Ice Formation in the Atmosphere Citation McNeal, Don (1935) Ice Formation in the Atmosphere. Master's thesis, California Institute of Technology. doi:10.7907/SX19-PN27. https://resolver.caltech.edu/CaltechETD:etd-04222008-104429 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: Meteorology Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Meteorology Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Group: GALCIT Thesis Committee: Unknown, Unknown Defense Date: 1 May 1935 Record Number: CaltechETD:etd-04222008-104429 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-04222008-104429 DOI: 10.7907/SX19-PN27 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1458 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 23 Apr 2008 Last Modified: 03 Oct 2019 23:08 Thesis Files Preview PDF (McNeal_d_1935.pdf) - Final Version See Usage Policy. 10MB Repository Staff Only: item control page

ICH FORMATION IN THE ATMOSPHERE by a 4 Don MeNeal Pasadena, California May 1935 Any discussion of the problem of ice formation in the atmos- phere should early treat of certain fundamental processes or phenomena inherent to the changes of state from water vapor to condensed water in droplet formations and, finally, to the various forms in the solid state--- clear ice, rime, and frost. These processes or phenomena are: (1), the condensation of water vapor in the atmosphere, (2), the existence of under-cooled water in the atmosphere, and (3), the processes involved in the freeze ing of under-cooled droplets. These will be discussed in the above order. Section I The Condensation of Water Vapor in the Atmosphere The amount of aqueous vapor that can exist in a given volume of the atmosphere depends upon the temperature. Supersaturation may be produced under laboratory conditions but is not believed to occur in the free atmosphere. If a’state of saturation is said to exist, a condition of equilibrium prevails, i. e. as Inany molecules of water are entering the free water surface, per unit time, as are escaping to the space above. These water molecules in the space above the water surface exert an inde- pendent pressure in accordance with Dalton's Law. This is called the vapor pressure and, since the number of molecules which contribute to this pressure is dependent upon the tempera- ture, we may say that the saturation vapoor pressure is also dependent upon the temperature. It is directly proportional to the temperature. If we start with a condition of saturation and -l- lower the temperature, we produce one of two conditions. Hither we bring about supersaturation or, if suitable nuclei are present, condensation of water vapor will take place thereon and small water droplets will be formed. The natural processes by which portions of the atmosphere are cooled sufficiently to bring about condensation are: (1), cooling by mixing or through contact with a surface which itself has lost heat by radiation or is otherwise cooled; (2), spontaneous cooling by radiation; and (3), dynamical cooling by expansion. Cooling by mixing or through contact with a cooled surface pro- duces advective sea and land fogs. Spontaneous cooling by radiation produces the fogs which are common on clear cool nights when the wind movement is light. This form of cooling, in conjunction with advective effects, is also responsible for the stratus clouds so frequently formed at the base of subsidence or turbulence inversions. These clouds are common around the perifery of polar air masses and semi-permanent anticyciones. Dynamical cooling by expansion is the most effective process of all. Such cooling may be due to the convective action resulting AZO eating of surface layers, producing cumulus clouds; to the convective overturning or the forcing aloft of warm air at the forward portion of the cold front type of discontinuity, producing cumulo-nigous clouds, or by the active upglide of warm moist air over the warm front or by the lifting of cold moist air under the warm front due to the convergence of stream lines along the warm front, producing nimbus, stratus, or alto-stratus clouds. The lifting of moist air in crossing mountain ranges is also impor- -2- tant in this respect-- the cloud types produced depending upon the stability of the air. The cooling of portions of the atmosphere, by whatever process, will yield condensation only provided nuclei in sufficient num- pers are present. any investigetions have been conducted in efforts to determine the exact nature of such nuclei. Recent discoveries have been made in this connection which prompt a radical revision of our ideas regarding the nature of these nuclei. It had formerly been believed that minute dust particles and ions of dissociated hygroscopic gases constituted the nuclei about which condensation takes place. It is true that conden- sation will take place about dust particles, provided other more effective nuclei are not available. The well known Aitken's "dust counter" had, for years, been used to determine the number of nuclei available in different samples of air. It has develop- ed, however, that the "dust particles" counted by this ingenious device are not dust at all but other more effective nuclei. Indeed it has been demonstrated that no increase in the number of nuclei wes observed in a sample of air that had been deliberately made dusty. Thus it is now believed that the particles counted by the Aitken device are not dust at all, but other forms of nuclei. Hence it is quite probable that the ordinary dust particles play ai unimportant role in condensation within the atmosphere. It