On the effect of topographie orientation on the variations of glacier length

World Glacier Inventory - Inventaire mondial des Glaciers (Proceedings of the Riederalp Workshop, eptember 978: Actes de l'atelier de Riederalp, septembre 978): IAH-AIH Publ. no. 6, 980. On the effect of topographie orientation on the variations of glacier length P. Kasser Abstract. The relation between the length changes of glaciers and their orientation was investigated for the observation network of glaciers in the wiss Alps for seven years within the period 946/947-976/977. The number of glaciers diverging positively (+) and negatively ( ) from the median value in their changes of length were counted and the ratio ^(+/ ) was tabulated for eight sectors of 90 each, each sector being designated by its central direction. The glaciers in the central direction are counted with weight whilst those in the two adjacent directions are added with weight 0.. The maximum of *?(+/-) is always in the northwest to northeast sectors, the minimum in the sectors southeast to southwest. This asymmetrical distribution is not due to climatic but to morphological factors, as is reflected in the inverse distribution of the sizes of glaciers in the network over the sectors. ur l'effet de l'orientation topographique sur les variations de longueur des glaciers Résumé. La relation entre les variations de la longueur des glaciers et l'orientation de ceux-ci a été étudiée pour le réseau d'observation comprenant glaciers des Alpes suisses, pour sept années comprises dans la période 946/947-976/977. On a compté les glaciers présentant un écart positif (+) et négatif (-) par rapport à la valeur médiane de leurs variations en longueur et regroupé dans un tableau les quotients ^(+/ ) obtenus pour huit secteurs de 90, chaque secteur étant désigné par sa direction centrale. Dans chaque secteur on a effectué une somme pondérée, attibuant le poids aux glaciers dans la direction centrale et 0. à ceux des deux directions adjacentes. Le maximum de ^(+/~) est toujours situé dans les directions nord-ouest à nord-est, le minimum dans les secteurs sud-est à sud-ouest. Cette distribution asymétrique n'est pas due à des facteurs climatiques mais à des facteurs morphologiques, ainsi que le montre la répartition inverse des dimensions des glaciers du réseau par rapport aux secteurs. ITRODUCTIO The investigations were based exclusively on the measurements made in the observation network of the Glacier Commission of the wiss Academy of ciences in the wiss Alps (Commission helvétique des Glaciers, 948-978). The ends of the glaciers are measured each autumn, and the years of measurement are designated below by the calendar year of the corresponding summer. The period of extreme shrinkage in respect of mass balances ended in 90, and from to 977 the sums of the balances are approximately zero to positive. In this -year period the number of advancing glaciers has increased and in 97, for the first time since 90, more than half of the observed glaciers were advancing. In a first publication (Kasser and Aellen, 976) a systematic dependence was found for the year 97 between the ratio +/- of advancing (+) to retreating ( ) glacier tongues and the topographic orientation, i.e. the directional exposure, of the glaciers. The results there obtained are briefly recapitulated in this study and the reasons for them are investigated. THE +/- RATIO I 97 The sign of the change of length in 97 is known for 07 of the glaciers of the observation network (Table ). ignificant values can hardly be expected for the quotient +/ in the directions southeast, south, southwest and west, since the samples, 0

06 P. Kasser TABLE. Dependence between the sign of the length change and glacier orientation in 97 umber of gl aciers per orientation In advance tationary In recession Total 9 E 9 E 7 6 4 E 0 W 0 W W 9 7 9 Total 6 40 07 with only five glaciers each, are very small. In addition, some glaciers are so situated that they might be allocated to either one or the next adjacent direction. For these reasons a kind of smoothing has been carried out by replacing the directions by sectors. These are named after the central direction but extend laterally to the lines of the adjacent directions. The number of advancing or retreating glaciers in a sector is determined by addition of the glaciers in the three directions, the glaciers being counted with -weight in the central direction and weight 0. in the adjacent directions. The results are shown in Fig.. There can be little doubt that the quotient varies systematically with orientation, having a maximum in the northeast sector and a minimum in the southwest sector. Why should the glaciers with northeast exposure have displayed this greater tendency to advance in 97? Is the cause climatic or morphological, or does it involve some more complex mechanism? 0.90.6 E FIGURE. Ratio +/ of the number of advancing to the number of retreating glaciers in the eight sectors for 97. THE RATIO M (+h) FOR EVE DIFFERET YEAR Evaluation with the quotients +/ of the signs of the length changes by the sector method is possible only in years in which a sufficient number of both advancing and retreating glacier tongues are available. The frequency distribution of the length changes now points the way to a general application of the method here described. The sign of the length change need only be replaced by the sign of the deviation from the median value to provide us with an ideal sample with an equal number of positive and negative signs. We select for our investigation three years of extreme shrinkage, three of extreme accumulation and one year with a small mass exchange and an almost zero mass balance (Table ).

