Diurnal Winds in the Himalayan Kali Gandaki Valley. Part I: Observations

1106 MONTHLY WEATHER REVIEW VOLUME 128

JOSEPH EGGER Meteorologisches Institut, UniversitaÈt MuÈnchen, Munich, Germany

SAPTA BAJRACHAYA Department of Hydrology and Meteorology, Ministry of Science and Technology, Kathmandu, Nepal

UTE EGGER,RICHARD HEINRICH, AND JOACHIM REUDER Meteorologisches Institut, UniversitaÈt MuÈnchen, Munich, Germany

PANCHA SHAYKA Department of Hydrology and Meteorology, Ministry of Science and Technology, Kathmandu, Nepal

HILBERT WENDT AND VOLKMAR WIRTH Meteorologisches Institut, UniversitaÈt MuÈnchen, Munich, Germany

(Manuscript received 4 February 1999, in ®nal form 28 May 1999)

ABSTRACT The diurnal wind system of the Kali Gandaki Valley in Nepal was explored in September and October 1998 in a ®eld campaign using pilot balloons as the main observational tool. This valley connects the Plateau of Tibet with the Indian plains. The river crosses the Himalayas forming the deepest valley on Earth. Intense upvalley winds blow up this valley during the day. Observations were made along the river at various spots selected between the exit point from the Himalayas and the source close to the Plateau of Tibet. The strongest upvalley winds were found between Marpha and Chuksang with typical speeds of 15±20 m sϪ1. The upvalley wind sets in ®rst at the ground but an upvalley wind layer of 1000±2000-m depth forms quickly after the onset. This deep in¯ow layer persists up to Lo Manthang, a town located a few kilometers south of the Plateau of Tibet. Deceleration in the late afternoon and evening also appears to commence near the ground. Weak drainage ¯ow forms late in the night. The causes of these phenomena are discussed.

1. Introduction The most conspicuous climatological feature of the region is the pronounced decrease of precipitation up The valley of the Kali Gandaki River in Nepal is pre- the valley. Monthly mean precipitation is given in Table sumably the deepest valley on Earth. The river originates 1 for six stations on the way up from Tatopani to Lo close to Tibet in the Mustang Himal and passes the town Manthang for the months September and October, that of Lo Manthang under the name Mustang Khola to ¯ow is, for the two months of the ®eld campaign to be de- then essentially southward through the Mustang district scribed below. While the summer monsoon clearly af- till the main barrier of the Himalayas is reached near fects the precipitation in Tatopani and Lete, there is little Marpha (Fig. 1). The Himalayan ranges are crossed be- impact in Marpha just a few kilometers farther north. tween Marpha and Ghasa. It is near Lete and Ghasa that There is virtually no precipitation in Lo Manthang in Annapurna and Dhaulagiri tower above the river making the fall. The same features are apparent in the climate the valley's depth more than 5000 m. The valley follows atlas of Nepal (ICIMOD 1996). a steep descent from Ghasa to Tatopani. The upper part of the valley is famous not only for its depth but also for its strong diurnal upvalley winds. These winds blow virtually every day and have been noted by travelers as a rather unpleasant feature of the Corresponding author address: Dr. Joseph Egger, Meteorologisch- es Institut, Arbeitsgruppe fuÈr Theoretische Meteorologie, UniversitaÈt area (Tucci 1977; Peissel 1992). In particular, the wind MuÈnchen, Theresienstraûe 37, Munich 80333, Germany. tends to raise a lot of dust in the afternoon. Figure 2 E-mail: [email protected] shows the monthly mean wind speed V as observed in

᭧ 2000 American Meteorological Society

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC APRIL 2000 EGGER ET AL. 1107

FIG. 1. Map of the Kali Gandaki Valley: dots, observation sites; crosses, villages and towns mentioned in the text. Height contours solid (m). Horizontal distances in (km). The map is based on topographic data with a resolution of 30Љϫ30Љ. These data have been averaged to a1kmϫ 1 km grid.

Kagbeni (see Fig. 1) in September and October 1990. the winds during the day. Strong upvalley winds set in Wind direction was not recorded so that it is not clear between 0800 and 1000 LST, and reach an impressive whether upvalley or downvalley winds prevailed during maximum of ϳ14msϪ1 at ϳ1400 LST to decay later the night. However, there is no doubt with respect to on. An inspection of the daily observations reveals rather little variability from day to day. The daily maximum speed varies only between 11.6 and 17.5 m sϪ1 within TABLE 1. Mean monthly precipitation along the Kali Gandaki Val- these two months. ley in (mm) as observed during the years 1974±96. From Department of Hydrology and Meteorology (1997). The strength of these winds is rather extreme. For example, typical valley winds in the Alps exhibit in- Lo Man- tensities of about 5 m sϪ1 (see Whiteman 1990 for a Tatopani Lete Marpha Jomsom Ghami thang review). The asymmetry between day and night is also Sep 189 137 52 41 13 10 extreme. Typically upvalley winds in the Alps are about Oct 64 59 40 32 29 10 as intense as downvalley winds (e.g., Dreiseitl et al.

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC 1108 MONTHLY WEATHER REVIEW VOLUME 128

topani) to Kagbeni, distinct upvalley winds were encountered only on 7 February 1985 when it was possible to ¯y into the valley in the afternoon. Additional surface observations were made in Jomsom for 4±7 February. Strong upvalley winds were observed with a pressure minimum in the afternoon. There was little pressure change in Pokhara during the day. In short, except for the near-surface wind data from Kagbeni as collected in 1990 and for the observations just mentioned, there are no further wind data available from the area. Nothing is known about the vertical structure of these winds and very little about changes of the winds along the valley. Given this lack of data on the wind ®eld a joint campaign was undertaken by the Meteorological Institute

