272 MONTHLY WEATHER REVIEW OCTOBER 1940 (2) The error is usually about 2 percent or less when the (3) The error is normally of the order of 1 percent a t the higher levels (5,000-20,000 feet) of an average curve. (4) When applied to the upper levels of a very stable curve (e. g. one featuring an extensive inversion), the rule leads to an overestimation of the height which may mount, to 4 percent or more in an extreme case. The formula i s least accurate when applied to the upper levels of such a curve. From the fact mentioned above, that in an average situation the percentage error is greatest in the lowest levels, it follows that the absolute error is small a t all heights in such a situation, and is usually of the order of 100-200 feet. rule is applied to the lower levels of an average curve. 1. 2. 3. 4. REFERENCES Shaw, Sir N. Manual of Meleorology, vol. 111. Cambridge Univerfiitv Press, 1930. Shaw, Sir R. Geopotential and Height in a Sounding with a Registering Balloon. Afemoir8 Roy. M e f . Society, vol. I, No. 8, 1930. Iieefer, P. J. Determination of Alt.itudes fron the Adiabatic Chart and the Refsdnl Diagram. MON. WEA. REV. vol. 64, 1936, pp. 69-71. Refsdal, A. Aerologische Diagrammpapiere. Geofysiske Pub- likasioner, vol. XI, No. 13, 1937. ilhaus, A. F,., Comment on Refsdals’ “Aerogram” and the spdTephigram. Bdl. Amer. Met. SOC. January 1940, pp. 1-3. Brunt, D. Physical and Dynamical Meteorology. Cambridge University Presfi, 1939, . 40. Gold, E. Letter to Melet. ifag., January 1939, p. 339. Gold, E. Height Calcillations; a Simple Method. Met. Mag., October 1938, p. 241. AN EVALUATION OF THE BERGERON-FINDEISEN PRECIPITATION THEORY By A. R. STICKLEY [Weather Bureau, Washlngton, May 19391 The fundamenta.1 concept of t,he Bergeron-Findeisen prec.ipit,ation theory was a,dva.nced by T. Bergeron (1) in 1935. As then foimulated, it n.sserted that, disregard- ing some rn.ther exceptional cases, the necessary condition for t,he formation of drops large enough to produce rain of any considerable intensity is that subfreezing tein- peratures exist in the c.loucl layer from which t8he rain descends. Fincleisen (2) (3) 1ia.s recent,ly ampliflecl this theory by introducing We,gener’s postulate 8s to the existence of two Ends of nuclei-c,ondensat,ion nuclei and sublimination nuclei-on which the water vapor of 6he en,rth’s a.tmosphere m8.y respectively condense n.nd sub- lime. The process t>lius 3mplified may be briefly described ns follows: Assuming that the dew-point of a mass of air is higher than the freezing point of water and that the mass of air contains both condensation nuclei (which are genemlly assumed to be ominipresent) and sublimation nuclei, let, it be supposed that it is being cooled by a.ny process or combination of processes. Under these c,onditions con- densation will first take place on the conde,nsation nuclei uiitil the point is reached where the vapor pressure es- ert8ed by the sublimation nuclei is less than t8he vapor pre.ssure exerted by the water drople.ts-this latter point, a.s will be shown late,r, seeming to be, in some cases at, le,&, not far below the temperat.ure of freezing. Aft,er t81& point is rea.ched, any furt,her cooling will ca,use the water vapor of the atmosphe,re to sublime on the sublinia- t8ioii nuclei and, a,t t,he same time, to be replenished by evaporation from the liquid drops. These latte,r processes will c.a.use the resulting ice pn.rt,ic,les to become so large thn.t they acquire a considera.ble rate of fall with respect to the wa,ter droplets, and, in their descent, t81iey will continue to grow, not only by the evaporahion-sublimation transfer of water from the surrounding water drops, but a,lso by overtaliing and coadescing with such drops as niay happen to be in their path of fall. Since their size will not be limited by their rate of fadl, these ice pellets can become quite large in the Subfreezing layers of the cloud. When they encounter tempera.tures above t,he free,zing point they will begin to me.lt a.nd, if the resulting wa.ter drops are larger t,lian the ma.ximum raindrop size, they will break up int,o smnller drops-thus rea.ching the ground as rain.2 2 If no sublimation nuclei had been present. under the clrcumstanws assumed above. the continuance of the cooling would bare resulted only in incrensing the size of the cloud droplets-the cloud particles thus continuing to exist in the form of undercooled liquid drops. That thiq latter process cannot lead to the formation of pmcipitatlon mas, how- ever, shown by Bergeron by a series of simple calculations and considerations presented in his orieinal paper (4). Neibher Bergeron nor Findeisen c1a.h that the presence of subfreezing temperatures and sublimation nuclei is always necessary for the formation of precipitation. Fhideison points out that if the humidities between the cloud hyer and the ground are high enough, the cloud elements themselves may become su5ciently large to reach the ground as light rain or drizzle. Bergeron sa.ys that there are two other processes which niay give rise to even heavy precipitation. The first process is instigated by what he ca.lls the Reynolds effect in which those ele- ments a t the top of the cloud n,re cooled by radiation with a conseqwnt, re.duction in the vapor pressure of the drop- letas so cooled a.nd an increased condensation on them. These droplets thus a.cquire a size which is sufficknt to cause t,hem to fn.11 t’hrough the lower part of the doud and to thereby collide with the smaller and more slowly falling droplets, thus creating the observed rain. Ber- geron points out, however, t,hat in order to obtain heavy rain by this process, t’he cloud must lime a great vertical thickness. Moreover, this process cannot set in unless some part of the cloud t,op is shielded from the sun’s ra.dia t’ion. The second e.splanation which Bergeron gives for t,he occurrence of heavy rain without, subfreezing tempera- tures is t,liat the ele.ctric field in the region mn,y become so gre.at the droplets aft,er t,he first coalescence. (e ) The circles designate the initial positions of the droplets afte,r the second coalescence. (d ) The triangles designate the initial positions of the droplets after the third codes- cence. (e ) The initial positions of the droplets after the fourth coalescence. The droplets nest may be assumed to have an initial radius of 1Op-this radius being a little greater t,hnn the mean droplet ra.clius found by Kohler in his cloud particle measurements (10). I n order to make the most likely assumption as to the distances between the droplet,s, the resultas of the cloud part,icle dcnsity measurements per- formed by Kohler, Conrad, and Wagner (11) may be used. These three investigators made a total of 59 measurements of the number of cloud pwticles per unit volume of air- the e.strernes of these measurements being 20/cni? and 580/~m.