On the effect of topographic orientation 07 TABLE. Years investigated, mean specific annual mass balances b of the Aletsch and ilvretta Glaciers, number of advancing, stationary and retreating glaciers, and median M of the length changes è[kgm- ] umber of glaciers measured M Year 947 4 97 97 976 977 Aletsch -40-69 + 78-8 + 9-688 + 476 ilvretta _ -409 + 8-6 + 79-0 + 60 + 0 7 4 46 tat. 8 6 8-69 78 60 8 68 47 Total 7 84 8 9 0 98 0 [m] -0.0-0.9 -. -.0 + 0.9-6. 0 The frequency distribution of the length changes in the extreme years 947 and 97 reveals a displacement of the maxima by three classes of m each (Fig. ). Representation of the frequency distribution in percentiles permits simple assessment of the length changes (Table ). Half of all the values are between the third and ninth duodeciles. Deviations from the median inside these limits may be classed -, /(Al - Al m ) V n - umber n - 8-7 o m -7.0 ±.4 7 97 -im +. ±. 0-0 -00-0 Length change AI FIGURE. Frequency distribution of the length changes Al for classes of m, in the years 947 and 97. TABLE. Frequency distribution of the length changes o. Years Year 947 4 4 97 97 6 976 7 977 + + 6 + + 7 to 7 Minimum [m] - 40.0-0.0-9. -4.0-8.0-7.0-6.0-7.0-9. -7.0-6.0 -. -7.6-4.8-9.0-4.6 -. -44. -6.8 -.0 Length changes in metres, m duodeciles t 6* 9* -.0 -.0-0.4 -.0-6. -7. -6.7 -.0-8. -6. -0.0-0.9 -. -.0 + 0.9-6. + 0. -. -0.6 -. -.0-6.4 + 0.0 +. + 8.6 ± 0.0 +. -4.0 +. +. -.0 -.0 +.0 + 6.0 + 7.0 + 6.0 + 4.0 +. + 6.0 +.0 Maximum [m] +. +. + 78.0 + 68.4 + 47.0 +.4 + 7.0 +. + 47.0 + 47.0 umber of glaciers 7 84 8 9 0 98 9 4 8 6 * Median t Lower quartile. + Upper quartile. In this case the eight stationary glaciers were not taken into account.

