February 1973 By T. Chiyu, H. Kon and C. Magono 43

The Moving Velocity of Cumulus Humilis Clouds

By T. Chiyu, H. Ikon and C. Magono Departmeutof Geophysics,Hokkaido University, Sapporo (Manuscriptreceived 4 May 1972,in revisedform 14 October 1972)

Abstract

The horizontalmovement of cumulus humilis clouds near Sapporo was measured by the stereophotogrammetricmethod in the summer seasons of the years 1969 to 1971 in Sapporo. The direction and speed of individual cloud movements were presented on charts. The environmentalmeteorological conditions were obtained from the Sapporo rawinsonde soundings. By comparingthe analyticalresults of clouds with the environmental meteorologicalconditions, the followingresults were obtained. The direction of horizontal movementof the higher cumulus humilis clouds was nearly the same as that of prevailingwind direction at the cloud level (exactly speaking, near cloud base level),however, the direction of the lower clouds was not in agreementwith the wind direction. The critical ground height for the agreementof cloud motion direction with wind direction was found to be about 700 meters. The speed of horizontal movement of cumulus humilis clouds was generally less than prevailingwind speed at the level of cloud base. It was also found that the speed of larger clouds was slower than that of the smaller clouds when their heights were the same. The generaltendency was that the lower the clouds, the lower the motion speeds, and the greater the vertical wind shear, the lower the cloud speed. The slowness of cloud speed was qualitatively explained by considering the upward transportation of low horizontal momentumin thermal convections under a condition of the positive vertical wind shear.

tainous terrain was studied by Glass and Carlson 1. Introduction (1963), and by Orville (1965). However, most of Cumulus humilis clouds are a species of these studies are concerned with the growth cumulus clouds. These clouds are generally seen characteristics, and give little insight into the in fine weather, particularly in the mountainous relation between horizontal movement of cumulus terrain during morning in the warm season. humilis clouds and the wind velocity. Observations show that the horizontal and the The study of the movement of cumulus clouds vertical dimensions of cumulus humilis clouds is of great importance in the field of cumulus are some tens to some hundreds of meters. The dynamics. This problem has long been the individual cloud bases are usually flat, and the subject of observation and speculation. In recent cloud edges appear sharp. years, the movement of clouds has been studied by Many years ago, Abe (1937 and 1941) observed Shenk and Kreins (1970), utilizing Nimbus II sat- clouds near Mt. Fuji, including cumulus humilis ellite infrared measurements, and by Leese et al. clouds, utilizing the stereoscopic method and (1971) and Endlich et al. (1971), utilizing sequences movies. Cumulus humilis clouds were also of geosynchronous satellite photographs. The aim studied by foreign investigators in the past of these studies is to determine the direction and several years, and their general features have speed of prevailing winds in the environment by been reviewed in detail by Khrigian and Shmeter measuring the motion of clouds. This method (1961). The effect of a mountain range on a small could be used to obtain the wind field pattern cumulus cloud was studied in detail by Braham over a wide area and could be especially useful and Draginis (1960). And the growth charact- in areas where radiosonde soundings are sparse. eristic of cumulus humilis clouds over moun- However, these studies focussed attention on 44 Journal of the Meteorological Society of Japan Vol. 51, No. 1

during the summer seasons of 1969, 1970 and 1971.