~ and the mean value being about 6 4 /~n i .~ When the mean value together with the assumed initial radius is used in Schmidt’s equation, it is found that it requires over 7 days for drops with a radius of 1 0 0 ~ to form a.nd over 75 days are required for the formation of drops with a radius of 1,000~. Even if the extremely great cloud par- ticle density of 8,OOO/cr11.~ estimated by Findeisen for cumulus clouds is assumed, it is found that over 3 hours are required for the formation of the 100p drops and over 32 hours are necessary for the formation of the 1,000~ drops. In view, then, of these results, and in view, espe- cially, of t,he highly improbable but most favorable assumptions as to the space distribution of the drops to start with, it would seem as though coalescence of equally large drops in accordance with the ordinaiy laws of hydro- dynamics is to be neglected as a factor contribut’ing to the formation of precipitation. Before discasding coalescence due to hydrodynamical attraction completely, however, the drop size distributions reported as being observe,d by Defant (12), Rohler (13) and Niederdorfer (14) a.re to be considered. These drop size distribut,ions iudic.ate that, starting with certain ba.sic drop size,s, a series of coalescences occurs which, up to certain limits, brings i t about that, in the ma,in, the mass of the larger drops is merely that, of the basic drop multi- plied by some power of 2.3 Although considerable dis- agree.ment as to the validity and acc.uracy of these obser- vations esists a,mong the observers themselves, it would seem that the very fact that t’he distributions have been observed by three independent investigators would war- rant the a.cceptmice of their redity. This being the case, one is then forced to conclude t1ia.t the ordinary laws of hydrodynamics, upon which Schmidt’s coalescence equa- tion is founded, are not applicable for droplets of the minute sizes composing these distributions. This being agree.d upon, the question now remains as to whether or 8 Accordina to KBhler, such a distribution occurs for four basic drop sizes-the mass89 of the hasic drop being related as 2, 3, 5, and 7, respectively (16). not, drops of the niasimum size observed in these distri- butions having been produced, the larger drops of rain can be formed by coalescence in accordance with Schmidt’s equation-it being assumed that Schmidt’s equation is valid for the drops whose sizes are greater than those within the size-distribution range. Consulting the results of the observations of Niederdorfer (who has conducted the most recent and, to all appearances, the most reliable set of size distribution observations) it is found that the size distribution no longer appears for drops whose radii are greater than, say, 640 p. It is hence to be determined whether drops with radii equal to or greater than 1,000 p can be formed by coalescence in accordance with Schmidt’s forniula-the 1,000 p radius being chosen since Nieder- dorfer found that almost 20 percent of the drop sizes measured during showers and thunderstorms exceeded this limit. In making this calculation it seems justi6able to assume that the spacing will be the same as that as- sumed in the preceding application of Schmidt’s equa- tion-allowing, of course, for the increased spacing r 1 . . . . . . . . x o x x o x x o x x o x . . . . . . . , A O A A O A . . . . . . . . x o x x o x x o x x o x -I . . . . . . . . . . . . . . . I x o x x o x x o x x o x ( I .. . . . . . .I :A :O :A : :A :O :A :I x o x x o x x o x x o x flgupe / between the drops as a result of the coa.lescence occurring within the size-distribution range. On the basis of this assumption-all other assumptions being the same as for the first application of Schmidt’s equation-it is found that with the average drop spacing for t,he observations of Kohler, Conrad and Wagner, about 5 weeks are required for the format,ion of the 1,000 p drops, while with the minimum drop spacing estimated by Findeisen for thun- derstorm clouds, 15 hours are necessary to produce the 1,000 p drops from the 640 p drops. It therefore appears that coalescence due to hydrodynamical attraction cannot produce the larger drops even when coalescences within the drop size distribution range are conceded to take place in mother manner than that prescribed by the ordinary laws of hydrodynamics. I n support of the ma,in feature of the Bergeron-Findeisen theory it is to be said that, if, as is usual, it is admitted that the condensation nuc.lei of the e.arth’s atmosphere con- sist of minute droplets of sadt or acid solution, it can be definitely asserted that, in some ca.ses a.t least, the sublinia- tion nuclei are quite distinct from the nuclei on which c.on- densation takes place. The foundation for this assertion lies in the fact that, according to Wegener (16), the water obtaineci by melting snow take.n from the firn re.gion of a glacier does not conduct electricity. That sublimation nuclei must, in general, have a nature whic,h is difTere.nt from that of condensation nuclei, is indicated by the fol- lowing considerations which are due, in the main, to Wegener (17), (18) : I n the first place, the molecu1a.r struc- ture of solids and crystals is considerably more complicated than that of the liquids. This