has been shown that a fourfold suversatureation is required before cordensation will take place on negative Lons, while a Sixfold supersaturation is required for condensation about positive ions. This relative effectiveness of ions of opposite charge has been misunderstood by some, leading to an erroneous conclusion -3. that negative ions could be regarded as nuclei of condensation for the atzosphere. But since there is no reason to believe that such a degree of supersaturation exists in the atmosphere, and which has never been recorded, it appears that such ions may be definitely eliminated from consideration here. What, then, are the effective nuclei within the atmosphere? Hygroscopic nuclei from evaporating sea-spray are, without doubt, carried into the atmosphere by turbulent and convective action. Also, more strongly hygroscopic nuclei are derived from the com- bustion of sulphur which is present in large quantities in coal and coke. In this connection it is interesting to note that minute particles of sodium chloride have been shown to become deliquescent and form water droplets when exposed in air with 2 relative humidity as low as 75 per cent. Other more strongly hygroscopic nuclei may result in condensation at still lower velues of humidity. Table No.l shows several examples of cloud formations existing at low humidities, that at Oklahoma City on April 6, 1935 being the most notable and indicating alto-cumulus clouds of 500 meters thickness in which the humidity ranged from 5l per cent at the base to 54 per cent at the top. Such observa- tions certainly suggest that the nuclei of condensation within the atmosphere consist of such hygroscopic material. K8hler hes conducted investigations concerning the nature of atmospheric nuclei wherein samples of cloud and cloud air have been analyzed. From such ahalyses he has not only provided. interesting and valuable information about the size and number of nuclei of condensation, end the size and number of cloud droplets ~4e per unit volume, but he has rather definitely shown that the for- mation of cloud and fog droplets are dependent upon nuclei of sodium chloride, magnesium Chloride, and calcium Sulphate, and, therefore, derived from Ssea-spray. The acceptance of the propo- sition that nuclei of condensation do consist very largely of these materials, with their varying degrees of solubility in water, will contribute to an understanding of the capricious be- havior of water in the liquid state at low temperatures. KOhler's measurements of the size of cloud droplets show a range in the diameter from 0.011 mm to 0.0638 mm, the average being 0.0276 mm. Many thousand such droplets could exist per cubic centimeter, the number depending upon the density of the cloud. KUhler has found that the water content of cloud ( ex- cluding water vapor) ranges from 0.12 gram per cubic meter in the less dense clouds to 1.84 grams per cubic meter in the most dense clouds. Conrad and Wegener have found maximum values approaching 5 gram per cubic meter. However, their values are based upon the assumption of 100 per cent relative humidity in clouds and, in some cases, of conditions of supersaturation, whereas Kohler, in no case, found a relative hunidity in clouds as high as 100 per cent. His values varied from 92 per cent to 97 per cent, whith are in close agreement with the values listed in table No. 1. The numerqus cases shown in this table wherein relative humidity values are considerably below 100 per cent in clouds show that it is decidedly unsafe to assume complete saturetion in all clouds Initially, cloud droplets formed on nuclei of the same Kind are uniform in size, soon, however, due to different rates of con- densation on the droplets in various portions of the cloud, a -~5- difference in size will result. Once this condition is establish- ed, it is interesting to note that, due to the larger vapor press- ure about the smeller droplets of greater convexity, these droplets will evaporate and the water vapor therefrom condense on the larger droplets. Thus the larger droplets are continuously being formed at the expense of the smaller ones. Through such processes we may expect to find cloud droplets within the atmosphere through a wide range of sizes. Droplets less than 0.025 mm in diameter are generally classified as cloud or mist. Larger droplets, ranging in size up to 5 mm, are found in various classes of rain. The larger drops, requiring for their support forces operating ageinst the acceleration of gravity, are associated with strong vertical motions and are, therefore, confined to regions where these currents are produced. The smaller droplets, on the other hand, are found in clouds or fogs which are produced primarily by radiational cooling and hence may be expected in regions not associated with strong vertical currents. Section IT The Existence of Under-cooled Water in the Atmosphere It has been a matter of common laboratory experience that water could be cooled far below its normal freezing point before solidi- fication took place. Further, that as soon as the smallest par- ticle of the substance in the more stable phase, (ice), is intro- duced, the under-cooled water is immediately transformed into it. The saturation vapor pressure over water in this under-cooled stage has a higher valee then over ice at the same temperature. ~b6a Thus when there is contact between this metastable phase and the stable phase the vapor of the former will diffuse toward the latter and there sublimate. This process willcontinue until all the under-cooled