08 P. Kasser as normal for the sample considered, values outside them up to the first or eleventh duodecile as a large recession or advance respectively, and values beyond the first and eleventh duodeciles as unusually large. The use of the sector method to determine the quotient M (+l~-) with the signs of the deviations from the median yields the values shown in Table 4 for the measurement intervals investigated and the eight main orientations. In Table 4 the highest values for quotient M (+/ ) occur without exception in the northwest to northeast sectors, while the minima are found in the southeast to southwest sectors. A trend associated with time, from 947 to 977, cannot be distinguished. The three shrinkage years 947, 4 and 976 show a similar behaviour to the three accumulation years, 97 and 977. For all these reasons the asymmetrical distribution of the quotient M(+/ ) over the orientations can hardly be attributed to a trend or singularity of climate but is more probably due to the influence of morphological parameters. TABLE 4. Quotient M (+h) for the sectors in the measurement intervals investigated, calculated from the signs of the deviations from the median values of the length changes Measuremen interval o. t Year E Quotient M (+h E E ) for the sectors W W W 4 6 7 + + 6 + + 7 to 7 947 4 97 97 976 977*.6..44....04...8.7.4.8..9...8.09.4 0.88 0.74 0.9 0.70.09 0.67. 0.94 0.94 0.87 0.60 0.4 0.0 0.6 0.86 0.4.00 0.74 0.7 0.6 0.7 0.7 0. 0.7 0.7 0.4 0.64 0.0 0.7 0.4 0.8 0.60 0.4 0.70 0.67 0.8 0.8 0.48 0.7 0.9 0.7. 0.76 0.87 0.70. 0.80.0.00.06 0.9.7.8.0 0.90.7..0.0.8 * In this case the eight stationary glaciers were not taken into account. THE RELATIO OF AREA, LOPE AD OUT ELEVATIO TO THE IG OF THE LEGTH CHAGE These relations were studied by categorizing the values of the four variables, i.e. signs, area, slope and altitude of the end of the glacier, by division into two classes according to magnitude and analysing their associations in contingency tables (e.g. see Kendall and tuart, ). The tongue measurements of 97 (Kasser and Aellen, 976) were used for the signs, while the morphological parameters of the network glaciers were taken from the Glacier Inventory (Millier et al, 976) with a few adaptions to the observation network (Kasser and Aellen, 976). The sample comprises 6 advancing glaciers (Class with values +) and 40 retreating glaciers (Class with values ). The three parameters, area, slope and altitude were divided according to magnitude into two classes each comprising 48 glaciers, with the higher values in Class. In Fig. the coefficient of association Q for several combinations of variables and the total number of cases are entered in the partial X table. The significance level of the association is also indicated. Each line in Fig. shows the result for one association. The horizontal strokes in the columns show which variables are being compared, the symbols indicate limitation of the sample to glaciers of the corresponding class. The associations between sign and area, sign and slope, and area and slope are particularly close. It seems quite possible that the distribution of the quotient +/ over the orientations might be

On the effect of topographic orientation 09 x Table o. 4 4- sign area a big small Vari ibles slope altitude k fc, steep gentle k fc^? V high low f V Q -.6 -.600 -.747 -.04 -.74 n i48_ 48 48 4 99 9 9 * 9 0 9 8 +. -.0G -.800 99 * 99.9 -.68 99.9 4 +. 60 * Association not significant. FIGURE. Coefficient of association Q for the relation of area, slope and snout altitude to the sign of the length change. dependent on the distribution of the areas over the orientations. This would be the case if the distribution of the reciprocals of the weighted areas over the sectors were similar to the distribution of the quotient +/. DITRIBUTIO OF THE WEIGHTED MEA OF J A OVER THE ORIETATIO Like the glacier area A, the magnitude J A is also closely related to the quotient +/ or M (+l~). The investigation is now continued with the values of J A in order to mitigate somewhat the influence of the few very large glaciers and to make allowances for the effect of the shape of the glacier surfaces. The weighted sum of JA is formed for every sector with weight in the central direction and weight 0. in the adjacent directions, and from this the mean (JA) m is determined. The distribution entered in Table is then obtained for the glaciers of the measurement network. It is clear from this that the northwest to northeast sectors contain on the average the smallest glaciers and the southeast to southwest sectors the largest ones. TABLE. Weighted mean of (JA) m and l/(ja) m in the sectors ector E E E W W W (JA) m [km] U(JA) m [km' ].8 0..89 0.. 0.4.80 0.6.68 0.7.4 0..7 0.46.9 0. COMPARIO OF THE DITRIBUTIO OF M(+/~) AD l/(^)m OVER THE ORIETATIO The sector values are now divided by the corresponding mean of the eight values to enable the two distributions to be better compared. With this normalization the value represents the average. After this adjustment we obtain Table 6 from the bottom lines of Tables 4 and. It may be concluded from the marked agreement between the two distributions and the close correlation between glacier area and the sign of