means, of course, that the 274 MONTHLY WEATHER REVIEW OCTO~ER 1940 collisions of the molecules which are favorable enough to produce a crystal are much more improbable than those which would produce a liquid drop. Secondly, consider- ing the formation of a solid from an under-cooled liquid, it is observed that, although the introduction of a solid body usually serves to bring about such a formation, not all solid. bodies have the same ability in this respect, and that the more carefully the body is rounded off and smoothed, the less capable it is of bringing about a “release” of the under- cooling. Evidence as to the truth of this assertion is fur- nished by the fact that water can be undercooled iU n smooth-walled glass vessel and that substances having sharp edges and being isomorphous with the ciystnlline form of the undercooled liquid possess the best relensing capabilities. Since, then, the nature of the resulting solid is the same regardless of whether it is formed by freezing from the undercooled state or by sublimation from the gaseous state, it would then seem that the effectiveness of the sublimation nuclei must be governed by the same lnws ATLANTA, GA. DEC. 12,1932 -1 1:01 -0 4 4 7 2 E s. -10:24 ?! 22 L c -9:s -20 -10 0 10 20 30 Temperature pC) --- o m Humidity (XJ Llght rain at surface at 9:44 a.m.. dimlnishin fo .sprinkling at IO:50am., und continuing ut ll:35%m. Figure 2 a.s the “releasing effectiveness” of foreign bodies in the cas of undercooled liquids. Indirect evidence as to the prevalence of the Bergeron- Fincleisen process in the formation of precipitation may be obtained in two wa.ys. The first of these is the correla.tion of the salt and acid content of rain with the intensity of t,he ra.infal1, i. e., if it is assumed, with Findeisen, that ice part,icles cannot be formed in the atmosphere by the spontaneous freezing of undercooled drops.4 If, as is supposed by Bergeron and Findeisen, most of the heavy rain originates ns ice pa.rticles, n low salt and acid content would be expected with high rainfall intensities while the rain collec,ted from light intensity falls of rain would be more likely to have a high acid and salt content. Un- fortunately, however, there have been no simulta.neous determinations of the salt and acid content which can be correlated with the intensity of the rainfall. However, in his paper on the chlorine content of rain, Israel (20) pub- lished the following set of chlorine determinations with 4 It may he contended that this assumption is incompatible with the flndings of Dorsey (19) as to the existence of a spontaneous freezing point for every sample of water. I t is to he pointed out, however, that, according to the account of his experiments, the samples tested were not shielded from the mechanical disturbances which might have been caused hy the action of microseisms and that although it was found that certain types of mechan- ical disturbances were without influen? on the temperature of the freezing point, other types were found to be extremely effective and t.hat it therefore appears possible that the spontaneous freezing observed by Dorsey could have been induced under the influence ol the microseisms. Since the cloud droplets are, of course, shielded from any such influence, DGrSey’S flnding of a spontaneous freezing point for his water sample does not, it would seem. indicate that such a spontaneous freezing point also exists for cloud droplets. the corresponding rainfall intensities in order to show how the chlorine content may vary within a single fall of rain: TABLB 1.-Strong upglide rain Leyden, Holland-Sept. 23, 1968 I As is indicated in the table, the collection of the water for the first annlysis terminated at 9:15 a. m. After this, the water for the various analyses was collected a t 15- minute intervals. I t will be seen that, considering only the period throughout which the water wns collected at 15-minute intervals, a well-defined inverse rehtionship exists between the amount of rain in the interval and the corresponding chlorine content. The high chlorine con- FEE. 17,1933 ATL A N TA, G A. Light min (misn -52:52 loo -20 -10 0 lo 20 Light mlst at 12:45pm..changing b light rain at 1:55 p.m. and to sprinkling at 2:29 pm. Humidity CX) Tempemlure K) Figure 3 tent found for the rain caught from 6 a. m. to 9:15 a. m. may well be explained in either or both of two ways. First, the average amount of rain for 15-minute intervals during this period is only 0.03 inches, which, on the inverse relationship hypothesis, would ca.11 .for a high chlorine content. Secondly, ma.king the likely supposi- tion that the nctual rainfnll intensities varied widely from the mean during this period, this high chlorine content could also have resulted from the cleansing of the im- purities from the air by the first part of the rainfall. If this is the accepted explanation, it is to be noted that., assuming no marked change in the direction and speed of the wind, this possibility cannot be used to explain the high chlorine content of the last three of the 15- minute intervals, since the air has presumably ahead been washed by the preceding part of the rainfall. A therefore appears that the high chlorinity for the last 45 minutes of the rainfall is only to be explained on the basis of the inverse relationship concept-which is in accordance with the Bergeron-Findeisen t h e ~r y .~ The second test as to the prevalence of the Bergeron- Findeisen process in the formation of precipitation is that 6 I t is to he remarked that even on the basis of the Bergeron-Findeisen theory. it is to be expected that the resultant raln will contain some chlorine-this being true sinm the Bergeron-Findeisen p r o m involves the coalescence of the dawnding ice particles or melted ice particles with the drops In the lower part of the c!oud. Besidss this, as has been pointed out, the descending drops will acquire an additional amount of chlorine due to the impurities in the lower atmosphere. OCTOBER 1940 MONTHLY WEATHER REVIEW 275 1. Precipitation WBS actually obaerved at a higheraltit~dethantheO~isotherm .