water is converted to ice. It is also well known that a slight agitation of under-cooled water will result in its almost immediate change to the solid state. Experimental researches have been conducted for the pur- pose of determining the tendency of under-cooled liquids to solidify by themselves, without the introduction of any crystall- ized particle. It has been found that microscopic crystalline nuclei make their appearance at different parts of the liquid and then grow until all the liquid has been solidified. It appears plausible that agitation, such as referred to above, might well assist in the arrangement of these crystalline nuclei, from which point the transformation is completed. A very important consideration in connection with the existence of under~cooler water in the atmosphere is the fact that, since the salts of evaporating sea-spray constitute the principle nuclei of condensation, each cloud droplet is in fact a salt solution. It is also well known that when a foreign substance is dissolved in a liquid, the freezing point of the solution is lower than that of the pure solvent. The solution will begin to freeze at that temparature where the vapor pressure of the solution and that of the pure solid solvent are the same. That is, where the solution is in equilibrium with the solid solvent. Only at this point can the two phases co-exist. Figure No.l will serve to illustrate this point. a Vavor Pressure Temerature Figure No. 1 The curve A-B shows the variation of vapor pressure of the solid solvent with temperature, while the curves coc, D-D, and E-E. represent vapor pressure variations with temperature ofisolutions of three different concentrations. The temperatures shown by the points C, D, and BE, where the vapor pressures of the solutions and the solid solvent coincide, are the freezing points for the three solutions. This phenomenon may be understood by considering that since the free surface of the solution must contain some molecules of the solute and therefore less molecules of the pure solvent, and since the vapor pressure of the solute is always less than the vapor pressure of the solvent, we may properly expect that as we add more of the solute, lower vapor pressures will be measured for the solution and hence the freezing point will be lowered. If P is the vapor pressure of the pure solvent and P' that of the solution, then ~Ba PePt 2£n P N where n is the number of gram molecules of the solute in N gram molecules of the solvent. It has been discovered that the depression of the freezing point of a given solvent is constant for the addition of one gram molecule of any solute to 100 grams of the solvent. For water, this value is 18.7 degrees Centigrade. This is designated by chemists as the molecular depression of the freezing point. Thus if the concentration of a given solution is that produced by the dissolving of one gram molecule of sodium chloride in 100 grams of water we would expect the solution to have its freezing point lowered 18.7 degrees C. This rule, however, holds only for dilute solutions and it is probable that the extreme under- cooling of water is due in part to the presence of other sub- stances in solution. Kéhler has said: "The small amount of other salts than sodium chloride, for very concentrated solutions, plays a not unimportant r6le. The magnesium salts on account of their great hygroscopic characteristics and the calcium salts on account of their relatively small solubilities”. The solubility of sodium chloride in water is such that the freezing point may be depressed as much as 22 degrees C. Other salts would cause depressions of the freezing point of their solutions in accordance with their molecular weights, provided ionization did not take place in solution. Indeed this relation- ship is used to determine the » lecular weights of solutes from the expression: tek ® where t is the depression of the freezing point, E the molecular depression, and m the number of grams solute of molecular weight M dissolved in 100 grams of the solvent. It is interesting to note that the lowest temperature recorded in Table No.1, at which ice was reported, was -22 degrees ©. Iwo observationsof rime are shown in this table with temperatures as low as -26 and -28. In this connection it should be pointed out that, due to the difficulty of observing the formation of rime in small quantities, it’may, at times, be confused with snow or ice crystals which already represent the crystalline state and do not show the existence of under-cooled water. L.T. Samuels, in his investigation of clear ice and rime deposits, found no temperatures lower than -23 degrees C. On the other hand many reliable observations have showm the existence of water in the liquid state at much lower temperatures. Kohler has reported cloud partivles in liquid form at temperatures as low as -28. Wegener, in his Greenland travels of 1912-13, found water drop- lets at -34.5 degrees, and W.C.Haines has reported observing fogs at Little America at temperatures of -26, -50, and -44, Several attempts have been made to explain the existence of under-cooled water in the atmosphere and some of these have attributed the phenomenon to the increased pressure resulting from the greater vapor pressure of very small droplets of great convexity. It would require a pressure of about 150 atmospheres to lower the freezing point as much as l degree. This feature of increased pressure is, therefore, of little -1l0— importance in accounting for the very low temperatures that have been observed. If, however, we accept the