FIG. 2. Monthly mean values of the hourly mean wind speed V (m of the University of Munich and the Department of Hy- sϪ1) as observed in Kagbeni in Sep and Oct 1990 at a height of 30 drology and Meteorology in Kathmandu in the fall of ft. 1998 to explore the three-dimensional structure of the diurnal wind ®eld in Mustang. The months of September and October were chosen to minimize the interference 1980; Whiteman 1990). In Kagbeni, the wind roars up the valley in the afternoon, while gentle breezes are of the monsoon with the valley wind system. Winter typical of nighttime ¯ow. conditions, however, may be found in upper Mustang Aside from these observations in Kagbeni little in- late in October so that the campaign could not be ex- formation is available on the diurnal winds along the tended beyond that month. Spring would be equally well Kali Gandaki River. Although winds are measured with suited for conducting such a campaign. high temporal resolution at the airport in Jomsom, these It was decided to cover as large a portion of the valley data are not recorded. Winds and other meteorological as possible. It is only in this way that wind differences data are collected by the Mustang Development Service along the river can be detected. Therefore, observations Association in Jomsom. However, these data have not were made all the way from Lete, close to the point of yet been published. The Department of Hydrology and the river's descent into the lowlands, up to Lo Manthang, Meteorology of H. M. Government of Nepal collects that is, close to the source of the river. Pibal ascents wind data in Lo Manthang and Jomsom. Wind roses were made at eight locations (see Fig. 1 and Table 2). show a clear preference for southwesterlies in Jomsom Major weather perturbations are unusual in this area at and southerlies in Lo Manthang in September and Oc- this time of the year. Thus there was good reason to tober with weaker winds in Lo Manthang. Ohata and expect that weather would be ®ne on a suf®ciently large Higuchi (1978) tried to infer the intensity of the upvalley number of days so that observations at different loca- wind from the deformation of trees. This method is tions would be comparable. The data to be presented bound to fail in the upper Mustang area to the north of, below were collected by the authors of this paper. say, Jomsom simply because there are few trees in this It was the primary goal of this ®eld campaign to extreme environment. However, Ohata and Higuchi ar- provide a gross description of the diurnal wind ®eld in rived at interesting results in the lower part of the valley, the upper Kali Gandaki Valley, with particular emphasis to be discussed further below. Neininger and Reinhardt on the diurnal evolution of the vertical structure of the (1986) report on attempts to probe the valley atmosphere wind and on its variation along the valley. In this paper, with an instrumented motorglider. On four ¯ights from we report the results of the campaign. Moreover, partial Pokhara (situated about 50 km to the southeast of Ta- explanations of the strength of the winds and the asym-

TABLE 2. Characteristics of theodolite baselines (see also Figs. 1 and 4): ⌬z is the height difference between theodolites T1 and T2 in m.

Negative values indicate that T1 is higher than T2.

T1 theodolite position Baseline Location N Lat E Long Altitude Length Direction (Њ) ⌬z Lete 28Њ37Ј50Љ 83Њ36Ј38Љ 2450 965.0 61.0 Ϫ106.0 Tukuche 28Њ42Ј17Љ 83Њ36Ј10Љ 2700 380.0 185.0 Ϫ2.5 Marpha 28Њ45Ј21Љ 83Њ41Ј21Љ 2700 879.2 125.0 Ϫ246.0 Jomsom 28Њ46Ј44Љ 83Њ43Ј13Љ 2800 793.5 155.0 Ϫ50.5 Kagbeni 28Њ48Ј48Љ 83Њ46Ј21Љ 2900 1078.8 319.0 67.2 Chuksang 28Њ55Ј03Љ 83Њ49Ј09Љ 3050 949.8 149.0 207.0 Nyi La 29Њ02Ј44Љ 83Њ51Ј15Љ 3900 1216.1 108.0 16.8 Lo Manthang 29Њ10Ј50Љ 83Њ57Ј14Љ 3800 980.0 98.1 Ϫ120.0

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC APRIL 2000 EGGER ET AL. 1109 metry between day and night are provided. These explanations will be tested in the more theoretically oriented Part II of this paper.

2. Equipment In Mustang there are no roads for vehicles and virtually no electricity. All equipment had to be carried by porters or by mules. Electric power had to be generated. It is impossible to use heavy equipment under such cir- cumstances. Moreover, demands on electrical power had to be low. Given these limitations with respect to weight and power supply, the double theodolite method (e.g., Reger 1935) seemed to be best suited for wind speed measurements. With this method, a helium-®lled balloon is released and tracked by two theodolites (Warren Knight FIG. 3. The 500-hPa geopotential height (g pdam) at 28Њ7ЈN lat, model 89 AFP). Of course, the helium had to be carried 83Њ15Ј E long; ECMWF analysis for the observation days. up as well. Each theodolite is connected to a 12-bit A/D- converter that transforms the potentiometer readings of azimuth and elevation into a digital signal. The data are experiments. Positions of all sites were determined via transmitted to a portable computer (serial RS 322 port). the Global Positioning System (GPS). Even this modest Speci®cally designed data acquisition software controls equipment had a weight of 350 kg. More than 10 porters the calibration procedure before each ascent as well as were needed to carry this load. Soundings of the thermal the data transfer and storage. It also provides an online structure of the atmosphere were not possible because display of data from the ascent. This enables an in situ the extra effort to put, say, a mobile radiosonde station check of data quality and ascent characteristics. Mainly, into operation would have been substantial. Thus, we Vaisala TA20-balloons were used during the day, but it decided to concentrate on the winds during this ex- was necessary to launch the larger TA30 balloons at ploratory campaign. night to compensate for the additional weight of a bat- Weather conditions were generally good during the tery and a lamp. Storage batteries for the portable com- campaign except for our stay in the entrance region puters were recharged with a wind turbine. All instru- where perturbations presumably linked to the monsoon ments functioned properly through the end of the cam- affected the valley ¯ow. Moreover, rain fell on 29 Sep- paign despite the fact that the equipment was exposed tember, 2 October, and 18 October. It is notoriously to strong and dusty winds on many occasions. dif®cult to relate such events to ¯ow patterns of larger The average ascent velocity of the balloons was ϳ2.5 scale in such extreme terrain. Nevertheless, the 500-hPa msϪ1. During an ascent measurements were made every heights taken from the analyses of the European Centre 10 s. The corresponding vertical resolution of the wind for Medium-Range Weather Forecasts (ECMWF) at a pro®le was ϳ25 m. The accuracy of the azimuth and grid point close to Jomsom show that these precipitation elevation angle readings was ϳ0.1Њ. events are linked to episodes with decreasing heights The datasets from both theodolites were combined to (Fig. 3). Inspection of the related weather maps yielded calculate balloon positions every 10 s and to derive wind additional clues to be described below. However, gra- velocity estimates from these data. Error estimates of dients are quite weak in this subtropical domain. position and speed were based on equations provided The expedition was conducted in a trek-type mode by Hennemuth et al. (1980). Corresponding error bars in which observations were made at individual locations are provided in most of the corresponding ®gures (e.g., as the expedition proceeded. Observations began on 19 Fig. 7). There is, of course, a tendency for error growth September. We arrived in Lo Manthang on 10 October, as the balloon's distance to the base line increases. The started downward on 17 October, and the last obser- error can be reduced by averaging over consecutive ob- vation was made on 24 October. servations. The error was kept below a threshold by selecting appropriate averaging intervals; Fig. 9, dis- 3. Observation sites cussed later, provides a good example. Close to the ground, the errors are small and the points are densely The choice of observational sites during this cam- packed. Higher up the distance between the data points paign was partly dictated by the observing system. A is relatively large in order to keep the error below the theodolite baseline of suf®cient length as necessary for threshold. reasonably accurate measurements was not always easy In addition to the theodolite equipment, a hygro- to ®nd in this rugged terrain. Moreover, one has to have thermograph and three anemometers were used in the a good view up the valley so that sight of the balloon

