INTRODUCTION

Ablation and snow accumulation are the basic processes that influence glacier mass variation. Their relation allows estimation of changes in a glacier i.e. mass balance of a glacier. Ablation is more or less responsible for ice mass decrement. This process is a main glaciological problem, which has been dealt with by many authors (Sugden 1976; John 1977; Jania 1993, 1994; Jania and Hagen 1996; Dowdeswell et al. 1997). Ablation is more and more often considered in mathematical and statistical formula, aiming to forecasting its occurrence in time (Konovalov 1987; Krenke and Menshutin 1987; Pelto 1988; Vincent and Vallon 1997). Many of the issues connected with the problem have not been, however, well recognised so far.
Studies of ablation should not only focus on a glacier surface but also on analysis of water conditions in a glacier catchment basin. Simultaneous measurements on surface and forefield of a glacier essentially increase accuracy of research (Sobota 1998).
In summer 1998 detailed measurements of ablation on the Waldemar Glacier were carried out in order to define its spatial and time variation (Fig. 1). Water discharge in streams that drained individual parts of a glacier was measured. Thus, it was possible to compare ablation of a glacier fragment with volume of outflowing water. Investigations included also the Waldemar River, which flows out from the glacier. The research focused mainly on correlation between intensity of water discharge and glacial ablation. An attempt to estimate ablation and outflow was done on the basis of temperature measurements of water in the Waldemar River. In order to carry out such research (which is a part of a program on ice mass balance of the Waldemar Glacier), an automatic gauging station "Davis" was used for the first time. It enabled to measure temperatures at 15' intervals.
Ablation of glaciers in Spitsbergen has been discussed in numerous papers (Baranowski 1977; Leszkiewicz 1982, 1987; Haeberli et al. 1991, 1994; Jania 1993, 1994; 1996; Jania and Hagen 1996; Bartoszewski 1998). In spite of many expeditions to Kaffioyra since 1975, glaciological research rarely concerned ablation of glaciers in this area. Since 1995 systematic research has been a part of ice mass balance estimation of the Waldemar Glacier (Grześ 1997; Grześ and Sobota 1997, 1998; Sobota 1997). However, water conditions in Kaffioyra have been widely discussed in literature, among others by Szczepanik (1977, 1982), Marszelewski (1987), Pietrucień et al. (1987), Skowron (1995), Sobota (1997, 1998) and Brykała (unpubl.).

STUDY AREA

The Waldemar Glacier is located in the northern Oscar II Land, northwestern Spitsbergen (Fig. 1). It is of the alpine type and flows down a valley to the Kaffioyra Plain. With the area of 2.66 km2, the Waldemar Glacier occupies 61% of a catchment basin closed by ice-cored moraines at the water gap. The firn field occurs at 380-490 m a.s.l. and the snout at 130 m a.s.l. The glacier is composed of two parts, separated by a median moraine, 1600 m long (Fig. 1). The foreland occupies 0.44 km2. A small ice-dam lake has been observed on the glacier since 1995, and its development was tightly related to glacier retreat, resulting in ice melting and outflow blocking. The catchment basin of the Waldemar River occupies an area of 16.5 km2 and its surface has been shaped mainly by meltwaters from the Waldemar Glacier. Within the catchment basin there are streams fed by ablation, rainfall and melting of the morainal ice-cores. Outlet of the river is influenced by sea tides.
Location of the glacier snout is also significant for regime of the glacial river. The Waldemar Glacier has been retreating intensively lately and the glacier surface has been lowered at 1% every year (Lankauf 1989, 1993, 1995). This process undoubtedly influences considerably the outflow from the catchment basin of the Waldemar Glacier.