demonstrated fact that salts of evaporated sea-spray constitute the principle nuclei of condensation, we can at least provide a partial explanation of the existence of under-cooled droplets in the atmosphere. Kéhler, in his paper " Zur Kondensation Des Wasserdampfes in der Atmosphare" says: "The introduction o@ salt particles here makes it very clear that fluid water can and must exist in-the atmosphere at very low temperatures". The full explanation seems to rest with the fact that the under-cooled droplet is not only a solution with the freezing point depressed on account of the addition of some foreign matter to the solvent, but also to the fact that the initial alignment of molecular agregates, so necessary for solidification, is being delayed. Section III Processes Involved in the Freezing of Under-Cooled Water on Aircraft. In the preceding sections of this paper it has bean shown that fog and cloud particles, ranging in size from 0.011 mm to 0.0658 mm in diameter, and rein drops up to 5 wm in diemeter, are formed principally about nuclei of evaporating sea-spray and therefore consisting of sodium chloride, magnesium chloride, and calcium sulphate; that the larger droplets are associated with strong vertical motions and are, therefore, confined to regions where these currents are produced; that the smaller dropletg may be expected in regions where radiation is the cooling process leading to condensation, or in regions where there is an absence -lile of strong vertical motion; finally, that the explanation of the existence of under-cooled droplets rests in the fact that these small globules of water are actually salt solutions of depressed freezing point wherein the alignment of molecular agregates has been retarded and which will be prompted to solidify by any form of agitation. It is now proposed to discuss the process of the freezing of such under-cooled droplets as they are encountered py aircraft in flight. Pilots have reported three different kinds of ice deposits encountered in flight, viz., clear ice, rime, and frost. Clear ice is smooth and glassy in appearance, although when mixed with sleet or snow, may assume a rough appearance. It is very tenacious end has a tendency to form in a mushroom shape with its frontal area enlarged. It forms near the leading edge of the airfoil or strut and, due to the irregular shape into which it builds, results in a loss in lift and an increase in drag. It is much the most dangerous type of icing. Rime is pure white, opaque, and granular in structure. It consists of tiny ice pellets which have little cohesion or ad- hesion. Rime builds into sharp-nosed deposits on leading edges and does not alter the form of the airfoil materially. Further, due to its granular structure, it is constantly being lost through vibration. This form of icing is seldom dangerous. Frost is a light crystalline formation which never developes in such quantity as to become of much importance. It is the least dangerous of the three forms. ~1l2— In order to demonstrate just what processes develop during the icing of aircraft, let it be assumed that we have water in liquid form, either as cloud, or, perhaps, falling rain, at a tempera- ture of -8 degrees C. which, from Table No. 1, will be seen to be within the average range of temperature for clear ice formation. Also, let it be assumed that the cloud particles encountered are of the average diameter of 0.03 mm. Each droplet then consists of 1.4 x 107° ce. As soon as the plane strikes such a droplet, there is provided the necessary agitation and freezing begins. But not all of the droplet will freeze at once. We kmow that to freeze l ec. of water we must remove 80 calories therefrom. We also know that at the instant the droplet begins to freeze the temperature of the mixture of ice and water will immediately rise to 0 degrees C. Actually the tempemature of the droplet will rise only to the freezing point of the particular solution with which we are dealing, because that is the only temperature at which ice and gur solution are in equilibrium. However, since we do not know the exact concentration of the solution let us, for simplicity, assume that the temperature rises to 0 degrees C. This rise in temperature to 0 degrees can only be accomplished as a result of heat being added, while at the same time heat is being taken away from a portion of the droplet in order to bring about the freezing. Assuming that no heat is provided from without, this added heat must be removed from that portion of the droplet which freezes. Thus the rise im temperature of the mix- ture from -8 degrees to 0 degrees will give us a measure of the number of calories required to produce this heating, and, thereby, ~1L3—- the fraction of the droplet which is immediately frozen on impact. In this example, since it requires l calorie to raise the tempera- ture of 1 cc. through 1 degree, it will require 1.4 x 107° x 8 or 11.2 x 1078 calories. And, since it requires the expenditure of 80 calories to freeze 1 cc., we have provided the cooling suffic- ient to freeze 11.2 x 107° ce. which represents 10 per cent of 80 the volume of our droplet. If we should assume the droplets to have a higher initial temperature, say -4 degrees C., we would find that only 4/80 or 5 percent of the water would be frozen on impact. On the other hand, if we should assume a cloud temperature of -20 degrees C., we would find that 25 per cent of each droplet would be frozen on impact. Thus we can say that the amount of water encountered by the plane in the form of cloud particles or