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC 1110 MONTHLY WEATHER REVIEW VOLUME 128 is not lost too early. In other words, observations can 200-m height extending from the bridge over the Kali be made only if the riverbed is reasonably straight and Gandaki toward the east (Fig. 4a). The slopes to the wide. All in all, eight locations were selected (see Table east of Marpha are covered by forest, while few trees 2 and Fig. 1). These will be described brie¯y in the are seen to the west. The northern slopes of the An- following, beginning at the lowest site at Lete to the napurna range are covered by forest as well. There is south and following the river up to Lo Manthang. little vegetation in the Mustang basin except near villages where irrigation systems are needed to grow crops on terraces. a. Lete As has been mentioned, the steep descent of the river d. Kagbeni begins at Ghasa. A gorge of a few hundred meters width and with rather steep sidewalls of about 1000-m height Shortly upstream of Jomsom one enters a winding leads downward from Ghasa to Tatopani. The gorge gorge with steep walls. A few kilometers to the south opens at Ghasa toward a basin situated between Dhau- of Kagbeni the valley widens again and becomes straight lagiri and Tukuche Peak to the west and the Annapurna (Fig. 4b). There, a baseline was established across the range to the east. The baseline was established in the river. Low-level upvalley winds to the south of the base- ®elds of the Lete village at a height of ϳ2500 m with line are perturbed by a sharp bend of the river. The a good view up the river. valley narrows again near Kagbeni. b. Tukuche e. Chuksang Tukuche is situated at the northeastern end of a rather The path to Lo Manthang is close to the river all the straight section of the river. The valley bottom is ¯at, way up from Lete to Chuksang, but climbs steeply near a few hundred meters wide, and covered by gravel. The Chele (Fig. 4c). The gorge to the north of Chele is mountains rise steeply along the river with Nilgiri as spectacular and so narrow that a passage is too dif®cult the towering peak above Tukuche (top height 7061 m). for standard travel and transport. However, a good spot Mountain slopes are covered by forest up to a height for establishing a baseline was found near Chuksang of about 4000 m. A rather short baseline was established where Narsing Khola joins the Kali Gandaki. to the south of Tukuche at a height of 2570 m. A dan- gerous crossing of the river with part of the equipment f. Nyi La pass would have been necessary in order to establish a longer baseline. After the climb from Chele the track to Lo Manthang continues at an altitude of about 3500 m with several passes to be overcome. Nyi La pass (3950 m) is the c. Marpha and Jomsom highest of these (Fig. 4d). Strictly speaking, Nyi La is Upstream of Tukuche a gorge leads to Marpha, a hardly a pass. One simply has to cross a shoulder pro- rather large and impressive village situated to the west truding from the western mountains. The river is a few of the river. Marpha may be seen as the gateway to the kilometers to the east of the pass. To the south, the Mustang area. While the valley is quite narrow in Mar- Annapurna Range is seen, while the Plateau of Tibet is pha it widens upstream (Fig. 1) and changes its char- clearly visible to the north. acter. One enters the world of the semiarid valleys to the north of the Annapurna range. For example, the g. Lo Manthang valley of Langpoghyun Khola (Fig. 4a) extends eastward from Kali Gandaki up to a height of almost 5000 The town of Lo Manthang is located on an eastward m over a distance of 12 km. The Jhong Khola River sloping plain in between two creeks ¯owing down from joins the Kali Gandaki near Kagbeni, originating 20 km the Mustang Himal (Fig. 1). The baseline was estab- to the east. Such long tributaries are not found to the lished to the south of Lo Manthang (Fig. 5). Theodolite south of Marpha where the main valley is quite narrow. T1 was placed on a ridge above our campsite. There is The peaks marking the border of the Mustang area (Fig. an east±west-oriented ridge to the south of the baseline. 1) typically reach heights somewhat above 6000 m and The winds blowing up the Kali Gandaki basin in the are about 20 km distant from the Kali Gandaki River afternoon have to cross this ridge. on its eastern side. In general, the terrain is much steeper In what follows, the section from Lete to Marpha will to the west and the peaks are relatively close to the river. be called the entrance region. The upvalley wind does

One theodolite (T1) was placed on a hill overlooking not reach full strength in this section, where the valley the valley both at Marpha and at Jomsom. The other is narrow and the ground is mostly covered by grassland theodolite was close to the river at Marpha. The baseline and forest. Marpha marks the beginning of the core extended over the river at Jomsom. Valley winds are section that extends to Chuksang. The valley is wide impeded between Marpha and Jomsom by a ridge of and many tributaries ¯ow into the Kali Gandaki from

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC APRIL 2000 EGGER ET AL. 1111

FIG. 4. Maps of the (a) Marpha and Jomsom, (b) Kagbeni, (c) Chuksang, and (d) Nyi La areas with baselines. The dot in (a) marks the same position as the dot in Fig. 18.