2. Observation method 2.1. Camera locations In 1969, the cloud observation was made with a single camera, however, in 1970 and 1971, it was made by the stereophotogrammetric technique. Figure 1 shows the location of the camera sites (F and V) and their normal field of view with respect to the mountainous area and the Ishikari Plain by broken lines. The photographing was made by means of a pair of Bronica-S 2 cameras with size of 60*60mm, and with 50mm focal-length lens. Each camera was fixed on a theodolite in order to determine the direction of the camera axis exactly. The base line VF was 1278 meters long. The camera axes were set horizontally and perpendicularly to the base line. Photographs were taken in 30, 60 and 120 second intervals according to the cloud speed. The simultaneity of the photograph was achieved by Fig. 1. Topographicmap of observationarea. a transceiver signal between two camera sites. Dashed lines show field of view of The cloud observation was made between 8a.m. stereo camerasF and V. Long arrows and 10a.m. local time, because routine rawinsonde represent camera axis. Hatched area shows height of topography over sounding was made at 9a.m. by the Sapporo 500m. Meteorological Observatory. large cloud masses whose patterns can be 2.2. Analysis method recognized from the satellite photographs, and Cloud observations in 1970 and 1971 were whose life cycles persisted longer. performed by stereophotogrammetry. Since the However against these studies, there is a severe optical axes of cameras were parallel and oriented criticism that individual cloud movements are horizontally and their heights were nearly the frequently different from the wind system, for same, compared with the base line between example a cap cloud. them, the normal photogrammetry equations Yates (1953) reported a paper of Ludlam who (American Society of Photogrammetry, 1952, or estimated that in a typical wind shear, the bubble Hallert B., 1960) were available in the analysis (or cumulus cloud) was moving over the ground (See Appendix). at a speed which was 3 to 4ft/sec (0.9 to The computations of many cloud positions 1.2m/s) slower than the wind at the bubble were done quickly on a computer. height, however, the cloud size is not given in this paper. On the other hand, cirrus clouds 2.3. Error analysis move with the same velocity as the environment Error analysis is especially of great importance wind, according to the observation of Yagi et al. in such measurements. The errors in stereophoto- (1968). Therefore it is important to clarify the grammetric measurements are composed of mechanism in which the cloud movement agrees many factors, such as inaccuracy in measuring or does not agree with the wind. The cumulus the base line, the focal length of camera, parallax humilis cloud is very convenient in checking between a pair of photographic papers and this problem by observations. The present paper human error in field-work operations. It is very is to describe the results of observations of difficult to estimate all of these errors. motion of cumulus humilis clouds made by Most of the cumulus humilis clouds observed photogrammetry in the vicinity of Sapporo City were located at distances of 5km to 12km February 1973 T. Chiyu, H. Kon and C. Magono 45 from the observational sites. Therefore, it was photographs. However, it was impossible to estimated the error in the horizontal distance estimate the error in this case. was under four percent. Actually, the error on The authors assumed that the error in the measurement of the horizontal distance from cloud height was of 50 meters in the range in observational sites to the known mountain was the present observations, according to the about one percent. experiences of measurements which were hitherto The estimation of error of height is more made by our laboratory in this field. complicated, because in addition to the horizontal distance the reading of the vertical displacement 3. Horizontal movement of cumulus humilis clouds in the photographs of a cloud is required. In During the observations of 1970 and 1971, 20 the present case, it was estimated that the error cases of cumulus humilis clouds were observed. of height was about six percent for a horizontal From the data obtained in the observations, 12 distance of 12km and a height of 1,500 meters. cases of horizontal movement of clouds were Actually, in the case of the measurement of the analyzed. height of known mountain peaks which were The measurement of cloud movement was based made for checking, the error was five percent. on the following procedure. The first step was Besides the errors described above, another to determine the horizontal outline of a cloud significant error may occur in the reading of by measuring the parallax of corresponding points a cloud position in the photographs. The stret- of the cloud in the photographs. Then, the ching and shrinking of photographic papers could center of the outline was assumed to describe be neglected, compared with other errors. The the position of the cloud. Exactly speaking, this most difficult estimation was in the identification position shows the position of cloud base, because of the same position of a cloud in the different the outline observed corresponds to the lower

Fig. 2a. Cumulus humilis clouds over mountains, 0856 June 27, 1970. Cloud A was measured.

Fig. 2b. Cumulus humilis clouds, 0905. Cloud B was measured. 46 journal of the Meteorological Society of Japan Vol. 51, No. 1

Fig. 3. Location of clouds A and B (left side), and their horizontal movement (right side) on June 27, 1970. Figures in parenthesis under description of movement show the mean width and mean depth of clouds. Cloud bases: 600m.

Fig. 4a. Cumulus humilis clouds over mountains, 0951 Sept. 7, 1970. Clouds A and B were moving to the left.