rain drops, and which is immediately frozen, is directly propor- tional to the degree of undercooling of the droplets. If it was only that portion of the droplet which freezes on impact that concerned us, and the remaining portion was permitted to run off as water, the icing of aircraft would not be of much imoortance. It is because a very large part of the remaining water freezes also that the icing conditions are considered such a hazard. It is through the operation of the process of evapora-~ tion that the remaining portions of each droplet are largely turned to ice. Let us consider, again, our original droplet, 10 per cent of which has been changed into ice, while the remaining 90 per cent exists as water at a temperature of 0 degrees C. Over this water -14- at 0 degrees C. we shall have a saturation vapor pressure of 6.11 millibars, whereas the surrounding cloud air will have a saturation vapor prewsure corresponding to the temperature of -&8 degrees, or only 3.12 millibars. Thus evaporation will take place from the water surface just as we observed in the section on condensation that the smaller cloud droplets with higher vapor pressure evapor- ated and condensed on the larger droplets of lower vapor pressure, Yo accomplish the evaporation of 1 cc. of water it requires the addition of 600 calories. For our particular average droplet it 8 x 600 or 8-4 % 107° calories. To freeze will require 1.4 x 107 the remaining 90 per cent of the original droplet we need to re- move 90 per cent of this amount, or 1.4 x 107° x 80 x .90 which equals 1.008 x 107° calories. Hence we need only to evaporate 1.008 x 107° or 12 per cent of the original droplet. Thus it is 8.4 x 107° clear that the process of evaporation is of first importance in any consideration of icing conditions. Under the conditions chosen for our example roughly 88 percent of the water encountered by the plane would be frozen, nearly nine tenths of which is caused by evaporation. The size of the cloud droplet has no influence on the proportion of each that is frozen either on impact or through subsequent evaporation. A particular size of droplet was used in the computation only for the purpose of making the illustration specific. Just as at was found that the portion of each droplet frozen on impact is directly proportional to the degree of under-cooling, so is it true that the rate of evaporation of the remaining liquid portion and the total amount to be frozen will be directly pro- -15- portional to the degree of under-cooling. If we start with a temperature of -20 degrees C, 25 percent of each droplet will be frozen on impact. Only one tenth of the droplet need be evap- orated to freeze the remaining portion and, due to the relative great difference between the saturation vapor pressure over water at 0 degrees C. (6.11 Mb.) and that of the cloud air at ~20 degrees C. (1.04 mb), this evaporation will take place about 5 times as rapidly as in the case where we assume a cloud air temperature of -8 degrees. It should be noted that in these examples we have assumed a relative humidity of 100 per cent in the cloud air. As has been mentioned above and as can be seen from Table No.1, clouds often occur with relative humidities considerably below 100 per cent. The values noted in the table for clear ice formations range from 51 per cent to 100 per cent, with the average being about 90 per cent. Under such conditions there would exist a still great- er difference in vapor pressure between that for the water on the wing and that in the free air. Hence evaporation and the resultant freezing would take place more rapidly. This considera- tion would seem to suggest that icing would take place more readily while flying through portions of a cloud or fog wherein the relative humidity is lower. This also explains the observed rapid formation of ice as the plane emerges from a cloud into the comparatively clear air above or below. In a few instances ice has been reported as occurring at temperae tures above freezing. This does not occur often but it is theoretically possible. Two cases of this kind are listed in ~1l6- Table No.l. The explanation of this phenomenon depends upon the assumption that the relative humidity within the cloud is less than 100 per cent. A temperature of 2 degrees is about the upper limit for ice formation. If we assume an air temperature of 2 degrees C. and a relative humidity of 100 per cent, the vapor pressure of any water striking the plane will be exactly the same as that of the cloud air. Hence there will be no evaporation and no freezing. If, however, we assume the same air temperature, but now a relative humidity of 90 per cent, we would have a difference in vapor pressure of 0.705 millibar. A certain amount of evapora- tion would take place and a very little freezing. fhe temperature of the ice and water on the wing would be reduced to 0 degrees. At this point the saturation vapor pressure of the ice and water mix- ture would be essentially the same as that of the cloud air. Hence no further evaporation would take place. Under such conditions, therefore, ice would form very slowly because of the small diff- erence in vapor pressure and the deposits would be small. The formation of ice at temperatures above 0 degrees C. is also, in part, caused by the evaporation brought about by the adiabatic cooling of air in passing over the vacuous space above the airfoil. If we assume a cloud air temperature of 0 degrees C. we see that there is no expenditure or gain of heat in bringing the water and ice mixture to a temperature of 