-.... 2. Clouds from which precipitation resuma- bly WBS falling were observed agove the 0” isotherm .___________________-.-------.- 3. Light rain or drizzle WBS falling from low clouds containing no subfreezing strata ... 4. The theory is neither supported nor contra- dicted due to the altitude of the cloud top an? the upper limit of the precipitation heingunknown ..... ...____.___._.__...._ 5. One or both cloud limits and precipitation limits coincide (and which, therefore, are assumed to he casea of “wet” clouds). ____ 6. Special considerations are required _____.____ Total _.__ ~ ._.._.________.___._._._._.-.. Total number of effective observations ........ of examining the records of the aerological airplane ascents made when rain was occurring to determine whether or not the clouds from which the rain was falling had their upper limits above the zero degree centigrade isotherni. That the presence of the zero degree centigrade isotherm within the cloud layer is sufficient, in some cases, a t least, to satisfy the hypothesis of the Bergeron-Findeisen theory is indicated by the consideration of the aerograms shown in figures 2, 3, 4, and 5. The only questionable region in the interval of subfreezing temperatures is, of course, that immediately below the freezing point. That sub- limation can take place on the sublimation nuclei at these CLEVELAND, 0. DEC.31.1933 I 61 35 79 29 204 25 20 18 25 88 6 0 10 3 2 12 11 8 5 36 4 I 7 n 12 6 0 4 0 10 111 69 121 59 360 99 58 113 54 324 ----- L’ ht rain, Take off, !o 9 0 4 3 d ’ ) kL ,I, Humidity @) Temperature (W Light rain ot surrace throughout fllght Figure 4 comparatively high temperatures is shown in the follow- ing way: In figures 2, 3, and 4 it will be seen that snow was forming in clouds which had temperatures bigher than -3’ C. a t the top. Now, according to the theory as developed by Wegener (21) [which theory has, in the main, been confirmed by the recent experiments of Nakaya of Japan (22)], the formation of snow requires a more intense supersaturation with respect to ice than the for- mation of plain ice crystals (the German volleliristalle). Since, according to these observations, it was possible to obtain these bigher supersaturations within the te.mper- ature interval from zero to -3’ C., without having the excess wa.ter vapor absorbed by condensation on the cloud droplets, it thereforc seems that the smaller supersatura- tions necessary for the formation of plain crystals without having supersaturation wit’h respect to any liquid droplets that may be present. The truth of this last assumption is well demonstrated in considering the observation shown in figure 5. Here,, it will be seen that what the pilot describes as a “few small pellets” of ice were observed at the top of a cloud whose indicated temperature was as high as -0.2’ C.-thus apparently demonstrating the validity of the assumption that sublimation ca,n tn.ke place at temperatures very near to that of the freezing In selecting the stations for this examination, all of the southern stations whic.h rendered a report as to the surface conditions a t the time of the flight a.nd which had tl latitude of less than 35’ were chosen. Besides these, cer- point.6 6 Theconclusion reached in this paragraph, of course, assumes-again with Findeism- that spontaneous freezing is nonexistent in the atmosphere. If, as is believed by many physicists. some mechanipal distvbance IS requued to produce the freezing of subwoled water, it is quite possible that some of the Ice pellets map have been formed due to the collision of subcooled drqps. I t does not. however, seem to be probable that this process could lead to the formation of a noticeable number of such pellets. tain northern stsations which were reputed to have made a large number of bad weather flight,s were also selected. The results of this investigation are shown in the following table: TABLE 2 Number of cases in which- Total South- North- South- North- ern sts- ern sta- ern sta- ern sts- I tions I tions I tions I tions I Southern stations: Atlanta, Dallas, E l Paso, Galveston, Miami, Montgomery, Ban Northern stations: Blllhgs, Chicago, Cleveland, Pembina, Sault Ste. Marie. Antonio, and Shreveport. In this table, the term “number of cases” refers to the number of airplane observations for which the observation of rain or drizzle was reported by the pilot during the flight or by the observer on the ground-all records up to and including the year of 1937 being used. If, now, the cases classified in the fourth of the six categories are discarded, we may call the remaining num- ber of observations the number of “effective observat,ions.” KELLY FI ELD(Sanhtonio),TEXAS. MAY 2,1935 mmldity (74 Temperalure CC) *Peaha of ACu axtending up out of ACU layer fiyum 5 It will t,hen be seen that of these 324 effective observu- tions, 302 are not contradictory to the requirements of the Bergeron-Findeisen theory. Furthermore, on the basis of the assumption made in connection with the fifth rate.gory, the 12 cases listed under it may be regarded as not being c,ontradic.tory to the Bergeron-Findeisen t,heory .’ 7 The term “wet. cloud” used in describing the clouds encountered in thH flights of this category means, of course that these clouds contained drops which were large. enough to penetrate the boundary dyer of air adjacent to the windshield, say, of the plane but which at !.he same time were not large enough to fall through the layer of dry air between the cloud and the ground without evaporating. I t appears allowable to assume t.hat the sizes of these drops lay within or not far from the “stte distribution range” of drop coalescence previously discussed and that, therefore, they could have been formed by the type of hydrodynamicnl-attraction coalescence mentioned there. 276 MONTHLY WEATHER REVIEW OCTOBER 1940 The permissibilit’y of this latter assumption is well dem- onstrated by the report of the pilot for the flight whose results are shown in figure 6. I n this case, as will be seen, the pilot reported ent,ering a stratus overcast a t 100 meters above the ground, and then, while still in this stratus he reported striking heavy rain a t 375 meters above BILLINGS. MONT. JUNE 7,1936 Lq? RUfD B /.2:38 a m - EZ-’/Oam /O 5f N€, 3:29 am. Take - Off 8Sf NE /:/5am 2 Sf NE /.