A Statistical Analysis-

April 1975 T. Yonetani 139

Characteristics of Atmospheric Vertical Structure on Days with Thunderstorms in the Northern Kanto Plain

A statistical analysis- -

By Tsuneharu Yonetani

National Research Center for Disaster Prevention, Tokyo (Manuscript received 7 September 1974, in revised form 10 March 1975)

Abstract

Vertical conditions on 248 days during two summer seasons are investigated to study the distinctive characteristics of the stratification on days with thunderstorms in the northern Kanto plain. For the sake of convenience atmosphere is divided into two layers, upper layer and lower layer. It is recognized that high degree of conditional instability of an upper layer is not the sufficient condition for the occurrence of thunderstorms. However, there are distinct differences of vertical stabilities of a lower layer between on days with thunderstorms and on days without a thunderstorm when an upper layer is conditionally unstable. Namely, it is shown that vertical movement of an air parcel in a lower layer on the former is easier than on the latter. It is also shown that the ratio of the degree of conditional instability of an upper layer to the degree of stability of a lower layer is an important factor affecting the occurrence of thunderstorms rather than their values. These conditions are interpreted into suggesting an interaction between a convective cloud and its subcloud layer, and an instability index is obtained by assuming the interaction. It is shown that this instability index has higher association with the occurrence of thunderstorms than Showalter stability index has. Therefore, the stronger relation is suggested between the occurrence of thunderstorms and the stability of the whole atmosphere than it has been pointed out.

Thus, the degree of over-all stability may be the 1. Introduction most important factor in the occurrence of con- The synoptic conditions favorable for the occur- vective storms among the conditions described rence of severe thunderstorms and tornadoes above. have been described by many authors (e.g. When we compute the stability of air masses Fawbush, et al. 1951; Means, 1952; Miller, 1959). for use in analysis and forecasting, a statical and Reviewing these, Newton (1963) summarized the macroscopical viewpoint is usually taken. Show- conditions as follows : alter stability index (Showalter, 1953) and energy (a) Conditional and convective instability; stability index (Darkow, 1968) are determined (b) Availability of abundant moisture in lower from 850- and 500-mb data. Lifted index (Galway, levels; 1956) is similar to Showalter stability index except (c) Bands of strong winds in lower and upper for the determination of the level where the parcel levels; is lifted. These indicies do not represent structural (d) Some dynamical mechanism which can characteristics like the existence of inversion. On cause the release of instability. the other hand, the presence of strong inversion Analysis done by Ninomiya (1971) shows that has been shown as one of significant features these are not phenomena occurred independently prior to the occurrence of tornadoes or large hail but moisture and wind fields are modified to (Fawbush and Miller, 1953). Discussing the evolu- intensify convections through the interactions tion of convective clouds dynamically, the energy between thunderstorms and large scale fields. supply may be a basic factor. The effects of the 140 Journal of the Meteorological Society of Japan Vol. 53, No. 2 energy supply on the behavior of clouds systems The days with thunderstorms are days when over the sea are analyzed by several authors thunderstorms or a thunderstorm occurred in (Matsumoto and Ninomiya,1966; Ninomiya, 1968 the northern Kanto plain during 09 to 21 JST and 1972). The purpose of this paper is to and the other days are regarded as the days investigate the characteristics of atmospheric verti- without a thunderstrom (refer to Fig. 1). Numbers cal structure on days with thunderstorms in the northern Kanto plain. The viewpoint will be rather dynamical and atmosphere will he divided into two layers, i.e. upper layer and lower layer. It will be simplified that an upper layer is environment in which convective clouds are embedded and a lower layer is a supplier of energy. We have many days with thunderstorms in the northern Kanto district in summer season and almost all intense thunderstorms are initiated in the mountainous area and move into the Kanto plain. Omoto (1971) showed the locations of preferred routes of severe convective storms in the Kanto plain which originated from several mountains. The upper layer is temporarily set as a layer above 1,800 m, noting the position of thunderstorms initiations relative to the mountains and their heights in the area under consideration. According to Kurihara (1962), the diurnal variation of temperatures and heights of isobaric surfaces at levels over 850 mb are fairly small Fig. 1. Topographic map of Kanto district and and the magnitudes are less than the probable location of weather stations used in the errors of upper air observations at that time. One analysis. Dotted area is northern Kanto of water vapor pressure is also small unless the Plain and shows a station whose exchange of air-mass does not occur. Thus, daily reports are used to know days assuming that meteorological elements except for with showers. Blacked triangles are the temperature at low levels do not change their peaks which is pointed out to be located values abruptly, we use aerological data taken at in the places from where preferred Tateno (646, 27 m MSL) at 09 JST as represent- routes of hailstorms start (Omoto 1971). ative of the stratification of atmosphere over the Kanto plain in day time, though it is desirable to of days with thunderstorms in 1967 and 1968 are use sounding data taken just before the occurrence 40 and 39, respectively. The following publica- of thunderstorms if we could. tions of the JMA and Tokyo Meteorological District Office are used: Aerological Data of 2. Data used Japan, Monthly Report of the Japan Meteorologi- The JMA (Japan Meteorological Agency) and cal Agency, Ijo-Kisho Chosa Houkoku (report on its cooperators hold a series of thunderstorm abnormal weathers) and Chijo-Kisho Nippo (daily observations in which about 20 regular weather weather report). stations and about 35 cooperative stations in Kanto district join and the results of the observa- 3. An instability index to an upper layer tions are published yearly as Denryoku Kisho We pursue a parcel method modified slightly Gaiho (weather report concerning electrical power). as described below to discuss the vertical stability It was carried out from 15 May to 15 September of an upper layer. Namely, we consider an in 1967 and 1968 and on these 248 days the ascending air parcel embedded in an environment investigation is made. A classification of days which is in hydrostatic equilibrium. Following into a day with thunderstorms and a day without assumptions are made. a thunderstorm is based on these observations. (i) The parcel is saturated. April 1975 T. Yonetani 141