0 degrees. But here any evap- oration which may be started by encountering cloud air of less than 100 per cent relative humidity will require the expenditure of the heat of evaporation. Since to freeze 1 cc. of water we need only remove 80 calories, only 80/600 or 13.3 per cent need -17- be evaporated. Cloud air with a temperature of O degrees must, therefore, be considered dangerous along with that found at lower temperatures. Section IV Discussion of Observational Data Table No.1 has been prepared from a study of teletype reports of upper air soundings made in the United States during the winter of 1954-35, and in which ice formations were reported. During the early part of this period reports from the eastern portion of the country were not available, but it is believed that the data are sufficient in volume to yield representative information. One of the most convincing features of these data is the close conformity of the regions wherein ice was encountered to the region of cloudiness. This may be seen from the following extract of Table No.l Avg. AVge AVE. Clouds elev.at elev.at Thick- AVE. AVE. AVS. which which ness elev. elev. thitk- formation formation of of ness began ended base top (meters) (meters) (meters) (meters) (meters) (meters) Clear ice 2890 3362 551 2824 3251 553 Rime 3205 3768 507 3128 3695 613 It has often been claimed that both clear ice and rime are form- ed, at times, above and below clouds. This, of course, may hapoen as is suggested by the explanation offered for the formation of ice at temperatures above O degrees C. That is to say, that under ~18. such conditions we must have first accumulated water on the aircraft and then encounter a zone wherein the relative humidity ig less than 100 per cent. This latter condition can be realized by going above or below the cloud. But here, by going above the cloud, there would be no new supply of water to be encountered and only that small portion which had adherea to the plane would be frozen. Hence under these particular conditions the danger of icing would be very small but the formation would take place very ‘rapidly. On the other hand one might argue that flying below a cloud and in rain would continuously provide a new supply of water spreading over the plane and thereby suggest that this might be a region of dangerous icing conditiogis. In the region of falling rain below a cloud the temperatures will usually be too high for ice to form and the relative humidity will also remain very high so that cooling by evaporation would be a very slow process. There is only one case listed in Table No.1 where ice was encountered below the base of the cloud, this being in the report for Cheyenne, Wyoning for April 8, 1935. There are only two case} where ice was reported in regions: above the cloud. The small differences in the levels of ice formation and those of cloud forms, noted in the above extract of Table No. 1, are, insinost every instance, due to ice being first noted within the cloud and not at the exact level of the base. Thus it apvoears that the hazard of ice formation may in most cases be avoided by avoiding flight through clouds. It is the realm of low temperatures that water exhibits its most capricious hehavior. Table No.l shows that clear ice has been observed forming at temperatures ranging from 2 to -22 -l19- degrees C., while rime has been observed at temperatures from -2 to -28 degrees C. Thus it would seem that temperature alone is not a safe criterion upon which to judge the type of ice formation to be expected. ‘Theoretically we would expect clear ice to be formed at higher temperatures than rime because, as explained in Section III, the smaller amount the temperature is depressed velow OQ degrees C., the smaller will be the portion of each droplet frozen on impact. Hence a telatively large amount is left in liquid fomto spread out in the familiar mushroom shape and freeze into clear ice by subsequent evaporation. In the case of a larger depression of the temperature of under-cooled droplets we have found that a very large portion of the droplet may be frozen directly on impact. And in the case of very small droplets the speed of crys- tallization may be so rapid as a result of the lerge amount of initial freezing and the relatively small amount rewuaining to be frozen through evaporation, which process will be aided by the large difference in vapor pressures at the lower tenrperatures, that there would be little or no spreading of water, but instead the almost imnediate and complete freezing of the entire small droplet, Thus with lower temperature and smaller droplets we might expect rime to form whereas with higher temperatures and larger droplets we should expect clear ice to form. The average temperature of the base of clear ice formation, as taken from Table No.1, was -6.6 degrees C., while the average temperature of the base of rime for- mation was -ll.l degrees C. Figure No.2 shows the percentage frequency of occurrence of clear ice and rime formations at the various temperatures. -20— Ot 1 fraley | rahctliniol Mola of 4 af Io val chal al cul rhst] ic WEP ayer ap ape] TVS A ah] ASST 8 SPS atl Uy pat] te RDO ORO MIRO eC RU =26 ~27 28 clear lide 20 Percentage Frequency WI 10 | H \ | 4 |] , } | Woe yy f Fig. No.2 Percentage frequencies for clear ice and rime formations at temperatures (degrees Centigrade) at which the formation beg. ~la This shows clearly the prevalence of clear ice at the higher temperatures. Seventy-eight per cent of the clear ice observed occurred at temperatures of -8 degrees C., or