0 P. Kasser TABLE 6. ormalized sector values of M (+/~)' and l/(ja)m ector E E E W W W..7 0.97 0.70 0.60 0.66.8. l/(v 4)m.7..04 0.8 0.6 0.74.07.0 the change of length that the distribution of the glacier areas over the orientations is one of the principal reasons why the glaciers in the northwest to northeast sectors were more prone to advance than those in the southeast to southwest sectors in the years under consideration, and in the observation network concerned. COCLUIO The results set forth are valid for the observation network of the wiss glaciers and for the years of measurement 947-977. In other observation networks account would have to be taken of the different distribution of the morphological parameters such as the size of the glaciers. The years of measurement 947-977 mark the end of a period of extreme shrinkage and lead into a period of approximately equilibrated mass balances. It was to be expected that the ends of the smaller glaciers would respond to the favourable growth years with advances more quickly than the large ones. But if the small glaciers react more quickly than the large ones to climatic changes, they must also be expected to be the first to retreat when a period of general advance comes to an end. The investigated observation network comprises predominantly of glaciers for which the sign of the annual change of length is determined by the difference between sliding movement and loss due to melting at the snout. Only very few glaciers in the network owe an advance to a deposit of névé in front of the snout. These two mechanisms are different with respect to the response time between mass balance and variation in the position of the snout. Investigations of the distribution of glacier parameters over the orientations of the glaciers, based on the Glacier Inventory, might be useful in the preparation of representative measurement networks. REFERECE Commission helvétique des Glaciers (948-978) Rapports no. 68 à 98 sur les variations des glaciers des Alpes suisses. Les Alpes, Rev. Club Alpin uisse, 4-4. Auteurs des rapports: Mercanton, P. L. (9-949); Mercanton, P. L. et Renaud, A. (90-94); Renaud, A. (9-); Kasser, P. (-97); Kasser, P. et Aellen, M. (97-978). Kasser, P. and Aellen, M. (976) Les variations des glaciers suisses en 974/7 et quelques indications sur les résultats récoltés pendant la Décennie Hydrologique Internationale de 4/6 à 97/74. Houille Blanche, no. 6-7, 467-48. Kendall, M. G. and tuart, A. () The Advanced Theory of tatistics, vol., pp. 8-6: Griffin, London. Mutter, F., Caflisch, T. and MiiEer, G. (976) Firn und Eis der chweizer Alpen (Gletscherinventar). Publ. no. 7, Department of Geography, wiss Federal Institute of Technology, Zurich. DICUIO Braithwaite: The glaciology textbooks since at least Heim's book (88) claim that the advance and retreat of glaciers is associated with topographic factors and orientation. However, in my opinion, they never proved this point but Kasser has now done it! I would like to ask how we can calculate a confidence interval for statistics like 'per cent of glaciers in advance'. I tried to do this under the assumption of a hypergeometric distribution but this is too simple as it excludes the 'stationary' case.

On the effect of topographic orientation Kasser: The aim of calculating a confidence interval is to assess the representivity of a sample. The sample of 0 glaciers in the observation network is mainly representative of those glaciers whose advance or retreat is controlled by the combined influence of movement and melting. The majority of the 88 inventoried glaciers in witzerland are small and advance due to snow accumulation in front of the snout. Reynaud: You have shown good agreement between the number of advancing glaciers and the inverse square root of the area: this last ratio is the inverse of a length. I think that this is important. For instance in the Mont Blanc area, three glaciers with the same orientation but different lengths (Bossons, Argentière and Mer de Glace) show very different features. Bossons is now retreating (40 to 0 m since 974) whilst Argentière is more or less stationary and Mer de Glace has advanced 00 m between 97 and 977 and 0 m in this last year. The same situation existed in 89 to 90: Bossons advanced first, Argentière -6 years later with Mer de Glace following by 0- years. Therefore, if we place the three glaciers in the same orientation sector it is difficult to obtain a significant average for the sector. Kasser: The investigated relation between the ratio +/ and the inverse of length is statistically valuable for the transition from a recession period to a period of advance. The fact that Bossons advanced first, Argentière later and Mer de Glace last is in full agreement with this relation. Radok: The different speeds of large and small glaciers in responding to changed climatic conditions have a complete analogue in the response of a single glacier: it is more rapid when the glacier is near its minimum than near its maximum extent. It might also be pointed out that the square root transformation used by Kasser is a well known device for normalizing a skew frequency distribution with sample standard deviation proportional to sample mean. An alternative parameter incorporating some of the glacier shape would be a sort of reciprocal 'hydraulic radius' L/A. Kasser: The 'hydraulic radius' seems to be a useful alternative parameter but the definition of the length of a glacier is sometimes much more difficult than the determination of the area.