the east. Upvalley winds reach maximum strength in the 4. Observations core region. Chuksang is a transition point where the exit section a. Entrance region begins. The river is winding through rather narrow The observations made in the entrance region, that gorges so that intense upvalley ¯ows at the ground is, at Lete and at Tukuche, do not contain a clear mes- cannot be maintained. As will be seen, there is, how- sage. In¯ow during the day was observed in Lete on 18 ever, a deep layer of ¯ow well above the gorge. The and 19 September, but ¯ow speeds where relatively valley basin is even wider in the exit section than in small. Wind observations near the Tukuche baseline the core section. were made for 17±21 September but the ¯ow was gen-

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC 1112 MONTHLY WEATHER REVIEW VOLUME 128

FIG. 5. Sketch of the Lo Manthang area with baseline. No map was available of suf®cient resolution to represent the small-scale features that are important in this case. This drawing is based on a photo taken from the hills north of Lo Manthang. The view is toward the south. The walls of Lo Manthang form a rectangle of 300 m ϫ FIG. 6. Near-surface wind speed V (m sϪ1) as observed in the camps

160 m in the north±south by east±west direction. Theodolite T1 is near Tukuche, Marpha, and Jomsom at the days indicated. The wind located 120 m above the base camp. direction changed in Jomsom from downvalley to upvalley between 0930 and 1000. Half-hourly mean values. erally perturbed by southeasterly ¯ow aloft. For ex- balloon was tracked to a large height to make sure that ample, the upvalley winds during daylight on 20 Sep- the situation was not perturbed on this day. The Marpha tember continued throughout the night (Fig. 6). During ascents of 24 September at 0911, 1000, and at 1124 this night, there was rain and the cloud base was rather LST document the growth of the upvalley wind layer low so that nighttime ascents had to be canceled. Lhasa with time (Fig. 8). At 0911 LST, the katabatic layer is reported weak southerlies at 500 hPa on 20 September completely replaced by upvalley ¯ow with V ϳ 5msϪ1 ahead of a weak trough over western Tibet. This trough at the surface. The southwesterlies aloft were slightly disappeared on 22 September (see also Fig. 3). Obser- stronger than the upvalley ¯ow. At 1000 LST, wind vations of cloud motion suggested that the in¯ow layer velocities have increased substantially over a depth of has a depth of at least 1000 m with typical velocites of about 1000 m. The surface wind observations at the 5±10 m sϪ1. Although there is no doubt that the upvalley Marpha campsite show also a rapid rise of wind veloc- wind system extends at least down to Lete there were ities at that time (Fig. 6). Wind speeds peaked at a height too many perturbations to allow for statements with re- of about 1000 m at 1124 LST. It is, however, dif®cult spect to the strength and depth of the in¯ow. One would to interpret such details since the upvalley ¯ow was have to stay longer in this region to make sure that rather turbulent at that time. The balloons underwent unperturbed days are part of the sample. However, Ohata rapid accelerations and decelerations during ascents be- and Higuchi (1978) found strongly deformed trees because of this turbulence. Wind velocities at the camp tween Tukuche and Marpha, while such deformations site reached maximum values near 1400 LST and de- are absent in the gorge downstream of Ghasa and are cayed slowly thereafter (Fig. 6). Parallel observations moderate at Ghasa and Lete. This indicates that winds of surface winds near the suspension bridge between become stronger between Lete and Marpha. Marpha and Jomsom ranged between 8 and 18 m sϪ1 on this day. It is not clear, however, whether this increase b. Core region of wind speed with upvalley distance re¯ects an overall acceleration. The valley is quite narrow at the bridge. As was mentioned, Marpha is at the transition from Ascents during the following night (0204, 0234 LST; the entrance region to the core region. We discuss the not shown) showed extremly weak winds in the lowest results from Marpha in this section because the ¯ow 500 m, which were replaced by downvalley winds by characteristics are rather similar to those found in Jom- the next ascent at 0617 LST (Fig. 9). At that time there som and Kagbeni. The ®rst ascent at Marpha on 23 was virtually no ¯ow aloft. Tibet was covered by a huge September (not shown) revealed vigorous upvalley high pressure system on this day. Weak northeasterlies winds throughout a layer of 500-m depth and south- prevailed at 500 hPa above Lhasa. Thus, this day (25 westerly ¯ow aloft. Wind speeds in this layer hardly September 1998) can be seen as a calm day without strengthened during the day and there was still upvalley noticeable large-scale perturbations. The balloon moved wind at midnight at least up to 1000 m. This suggests down the valley during the ascent shown in Fig. 9 for that the valley circulation was perturbed on this day as about 15 min and then climbed up one of the slopes. well. Weak drainage ¯ows evolved during the morning Finally the balloon crossed the baseline. of 24 September (Fig. 7). This downvalley ¯ow had a A rapid buildup of the upvalley wind system was Ϫ1 speed of ϳ4ms and a depth of almost 1000 m. The observed on this day. The depth hu of the upvalley wind balloon moved about 2 km down the valley until en- layer was 500 m at 0911 LST, 900 m at 0948 LST, 1500 tering a layer of rather weak southwesterly ¯ow. The m at 1029, and more than that at 1128 LST and possibly

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC APRIL 2000 EGGER ET AL. 1113

FIG. 7. Pibal ascent at Marpha at 0616 LST 24 Sep 1998: (a) wind speed V (m sϪ1) and (b) direction as a function of height z (m). Upvalley direction: ϳ220Њ. Only the lower 2000 m of the ascent are shown out of a total of 10 000 m.

2500 m at 1413 LST (Fig. 10). Wind speeds in the lowest clouds to the south but to have clear sky from, say, 1000 m were quite high in this case, leading to a rapid Tukuche toward the north. Mean sunshine duration ex- increase of the balloon's distance from the baseline and hibits a distinct minimum to the south of Jomsom in to a correspondingly rapid error growth. The surface October (ICIMOD 1996). pressure dropped by 5 hPa between morning and after- Observations in Jomsom commenced on the morning noon on 24 and 25 September. of 27 September. Weak northwesterly winds were re- Our observations in Marpha strongly suggest that the corded at 0924 LST (not shown) throughout the lowest total mass ¯ow in the valley wind system in the lowest 3000 m. The following ascents until noon were rather 1500 m above ground increases between, say, Lete and similar to those of 25 September in Marpha except that Marpha. If so, air must descend into this layer from the ¯ow speeds were somewhat higher. The upvalley above. Supporting evidence for this downward ¯ow ¯ow sets in close to the ground. The in¯ow layer grows comes from cloud observations. It is typical to see afterward to a depth hu of almost 2000 m. The wind speed pro®les throughout the day are presented in Fig. 11. The layer's depth was less than 500 m at 0956 and about 500 m at 1029. Note the strong acceleration of