(ii) The forces acting on it are gravity, buoy- velocity and zero liquid water content at zi. The ancy and no frictional force. equations (1)-(4) are essentially similar to those (iii) In its ascending, all excess water vapor over of one dimensional cumulus model used by saturation condenses to liquid which is Squires and Turner (1962), Simpson and Wiggert retained in the parcel. et al. (1969). In one dimensional cumulus model, (iv) It has no ice phase process. it is assumed that entrainment rate is in inverse (v) It entrains environment air at a rate of 100 proportion to the updraft radius R, namely percent per 5,000 m ascent. The last corresponds to that environment air is entrained into the growing cumulus at a rate of approximately 100 percent per 400 mb, that is So we could take this instability index as the doubling of the mass for a rise of 400 mb (Byers maximum vertical velocity in an imaginary and Braham, 1948). The vertical motion of this convective cloud with 1,400 m radius of updraft. parcel can be expressed by a set of equations (1)-(4) (for example, see Mason and Emig, 1961). 4. Vertical structure on days with thunderstorms and on other days The correlation coefficients between Wm(0.0, 1800) and Wm(0.5,1800) and between Wm(1.0,1800) and Wm(0.5, 1800) are 0.98 and 0.99, respectively. The regression equations of Wm(0.0, 1800) and Wm(1.0, 1800) on Wm(0.5, 1800) are Wm(0.0, 1800) =1.00 • Wm(0.5, 1800)-2.8 and Wm(1.0, 1800) = 0.97 • Wm(0.5, 1800)+2.7. These show that the variation of Wm(d T, 1800) is in proportion to AT. However, we have a few exceptions. The relation between Wm(d T, 1800) and d T on such days with thunderstorms is shown in Fig. 2. where Cpm is specific heat of moist air at constant pressure, q acceleration of gravity, L liquid water content, Lh latent heat of condensation, Q specific humidity of a parcel, Qe specific humidity of environment air, R gas constant of air, T temperature of a parcel, Te temperature of environment air, Tv virtual temperature of a parcel, Tve virtual temperature of environment air, t time, W vertical velocity of a parcel, z height and p entrainment rate. The entrainment rate is give by Fig. 2. Dependence of maximum vertical velocity on temperature excess at 1,800 m (AT). The dashed line is a typical one and the others Noting the nature (v) of the parcel and assuming are exceptional ones on days with that the entrainment rate is independent of height, thunderstorms. integration of Eq. (5) with height gives p=0.00014. In this paper we take the maximum vertical We adopt Wm(0.5, 1800) as an instability index velocity calculated from equations (1)-(4) as an to an upper layer and it is referred to as Iu. index to the degree of conditional instability of The distribution of Iu on days with thunder- an upper layer. Hereafter we use a notation storms and their occurrence ratio are shown in Wm(d T, zi) to represent maximum vertical velocity Fig. 3. Fig. 3 shows that the probability of the calculated under a set of initial conditions: d T occurrence of thunderstorms is low on a day temperature excess from environment, zero vertical when Iu is small. However, the converse is not 142 Journal of the Meteorological Society of Japan Vol. 53, No. 2

Table 1. Statistics of Iu and the maximum vertical velocities calculated under five different initial conditions. Row A is the number of days with thunderstorms and the mean, row B is the number of days without a thunderstorm and the mean.