ABLATION OF THE WALDEMAR GLACIER

Similarly as in previous years, measurements of summer ablation in 1998 were carried out in 5 days' intervals at 30 sites on the glacier (Fig. 1). Aluminium poles were installed at depth 1.5 m in April and May 1998. In result, total surface ablation could be estimated for the whole summer. Investigations aimed to determine a course of ablation in time and its variation with altitude, as well as to estimate average ablation in summer. This detailed research enabled comparison of ablation with runoff from a given part of the glacier.
Many agents, both morphological (morainal cover, slope, density of supraglacial streams, shielding) and meteorological (mainly air temperature) influence the ablation. High cloudiness occurred in summer 1998. As far as average air temperatures are concerned, they were also high and equal to 5°C on surface of the Waldemar Glacier, 5.7°C at the snout and 4.2°C at the firn field (according to measurements at the automatic meteorological gauging station "Davis"). Meteorological measurements enabled evaluation of tangible relation between air temperature and ablation (Fig. 2). Regardless of a part of the glacier, ablation increases distinctly with rising temperature. Air temperature, often modified by local conditions on a glacier, is the most important factor for the ablation.
High intensity of ablation and lack of this phenomenon are observed on the Waldemar Glacier irrespectively of altitude. Unlike the previous summers, ablation was relatively constant. The highest ablation was noted at the beginning of the analysed period. Next, the decreasing ablation followed by a slight increase at the end of the investigated period was observed. The lowest ablation, both at the snout and in the firn field, was ascertained between 29th July and 2nd August 1998 (10.6 cm w.e. and 9.0 cm w.e., accordingly). The highest ablation in these parts of the glacier was noted at the beginning of the analysed season (20.7 and 20.1 cm w.e.). The five-days' average ablation for the entire glacier was equal to 14.7 cm w.e. Contrary to the previous summers, ablation started nearly at the same time on the whole glacier and lasted for nearly the same period. It is the result of similar tendency in temperature changes at individual parts of the glacier.
Ablation is dependent also on the so-called ablation layer. Ice melting occurs on ice crystals too, and white colour of glacier surface is due to this process. In summer 1998 the ice layer was to 20 cm thick. It disappeared completely during rain and its thickness was generally considerably varying. Real surface of ablation occurs only in case of absence of ablation. Both the Waldemar Glacier and altitude difference between the firn field and the snout (365 m) are relatively small. Nevertheless, spatial variation of ablation is observed. Besides the altitude gradient, variation was caused by local conditions including exposition, selective melting, slope and pattern of supraglacial streams.
The map of ablation of the Waldemar Glacier presents decreasing ablation with increasing altitude (Fig. 3). The highest ablation was noted at the glacier snout up to 250 m a.s.l.. The maximum total ablation was equal to 160-180 cm w.e. at 200 m a.s.l., whereas the lowest one to 106 cm w.e. at 350 m a.s.l. The gradient of ablation for the whole research period was only 10 cm w.e. at 100 m a.s.l., it was 22 cm w.e. at the same altitude in summer 1997. The lowest total ablation was not noted at the highest point of the firn field but a bit lower (Fig. 4). Ablation on the firn field was observed from the beginning of the ablation season. This process was so intensive that dense network of supraglacial channels developed together with a few ice crevasses, influencing a considerably varied ablation. Distribution and variability of glacial zones, characteristic for the previous seasons, could not be observed. Throughout the whole summer, the glacier occurred within the ablation zone. Additionally, small patches of water-ice pulp were formed but disappeared very quickly.
In summer 1998 the altitude did not influence much a spatial variation of ablation. Local conditions, mainly air temperature and foehn winds played much greater role, especially in the glacier firn field. This conclusion is based on total ablation in the firn field, equal to 122 cm w.e., and was higher than the average total ablation for the whole glacier (120.5 cm w.e.). The correlation coefficient between altitude and ablation during the analysed period was equal to 0.53 only, whereas it was 0.93 during the previous summer. It confirms much lower spatial variation of ablation.