‘/5 0. m 6Sf NE &45fCuhE/Z.’38am Observed from Ground i figure 6 the ground-both the rain and the stratus being reported as ending a t 620 meters above t,he ground. A consulta- tion of all available records reveals that no rain fell during the period of the flight-thus indicating that a pilot may even go so far as to term a wet layer of the cloud “heavy rain.” This, then, leaves the 10 cases of the sixth cate- gory to be accounted for. In four of these cases, the temperatures indkated a t the top of the cloud layer were 1’ C. or less above the freezing point. Since the error in the c,alibration of the tempera- ture elements may be as much as 2OC., it is therefore possible that, for the.se four cases, the required subfreezing temperatures could have been present. EL PASO, TEXAS. J U LY 6,1935 5190, Clear above RCu 4890- 47xk\. 4630,:. -&aOs- -I 4440- g4f90- L3920- ? 2 F 4 c w 1194- 0 100 -20 -10 0 10 20 30 Humidity (7.) Temperature (‘C) Lightnlng throughout flight. fiyure 7 Two more of the, cases in the sixth category are shown in figure.s 7 and 8. In these two c.ases, an increase in the. hunliclity and fairly good lapse rates make it appear that., considering the tolerances for instrumental error just mentioned, the upper cloud limit really c,ould have been above the 0’ C. isotherm although the pilot’s reports incli- cat8e the upper cloud limit to belelow this isot,herm. Bar- ing in mind the multiplicity of t,he duties of the weather flight-pilots, and bearing in mind also the trying conditions under which these bad-weat,her flights were macle., it is bo be expecked that, in t8he 360 cases inve.stigate,cl,, some of the pilot’s reports will be in error. That there should be two c,ases of this nature is therefore not surprising. Figures 9, 10, 11, and 12 show the rexmining four of the 10 ca.ses. In the flight of figure 9 the pilot merely st.at.es that clouds were encountered a t about 2,000 feet and that rain was encountered a t about 10,000 feet without indicat- ing whether he left the lower cloud layer or the rain and, if so, when. Considering the scnrcit,y of the notes along with the probability of their inaccuracy-as is revealed, for instance, by the lack of saturation a t the stated eleva- tion of the cloud base-no definite conclusions appear to be warranted, and it would seem t’h8.t this flight co~lcl, EL PASO, TEXAS. AUG. 19.1936 Observed pllot 5440- -2:34 - - -1 4720- Y C 3990‘ ‘2:06 $M90- --1:57 3 2680- % t t 4130c I-2.08 $3560- --2:02 $ -l :5 0 u E c --I :3 4 1194- MO -20 -10 0 IO 20 30 0 Iiumldliy (?.I Temperature (‘C) Clwdless at 12:91% l :~a m .-3 S t C u /S W ~2 ;~6 a .~-O b s e r ~d fmm ground. fipm a therefore, be classified with those flights which neither confirm nor deny the theory being evaluated. The clifiiculty with the flights shown in figures 10, 11, and 12 is, of course, that rain-light though it is-is ob- served a t the surface even though the zero degree isotherm is above the cloud layer from which the rain appears to be coming and even t,hough low humidities exist between the base of the cloud layer and the ground. In all three cases, the thickness of the cloud layer would seem to be great enough to account for the formation of the rain either by the Reynolds eft‘ect or perhaps by coalescence wit,hin the size-distribution range. Although the flight GALVESTON. TEX. JULY II, 1934 figure 9 shown in figure 12 was macle in cloylight, attributing the formation of the rain to the Reynolds effect is not exclud- ed here since the pilot’s report shows that, these were scattered tops of the “stratus” extending considerably above the general layer of the ‘%tratiis”-which means that those portions of the top of the general la er which losing a sficiently great amount of heat by radiation for the Reynolds effect to set in and produce the occasional light rain a t the surface. However, it will be noted that in both figures 11 and 12, no inversion exists at the top of the cloud layers. If the Reynolds effect were active, one might reasonably expect that its activity woulcl be evi- denced by the presence of such an inversion. But if certain fairly plausible assumptions are made, it can be were in the shade of these scattered tops might K av.e been OCTOBBR 1940 MONTHLY WEATHER REVIEW 277 Wave length (microns). Elm. (O.(fil ~m . pfi- cipitablewaters) .____. EIE. (0.06 cm. precipi- tablewater) ._._______ shown that this is not necessa,rily the case. The required nssumptions nre, briefly, thnt, first, in accordance with the results of the water content measurements of Kohler, Conra.d, and Wsgner (ll), the mass of the liquid water and the mass of the wat,er vapor in a c.loud are of the same order of magnitude; nncl second, that, in accordance with an nssertion mnde by Brunt (23), no great change is pro- duced in the emissive power or nbsorptivity of liquid wnter DALLAS, TEX. FEB. 24, 1934 3-4 4-5 W 5 7 7-8 8-9 9- IC- 11-12 12-13 13- 14- 1 5 16. 17- 10 11 14 15 I6 17 19 - - - - - - - - __ - - - - - - 15.6 4.9 10.25.0 10.2 co m m m m m ___ ___ ___ ___ '2.82.5 2.01.1 1.925.0 m m 1M).0100.016.74.0!2.22.01.3 ,54/0 5:/0 ; -? \ % e ? 