Fig. 4. Distribution of Iu on days without a thunderstorm. A histogram dotted denser shows distribution on days when a shower or showers are Fig. 3. Distribution of Iu (histogram) on days observed at one or more weather with thunderstorms and their occur- stations or/and thunderstorms or a rence ratio to all days belonging to the thunderstorm occurred in the moun- same Iu class (polygon). The days tainous area. N in the figure shows when Iu exceeds 26 is taken as one the total number of days. class in the calculation of the occurrence ratio. N in the figure shows the reports of one or more weather stations in the total number of days. northern Kanto district during 09 to 21 JST (the true. When Iu exceeds 12, the occurrence ratio weather stations are shown in Fig. 1). The of days with thunderstorms is 40-60 percent distribution of Iu on such 81 days is similar to independently of Iu. This situation holds true one on the whole days without a thunderstorm when we adopt other initial conditions, as is seen and the means are 8.9 and 8.8, respectively (Fig. 4). from Table 1. It is evident that the high degree The numbers of days when Iu exceeds 10 in the of instability of an upper layer is not a sufficient former and in the latter are 25 and 54, respec- condition for the occurrence of thunderstorms in tively. The distribution of Iu on the 50 days the northern Kanto plain. without a thunderstorm when showers or a shower The 169 days without a thunderstorm contains are observed at one or more stations in the 81 days when thunderstorms or a thunderstorm northern Kanto plain is also similar to one on the are observed in the mountainous area or/and a whole days without a thunderrtorm and the mean shower or showers are recorded in daily weather is 8.5. Above results suggest that there may exist April 1975 T. Yonetani 143 some basic factors affecting the evolution of convective clouds besides the stability of an upper layer. Hereafter we call the days without a thunderstorm when Iu exceeds 10 as the days with an unstable upper layer and no thunderstorm.

Fig. 6. Scatter diagram showing the relation between Iu and SIL on days with thunderstorms.

Temperature has systematic diurnal variation and the diurnal variation of the frequency of thunderstorms has a sharp rise in the afternoon in the Kanto district. It is said that temperature subjects considerable diurnal variation in the lower 1,000 m layer next to the ground (Takahashi, 1969). An air parcel described below may represent the averaged state of the layer below Fig. 5. Distribution of stability index of a layer extending from 1,200 m 1,000 m at high noon. The parcel has the mean to 1,800m. Upper histogram is specific humidity observed in the 1,000 m next one on days with thunderstroms to the ground and has the mean value of potential and the mean is 1.6*. Lower temperature between one observed at 1,000 m histogram is one on days with an and the maximum one observed at Maebashi. It unstable upper layer and no thun- is assumed that this air parcel represents the derstorm. The mean is 2.5*. averaged state of a layer below 1,000 m not only Ns in the figures show the respective total numbers of days. Fig. 5 shows a difference in the degree of stability of the layer extending from 1,200 m to 1,800 m between on days with thunderstorms and on days wiht an unstable upper layer and no thunderstorm. SIL which is an index to the degree of stability of the layer is computed as follows : An air parcel at 1,200 m is lifted dry adiabatically to saturation and then wet adiabatically to 1,800 m. When its lifting condensation level is above 1,800 m, dry adiabatically to Fig. 7. Comparison between distributions 1,800 m. The temperature of this air parcel is (histograms) and cumulative fre- then subtracted from the observed temperature quencies (polygons) of LFC of an at 1,800 m. A negative number indicates rising air parcel representative of the air is warmer than its surroundings. Fig. 5 averaged state of a layer below suggests that it needs less energy to lift up the 1,000 m on days with thunder- parcel of air at 1,200 m on days with thunderstorms (full lines) and on days storms than on days with an unstable upper layer with an unstable upper layer and no thunderstorm (dashed lines). and no thunderstorm. And on days with thunder- The total numbers of the former storms it is suggested that there exists a relation and of the latter are 79 and 54, between the degree of stability of a lower layer respectively. Parenthesized num- and the degree of conditional instability of an bers of days in the figure are upper layer, which could be expressed as numbers of days with an unstable SIL <0.075*Iu+ 2 in terms of Iu and SIL (Fig 6). upper layer and no thunderstorm. 144 Journal of the Meteorological Society of Japan Vol. 53, No. 2