Varying ablation with the altitude, dissimilar to the previous seasons, was a reason for detailed analysis of the Waldemar Glacier. It seems characteristic that ablation indicates strong diversity at the same altitude (Table 1). Sometimes these differences are significant as e.g. in summer 1998 when ablation was equal to 58 cm w.e. at 200 m a.s.l. In accordance with a general trend towards ablation getting lower with altitude, the ablation diversity increases. This situation is tightly connected with local conditions on the Waldemar Glacier. Its lower part, showing the most intensive ablation, stretches up to about 300 m a.s.l. It is generally covered with surface moraine. The fact that at different altitudes similar features exist makes for ablation a role of the altitude gradient insignificant. Participation of different fragments of the glacier in total ablation gives similar results to the quoted above. The whole central part of the Waldemar Glacier, irrespectively of its altitude, shows similar ablation. These observations, however, do not exclude general decrease of ablation with altitude.
The estimated ablation for the Waldemar Glacier resulted in a simplified scheme of glacier ablation variability with altitude (Fig. 5). Weather conditions and particularly air temperature during summer were accepted as the most important factor for ablation distribution. Meteorological factors were treated together. Summers were divided into three types including cold summer with average temperature lower than a multi-annual average one, average summer with average temperature similar to a multi-annual one, and warm summer with average temperature higher than a multi-annual one.
The second examined factor included local glacier conditions that more or less influenced variability of ablation with altitude. Snow accumulation in winter does not play any significant role and ablation is more or less intensive, depending on meteorological conditions in summer. Ablation drops with air temperature decreasing with altitude. Thus, air temperature is so low during a cold summer that from certain altitude melting does not occur on a glacier surface. The presented scheme shows three variants of altitudinal distribution of ablation (Fig. 5). During a cold summer ablation decreases distinctly up to a certain altitude (in most cases to a firn field), above which it does not take place at all. The ablation gradient is quite high, but not the highest one. During an average summer ablation decreases considerably with altitude, its values are big and the gradient is the biggest. Warm summer is characterised by most intensive ablation, taking place on the whole glacier but its variability is smaller with increasing altitude and the ablation gradient is the lowest one. Thus, as far as other glaciers similar to the Waldemar Glacier are concerned, various courses of ablation changing with altitude are expected in accordance with thermal conditions in summer. Such variability can be expressed by the ablation gradients GB > GA > GC, where GB is typical for average, GA - cold, and GC - warm summer.
The scheme presented above is modified slightly if completed with local conditions on a glacier. The lines for individual summers (A, B and C) are similarly inclined. Additionally, relations of their ablation gradients do not change, but their values are lower. Up to a certain altitude, ablation does not change and its values are similar. The zone of similar ablation stretches up highest during a warm summer while lowest during a cold one. The presented scheme was based on detailed measurements of ablation on the Waldemar Glacier. A small size of the glacier plays a significant role, as the whole glacier is located in similar weather conditions. The other glaciers in Spitsbergen, size and altitude of which are similar to those of the Waldemar Glacier, present similar distribution of ablation with altitude.
During the whole period of examination (last measurements taken on August 31) ablation of the Waldemar Glacier was equal to 120.5 cm w.e., and was much higher than during the two previous summers. Variation of ablation was also lower with time. The cumulated ablation of the Waldemar Glacier during the last three years was about 280 cm w.e., half of which occurred during the analysed season.