Fig. 4b. Cumulus humilis clouds, 0955. Cloud B was separating from cloud A. portion of clouds. The movement of individual means the movement of cloud base, exactly clouds was then measured by the displacement speaking. of the positions of clouds in successive photo- It should be pointed out that the life cycle of graphs. Therefore the cloud movement measured, cumulus humilis clouds froms their birth to disso- February 1973 T. Chiyu, H. Kon and C. Magono 47

lution is fairly short, often only several minutes. base, but are deviated to the left (east) side of Therefore, the cloud speed was measured as an the wind. average speed for a few minutes. The size of a cumulus humilis cloud was Some examples of cumulus humilis clouds on represented by the apparent area of clouds e.g. June 27, 1970 are presented in below. Figs. 2a mean horizontal width times mean vertical and 2b, respectively, show selected cumulus humilis depth, because the width and depth of clouds clouds as indicated by A and B. These photo- changed during the observation. The size of graphs are one of a pair stereoscopic photographs. clouds A and B is given near the description of The horizontal movement of these two clouds cloud motions. In this case, the size of cloud A was analyzed, as shown in Fig. 3. In the left was approximately equal to that of cloud B, It is side of this figure, the contour of topography noted that clouds of nearly the same size moved around Sapporo is pictured. A and B show approximately at the same speed. the location of clouds A and B, and the broken In Fig. 4a, cumulus humilis clouds A and B arrows indicate the direction of the cloud on Sept. 7 were moving to the left. As seen in movement. And F and V show the location of the the photograph, the position of cloud B was photographing sites. It may be seen in this figure located just ahead of cloud A. Figure 4 b shows that clouds A and B were located over the lower the position of the clouds after four minutes. area. The base height of these clouds was It is clearly seen that cloud B was separating 600 meters, and their tops reached 800 meters from cloud A. According to the analysis, cloud above sea level. A was about four times larger than cloud B. The successive movement of couds A and B is shown in the right side of the figure. In the figure, horizontal and vertical axes show the distance along the base line and the distance along the camera optical axis, respectively. The hodograph in Sapporo is also given in the right side together with the vector of cloud movement. According to the calculation, the speed of couds A and B was 2.4m/s and 2.2m/s, respectively. The wind speed at the cloud base and top is shown at the end of the arrows. It may be seen that the speed of these two clouds was slower than the wind speed at the cloud base. In Fig. 5. Description of successive horizontal addition the directions of these clouds are not motion of clouds A and B on Sept. in agreement with the wind directions at the cloud 7, 1970. Cloud bases: 1700m.

Fig. 6. Cumulus humilis clouds over plain area, 0937 Sept. 13, 1970. Cloud A was measured. 48 Journal of the Meteorological Society of Japan Vol. 51, No.

The successive movement of these clouds is tops were 2,000 meters. The speed of clouds A shown in Fig. 5. The base of both these clouds and B was 8.3 and 11.4m/s, respectively. The was at 1,700 meters above sea level, and their hodograph of wind and the cloud movement are shown at left bottom of the figure. It is apparen that the speeds of clouds were slightly slowen than the wind speed at the cloud base. As shows in the hodograph, the directions of these two cloud motions were well in agreement with the wind direction at the cloud base. It will be seen that the speed of the larger cloud was less than that of the smaller cloud. It is also noted that the speed of the small cloud was approximatelly equal to the wind speed at the cloud base. Fig. 6 shows an example of cumulus humilis clouds over the Ishikari Plain. The horizontal Fig. 7, Description of successive horizontal movement of cloud A in the photograph was motion of cloud A on Sept. 13, measured. The data about the motion of this 1976. Cloud base: 900m. cloud is shown in Fig. 7. The base of this

Fig. 8. Motion sequence of a cumulus humilis clouds, Sept. 27, 1976. Cloud A separated into clouds A and A' at 0829, and older cells became smaller as it moved alone. February 1973 T. Chiyu, H. Kon and C . Magono 49

Table 1. Summary of analytical results of horizontal movement of cumulus humilis clouds in 1970 and 1971

