26 Journal of the Meteorological Society of Japan Vol. 59, No. I

Non-Melting Phenomena of Snowflakes Observed in Subsaturated Air below Freezing Level

By Takayo Matsuo and Yoshio Sasyo

MeteorologicalResearch Institute, Yatabe-cho, Tsukuba-gun,Ibaraki-ken, 305, Japan (Manuscript received 16 July 1980, in revised form 30 September 1980)

Abstract

The analyses of the meteorological surface data at Wajima, Matsumoto, and Nikko Weather Stations in Japan were made in order to examine the effect of relative humidity of air on melting of snowflakes below freezing level in the atmosphere. The results showed that the types of precipitations (rain or snow) observed on the ground were closely de- pendent on surface relative humidity as well as surface air temperature. When surface relative humidity was below a certain critical humidity, even at a higher surface air tempera- ture above 0* precipitations were snow. Using the regression analysis, the relations of the critical relative humidity RHcri to surface air temperature T could be obtained at each Weather Station in the following forms, RHcri=-7.5T+93, Wajima, RHcri= -7.3T+96, Mtsumoto, RHcri=-6.2T+91, Nikko. The relations thus obtained agreed well with that obtained previously from the theo- retical calculations by Matsuo and Sasyo (1981).

should be considered. 1. Introduction Matsuo and Sasyo (1981) showed theoretically The prediction of the types of precipitations the importance of relative humidity of air in the (rain or snow) on the ground has been made so melting process of snowflakes below freezing far on the data of air temperature (e.g., Hand- level. According to the theoretical calculations, book of Weather Forecasting, Japan Meteoro- it was shown that the ambient air temperature logical Agency, 1976, p. 207-208). at which melting commenced depended on rela- From statistical analyses of air temperature tive humidity and it increased nearly linearly when rain or snow was observed on the ground, as relative humidity decreased. For example, at it was shown that the types of precipitations a relative humidity of 90%, melting of falling were closely dependent on surface air tempera- snowflakes did not take place until the ambient ture. Snowfalls were frequently observed at air temperature rose up to about 1*, and at a surface air temperature below 2.5*: rainfalls humidity of 50% until up to about 4*. Thus, were frequently observed above 2.5*. This the presence of a non-melting layer, formed in critical temperature is utilized in the present subsaturated air below freezing level was pre- routine work of weather forecasting for the dicted. prediction of types of precipitations on the The purpose of this paper is to confirm the ground. prediction obtained previously from the theo- However, it is not unusual to actually ex- retical calculations with the analyses of meteoro- perience the phenomena that snowfalls appear logical surface data. even at higher surface air temperature of 4-6*. 2. Analyses of the surface meteorological data There are few explanations of the cause of the at Wajima, Matsumoto, and Nikko Weather phenomena. In order to understand the phe- Stations nomena, some other physical factors affecting the melting of snowflakes, except air temperature, The surface meteorological data in winter February 1981 T. Matsuo and Y. Sasyo 27

1292m for Nikko. The difference in the locations may give rise to the differences in physical properties of snowflakes (i.e., size, density) and in air conditions between these Stations, and the effects of the differences on melting, if any, can be examined. The analysed periods are as fol- lows: January-March from 1975 to 1978 at Wajima, October-May from 1970 to 1977 at Matsumoto, and October-May from 1963 to 1978 at Nikko. The length of the periods required for analyses was dependent on the amount of data available. Figs. 2(a), (b), and (c) show the relationship at three Stations between the type of precipita- tions and the corresponding surface air tempera- Fig. 1 Map showing the locations of three ture and relative humidity which were obtained Weather Stations used in analyses from routine surface data. All precipitations, (Wajima, Matsumoto, and Nikko). except graupels, observed at surface air tempera- ture below 0* were snowfalls, and were ex- seasons at three different Weather Stations were cluded from the figure. The types of precipita- analysed in order to investigate the relationship tions were determined routinely from eye ob- among the types of precipitations on the ground, servation by the staff members of the Weather surface relative humidity, and surface air tempera- Station. As is shown in the figure, the frequency ture (Fig. 1). Wajima is located at the sea shore of the occurrence of snowfalls decreases with of the Japan Sea and Matsumoto is about 90km increasing surface air temperature. At surface inland from the sea share, Nikko being 120 km air temperature below 2-3*, snowfalls are seen inland. The heights of the Stations are 5m above frequently and at surface air temperature above sea level for Wajima, 610m for Matsumoto, anc 2-3*, snowfalls are infrequent. This tendency

Fig. 2(a) Relationship between the types of precipitations and the corresponding surface air temperatures and relative humidities at Wajima Station. Data were collected in the winter seasons (January-March), from 1975 to 1978. 28 Journal of the Meteorological Society of Japan Vol. 59, No. 1

Fig. 2(b) Same as Fig. 2(a) except for Matsumoto Station.