higher, while only thirty-six per cent of the rime occurred in this temperature range. No date are available showing the relative size of cloud drop- lets during ice deposits but it appears reasonable to assume that the smaller sized droplets are associated with rime deposits, while clear ice may be expected when larger droplets are encount- ered. In agreement with this we might expect rime to be encount- ered most often in the regions where convective action, sufficient to support the larger droplets, is absent, and clear ice to be found most often where relatively strong vertical currents, are encountered. It is misleading to attempt to show any correlation between the existence of icing conditions and the various types of clouds. This results from the difficulty of definitely classifying the clouds under all conditions, as well as the fact that flights are seldom made through certain kinds of clouds. For example, any curve Showing the percentage frequencies for both clear ice and rime formations in the verious cloud forms will show pronounced high frequency for A.St. clouds and pronounced low frequency for Cue Clouds. The high frequency recorded for A.St. will undoubt- edly be largely due to the fact that this type is a formless cloud which may often be reported when the observer hes not been in position to observe the true form. The spreading top of the CueNb.or the base of a wide-spread layer of thick A.Cu. clouds -22- may often quite reasonably be mistaken for A.St. clouds. On the other hand, the very nature of Cu. clouds, being considerably separated one from enother, makes it almost always possible for the pilot to avoid flying through such clouds. Hence we find very few reports of icing conditions in Cu. clouds. Providing temperatures are appropriate, there is no reason to say that any one type of cloud will yield icing conditions more often than enother. We can only state that the type of ice encountered will be governed by the degree of turbulence or vertical motion associated with the cloud forms. Thus we should expect clear ice to be associated with those clouds wherein considerable vertical motion is encountered and rime to be found most often in clouds wherein there is the absence of any considerable vertical motion. A large number of characteristic curves were plotted for sound- ings in which ice was reported. These curves were studied in connection with the synoptic weather maps which agreed in time nearest to that of the sounding. The following relations were discovered: le. Clear ice occurs in unstable air or in a cloud which has been developed by instability just below the ice level and which has, through momentum, carried through a short distance into stable air. 2. Clear ice occuisg where considerable turbulence prevails. oS. Rime occurs in steble air and where little or no turbulence prevails. ~ 235. Figures Nos. 3 to 17 show the synoptic maps and the character- istic curves for a number of the observations listed in Table No.l. Figure No. 3 shows a situation on November 25, 1934 where clear * a ice was reported at Spokane, Wash. The map shows Spokane to be in 4Ppy air a short distance behind a cole front type occlusion. Woile the upper wind data are not shown the pressure distribution indicates that fairly high upper winds from the Wor WNW, with resulting turbulence, must have prevailed. Further, the lifting of this air, which has had a four day trajectory over a water area and is therefore very moist, as it passes over the occluded front and the mountain ranges may be expected to result in de- veloping consideratle instability. The characteristic curve shows both instability and turbulence. Clear ice was encountered in A.eCu. clouds in potentially unstable air between 2750 meters and 5000 meters. Figure No.4, for November 29, 1934, shows much the same con- dition at Spokane es in the preceding case, except that a lesser degree of turbulence,due to smaller values of upper wind speeds, will prevail. Clear ice was reported in A.Cu. clouds between 52450 meters and 2800 meters. Here the characteristic curve shows the ice to have formed in air that is practically in equilibrium but which is immediately above an unstable stratum. Rime was reported at Billings, Mont. on December 6, 1954. Both the synoptic mes and the characteristic curve of Figure No.5 show this sounding to have been made in stable air throughout. Note that the winds at upver levels are nearly parallel to the mountains and therefore can not be expected to produce much turbulence. It should be noted also that the rime was reported in St. clouds between 1700 meters and 1900 meters. St. clouds are distinctly lacking in any vertical motion, which condition we have observed is favorable for the formation of rime. Figure No. 6 shows the conditions prevailing when clear ice was observed in a sounding made st North Island, California on Dec- ember 8, 1934. This is a case where ice was observed in a zone where stable conditions prevailed, but where unstable conditions are shown below. Extreme turbulence was reported between 2800 meters and 4200 meters. Ice was encountered between 3700 meters and 4200 meters. Figure No. 7 shows the conditions prevailing when clear ice was observed at Spokane, Washington on December 15, 1934. Note that this ice was observed in stable air, but air which was well mixed through turbulence. This ice was reported in A.St. clouds between 2000 meters and 2820 meters. Clear ice was reported in a sounding made at Spokane on December 25, 1934. Figure No. 8 shows that the ice formed in stable air