2 p 3670 e 1, $2470 4.26 -? h QJ I I I I \IZkelOFF, 100 -30 -20 -10 0 /O 20 Humidify (%) Ternperdure C°C/ Figure 10 by the fact thnt it consists of sma.11 drops such as those found in fogs and clouds. These assumptions hnving been made, an application of Kirchhoff's law shows that the emissive power of the liquid wnter drops has the same ratio to the emissive power of the wnter vapor as the ab- sorptivities of liquid water and wnter vapor, respectively. MONTGOMERY, ALA. JAN.18.1935 0 I O 0 -20 -/0 0 10 20 30 Hurnidity/7J fimperufure PCI ruth ended at 4-50 am. Occosiono/ /;qbf r a h of surfore durihg first portion of fh9hfi Figure I I Utilizing the liquid water absorptivity meusurenients of Reubens and Laden burg (24) nncl the corresponding meas- urements of Fowle (25) for the water vapor in the earth's atmosphere, the ratio of the emissivities is then found to have the vnlues given in the following t,nble for the incli- cated radiation ranges: Considering the ratios given for the smaller quantities of liquid water and water vapor (which, of course, are those most nearly applicable to the conditions in questmion), it will be seen that this ratio is quite large for all the radi- ation rnnges. This, then, nieans that the cloud droplets can cool more rapidly by radiation than the surrounding air a.nd thnt, ns a consequence, it seems possible that t8he water droplets themselves may experience a loss of lient by radintion without the occurrence of a c.orresponding loss of heat in the air surrounding the droplets. When it is aclditionally borne in mind that, under the rtssumed conditions, a minute fall in the tempernture of t,he drop- Lets will result in a c,orre,sponding condensat,ion of the vapor surrounding the drops on the drops together with a corresponding liberation of the heat of condensation, it would consequently seem that the act,ion of the Rey- nolds effect is not necessarily accompanied by t'he forma- tion of an inversion. It will finaIly be noted that for a t least one of these three cases (that shown in fig. 11) rain is reported as being encountered very near the top of the doud layer. On first consideration, this phenomenon dso does not appear to be explainnble by any of the processes whkh SHREVEPORT, LA. NOV. 6,1935 5300 IO 01 7 .I Y 3 2 % 2310 9 24 r 5 .p s y /2/0 9 1.2 ; 23830 % $2840 I 930: .t. k 0 91 9 01 5 2 ~ m0 +O /O BO Humtd///y/%] Temperdue /*C) Occusiond Ltqhf ruin fo 9 /0 a m RE I2 30om R Conf'd Figure 12 have been listed thus far. For, both in tlie case of conles- cenc.e within the size distribution rnnge and in the cme of tlie action of the Reynolds e,ffect,, a c,onsiderable fall of the coalescing droplets with respect to the surrounding nir- and therefore with respect to the unused nulcei-is re- quired before drops large enough to be ac.countec1 as rain result, nnd, since there is no reason to suppose t81iat con- densation willnot continue to take plnce on the portion of the unused nudei which nre thus nscencling with respect to the coalescing droplets, it would t,lierefore seem thnt none .of the proc,esses so far outlined serves to esphin this phenomenon. If, therefore, the phenomenon is red, the existence of some unknown rain formation process would seem to be indicated. However, if the c.ircumsta.nces under which these flights are made are borne in mind, it would seem that there is n considera,ble c.hnnce thnt t,lie phenomenon may no be real. For, in the first plnce, due to the hrge horizontal component of the velocit8y of thc plane with respect, to the surrounding air, the observed vnrintions in the weather may frequently be those wit'h re,spec,t t80 the horizontal rnt'her t,hnn with respeci to the vertkal. In the second plnce, owing to the multifarious duties of a pilot in these bad-weathe,r flights, it is quitme c.onceiva.ble that changes in the weather (and grndua.1 c,hmges in particu1a.r) ma.y set in considerably earlier than t,he time a t which they are observed by the pilot-this being especially the case if the attention of the pilot is not con- fined to the oc,currence or nonoccurrence of the phenomenon in question. It is therefore quite possible that, 111 the case being considered, the pilot may have flown unde,r the crest of one of the rolls of the strnto-cumuli (at the top of which the action of the Reynolds effect would, of course, be con- 278 MONTHLY WEATRER REVIEW OCTOBER 1940 siderably more inte,nse than it wpuld in t’hose portions of the upper cloud surface which Intervene between these crests) a t the time a t which the beginning of the rain was observed and that he nlso emerged from the strnto- cumulus layer in one of the troughs in between these crests therewith failing to notice the gradual diminut,ion of the rain owing to his absorption in the remainder of his dut’ies connected with b nd-w ea tjher flying. The only wa.y to be sure in instances of this sort is, of course, to devise a means of measuring drop sizes in con- nection with these flights. Such a procedure does not appear to be impossible. Besides the foregoing indire.ct evide,nce as to the prev- alence of the Bergeron-Findeifen process jl;l the formation of precipitation, a consideratlon of the flights shown in figures 2 and 13 furnishes evichce as to the existence of this process which is somewhat more direct. In figure 2 it will be noted thnt an accumulation of ice was obtained ATLANTA, GA. JUNE 26,1933 - c g P .) - 2 L i i= [Tnin layer S t 0 yx) -20 -10 0 IO 20 30 Humldo (%) Temperature (u) Moderate io heovy rain of surface from 3:38 a.m. t 0 4 :/5 ~m .~ light ruin from 415 u.rn.t04:48 a.m. Figure i3 in a layer of alto-stratus which lay considerably above the cloud layer from which snow wns falling. Since the presence of liquid drops is necessary for the formntion of ice, on airwaft, we thus have a. case of the existe,nce of liquid clrops a t a temperature lower than that a t which snow was forming. As far as the author is awnre, the only explanation for this is that effective sublimation iiuc.lei were lacking a t the higher levels and hence under- cooled droplets instead of ice cryst,a.ls or snow flakes were formed. I n figure 13, it will be seen that the pilot in his ascent first encountered snow and then rain and finally snow again just before he reached the top of the flight. Again, suc.11 nn alternation in the occurrence of water in the solid a.nc1 liquid states can, it would seem, only be accounted for by the lack of effective sublimation nuclei in the region in which the liquid clrops we,re fonnecLs These two cases, therefore, furnish fairly positive evidence as to the: 0ccurre.nc.e of the Bergeron-Findeise.n proce,ss a.nd it thus follows that considera.bly mor? importance than otherwise may be attached to the clrc,umstantial evidence furnished by both the chlorine content observa- tions and by the d&a 8.s to t,he