the ¯ow near the ground. Forty minutes later hu grew to about 800 m with an overall increase of speed of about 3 m sϪ1. In the afternoon, the ¯ow velocities were high throughout a layer of 1300-m thickness. Flow speeds are reduced ®rst near the ground in the evening (not shown). The surface observations during the day reveal a more dramatic rise of wind velocities between 1000 and 1100 LST than had been observed at Marpha (Fig. 6). How- ever, the anemometer was placed in a maize ®eld in Marpha while there was little surface roughness near the observation site in Jomsom. Thus the increased ¯ow strength in Fig. 6 presumably re¯ects the choice of site. After sunset, the ¯ow speed decreased quickly. How- ever, there was no katabatic ¯ow in the morning. The next day brought little change when compared to 27 September except that ¯ow velocities were above 20 m sϪ1 in the afternoon. The pressure fall in Jomsom was FIG. 8. Pibal ascents at Marpha at 0911, 1000, and 1124 LST 24 Sep 1998: Wind speed V (m sϪ1) as a function of height z (m). Ascents ϳ5 hPa between morning and afternoon. are interpolated manually for the sake of clarity. On 1 October an attempt was made to explore the

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC 1114 MONTHLY WEATHER REVIEW VOLUME 128

FIG. 9. Pibal ascent at Marpha at 0617 LST 25 Sep 1998: (a) wind speed V (m sϪ1), (b) direction as a function of height, and (c) trajectory. Upvalley direction: ϳ220Њ. The balloon was tracked up to 7000 m above the ground. Only the lowest 2000 m are presented.

variability of the valley winds along the valley. Near- day upstream of this point. It is virtually certain that surface winds were recorded near Tukuche, Jomsom, winds were much stronger in this part of the valley than and Kagbeni (Fig. 12) simultaneously. Winds in Tuk- in Jomsom, let alone in Tukuche. This raises the ques- uche and Jomsom turned out to be relatively weak on tion how this acceleration comes about, given the wid- that day. Strong winds were recorded in Kagbeni. In ening of the valley near Marpha and the small slope of particular, the increase of wind speed in Kagbeni be- the valley ¯oor. Mass continuity requires descending tween 1000 and 1130 LST is quite dramatic. It must be motion between Jomsom and Kagbeni. pointed out that the spot chosen for observations near Theodolite observations in Kagbeni began on the Kagbeni was at a relatively narrow gap underneath the morning of 3 October. However, clouds were so low spot where theodolite T1 was placed a few days later and the situation appeared to be so strongly perturbed (see Fig. 4). Wind speeds tend to be high at this spot. that we decided to save helium. The Mustang area was Nevertheless, there was a lot of dust raised during the located ahead of an extended trough on that day. Upper-

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC APRIL 2000 EGGER ET AL. 1115

FIG. 10. Wind speeds in the lowest 1500 m above Marpha on 25 Sep 1998 as obtained from four consecutive ascents. Wind directions (not shown) indicate the depth of the in¯ow layer of 600 m, 1200 m, Ͼ1500 m, and Ͼ1500 m. FIG. 11. Wind speed V as a function of height on 27 Sep in Jomsom at various times as indicated. For the sake of clarity, the 0956 winds level winds on 4 October were from the WSW with are presented for the lowest 400 m only. Manual interpolation. speeds of 5±10 m sϪ1. The 500-hPa ¯ow above Lhasa had the same direction. The low-level ¯ow accelerated and a deep upvalley ¯ow layer was established by 1151 LST (Fig. 13). The southwesterly layer on top is clearly visible in Fig. 13. Later in the day wind speeds were larger than 15 m sϪ1 at least up to 1300 m except for the lowest 200 m (not shown). Surface wind observations at theodolite T1 on 4 October showed rather similar characteristics as those obtained 120 m below on 1 Oc- tober (see Fig. 12). In particular, there were also two separate phases of rapid increase. Weak downvalley winds were found in the morning of 5 October. The ensuing buildup of the upvalley ¯ow layer did not differ much from that of the previous day. A rather clear picture emerged for the core region. Late in the night, a weak drainage ¯ow tends to occur. The upvalley acceleration sets in ®rst near the ground. After that, the in¯ow layer grows rapidly reaching typical depths of hu ϳ 1000±1500 m in the afternoon. Deceleration appears to set in ®rst near the ground. c. Exit region Observations in Chuksang were made on 23 and 24 October after the return from Lo Manthang. As was mentioned, Chuksang is close to the northeastern end of that section of the valley where the river meanders through a relatively wide ¯at bed covered with gravel. The gorge near Chele blocks all upvalley ¯ow close to the river. So Chuksang is a transition point between the core region and the exit region. FIG. 12. Wind speed V as recorded on 1 Oct in Tukuche, Jomsom, Wind speeds were found to be somewhat weaker in and Kagbeni. Also given are the observations at theodolite 1 at Kag- Chuksang than in Kagbeni and Jomsom. For example, beni on 3 Oct. Ten-minute mean.

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC 1116 MONTHLY WEATHER REVIEW VOLUME 128

FIG. 13. Pibal ascent at 11:51 4 Oct 1998 at Kagbeni: (a) wind speed and (b) direction as a function of height z (m). Upvalley direction: ϳ220Њ.

the speed of the surface winds in the camp in Chuksang did not exceed 5 m sϪ1 on 23 October. Additional observations on the slopes at a height of ϳ400 m above the river gave maximum winds of 9 m sϪ1. This is def- initely less than that observed at Kagbeni. However, there appears to be rather little wind in Chele just a few kilometers up the river. Observations were made on the buckwheat terraces immediately to the north of Chele at the rim of the gorge about 100 m above the river. Maximum wind speeds were 2.7 m sϪ1 on 23 October. A special effort was made in Chuksang to document the deceleration of the wind in the afternoon. The ascent at 1735 LST on 23 October showed the familiar pro®le of a deep anabatic layer with southwesterlies aloft (Fig. 14). At 1951 LST the low-level winds speeds were reduced substantially. The upper branch of the in¯ow was still quite strong at that time. Rather weak anabatic ¯ow was recorded up to a height of 1500 m at 2200 LST and even lower speeds were encountered at 2300 LST. This series demonstrates clearly that the deceleration sets in at the ground. The ¯ow acceleration the next day followed the familiar pattern but maximum ¯ow speeds did not exceed 15 m sϪ1 in the lowest 1500 m. Although the low-level winds at Chuksang cannot penetrate the gorges north of Chele, there are sections farther north where the river is relatively wide. Occa- sional observations from higher terrain showed that dust FIG. 14. Pibal ascents of 23 Oct in Chuksang. Wind speed (m sϪ1) at various times as indicated. Upvalley direction: ϳ220Њ. Manual is raised there. However, no data were collected close interpolation. to the main river in the exit region. An excursion on 18