at near Maebashi but at the inner Kanto plain, convective cloud develops. On the other hand, as the correlation coefficient between the if subcloud layer is stable enough against the maximum temperature observed at Maebashi action, it cannot form updraft and dissipates. (TMae) and one observed at Utsunomiya (Tut, This hypothesis is one that gives an explanation their locations are shown in Fig. 1) is 0.95 and to what is shown in Fig. 6. In this section we the regression equation is TUtsu=0.89*TMae+2.0. lead an index to the degree of instability of the Fig. 7 shows distributions and cumulative whole atmosphere based on the hypothesis. frequencies of the LFC (level of free convection) Consider a convective cloud and its subcloud of this air parcel. It is shown that the LFC on layer. The former has energy Ec and acts on a day with thunderstorms is below 3,000 m with subcloud layer, and the state of the latter needs 90 percent certainty, while the probability that the energy ESL to be lifted up to the height of the LFC on a day with an unstable upperr layer and cloud base. Ecs, surplus of energy over the no thunderstorm is below 3,000 m, is 61 percent. requisite energy to lift up subcloud layer, is This suggests that less amount of energy should be supplied to a mean parcel in the lower layer before the parcel acquires an excess temperature The problem is whether convective clouds form and is accelerated upwards on days with thunder- new upcurrents or not, and they need to form storms than on days with an unstable upper layer upcurrents in the area proportional to their cross and no thunderstorm. sections. So restricting a discussion to one dimen- 5. An instability index, IW sion, we may write Concerning the maintenance of convective storms, observations show that many thunderstorms contain several cells and that there is a distinct tendency for new cells to form in the immediate vicinity of existing cells. This is commonly explained that cold downdraft air spreads out on approaching ground and lifts the neighbouring warm air with the result that a new convective cell is initiated. This is a case of According to the first mean value theorem there thunderstorms of multicellular type. A numerical exist * and * which satisfy simulation of convective clouds (Takeda, 1971) shows that the type of thunderstorms is determined by the relative positions of pre-existing updraft, downdraft and new upcurrent which is initiated by downdraft. At any rate, it is important for the evolution of thunderstorms whether new upcurrent where ac and aL are constants, E0 the minimum is formed or not and as to its initiation the energy that a convective cloud has, T v(z,z1) virtual downdraft is considered to play a major role. temperature that a parcel of air at z1 would Some statistics shown in section 4 suggest that acquire if it were lifted adiabatically up to z, there may exist some dominant factors affecting Tvc(z) virtual temperature in a cloud at z, the evolution of convective clouds besides the Tve(z) = Tve; virtual temperature of environment stability of an upper layer. It is also shown that air at z, zs height of the ground, zb height of less amount of energy should be supplied to lift cloud base, zm height of level where Tvc(zm) up a lower layer on days with thunderstorms = Tve(zm) and p(z) density of air at z. We may than on days with an unstable upper layer and assume Ecs*E0 when a convective cloud develops. no thunderstorm. Then we may be able to Defining Was as ac. Wcs2=Ecs-E0 analogously to develop the explanation as to development of Eq. (8), Wcs is expressed from Eqs (7), (8) and thunderstorms as follows : (9) as A formed convective cloud acts on subcloud layer. When subcloud layer is not stable against the action, updraft is formed newly and a April 1975 T. Yonetani 145

A condition Ecs*E0 is equivalent to that Wcs is relation is SIL = 0.075*Iu+2u and we obtain Eq. a real number. Ecs is the energy of a convective (15) from Eq. (11). cloud that has just used energy in order to lift up subcloud layer, so