* A , A' and B indicate notations of clouds in photographs. ** Figures in parentheses mean ground heights . cloud is at 900 meters , and its top reached 1,400 meters. The speed of this cloud was 5.0m/s. It is seen in the figure that this speed is less than the wind speed at the cloud base . As seen from the hodograph, the direction of the cloud movement approximately coincided with the wind direction at the cloud base. Fig. 8 shows an example of the motion sequence of cloud A on Sept. 27, 1970. As seen from the photographs , cloud A separated into two cells at 0829 JST, then the cell in the left side of cloud A' soon after disappeared . Cloud A' became smaller as it moved along Fig. 9. Description of successive horizontal . motion of clouds A and A' on Sept The successive horizontal movement of the 27, 1970. Cloud bases: 1900m. い50 Journal of the Meteorological society of Japan Vol. 51, No. 1 clouds is shown in Fig. 9. The base of these large and the cloud direction was generally clouds was at 1,900 meters above sea level. The deviated counter clockwise from the wind direc- speed of cloud A was 9.5m/s and that of cloud tion, however, in the case of higher clouds with A' was 12.9m/s. As shown in the hodograph, ground height heigher than 700 meters, the the speed of these clouds was less than the wind direction of cloud movement almost coincided speed at the cloud level. It is noted that when with that of wind direction. This tendency is the cloud was greater, the movement was slower, described more clearly in Fig. 10. The vertical however when it became smaller, the speed axis shows the magnitude of difference of cloud increased. The direction of these cloud move- movement direction from wind. The horizontal ments coincided with the wind direction at the axis shows the ground height of cloud base. It cloud base. is immediately seen that the direction of cloud Besides the examples described above, other movement is nearly the same as that of wind in cumulus humilis clouds were analyzed. All the higher clouds, however, when the ground height results of analyses are summarized in Table 1. is lower than 700 meters, the deviation rapidly This table lists the data for comparison of cloud increases to 40 degrees. According to the result, movements with wind at the cloud base. Cloud it is considered that the topography has a great size is shown by the product of mean width influence on the direction of the lower clouds. and mean depth of cloud. Figures in parentheses The topographic influence on cloud direction was of column of cloud base height mean the ground pointed out by Shenk and Kreins (1970). They height e. g., the difference between the cloud found, utilizing satellite measurements that on base and the terrain height. The difference the whole the directional difference was of 30-40 between the cloud movement and the wind is degrees for cloud over land between the surface shown in the right end of the table. In the case and 850mb levels. If we take account of the of the difference in speed, the values were average height of mountains of about 500 meters rounded off to the nearest whole number. above sea level which are seen in Fig. 10, the Negative signs in the column of difference critical value of 700m in the ground height between cloud and wind direction indicate the coincides with their result described in atmos- anti-clockwise deviation of cloud motion from pheric pressure for large scale clouds. the wind direction. 4.2. Speed of cloud movement. 4. Discussion Fig. 11 shows the relationship between the 4.1. Direction of cloud movement speed of cloud movement and the size of clouds. Let us first consider the directional deviation The vertical axis shows the ratio of cloud speed between the cloud movement and the wind. (Uc) to the wind speed (Uw) at the cloud base. It may be seen in Table 1 that in the case of The horizontal axis shows the cloud size indicated lower clouds with ground height lower than by apparent area. As described in Section 4.1., 400 meters, the directional deviation was fairly clouds were classified into higher clouds with

Fig. 10. Deviation in direction of cloud motion from wind direction vs Fig. 11. Ratio of cloud speed to wind ground height of cloud base. speed vs cloud size. February 1973 T. Chiyu, H. Kon and C. Magono 51