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC APRIL 2000 EGGER ET AL. 1117

FIG. 15. Ascents at 1013 and 1529 LST 20 Oct at Nyi La pass: (a) and (c) wind speed V (m sϪ1) and (b) and (d) wind direction as a function of height z (m).

October to Yara at the eastern side of Kali Gandaki lowest 1000 m above the pass (Fig. 15). This demon- turned out to be a failure. It began to rain before noon. strates clearly that the upvalley winds extend horizon- There was little wind during this day. tally at least from the riverbed to the mountains to the Figure 15 shows the wind observations taken on 20 west. The top of the in¯ow layer was at 5000 m above October at Nyi La pass. The situation at this pass differs sea level on that day. profoundly from that in the valley. The air ascends from The observations at Lo Manthang support the ®ndings the south and descends toward the north. One balloon at Nyi La pass. Early on 12 October little wind was ascent failed because the balloon disappeared into the found below a height of 1000 m. Upvalley winds linked valley leading toward Nyi La from the north. The ascent to the local topography were quite weak. Aloft, there at 1013 LST revealed a layer of southerly ¯ow up to were westerlies of ϳ10 m sϪ1. Winds remained weak 2300 m above the pass. Aloft, winds were westerly (not until noon but there was at least some southerly in¯ow shown). The turning of the wind occurs roughly at the at 1122 LST (Fig. 16a,b). Note the pronounced turning height of mountaintops bordering the valley to the west. of the wind at 1000 m above the ground. This in¯ow The acceleration during the day was substantial in the became rather vigorous in the afternoon (Fig. 16c,d) but

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC 1118 MONTHLY WEATHER REVIEW VOLUME 128

FIG. 16. Ascents of 12 Oct in Lo Manthang at various times as indicated. Wind speed V (m sϪ1) and wind direction as a function of height z (m).

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC APRIL 2000 EGGER ET AL. 1119

FIG. 17. Cross sections of the Kali Gandaki Valley at Marpha and Jomsom (dashed). disappeared completely at low levels after sunset (Fig. cise review of this concept). For example, McKee and 16e,f). The next day, a buildup of the southerlies was O'Neal (1989) demonstrated that drainage ¯ow can be observed again. However, velocities were less than 10 closely related to local values of the topographic am- msϪ1 in the lowest 1000 m. pli®cation factor. This explanation is not readily com- The observations at Chele revealed a complete block- patible with the shape of the valley between Tukuche ing of the low-level ¯ow at the entrance to the Chele and Kagbeni. Cross sections of the valley are shown in gorge. However, vigorous diurnal upvalley ¯ow was Fig. 17 for Marpha and Jomsom for H ϭ 2500 m. The found at Nyi La and in Lo Manthang within a deep layer valley is essentially v-shaped in Marpha and u-shaped extending vertically up to at least 5000 m above mean in Jomsom so that the ¯ow enters between Marpha and sea level and horizontally to the mountains to the west. Jomsom a section with reduced topographic ampli®- It is obvious from the trajectories that this diurnal south- cation factor. Despite this, the upvalley winds appear to erly ¯ow reaches Tibet. It is also obvious that this ¯ow accelerate on their way to Kagbeni instead of slowing is an extension of the upvalley winds in the core region. down. There are no observations available in the eastern part It is not obvious, however, whether the evaluation of of the exit region. Thus it is impossible to estimate the topographic ampli®cation factors on a local basis is ap- width of the in¯ow layer. propriate for the Kali Gandaki Valley. Roughly speaking, the Lete basin opens toward the free atmosphere to the south at the gap near Ghasa and is connected to 5. Discussion the large Mustang basin by a narrow and winding valley Two of the most surprising features of the Kali Gan- tube. Vergeiner (1987) has proposed a conceptual model daki diurnal wind system were known before our cam- for such situations. He considered a basin linked to the paign, namely the asymmetry between day and night foreland by a narrow valley. According to Vergeiner it and the extreme intensity of the winds (see Fig. 2). We is the topographic ampli®cation factor of the basin that have found in addition that there is a strong acceleration is important and not the width and shape of the con- between, say, Tukuche and Kagbeni. This a truly sur- necting valley tubes. The temperature in the basin is prising feature. It is a generally accepted explanation of higher during the day than that over the plain at the diurnal valley winds that their intensity is closely linked same altitude. This leads to a pressure difference and to the so-called volume effect [also called the topo- to corresponding upvalley winds. However, it must be graphic ampli®cation factor; Whiteman (1990)] as pro- kept in mind that the Kali Gandaki Valley opens to the posed by Wagner (1932) and as demonstrated quanti- free atmosphere and not to a plain in Ghasa. It is this tatively by Steinacker (1984). The topographic ampli- access to the free atmosphere where the topography of ®cation factor can be evaluated locally per unit length the Kali Gandaki Valley differs from that envisaged by of the valley. One has to determine the cross-sectional Vergeiner (1987). The free atmosphere to the south of area A(H) of the valley up to a height H assumed to be Ghasa is hardly heated up during the day. Because of the depth of the diurnal circulation systems. Let L be this a strong upvalley wind would have to be expected the width of the cross section at height H. The area A into the Mustang basin even if this basin were like a must be compared to the corresponding area HL out in box with vertical walls. The temperature in this box the plain. Thus HL/A is the local topographic ampli®- would be considerably higher than in the free atmo- cation factor. The larger this factor, the smaller is the sphere to the south of Ghasa. Therefore the pressure mass of air to be heated in the valley and the larger the would be lower and winds begin to blow in the valley temperature excess of the valley atmosphere with re- tube. spect to the atmosphere outside the mountain massif. However, even a cursory inspection of the terrain Finally, the larger the temperature excess the stronger shows that there is also substantial topographic ampli- the wind into the valley (see Whiteman 1990 for a con- ®cation in the Mustang basin. In particular, there are