We may make on more assumption that subcloud layer has its level of free convection when a convective cloud develops. Then, in the stage when energy is supplied from subcloud layer, the energy that the convective cloud has may be

where Ws is the maximum vertical velocity of a As is known from the process of leading the subcloud layer when it were lifted up to a level instability index, the larger is Iw, the more energy where it is accelerated upwards and starts free an imaginary convective cloud could have after vertical movement in the environment air. Thus, the cloud derives the supply of energy from its the value computed from Eq. (14) may be suitable subcloud layer in the inner Kanto plain. for an index to the degree of instability of the whole atmosphere. 6. Dependence of thunderstorms on l y The statistics on Iw on days with thunderstorms and without a thunderstorm are shown in Fig. 8

In calculation of the instability index Iw, the values of W~ and WS are estimated at the values of Iu and Wsm, respectively. Here, Wsm is the maximum vertical velocity of the air parcel representative of the averaged state of a layer below 1,000 m described in section 4. It is obtained by solving the equations (1)-(4) under an initial condition as in the following. The initial height is a level where the excess of temperature of the air parcel over temperature of environment is largest above its lifting condensation level when it is lifted dry adiabatically to saturation and then wet adiabatically. The initial temperature and liquid water content are those that it has at the initial height, and initial velocity is zero. {Tv(*, )-Tve(*)}/Tve(*) may be estimat- Fig. 8. Distribution of Iw on days with ed at **/T, where ** is excess of temperature that thunderstorms (upper) and on a parcel of air at a certain height (1,200 m) would days without a thunderstorm acquire if it were lifted adiabatically up to a (lower). The means are 11.8 on days with thunderstorms and 3.6 certain height (1,800 m) over temperature observed on days without a thunderstorm. at this level, and T is temperature averaged on Polygon shows occurrence ratio duration. When we take zb as a constant and of days with thunderstorms with neglect the variation of density of air, ESL may be over Iw value to all days with estimated at aL'*SIL . We may conclude that a the same Iw class. Ns in the convective cloud cannot form new upcurrents figures show the respective total unless SIL < 0.075*Iu+2urom Fig. 6. The critical numbers of days. 146 Journal of the Meteorological Society of Japan Vol. 53, No. 2

Table 2. Cumulative frequency table. Rows A and B are cumulative number and percentage frequency of days with thunderstorms, respectively. Rows C and D are the same as rows A and B, respectively, but of days without a thunderstorm. Row E is occurrence ratio of days with thunderstorms. Parenthesized numbers are cumulative numbers of days with frontal thunderstorms.

Table 3. Same as Table 2, but classified by Showalter stability index.