Fig. 12. Vertical distribution of wind speed Fig. 13. Ratio of cloud speed to wind speed over Sapporo during day of cumulus vs wind shear 1,000mb to cloud humilis clouds. base. Figures in parentheses show temperature lapse rate between ground height of >700 meters and lower clouds surface and 900mb level. with ground height <700 meters. The higher and lower clouds are shown with dots and cross smaller the cloud speed, compared with wind marks, respectively, in the figure. It can be speed. It is noted that in the case of a negative seen from the figure that the ratio of the speeds wind shear, the cloud speed was nearly equal to of higher clouds gradually decreases as the cloud the wind speed at the level. size becomes large, while the ratio of lower It is noted in Fig. 13 that when the lapse clouds rapidly decreases. It is seen that the rate was as small as 0.6*/100m, the wind cloud speed was always lower than wind speed, shear was much greater, whereas when the lapse and the lower the clouds,the greater the influence was as great as 0.9*/100m the wind shear of the cloud size. It seems likely that the was very small. About this it is considered that topographic features influence not only the lower when the lapse rate is great, the convective cloud direction but also the speed of the cloud motion may be strong, then vertical mixing of movement. momentum occurs strongly over a wide area. As As described above, the speed of all clouds a result, the vertical wind shear becomes small. was actually slower than that of the wind, in the It is, therefore considered that when the wind case of cumulus humilis clouds. This result can shear was small, owing to strong vertical mixing, be easily understood by considering the vertical the horizontal motion of air was uniform transportation of horizontal momentum from the through out the cloud and surrounding air. As root of convection under a positive wind shear. a result of this, the cloud speed was nearly the Fig. 12 shows the vertical wind distributions same as the wind speed. between surface and 800mb level observed on On the other hand, when the wind shear is the cumulus humilis cloud days in Sapporo. It great in an adiabatically stable condition, the is seen that all the vertical distributions, except vertical mixing may be great only inside a two, represent the positive wind shear. thermal whose top corresponds to a cumulus, In order to analyze the relationship between then low horizontal momentum is transported the positive wind shear and the excess of wind upward only inside the thermal, while there may speed over the cloud speed, the Uc/Uw is shown be not strong vertical mixing outside of the against the degree of wind shear between the thermal. Accordingly, the cloud speed was much cloud base and 1,000mb level over the plain slower than the wind speed in the surrounding area in Fig. 13. Figures in parentheses near air. The result in Fig. 13 supports this con- black dots show the temperature lapse rate sideration. It should be pointed here that the between 900mb and 1,000mb level. The lapse energy is mainly supplied from the base and the rate represents the thermal stability. It is seen sideward entrainment is small in case of cumulus in the figure that the greater the wind shear, the clouds in early stage. It should be also pointed 52 Journal of the Meteorological Society of Japan Vol. 51, No. 1 out that the cumulus cloud corresponds to the the greater the vertical wind shear in the environ- upper portion of the respective convection, ment, the lower the cloud speed. although the speed was measured in the cloud The observational results described above were base level in this paper. understood by considering the upward transporta- In the present paper it is assumed that the tion of low horizontal momentum in a cloud direction and speed of air around a cumulus convection under a condition of positive vertical humilis cloud is described by those of wind wind shear. which were measured by the rawinsonde measure- ment at the Sapporo Meteorological Observatory. Acknowledgements This assumption may be the case when the cloud This work was made as a part of CARP. The is high. Therefore the data shown in Fig. 13 authors wish to express their thanks to Mr. T. are all limitted to clouds whose ground height Yoshida, the Sapporo Meteorological Observa- of the cloud base is greater than 700m. tory, for his help in collecting radio sounding data. From the considerations described above, it Computations in the analysis were made on was considered that under the positive wind the FACOM 230-60 in Hokkido University shear, the cloud speed is always slower than the Computing Center. wind speed at the cloud base. If this consideration is the case, when there is References a negative wind shear, the cloud speed would be Abe, M., 1937: Mountain clouds, their forms and greater than the wind speed at the cloud level. connected air current, Part I. Bull. Central Meteor. However, the actual cloud speed observed was Observatory of Japan, 1-466. slightly slower than the wind speed as shown in 1941: Ibid, Part II, -,93-145. Fig. 13, although nearly the same. This discre- American Society of Photogrammetry, 1952: Manual of Photogrammetry. New York, G. Banta Publ. pancy may be caused by observational error. Co., p. 876. Sometimes it is observed in a time lapse movie Braham, R.R. and Draginis, 1960: Roots of orographic picture that the windward portion of a moving cumuli. J. Meteor., 17, 214-226. cumulus cloud is growing, while the leeward Endlich, R.M., D.E. Wolf, D.J. Hall and A.E. Brain, portion of cloud is disappearing. However the 1971: Use of a pattern recognition technique for observational error due to this factor is not so great determining cloud motions from sequences of that it disturbs the point of arguments of this paper. satellite photographs. J. Appl. Meteor., 10, 105- As mentioned in Section 3, the greater the 117. size of clouds, the smaller the cloud speed. It is Glass, M. and T.N. Carbon, 1963: The growth considered that the greater the size of cloud, the characteristic of small cumulus clouds. J. Meteor., deeper the root of the thermal (cumulus cloud), 20, 397-406. in other words, the effect of the upward trans- Hallert, B., 1960: Photogrammetry. New York, Toronto, London, McGraw-Hill Book Co., Inc., portation of low momentum is stronger. If this p. 340. consideration holds, a decrease in speed in the Khrigian, A. Kh. and S.M. Shmeter, 1961: Cloud large clouds is easily understood. It is, of Physics. (Translated from Russian), IPST, p. 392. course, true that the motion of the lower clouds Leese, J.A. et al. 1971: An automated technique for is strongly influenced by the ground friction obtaining cloud motion from geosynchronous compared with the higher clouds, if the sizes are satellite data using crosscorrelation. J. Appl. the same. Meteor., 10, 118-132. Orville, H.D, 1965: A photogrammetric study of 5. Concluding remarks the initiation of cumulus clouds over mountainous The direction of horizontal movement of terrain. J. Atmos. Sc., 22, 700-709. Shenk, W.E. and ER. Kreins, 1970: A comparison cumulus humilis clouds was nearly the same as between observed winds and cloud motions derived that of wind at the cloud base level, when their from satellite infrared measurements. J. Appl. ground height was greater than 700 meters. Meteor., 9, 702-710. The speed of horizontal movement of the clouds Yagi, T., T. Harimaya and C. Magono, 1968: On was generally lower than the wind speed at the the shape and movement of cirrus uncinus clouds cloud base level. The tendency was as follows, by the trigonometric method utilizing stereopho- the lower the clouds, the lower their speed, and tographs. J. Meteor. Soc. Japan, 46, 266-271. February 1973 T. Chiyu, H. Kon and C. Magono 53