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC 1120 MONTHLY WEATHER REVIEW VOLUME 128

FIG. 18. Tree deformations to the south of Langpoghyun Khola. The direction of the trunk's declination is given by the arrow. The maximum deviation of branch directions is indicated by the two straight lines. Tree 10 is also strongly deformed but there were little branches growing opposite to the directions of trunk declination. Creeks are denoted by dashes. The locations of the trees were determined using GPS. The dot marks the same position as the dot in Fig. 4a. several valleys leading from the Kali Gandaki toward there must be compensating return ¯ow aloft with de- the east (see section 3c). These valleys are 10±20 km scent above the main valley. Adiabatic warming and a long and at least the valleys near the Annapurna Range corresponding decrease of pressure are induced in the have a strong diurnal circulation of their own. These main valley by the tributaries (Egger 1990). This warm- diurnal winds are so strong that a remarkably clear de- ing is part of the volume effect of the larger basin. It formation of trees results. These deformations have been contributes to a northward upstream acceleration of the documented for that valley which joins the main valley winds at the exit of the valley tube near Marpha. south of Lhungpoghyun Valley (Fig. 18). Ohata and All this suggests that the strength of the upvalley ¯ow Higuchi (1978) did not perform their deformation anal- is at least partly due to the speci®c topography. More- ysis in this valley. The valley bottom ascends toward over, as has been mentioned, the Mustang basin is dry the east so that upvalley winds are westerly. Pine trees so that ¯uxes of sensible heat are larger there than, say, of about 10-m height were selected to measure these in the Lete basin where the ground is covered by veg- deformations. Most trees show an eastward inclination etations. This leads to additional acceleration. On the of their trunk (arrows in Fig. 18). There are many trees other hand, the albedo of the arid slopes of the Mustang without branches pointing toward the west. Instead, the basin is larger than that of the forests farther south. The branches form an angle within which all the twigs are relatively high altitude of the basin is an additional fac- found. This angle has been determined simply by using tor. Given the solar input, the increase of temperature a compass. Of course, one tends to select good exam- during the day is larger the less dense the air. Corre- ples. However, these good cases would not have been sponding accelerations are also larger and so are the found if these diurnal winds were not extremly strong. wind speeds. This argument applies, of course, to all Trees 5, 14, and 13 belong to the wind system of Lang- valleys in the area and may explain the strong defor- poghyun Khola while nearly all the other trees are de- mations of the trees displayed in Fig. 18. Smith and Shi formed by the winds blowing up the slopes of the neigh- (1992) have shown that the bulk longwave cooling at boring valley to the south. The ridge to the northwest high elevation sites may be smaller if the surface is of trees 13 and 14 is covered by forest, which shows mostly covered by rocks as in upper Mustang than by little wind impact. The evaluation of tree deformation leaf vegetation as in Lete. Again, this might contribute was performed on a cloudy day without winds (29 Sep- to enhanced upvalley winds during the day and weaker tember 1998). However, two of us (JE and UE) were katabatic winds at night. Cloud formation was observed measuring wind speeds in this valley on 24 September quite often during the night throughout the experiment. 1994, a ®ne day. Then upvalley winds up to 23 m sϪ1 This hinders the development of katabatic winds. Our velocity were observed. We conclude that this tributary stay in the area was too short, however, to see how the has diurnal upvalley winds at the surface that are similar intensity of katabatic winds in the morning is related to in strength to those found in the main valley. Although nighttime cloudiness. nothing is known about the depth of the upslope ¯ow, The speci®c topography of the Kali Gandaki Valley