relative alt,itudes of the tops of the precipitat’ion producing c.loucls R;nd those of the 0’ C. isotherm. IA closing, a discussion of-this nature would not be corn- plet)e wit,hout a considera.tion of a. crit,icism of- Bergeron’s the.ory published by Holznmn in 1936. (26) -Those por- e It is to be noted here that this alternation of rain and snow was apparently one with respect to the horizontal instead of with respect to the vertical and that furthermore the ohserved rain could not. have heen formed by the Bergeron-E’indeisen ;)recess since‘this process requires a melting 01 the snow flakes or ice crystals and. owing to the altitudes and t.emperatures at which it was observed such a melting is quite improhahle. tions of the criticism which deal with the theoretical aspects of Bergeron’s theory, have, in general, been answered by the developments in the theory, subsequent to the publication of Holzman’s article. A closer exam- ination of the two examples which he cites as being contrary to the theory will, however, be found to be worth while. As the first of these examples, he gives the following: On June 15, 1936, in a flight made from Albany to Newark during the hours 5 to 6 a. m., a moderate rain was encountered in ascending and descending through a strato-cumulus deck. There were some low ragged stratus clouds extending from 600 to approximately 1,500 feet with the base of the strato-cumulus near 1,800 to 2,000 feet but frequently merging with the low stratus. The flight mas made at 8,000 feet with the temperature at or near 45’ F. At this elevation the plane waa generally above the cloud deck but, due to the undulating upper smface, an occasional cloud roll would sub- merge the ship. Aloft were a few cirrus and a few altostratus clouds that thickened to a near overcast far to the east, but pre- cluded the possibility that the rain that was encountered both on ascent and descent could have originated from an upper cloud system. Upon approaching Newark the strato-cumulus layer seemed to be rapidly dissipating, and by the time the landing was made the sky condition could be described as hroken. J UN E 15, I936 MITCHEL FIELD, N.Y -2 ASt/u above max. altitude:, -845 e 4 n 3 Y -7:32 u E L -7:28 I= -7:25 0 IO0 -20 -10 0 10 20 Figure 14 The 8 a. m. synoptic chart indicated 0.08 iiirhes of rain at Albany and 0.33 inches at New York City. The Mitchell Field sounding on June 15 taken at 7 a. ni. reached a height slightly over 11,500 feet at which elevation the temperature was 34O F. Extrapolation of the lapbe rate curve would place the freezing isotherm well above 12,000 feet. The temperature at 5,000 feet was 46O F., in very good agreement mith the temperatures as observed during the above- iiielitioned flight at this altitude. The cloud observations indicated only two-tenths altostratus above a rather low overcast stratus deck that extended from 1,500 to 3,000 feet. Regarding this flight i t is to be considerccl that moderate rain was not reported either a t Albany or New York a t the times in question. The 0.0s inch of rain mentioned a t Albany occurred between 1:OO and 5 :O O p. m. of the 14th-only a trace being recorded from 6:08 a. m. to 8:56 a. m. of the 15th. Also, the bulb of the 0.32 inch of rain reported a t New York City occurred before the night observation of the day before. Only 0.06 inch occurred after this, nnd all of this occurred before 2:30 a. m. of the 15th-traces of rain being reported from then until 8:45 a. m. Furthermore, the Mitchel Field aerograph flight shown in figure 14 only indicates “light mist” between the cloucl layer and the ground-the hu- midity throughout the stratum being approximately 100 percent. It would therefore seem that the “modernte rain” encountered in the strato-cumulus during this flight was probably a very light rain due to one of the two processes Hurnldity (3) Ternpemture yC) 0 Thrse are the examples referred to by “C. F. D.” in the 3ulletin of the American Meteorological Society (27) where. in his necounq of the pro$ee&ngs of the 1939 meet.mg of the Institute o f the Aeronautical Sciences (st which the main part of the above mwldera- tions was presented in connection with thelr applmatlon to the aucrdt icim3 problem). he says that: “H. 0. Houahton and Ben Holzmen, however, pointed .to the occurrence of rains from clouds entirely ahove freezing, which does not permit so simple an explana- tion of precipitation.” OCTOBER 1940 MONTHLY WEATHER REVIEW 279 already mentioned as being alternate to the Bergeron- Findeisen process and that, as in the case of the Billings flight previously mentioned, the apparent int'ensity of the rain was increased by the speed of the plane. Judging by the Mitchel Field ascent, this case would therefore be listed in that category of table 2 which was allotted to those cases in which light rain or drizzle was falling from low clouds with high humidities between the earth and the cloud. KELLY FI EL D (San Antonio),TEX. JULY 1.1936 Humidity (2) Temperature ['C) Light rain and IO St/SW observed from surface at: 542 a.m., 6:IOa.m.. 708 a.m. Rain ended -7:52 am. fiyure 15 The second example mentioned by Holzman is shown in figure 15. As is indicated, light rain was-reported both by the observer on the ground and by the pilot, and the humidities between the cloud base and the ground lay between 92 percent and 97 percent. The San Antonio precipitation record for the early part of the day of the flight reads as follows: Period: Amount of rain Midnighel a. m- ____________._______________ 0.02 inch. 6 a . m.-7a. m _______________________________ trace. 7 a . m.