Yates, A. H., 1953: Atmospheric convection; the structure of thermals blow cloud-base. Quart. X=Lx1/x1-x2, Y=Lf/x1-x2 and Z=Ly1/x1-x2 J. Roy. Meteor. Soc., 79, 420-424. where X, Y and Z are components of actual Appendix position of a cloud, respectively, and (x1,y1) and Because the axes of two cameras were perpen- (x2,y2) are horizontal and vertical components of dicula to the base line between camera sites 1 the cloud images in the two photographs, and 2 and the cameras were at the same respectively. L is the distance between sites 1 level, the normal photogrammetry equations are and 2, and f is the focal length of the cameras. available as follows,

晴 天 積 雲 の 移 動 速 度

周 徳 ・今 久 ・孫 野 長 治 北海道大学理学部地球物理学教室

1970,71年 の夏季,札 幌において晴天積雲の移動速度をステ レオ写真方式で観測 した.ま た雲の周辺の気象条件と して札幌管区気象台の レーウインゾンデの資料をつかって解析して次の結果を得た. 1.雲 底が地上高700m以 上の高い晴天積雲では,そ の移動方向は,そ の雲の高度(雲 底)の 風向とよく一致す るが,700m以 下では地形の影響が大きい. 2.晴 天積雲の移動速度は一般に雲底高の風速よりおそいが,そ のなかで次の傾向が認められた.低 い雲ほど, また大きい雲ほどおそい傾向がある.ま た風の垂直 シャー(上 方が速い)が 大きいほど雲速に比べておそく なる. これらの傾向は,雲 内で小さい運動量が下方から輸送 され るということで理解される.