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC APRIL 2000 EGGER ET AL. 1121 appears to be partly responsible for the observed asym- or winter but not in fall. What we found, however, is metry between day and night. The upvalley ¯ow passes the existence of a deep layer of upvalley ¯ow in the Marpha almost at full strength and forms essentially a upper Mustang region. This ¯ow extends at least to the jet after its exit from the valley tube there. Such jets Plateau of Tibet. There are, however, no observations maintain their intensity mainly through their inertia, available to determine whether the atmosphere above loosing momentum via friction. Additional acceleration the plateau is affected by this airstream. through tributaries as discussed above helps to strength- en the jet. This appears to be the only example of an 6. Conclusions upvalley jet known up to now. On the other hand, downvalley jets are rather common. They tend to form at In this concluding section, we summarize our ®nd- valley exits during the night. For example, Pamperin ings: and Stilke (1985) report on the cold air jet caused by the nocturnal out¯ow from the Inn valley into the Alpine 1) The upvalley ¯ow in the Kali Gandaki is accelerated forelands. This jet is observed over the plain at distances between Lete and Marpha. There is some evidence up to 20 km from the mouth. There is no symmetry for descending motion in this entry section. between day and night in this case. The diurnal in¯ow 2) The upvalley ¯ow is fully developed in the core to the Inn Valley is accelerated gently and does not form region. Acceleration in the morning and deceleration a jet in the plain. Just as one would not expect that a late in the day commence near the ground. The depth downvalley jet forms, say, in Jomsom. These ideas will of the in¯ow layer may be more than 2000 m. The be tested in Part II of this paper. upvalley jet extends to the mountains to the west. There are, however, also open questions. For example, 3) Although low-level ¯ow is partially blocked in the drainage ¯ow from the Mustang basin would enter the exit region, the deep in¯ow layer can be identi®ed Lete basin and one would expect to ®nd a nocturnal jet up to the Plateau of Tibet. There are indications that there. There is no evidence of such ¯ows. It is con- this exit branch reaches full strength later in the day ceivable, however, that the nocturnal cooling in the Lete than in the core region. basin is as strong as that farther north. In that case, there 4) Weak drainage ¯ow of ϳ1000 m depth was found would be little reason for strong out¯ows. A similar on several occasions early in the morning. situation is found near Ghasa. Again one would expect We hypothesize that the upvalley ¯ow is induced in that the cold air would rush through the gap near Ghasa the valley tube linking Marpha and Lete by the heating to ¯ow down the steep canyon there. Again, there is no of the Mustang basin. The upvalley ¯ow throughout the evidence of such ¯ows. Quite to the contrary, trees are core region is essentially a jet that is based on inertia. deformed by upvalley winds in Ghasa (Ohata and Hi- This explains part of the asymmetry between day and guchi 1978) albeit weakly. The absence of this down- night. These speculations will be exposed to tests in a valley ¯ow may be explained by the fact that clouds forthcoming second part of this paper where numerical tend to form in the Lete basin in the afternoon. This experiments on the Kali Gandaki Valley winds will be would reduce the nocturnal cooling. However, further described. observations are required to elucidate this point. The wind system of the Kali Gandaki Valley is em- Acknowledgments. We are grateful to M. Reinhardt bedded in the diurnal circulation of the Plateau of Tibet. for his enthusiastic support of the campaign, to J. Even in winter, there is low-level in¯ow (Murakami Schween for writing most of the data evaluation pro- 1981) toward the plateau in the afternoon and out¯ow grams, and, above all, to the supporting team for perfect late in the night. It has been suggested, for example, by help. The comments by all the referees and by G. ZaÈngl Reiter and Tang (1984) that the daily circulations of the were most helpful. North American plateaus affect local valley wind systems and that this might apply as well to the Plateau of Tibet. Calculations with a simple model by Egger (1987) REFERENCES support this suggestion. It is, therefore, conceivable that Department of Hydrology and Meteorology, 1997: Precipitation re- the valley winds explored here re¯ect at least partially cords of Nepal, 1991±1994. Ministry of Science and Technology, the impact of the Plateau of Tibet. For example, pressure Nepal, 402 pp. [Available from His Majesty's Government of is relatively low over the plateau in summer. This im- Nepal, Ministry of Science and Technology, Department of Hy- poses a pressure gradient in the upper part of the Kali drology and Meteorology, Babar Mahal, Kathmandu, Nepal, 2044.] Gandaki that might in turn drive upvalley winds and Dreiseitl, E., H. Feichter, H. Pichler, R. Steinacker, and I. Vergeiner, weaken downvalley ¯ow. However, September and, in 1980: Windregimes an der Gabelung zweier AlpentaÈler (Wind particular, October are months of transition from the regimes at the bifurcation of two Alpine valleys). Arch. Meteor. summer situation to the winter, when the air on the Geophys. Bioklim., 28B, 257±274. Egger, J., 1987: Valley winds and the diurnal circulation over plateaus. plateau is cold and the surface pressure is relatively Mon. Wea. Rev., 115, 2177±2185. high. Therefore, a search for in¯uences of the circulation , 1990: Thermally induced ¯ow in valleys with tributaries. Part of the Plateau of Tibet should be conducted in summer I: Response to heating. Meteor. Atmos. Phys., 113±125.

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC 1122 MONTHLY WEATHER REVIEW VOLUME 128

Hennemuth, B., H. Oberle, and C. Freytag, 1980: An error analysis Peissel, M., 1992: A Lost Tibetan Kingdom. Book Faith India, 288 of the double-theodolite pibal method with examples from the pp. Slope-wind Experiment Innsbruck 1978. Contrib. Atmos. Phys., Reger, J., 1935: Messung der LuftstroÈmung mittels Pilotballonen 53, 335±350. (Measurement of air ¯ow by aid of pilot balloons). Handbuch ICIMOD, 1996: Climatic and Hydrographical Atlas of Nepal. Inter- der Meteorlogischen Instrumente und ihrer Auswertung, E. national Centre for Mountain Development, 261 pp. [Available Kleinschmidt, Ed., Springer, 446±472. from ICIMOD, 4/80 Jawalakhel, G. P. O. Box 3226, Kathmandu, Reiter, E., and M. Tang, 1984: Plateau effects on diurnal circulation Nepal.] patterns. Mon. Wea. Rev., 112, 638±651. McKee, T., and R. O'Neal, 1989: The role of valley geometry and Smith, E., and L. Shi, 1992: Surface forcing of the infrared cooling energy budget in a mountain valley. J. Appl. Meteor., 28, 445± pro®le over the Tibetan Plateau. Part I: In¯uence of relative long 456. wave heating at high altitude. J. Atmos. Sci., 49, 805±822. Murakami, T., 1981: Orographic in¯uence of the Tibetan plateau on Steinacker, R., 1984: Area height distribution of a valley and its the Asiatic winter monsoon circulation. Part II. Diurnal varia- relation to the valley wind. Contrib. Atmos. Phys., 57, 64±71. tions. J. Meteor. Soc. Japan, 59, 66±84. Tucci, G., 1977: Journey to Mustang 1952. Bibliotheca Himalayica, Neininger, B., and M. Reinhardt, 1986: Meteorological aircraft data Ser. I, Vol. 23, Ratna Pustak Bhandar, 85 pp. set of the ``First Himalayan Soaring Expedition.'' Deutsche Vergeiner, I., 1987: An elementary valley wind model. Meteor. Atmos. Forsch. Vers. Anst. Luft-Raumfahrt, Forschungsbericht, DFW- Phys., 36, 255±263. 86-39, 149 pp. [Available from Wissenschaftliches Bericht- Wagner, A., 1932: Der taÈgliche Luftdruck- und Temperaturgang in swesen der DLR, 51140 KoÈln, Germany.] der freien AtmosphaÈre und in GebirgstaÈlern (Diurnal variation Ohata, T., and K. Higuchi, 1978: Valley wind revealed wind-shaped of pressure and temperature in the free atmosphere and in val- trees at Kali Gandaki valley. Seppyo, 40, 37±41. leys). Gerlands Beitr. Geophys., 37, 315±344. Pamperin, H., and G. Stilke, 1985: NaÈchtliche Grenzschicht und LLJ Whiteman, C. D., 1990: Observations of thermally developed wind im Alpenvorland nahe dem Inntalausgang (Nocturnal boundary systems in mountainous terrain. Atmospheric Processes over layer and LLJ in the Alpine foothills near the mouth of the Inn Complex Terrain, Meteor. Monogr., No. 45, Amer. Meteor. Soc., Valley). Meteor. Rundsch., 38, 145±156. 5±42.

Unauthenticated | Downloaded 09/30/21 12:10 PM UTC