Fig. 2(c) Same as Fig. 2(a) except for Nikko Station. February 1981 T. Matsuo and Y. Sasyo 29 agrees with the results obtained so far. It should ly expressed in terms of a linear function. The be noted here that the occurrence frequency of regression equation and correlation coefficient for snowfalls is also influenced by surface relative these plots are, humidity. Lower humidity results in an increase RHcri= -7.5T+93, r=0.94, Wajima, in the occurrence frequency. In the region of where RHcri is the critical relative humidity, T low humidity below 60%, snowfalls are seen surface air temperature, and r correlation co- even at high surface air temperature of 4-6* efficient. Below the critical humidity, precipita- as is shown by dashed circles in the figure. tions are all snow and above it they could be In order to obtain the relative frequency snow, sleet, and rain according to the situation. distribution of the occurrence of snowfalls as a In the same way as above, the critical relative function of surface air temperature and relative humilities at Matsumoto and Nikko Stations can humidity, the data are divided into small classes. be obtained. The results are as follows: The intervals of a class are 0.2* in temperature RHcri =-7.3 T+ 96, r= 0.96 Matsumoto, and 5% in humidity. The result at Wajima is RHcri =-6.2T+91, r=0.93 Nikko. tabulated in Table 1 as an example. Fractional numbers in classes indicate the relative frequency 3. Theoretical treatment of formation of a non- of the occurrence of snowfalls. A denominator melting layer below freezing level and a numerator indicate the frequency of all In saturated air below freezing level, water precipitations and the occurrence frequency of vapor density of the air is always higher than snowfalls respectively. In the columns of the that of snowflakes at the freezing point, and same air temperature range, the relative frequency condensation of water vapor takes place on increases as humidity decreases and becomes snowflake surface. Snowflakes commence melt- unity at a certain humidity which we define as ing from just below freezing level owing to the critical humidity, remaining the value of unity heat transfer from the ambient air and release below the critical humidity. The critical humidity of latent heat due to condensation of water thus obtained decreases with increasing air vapor on snowflake surface. In subsaturated temperature of classes. air, on the other hand, water vapor density The critical humidities in each column are of the ambient air around freezing level is plotted against the corresponding surface air lower than that of snowflakes at the freezing temperatures (open circles) in Fig. 3, The air point, and sublimation of water vapor occurs temperature is represented by mean temperature from snowflake surface. Cooling of snowflakes of the column. The relation can be approximate- due to sublimation takes place and snowflake temperature is reduced below freezing point, and consequently melting does not take place. In this case, heat required for sublimation is supplied with heat transferred by heat diffusion from the ambient air and in the steady-state condition, these heats must be balanced. Using the equation of the heat balance, steady-state temperature of snowflakes can be numerically obtained under a given condition of air tempera- ture and relative humidity. From this, we can obtain the relation between air temperature and relative humidity (critical humidity) in the com- mencement of melting. The details of the calcu- lations were described by Matsuo and Sasyo (1981). The calculated result previously obtained is shown by a solid line in Fig, 4, A solid line is the critical line for melting obtained from the Fig. 3 Critical relative humidity (open circles) calculations. Below the line melting does not take as a function of surface air tempera- place. The relations obtained from analyses at ture. In the region below the critical three Stations are also shown by dashed lines. line (dashed line), all precipitations There is in fairly good agreement between the observed were snowfalls. line obtained from the calculations and those 30 Journal of the Meteorological Society of Japan Vol. 59, No. 1

Table 1. Probability of snowfalls being observed in precipitations at Wajima Weather

from the analyses. that melted snowflakes or raindrops fall on the 4. Discussions ground where relative humidity is low enough for these precipitation particles to situate in the As mentioned before, we showed by numerical non-melting region shown in Fig. 4, possibly simulation that the commencement of melting of snowfalls are not observed on the ground be- snowflakes depended only on ambient air tem- cause of the time lag of the response. This case perature and relative humidity. If the melting will happen under the air condition of relatively process responds quickly to change of ambient high temperature and humidity around freezing air condition, we can judge for the commence- level (the air condition is situated in the melting ment of melting based on the air condition on region in Fig. 4) and low temperature and the observation place and do not need to pay humidity near the ground (the condition in the any attention to the air condition below freezing non-melting region). In this case, the atmos- level. pheric condition below freezing level exerts some It is considered, however, that practically such influence on the occurrence frequency of snow- quick response is not always feasible. In the case falls on the ground. However, this situation seems to be rare generally. An analytical example of the atmospheric con- ditions at Wajima in presence of precipitations will be shown below. At Wajima Weather Station, in parallel with meteorological surface observa- tions, the aerological observations of air tempera- ture and relative humidity by radiosondes are also carried out routinely two times a day (9h, 21h). The aerological data used here are those at the times nearest to the times when precipitations are seen in the hourly surface meteorological data. The analysed period is from January to March in 1975. The lapse rates of air temperature were deduced from the difference between surface air temperature and air temperature at 900mb level. Most of the lapse rates obtained distributed nearby wet adiabatic lapse rate and the average Fig. 4 Dependence of melting of snowflakes was 5.8°C/km. In very rare cases (only a few on air temperature and relative cases), air temperature inversions between the humidity. A solid line and dashed lines are critical lines obtained from surface and 900mb level were found. This indi- the calculation and the analyses for cates that generally warm air of the same degree three Weather Stations, respectively. as surface air is unlikely to exist near freezing February 1981 T. Matsuo and Y. Sasyo 31