OUTFLOW FROM THE WALDEMAR GLACIER

In summer supraglacial streams are the main morphological elements on a glacier surface, especially in a frontal part. Intensified ablation creates or renews network of meltwater streams. A scheme of stream development, their number, depth and time variation reflect a rate of ablation. This paper focuses predominantly on volume of water transported in selected streams on the Waldemar Glacier and their relation to the outflow from individual parts of a glacier. The ablation based on the runoff hydrogram was estimated due to analysis of discharge from individual fragments of the catchment basin. Such approach enables determination of relation of ablation to partial outflow. This issue is very complicated and it allows only for rough comparison of the above parameters. Discharge from a given part of a glacier may indicate the ablation rate as well as its share in feeding the supraglacial streams with meltwater (Sobota 1998). Moreover, knowledge of partial outflow of streams directly at water outbursts from a glacier allows estimating the share of surface ablation in the total outflow from the drainage area. It also enables to assess the share of melting icings, which seems to be quite large. A precise estimation of volume of englacial water seems also possible.
In order to estimate outflow of streams the glacier was divided into characteristic balance areas (Fig. 6), borders of which follow roughly the watersheds on the glacier. Not only ablation for each fragment of the glacier was assessed within a research period but also outflow of streams draining those areas. Distinct relation between time variation of ablation in the defined areas and outflow rate of streams draining those areas was ascertained. This relation, however, was ambiguous. In some areas ablation was higher than outflow (Fig. 7) but the opposite relation occurred occasionally too. For instance, share of ablation in outflow from the area BA was equal to 19% only while in the area A - as much as 134%. Similar analysis was carried out for the previous season (Sobota 1998). All these differences are tightly correlated with local conditions of individual catchment basins and have their justification. The above relation can create the basis for estimating the outflow from the glacier as well as the englacial outflow. This issue, however, is very complicated.
In summer 1998 standard measurements of discharge in the Waldemar River were taken, and relation of river outflow to glacial ablation was determined. Additionally, several physico-chemical properties of river water were examined. The investigations also included the ice-dam lake, outflow from which plays significant role in total outflow from the Waldemar Glacier and in feeding the analysed river. The "Davis" measuring equipment enabled the very detailed water temperature measurements that were taken for the first time and every quarter of an hour. Such frequency allowed drawing conclusions on relation between river water and air temperature, and ablation.
Considerable time variation in discharge, especially up-stream, is characteristic for glacial rivers and the same is typical for the Waldemar River (Fig. 8). There were several alternate periods with high and low discharge. The course was tightly related to ablation, which is particularly visible in relation to the average 5-days' discharge and ablation (Fig. 9). High variability of discharge causes great morphometric changes of the riverbed and difficulties in measurements. Changeability of discharge of the Waldemar River is similar to the ones during the previous summers. Ablation is the main factor responsible for discharge. Strict dependence between ablation and discharge allows determining a share of surface ablation in total runoff from a glacier. Significantly, the river reacts very quickly to all hydrological changes on the glacier: small distance results in slight delay only between maximum discharge and maximum ablation.
Distinct relation between water temperature in the Waldemar River and air temperature, and their relation to water discharge and ablation could be determined. The greatest discharge occurred when water temperature was the highest (Fig. 10) and this relation allows for treating the water temperature as an indicator of ablation and time variation in its intensity.
Feeding and outflow from the ice-dam lake on a glacier plays significant role in regime of the Waldemar River. Ice-dam lakes influence much a runoff from the glacial catchment basin. They are water reservoirs, mainly with seasonal runoff (Banach and Grześ 1974). The lake on the Waldemar Glacier is located at the foot of a median moraine. The area of the lake is about 0.5 hectares. It is fed directly by meltwaters flowing out from the western, mainly frozen part of the glacier. As much as 38% of discharge from the Waldemar Glacier was estimated to come from the lake in summer 1998. This fact stresses a role of the ice-dam lake in feeding and shaping the Waldemar River.
From about 4800000 m3 of water flowing out through the Waldemar River as much as 67% was estimated to come from surface ablation of the Waldemar Glacier, comparing with 60% during the previous summer. The other 33% means feeding with rain as well as with water from melting icings. The latter, thanks to detailed analysis of the runoff from the glacier, was assessed to 250,000 m3, which makes up about 6% of outflow. Rainfall feeding in 1998 was 133,000 m3 (about 3% of the outflow). Circulating englacial water seems to play an important role in river feeding. A discharge from the Waldemar River can be expressed with the following equation:

where : Q - river discharge, A - surface ablation, W - englacial water, H - precipitation, N - water from melting of icings, R - local sources of feeding (e.g. water from streams on valley slopes). These relations indicate an important role of ablational feeding in regime of a glacial river.

CONCLUSIONS

There is tight correlation between river water temperature, discharge and ablation. During the analysed season a high average air temperature was observed. It resulted in increased ablation if compared to the previous seasons. The ablation is not greatly varied in time. Maximum total ablation reached 160-180 cm w.e. at 200 m a.s.l., and the lowest total ablation equal to 106 cm w.e. occurred at 350 m a.s.l. Ablation changeability with altitude enabled to present a scheme of ablation for three types of summer. Average air temperature and local glacier conditions were accepted as the main factors of ablation. The described scheme can be used for the other glaciers in Spitsbergen, having similar area and altitude.
Taking into account the whole research period, ablation of the Waldemar Glacier accounted for 120.5 cm w.e. in 1998 and was nearly two times higher than during the previous season. Basing on detailed analysis of ablation and discharge, similar time variation of both was observed. Catchment basins with ablation higher than discharge and the ones with discharge much higher than ablation were determined. This analysis allows therefore for estimating the englacial flow. From about 4800000 m3 in the Waldemar River in 1998, 67% comes from surface ablation on the Waldemar Glacier. During the previous summer this share was similar and accounted for 60%. The other most important sources of river feeding comprise melting of icings, precipitation and water runoff down the surrounding slopes.

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