and Table 2. The days with thunderstorms when Table 3 shows the statistics on SI (Showalter Iw exceeds 21 amount to 17 percent of the whole stability index). The occurrence ratio of thunder- days with thunderstorms, while the number of the storms on a day when SI is less than or equal days without a thunderstorm belonging to the to -4 is 100 percent. However, the number same Iw class is 0. The days with thunderstorms of the days belonging to this SI class is only 2. when Iw exceeds 6 amount to 81 percent of the The days with thunderstorms when SI is less than whole days with thunderstorms and the days or equal to 4 amount to 81 percent of the whole without a thunderstorm belonging to the same days with thunderstorms and the days without a Iw class amount to 27 percent of the whole days thunderstorm belonging to the same SI class without a thunderstorm. The occurrence ratio of amount to nearly half of the whole days without thunderstorms on a day when Iw exceeds 6 is 59 a thunderstorm. The occurrence ratio of thunder- percent. It is obvious that the higher value of storms on a day when SI is less than or equal this instability index has the higher association to 4 is 44 percent. It is clearly evident from the with the occurrence of thunderstorms in the tables 2 and 3 that the occurrence of thunderstorms northern Kanto plain. has stronger relation to Iw than to SI. On many The investigation is made setting the boundary days without a thunderstorm when SI indicates of upper and lower layers at 1,800 m. Iw' is the occurrence of thunderstorms, Iw does that the calculated following the same method of calcula- stratification of atmosphere is not so unstable. tion for Iw except that the height of the boundary For example, the 93 days without a thunderstorm varies between 1,600 m and 2,000 m at random when Iw is equal to 0 contains 23 days when SI on each day. There is no significant difference is less than or equal to 2. Thus, it is suggested between the distributions of Iw and Iw' both on that the dynamical mechanism which can cause days with thunderstorms and on days without a the release of instability may not contribute so thunderstorm. The means of Iw'(Iw) on days largely to the occurrence of thunderstorms as we with thunderstorms and on days without a thunder- have considered. strom are 11.6 (11.8) and 3.8 (3.6), respectively. Thus the instability index may not depend on the 7. Concluding remarks height of the boundary if it is held between It is shown from a statistical analysis that the 1,600 m and 2,000 m at least. vertical conditions described below are satisfied April 1975 T. Yonetani 147 when thunderstorms occurred in the northern (This is the same as what lies at the base of the Kanto plain. hypothesis in section 5). This gives thunder- 1. The degree of stability of a lower layer does storms the character of frontal ones when thunder- not exceed a certain value which increases storms occur. The number of days with frontal proportionally to the degree of conditional thunderstorms among the days with thunderstorms instability of an upper layer. is 10 according to Dneryoku Kisho Gaiho (refer 2. The level of free convection of the air parcel to section 2). As is known from Table 2, the representative of a lower layer in midday is existence of 10 days with frontal thunderstorms less than 3,000 m with 90 percent certainty. may not bring about any change in the results. These conditions are interpreted into suggesting It has been shown that abundance of water an interaction between a convectioe cloud and its vapor content in a lower layer is not necessarily subcloud layer, and an instability index is obtained. a condition favorable for the occurrence of This instability index has higher association with thunderstorms with hail (Yonetani, 1974). This the occurrence of thunderstorms than Showalter is suggested more clearly by plotting Iw vs. stability index has. Therefore, the stronger rela- precipitable water vapor in a lower layer. tion is suggested between the occurrence of Namely, the conditions described below are thunderstorms and the stability of the whole represented as conditions the more favorable for atmosphere than we have considered. the occurrence of thunderstorms, which have the Temperature difference is used to indicate the stronger tendency to be accompanied with hail. degree of stability of a lower layer. When the (1) The larger of the instability index when the LCL (lifting condensation level) of air at 1,200 m precipitable water vapor in a lower layer is exceeds 1,800 m, the same temperature difference the same. may not always indicate the same degree of the (2) The less of precipitable water vapor in a stability of a lower layer. However, the difference lower layer when the instability index is the of the height of the LCL in such case is neglected same. in leading the instability index to the whole at- What this means is studied and will be reported mosphere, because the mean of the LCL is 1,680 m in near feature. and the number of days when the LCL exceeds 2,200 m is only 20. The 20 days when the LCL Acknowledgements exceeds 2,200 m contains 9 days without a thunder- The author wishes to thank to the Forecast storm when Iw is equal to 0, 4 days without a Division of JMA for making the thunderstorm thunderstorm when Iw exceeds 10 and 6 days with observations data available. The author also ex- thunderstorms. On the 6 days with thunderstorms, presses his thanks to refrees for their comments Iw exceeds 9 and thunderstorms occurred in a and Mr. K. Ohmura for his help with computer few places regardless of the value of Iw. The 4 programs. The computations were made with the days without a thunderstorm contains 2 days when use of the TOSBAC 3400 at the National Research Iw is larger than 16 and less than 18. This sug- Center for Disaster Prevention. gests that the relation between the occurrence of thunderstorms and the stability of the whole at- References mosphere may be stronger than what is suggested Byers, H. R. and R. R. Braham, 1948: Thunderstorm in section 6. structure and circulation. J. Meteor., 5, 71-86, We can classify types of thunderstorms into Darkow, G. L., 1968: The total energy environment two large groups, air mass thunderstorms and of severe storms. J. App!. Meteor., 7, 199-205. frontal ones. Pure air mass thunderstorms or Fawbush, E. J. and R. C. Miller, 1953: A method for forecasting hailstone size at the earth's surface. pure frontal thunderstorms scarcely occur and Bull. Amer. Meteor. Soc., 34, 235-244. typical development of thunderstorms in high and L. G. -,-, Starrett, 1951: summer is as follows (Takahashi, 1969) : Sunshine An empirical method of forecasting tornado forms upcurrents in mountainous areas and development. Bull. Amer. Meteor. Soc., 32, 1-9. cumulus clouds grow into ones with precipitation. Galway, J. G., 1956: The lifted index as a predictor Then cold air generated by precipitation moves of latent instability. Bull. Amer. Meteor. Soc., 37, down along valleys and it pushes warm air in 528-529. lower levels upward in a plane as cold front does Kurihara, Y., 1962: On the diurnal variation in the 148 Journal of the Meteorological Society of Japan Vol. 53, No. 2