Station in given ranges of surface air temperature and relative humidity.

level. freezing level to the ground. The lapse rates of relative humidity were also From above discussion, it is considered that deduced from the humidity difference between generally the prediction of snowfalls can be made surface and 900mb level. In order to discuss only by the air conditions near the ground. This the relative humidity below freezing level, the consideration is supported by the analytical height of freezing level is required. The heights results that the relations obtained at each Station were calculated using an interpolation method are almost the same in spite of the difference of between surface and 900mb level and then rela- the locations. It is further supported with the tive humidities at the freezing level were also result that the obtained relations almost coincide calculated using the same method. with the relation obtained by calculations. Fig. 5 shows the relative frequency of the humidity difference (RHg-RH f) between the 5. Conclusions ground and freezing level. The difference ranges The results of the analyses of the meteoro- from -15% to 12.5%. The mode of the dif- logical surface data at three different Weather ference is -2.5% and there is no great humidity Stations showed that the types of precipitations difference between the surface and freezing level. observed on the ground were closely related to This example shows that precipitation particles surface relative humidity as well as surface air do not generally experience two regions (both temperature. Even at high surface air tempera- melting and non-melting) in falling from the ture above 0* (for example, several degrees centigrade), snowfalls were always observed when relative humidity was low and below the critical relative humidity. The critical humidity was obtained as a linear function of surface air temperature T. The relations at three Weather Stations are as follows: RHcri=-7.5T+93, Wajima, RHcri =-7.3T+96, Matsumoto, RHcri= -6.2T+91, Nikko. The present relations are in good agreement with that obtained previously from the calcula- tions (Matsuo and Sasyo (1981)). The present work will contribute to the improvement of the Fig. 5 Frequency distribution of humidity prediction of the types of precipitations on the difference between the ground and the ground. freezing level (RHg-RH f) in presence of precipitations from January to Acknowledgements March in 1975 at Wajima Weather Station. The authors would like to thank the Staff 32 Journal of the Meteorological Society of Japan Vol. 59, No. 1 members of Investigation Division, Technical are extended to Mr. Yasuhiro Sato of Saitama Department, Tokyo District Meteorological Ob- University for his assistance. servatory of Japan Meteorological Agency for References their offering surface meteorological data at Weather Stations. The authors also would like Japan Meteorological Agency, Forecast Department, to thank Mr. Jiro Kubo (Head) and the Staff 1976: Handbook of Weather Forecasting (in members of Physical Meteorology Division, Japanese), 207-208. Meteorological Research Institute of Japan for Matsuo, T. and Y. Sasyo, 1981: Melting of snow- flakes below freezing level in the atmosphere. J. their valuable comments and discussions. Thanks Meteor. Soc. Japan, 59, No. 1, 10-25.

0℃高 度 下 の 未 飽 和 大 気 中 で 起 こ る雪 片 の非 融 解 現 象

松 尾 敬 世 ・佐 粧 純 男 気象研究所

輪 島,松 本,日 光 測候 所 の地 上 気 象 観 測 デ ー タを 使 用 し て,雪 片 の 融 解 に 与 え る湿 度 の 影 響 を 解 析 的 に調 べ た。 地 上 で 観 測 され る降 水 の タイ プ(雨,雪)は,地 上 気 温 の み な らず 湿 度 に 依 存 して 変 化 す る こ とが 明 らか に な っ た 。 降 雪 は 地 上 気 温 が0℃ 以上 のか な り高 い場 合 に も見 られ,こ れ は 低 い 地 上 の 湿 度 と関 連 して い た。 これ ら の降 雪 は,地 上 の湿 度 が あ る臨 界 値 以 下 で あ れ ば 必 ず 見 られ た 。 三 地 点 の 臨 界 湿 度 と地 上 気 温 の 関 係 を 回 帰分 析 に よ り求 め る と次 の よ うに な った。 RHcri=-7.5T+93,輪 島 RHcri=-7.3T+96,松 本 RHcri=-6.2T+91,日 光

得 られ た 関 係 は松 尾,佐 粧(1981)が 計 算 に よっ て 求め た 雪 片 の融 解 開 始 時 の 温 ・湿 度 の 関 係 式 と良 く一 致 した。