or comparable to, that of a few large defined concentric Iayers resulting frorn final freezing bubbles. Opaque ice can also be obtained by freezing of wetted snowballs. Although the structure of dry bulk. water under specific conditions. wetted growth is different, an analogy exists in heat ex­

Our findings indicate tha t consistent layers of wet or initially spongy growth are not present in the examined hailstones. This condusion from local density measure­ments confirms Browning's (1967) premise that initially spongy growth cannot account for the regular tbree­dimensionaI array of lobes. Our accretion experiments also show (Fig. 3) that wet growth tends to attenuate the lobes fOlmed by dry growth, giving the hailstone a smooth surface.

The cffectiveness of an aerodynamic shedding of in­ternaI water proposed by List (1961b) to explain large bubbles or cavities in natural hailstones seems improb­ab le for hailstones !rom the Colorado-Nebraska region. Their outer layer seems always to be frozen, undoubt­ed.ly preventing the exchange of any kind of liquid water with the environment.

Two processes remain possible : dry growth dose lO the wet limi t, and liquid water penetration into the porous structure fonned by the first dry growth.

Artificial hailstones very similar to natural ones have been reproduced by Bailey and Macklin (1968a) in conditions of dry growth, tending toward wet growth in a final stage. Even in the most opaque stones, densi­ties >0.875 gm cm-a were measured; this suggests that each !ayer, when formed, has its own density,.··thus rul­ing out the possibility of subsequent penetration of liquid water.

However, our experiments show that the x-ray images of the air inclusions in a high-density dry structure are different from the images of bubbles in natural hail­stones, and that the local density frequently decreases from outside toward the interior of the hailstone. These results also demonstrate the effectivenes5 of a process of final freezing of water penetrated in to a previously formed p:>rous structure. In a Jirst stage the hailstone could grow in a dry condition, developing lobes and protuberances, and being sustained by a smaller up­draft with the lower density. H aving once reached maximum size, it could be wetted either in a final stage of growth or by melting during its fallo The external

change wi th the environment, and tbeir experiment suggests that a layered structure does not imply abrupt variations in growth condi tions.

Computations by Bailey and Macklin (1968b) show that when large hailstones fall through still air, melting is severe, giving rise to changes in radius up to 30% wilh high heat transfer coefficien ts. In a dry accretion the decrease in radius due to melLing during descent do es not cause a decrease in mass, because tbe liquid wa ter is immediately absorbed by the capillary structure, thus increasing tbe density to the observed values. A dry growth that is not wetted in the updraft by supercooled droplets may be wetted by melt ing during fall , giving tbe hailstone the slushy property sometimes observed.

Tbe process of penetra tion of water into a porous structure was experimentally investigated by Kidder and Carte (1964) who also studied the implications of tbis process in the interpretation of hailstone structure. They conduded that quant itative data on air bubble size and concentrations were necessary.

More experimental work is needed on several aspects of the penetration process such as the increase in den­sity, the final rearra.ngement of the crystal structure, and the optical characteristics of the resulting ice (abil­i ty of producing dear ice la yers).

4. Conclusion

A densitometric technique applied to x-ray micro­graphs appears suitable for local density measurements on hai lstone slices. Results have been explained by two processes: a dry growth dose to the wet limi t in a final stage, and a process of final freezing of water penetrated into a porous structure formed by tbe first dry growtb. We propose that layers could form during the final freez­ing rather than develop as a result of abrupt variations in growth parameters.

More study is needed on the stage of fina l freezing of large dry-wetted structures to darify the process of layer formation . A measure of air pressure on tbe large internai bubbles would contribute helpful data.

910 JOURNAL OF APPLIED METEOROLOGY VOLUME 9

Acknolwedgments. The author is deeply indebted to Mr. C. Nagamoto for his suggestions, his aid during the experiments, and for many helpful discussions.

REFERENCES

Bailey, L H. , and W. C. Macklin, 1968a: Surface configuration and internai structure of artificial hailstones. Qu,art. J . Roy. M e/eor. Soc ., 94, 1-11.

--, and --, 1968b: Heat transfer from arti1:icial bailstones. Quart. J . Roy. Me/eor. Soc., 94, 93-98.

Browning, K. A., 1967: The growth environment of hailstones. Me/eor. Mag., 96,202-211.

Goyer, G. G., S. S. Lin, S. N. Gittin and M. N. Plooster, 1969: On the beat transfer to ice spheres and the freezing of spongy hai!. J . A tmos. Sci ., 26, 319-326.

Kidder, R. E., and A. E. Carte, 1964: Structures of artificial hail­stones. J. Ree". Atmos., 4, 169-181.

List, R., 1958: Kennzeichen atmospharischer Eispartikeln, II Tei!. Z. A ngew. Ma/h. Phys., 9a, 217-234.

--, 1961a : On the growth of hailstones. N"bua, 4, 29-38. --, 1961h: Physical methods and instruments for characterizing

hailstones. Bull. Anter. Meleor. Soc., 42, 452-466. Macklin, W. c., 1962 : The density and structure or ice formed by

accretion. Quart. J . Roy. M e/eor. Soc., 88, 30-50. Mossop, S. c., and R. E. Kidder, 1961: Hailstorm al Johannesburg

on 9th November 1959, Part II-Structure 01 hailstones. N1tbila, 4, 74-g6.

Prodi, E'., 1969: X-ray images 01 bailstones. J . Appl. Meteor., 8, 458-459.

--, V. Prodi and G. Fiore, 1970 : Distribution 01 contaminants in ice grown by accretion. J . Appi. Meteor., 9, 283-288.

Vittori, O., and G. di Caporiacco, 1959: The density or hailstones. Nu.bi/a, 2, 51-57.