which was immediately above a zone of potentially unstable air. Also the characteristic curve shows that considerable turbulence prevailed, as might be expected from the strong pressure gradient and the general orientation of the isobars. Figure No. 9 shows the conditions for soundings made at Spokane, Washington and Murfreesboro, Tennessee on January 27, 1935. Clear ice was observed in over-running Rpp air at Spokane in a zone which was if equilibrium and above a turbulent stratum of 1380 meters thickness which latter was potentielly unstable. Rain was observed 25 falling during this sounding between 3700 meters and 5110 meters. Rime was observed at lurfreesboro in stable Pe air. It is inter- esting to nate that on this date clear ice formed at Spokane at a temperature of-10 degrees C. while rime formed in the stable air at Murfreesboro at a temperature of -8 degrees CG. , thus showing that the degree of stability or instability of the air is a better eriterion of the type of ice to be expected than is the temperature alone. Figure No. 10 shows another condition for clear ice formation at Spokane on February 21, 1935. The characteristic curve shows the ice forming in absolutely unstable air which appeared well mixed by turbulence. Rime was reported in the sounding made at Selfridge Field, Mich- igan on February 28, 1935. Figure No.11 shows this formation to have occurred in stable Pe air. Figure No. 12 shows the condition prevailing when ice was encount- ered on March 17, 1935 at Spokane, Pargo and Selfridge Field. Clear ice was found in unstable air at Spokane, while rime was observed at Fargo and at Selfridge Field in stable Pe air. Figure No. 13 shows the conditions on March 19, 1935 when clear ice was reported at Spokane, North Island and Murfreesboro. The character istic curve for the Spokane sounding shows clear ice forming in an unstable zone. In this case the cloud type noted was St.Cu. which had formed below a subsidence inversion and had carried through the base of the inversion for 100 meters, thus accounting for the ice observed in the stable stratum just above the inversion. Rime was observed at North Island in stable air. Clear ice was observed at ~-26@< Nurfrees vporo in a thick stratum of unstable over-running Tg air. Figure No. 14 shows the condition at Oklahome City on March 2l, 1935 when clear ice was reported. The characteristice curve shows the ice to have formed in a stable stratum but that this air was immediately above a deep zone of very unstable Tg air. Clouds were encountered during this sounding at 3560 meters and the plane was still within the cloud at 5020 meters wheh the descent was started. Clouds of such thickness show clearly evidence of con- siderable vertical motion. Figure No. 15 shows the condition for clear ice formation at Cheyenne on April 1, 1935. The characteristic curve s!:ows the ice forming in an unstable stratum. Figure No. 16 shows the condition for clear ice formation at Murfreesboro on April 11, 1935. The characteristic curve shows clearly that the formation occurred in very unstable Tg air. Turbulence was reported between 1350 meters and 4670 meters. Ice was encountered at 5450 meters. ‘Figure No. 17 shows the conditions prevailing at Murfreesboro on April 12, 1935. In this case we observe that stable Pog air now occupies this area and rime, as is to be expected, is the type of icing observed. In summery the following may be said: l. Icing conditions may be expected in any form of cloud wherein the temperature is 2 degrees C. or below. 2. The danger of icing conditions in regions aoove or below cloud forms is not great. 5.a.-Clear ice will predominate at temperatures of ~2'/— .78 degrees ©. or above. b.Clear ice may be expected in clouds, with approp- riate temperatures, where we have vertical currents strong enough to support the larger cloud droplets. These conditions may be expected where we have: (1) Convective action resulting from the heat- of surface layers. (2) Convective overturning or the forcing aloft of warm air at the forward portion of the cold front. (3) Active upglide of warm moist air over a warm front. (4) The lifting of cold moist air under the warm front due to the convergence of stream lines along the warm front. (5) The lifting of unstable air over mountain Tanzes. (6) All of these conditions will be shown on the ®, diagram as being within a layer of unstable air or, if in a stable layer, this latter will be immediately above an unstable ZONE» ‘S.aRime will predominate at temperatures below -8 degrees C. bRime may be expected in clouds, with appropriate temperatures, wnerein vertical currents are not -28- strong enough to support the larger droplets. @ The Ogdiagrems will indicate stable con- ditions within the zone of rime formation. BIBLIOGRAPHY Nernst, W. : Theoretical Chemistry. Ewell, A.W. Physifel Chemistry. Walker, J.S. : Introduction to Physical Chemistry. Shaw, N. ¢ Manual of Meteorology, Vol. III Humphreys, W.d. : Fogs and Clouds. Lange, K.0. s: Talk on Ice Formation Kohler, H. : Zur Kondensation des Wasserdampfes in der Atmosphére. (Erste Mitteilung) Konler, H. : Zur Kondensation des Wasserdampfes in der Atmosphére,. (Zweite Witteilung) KOhler, H. : On Water in the Clouds. Samuels, L.T. : Meteorological Conditions During the Formation of Ice on Aircraft. N.A.C.A. Technical Note No. 439 Kopp, W. : Danger of Ice Formation on Airplanes. N.A.C.A. Technical Memorandum No. 499. Carroll, Thomas and iicAvoy: The Formation of Ice upon Airplanes in Flight. N.A.C.A. 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