-8a. m ___-____-______-_______________ 0.01inch. In compiling table 2, therefore, this case also came under the third category, i. e., in the category of being, therefore, comput'ible wit,h t.he theory as outlined by Findeisen. Summarizing then it has first been shown t,hat, assuming Schmidt's equation for the distance of fall required for t.he coalescence of two equally large drops by hydrodynaniical attraction to be valid, the process which has been the main rival of the Bergeron-Findiesen process, i. e., t,he coales- cence of drops of equal size-cannot produce the large drops which are observed in heavy rains-this being true even if, in consideration of t8he drop size measurement.s of Defant, Kohler, and Niederdorfer, such a coalescence is conceded to have previously taken place up to the top of the range in which the size distributions indicative of such a coalescence are observed. Sec.ondly, it has been pointed out that the nomonductivity of the water obtained by melting the snow tn.ken from the firn region of a glacier indicates that, in some cases a t least, the duality of the nuclei required for condensation and sublimation is real, a.nd it has been further pointed out that such a duality is to be expected from a consideration of the more compli- cated molecular structure of solids 8,s compared with liqiiids. In the third place, it has been shown that such indirect evidence as is available, i. e., t'hat to be derived from the chlorine content observations and that derived from the data as to the relative altitudes of the top of the precipitation producing douds and those of the zero degree, centigrade isotherm-points to the prevalence of the Ber- geron-Findeise.n process in the proc1uct)ion of rains of any considerable, intensity. Fourthly, it has been indicated that the only a,ppare.n t e.xpla.nation for the appearance of n9210-41-2 undercooled water drops at higher and colder altitudes than those at which snow is simultaneously observed is that effective sublimation nuclei are lacking in those park of the atmosphere in which the undercooled drops originat,e-this phenomenon dso, therefore, confirming the, existence of t,he Bergeron-Findeisen process in the earth's atmosphere and lending considerably greater weight to tho circumstantial evidence previously presented. Finally, it has been demonstrat,ed t,hat a more dekailed consideration of the examples cited by Holzman as being contrary to the the,ory shows that such is not the case a t d l . CONCLUSIONS On the basis of the evidence presented, it therefore must be concluded that the Berge,ron-Findeisen process actually takes place in the atmosphere. Furthermore, the results of the chlorine content observations together with the relationship of the altitudes of the Oo isotherni to the altitudes of the tops of the precipitation-producing clouds seem circumstantially, to indicate that the process is, at lea.st, the main one in the production of rains of any considerable intensity and that any alternative proc.esses, such as the action of the Reynolds effect and coalescence within the size-distribution range, are confined mainly to the production of light rains and drizzles. As has been suggested, however, the inferences drawn need to be con- fimed by more accurate observations-it being particu- larly necessary to judge the occurrence or nonomurrence of rain as observed from an airplane by some other means than by the amount of water striking the plane. Also, of course, an investigation as to the nature of the sublima- tion nuclei is needed. When this has been done, it would seen as though it should be possible ultimately to con- siderably extend the accuracy of precipitation forecasts. ACKNOWLEDGMENTS The author f i s t desires to acknowledge the large amount of cooperation furnished in the earlier part of these studies by his coworker at, tha.t time, P. F. Clapp of the Meteoro- logicad Research Division. In a.ddit>ion, L. P. Harrison of t>he Aerologicd Division read the manuscript and of- fered many suggestious which led to its clarification. Finally, indebtedness is expressed to H. R. Byers of thc Meteorological Research Division for the aid and advice received from him, this aid a.ncl advice having contributed much to expediting and improving the resiilts obbained. References to Literature Cited (1) Rergeron, T., On the Physics of Cloud and Precipitat,ion, Proc6s-Verbaux des Seances de 1'Associat.ion de MBtBoro- logie, Cinquiime AssemblBe GBnBrale de 1'Union G6o- desique e t GBophysique Int,ernationale, M6moires et, Dis- CUSSIO~~S, 156, Paris, 1935. (2) Findeisen, %., Die kolloidmeteorologischen Vorgange bei der Niederschlagsbildung, Meteorologische Zeitschrift, Bd. 55, S. 121, Braunschweig, 1938. (3) Findeisen, W., Der Aufbau der R.egenwolken, Zeihchrift, fur angewandte Meteorologie, 55. Jahrg., Heft 7, S. 208, Leipzig, 1938. (4) Op. cit. in reference (l), pp. 161-162. (6) Hohler. H.. nber die Chlorverteiluna und die TroDfeneruDDen .I im Nebel, Arkjv for Matematik;Astronomi och FGik; kd. 24 A, No. 9, S. 8, Stockholm, 1933. (6) Bjerknes, V., Bjerknes, J., Solberg, H., und Bergeron, T., Physikalische Hgdrodynamik, S. 252, Berlin, 1933. (7) Op. cit. in reference (5), 8. 46-48. (8) Gish, 0. H., and Sherman. K: L., Electrical Conductivity of Air to an Altitude of 22 Kilometers, National Geographic Society, Technical Papers, Stratosphere Series, No. 2, p. 111, Washington, 1936. (9) Schmidt, W., Zur Erkliirung der gesetzmiissig Verteilung der Tropfengrossen bei Regenfallen, Meteorologische Zeit- achrift, Bd. 25, S. 498, Braunschweig, 1908. 280 MONTHLY WEBTHER REVIEW OCTOBER 1940 Kohler, H., Untersuchungen uber die 14701~enbildung auf dem PIrtetjbkko in] August, 1928, nebst einer erweitert,en Untersuchung der Tropfengruppen, Nat,urwissenschaft,liche Untersuchungen des Sarekgebirges in Schwedisch-Lappland, Bd. 2, No. 21, 8. 84, Stockholm, 1930. Iiohler, H., On Water in the Clouds, Geofysiske Publikasjoner, Defant, A., Gesetzmiissigkeiten in der Verteilung der ver- schiedenen Tropfengrossen bei Regenfallen, Sitzungsbericht,e der mathematisch-nat,urwissenschsftlichen Iclasse der Kaiserlichen Akademie der Wissemchaften, Bd. 114, S. 585, Vienna, 1905. Kbhler, H., tfber Tropfengruppen und einige Bemerkungen zur Genauigkeit der Tropfenmeesungen, besonders mit Rucksicht auf Untersuchungen von Richardson, Meteoro- logische Zeitschrift, Bd. 42, S. 463, Braunschweig, 1925. Niederdorfer, E., Mcssungen der Grosse der Regentropfen, Met,eorologische Zeitschrift, Bd. 49, S. 1, Braunschweig, 1932. Ih. Tracks of tropical storms of October 1MO.