reported heights of isobaric surfaces, temperatures Meteor. 10, 1103-1121. and winds in the troposphere. J. Meteor. Soc. 1972: -, Heat and water-vapor budget over Japan, 40, 213-221. the East China Sea in the winter season. J. Meteor. Mason, B. J. and R. Emig, 1961: Calculations of the Soc. Japan, 50, 1-17. ascent of a saturated buoyant parcel with mixing. Omoto, Y., 1971: Hailstorms in the Kanto-Koshin Quart. J. Roy. Meteor. Soc., 87, 212-222. District (3) (in Japanese). J. Agri. Meteor., 26, Matsumoto, S. and K. Ninomiya, 1966: Some aspects 211-218. of the cloud formation and its relation to the Showalter, A. K., 1953: A stability index for thunder- heat and moisture supply from the Japan Sea storm forecasting. Bull. Amer. Meteor. Soc., 34, surface under a weak winter monsoon situation. 250-252. J. Meteor. Soc. Japan, 44, 60-75. Simpson, J. and V. Wiggert, 1969: Models of precipitat- Means, L. L., 1952: On thunderstorm forecasting in ing cumulus towers. Mon. Wea. Rev., 97, 471- the Central United States. Mon. Wea. Rev., 80, 489. 165-189. Squires, P, and J. S. Turner, 1962: An entraining jet Miller, R. C., 1959: Tornado-producing synoptic pat- model for cumulonimbus updraughts. Tellus, 14, terns. Bull. Amer. Meteor. Soc., 40, 465-472. 422-434. Newton, C. W., 1963: Dynamics of severe convective Takahashi, K., 1969: Soukan-Kishogaku (synoptic storms. Meteor. Monogr., 5, No. 27, 33-58. meteorology), Iwanamishoten, Tokyo, 385 pp. Ninomiya, K., 1968: Cumulus group activity over the Takeda, T., 1971: Numerical simulation of a precipitat- Japan Sea in wintertime in relation to the water ing convective cloud: the formation of a "long- vapor convergence in subcloud layer. J. Meteor. lasting" cloud. J. Atmos. Sc., 28, 350-376, Soc. Japan, 46, 373-388. Yonetani, T., 1974: Atmospheric stabilities on days 1971: Mesoscale -, modification of synop- with thunderstorms in the northern Kanto district tic situations from thunderstorms development as (in Japanese). Report of the National Research revealed by ATS III and aerological data. J. Appl. Center for Disaster Prevention, 9, 47-53.

関東平野北部の雷雨日に特徴的な大気垂直構造 -統計的解析

米谷恒 - 春国立防災科学技術センター

関東平野北部に雷雨が発現した日に特徴的な大気垂直構造を知ることを目的として,館野の9時の高層データと前橋で観測された最高気温を使用して,1967年および68年の5月15日～9月15日の248日間について,大気の垂直安定度を求めた. 大気は1,800mを境として上層と下層に分けた.対流雲を取り囲んでいる環境である上層では,湿潤不安定度を問題とした.下層は,対流雲へエネルギーを補給する層であることを強調して,層中の気塊の垂直移動の難易を問題とした.上層における垂直不安定度を表わす指標として,周囲大気の吸い込みを行なう飽和気塊の上昇速度を計算し,これの最大値を採用した.

上層がかなり湿潤不安定であった日のうち,雷雨が発現した日はその約半数の日であった.しかし雷雨日と上層が不安定であった無雷雨日とでは,下層の状態が異なっていた.すなわち,上層が不安定であった無雷雨日は,雷雨日に比して下層がより安定であり,前橋での最高気温を用いて地上から1,000mまでの層を代表させた気塊の自由対

流高度は,平均的に高かった.さらに雷雨日には,上層の湿潤不安定度(Iu)と下層の安定度(SIL)とは,.SIL<0.075* Iu+2なる関係を満していた.

これらの特徴は対流雲と雲底下層との相互作用を示している,と解釈し,不安定指数を定義した.この不安定指数の平均値は,雷雨日では11.8無雷雨日では3.6となり,不安定指数の大きい口に雷雨の発現する確率は高くなった. この不安定指数と雷雨の発現との相関は,Showalterの安定指数と雷雨の発現との相関より,はるかに強かった .従って,雷雨の発現と大気の垂直安定度との間には,今まで考られていた以上に強い関係が存在すると考えられる. この報告は,国立防災科学技術センター気象調節に関する特別研究の1部としてなされたものである.