Elevational changes in meteorological variables along a midlatitude glacier during summer

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. D22, PAGES 25,941-25,954, NOVEMBER 27, 1997 Elevational changes in meteorological variables along a midlatitude glacier during summer Wouter Greuell and Wouter H. Knap Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands Paul C. Smeets Faculty of Earth Sciences, Vrije Universiteit Amsterdam, Amsterdam Abstract. During the summer of 1994 a glaciometeorological experiment was carried out on the Pasterze (a glacier in Austria). This paper reports on the data from six energybalance stations ranging in altitude from 2075 to 3225 m above sea level (asl). The wind regime was dominated by the glacier wind. On the tongue, directional constancies ranged between 0.94 and Mean 2 m wind speed and specific humidity were almost constant along the glacier. The variation in the 2 m temperature along the glacier cannot be described by the usually assumed constant decrease with elevation. On the tongue the 2 m temperature even increased with elevation. A much better description of the temperature distribution is given by a linear relation between the potential temperature and the distance along the flow line. This can be understood from a simple thermodynamic analysis of the glacier-wind layer. It is further shown that changes in clear-sky global radiation with elevation are due mainly to changes in local albedo and relief and hardly at all to changes in absolute optical path length and atmospheric water vapor and aerosol content. On the tongue the laterally averaged ice albedo is almost constant with elevation. The flux of incoming long-wave radiation during clear-sky conditions at U2 (2310 m asl) was 48 W/m 2 higher than the flux at U5 (3225 m asl), on average. More than half of the difference was due to systematic differences in the shape of the temperature profile (probably the inversion depth is larger at U2). The rest can be ascribed to higher 2 m temperatures and larger amounts of upper hemisphere slopes at U2. The distributions of the meteorological variables and the parameterizations described in this paper might be incorporated in surface energy-balance models designed to simulate the surface mass balance. 1. Introduction During the summer of 1994, roughly between mid-june and mid-august, a glaciometeorological experiment, called PASTEX, was carried out on the Pasterze, Austria's largest glacier. In order to study the climate and mass balance and their mutual relation as a function of elevation, six energybalance stations were established along the center flow line of the glacier, distributed over elevations ranging from 2075 to 3225 m asl. This paper deals with some of the meteorological variables, measured at the energy-balance stations, namely, 2 m wind direction, 2 m wind speed, 2 m temperature, variables that quantify 2 m humidity, surface fluxes of incoming short- and long-wave radiation, and surface albedo. These variables have often been measured on glaciers, but to the authors' knowledge, simultaneous measurements at more than two elevations on a melting glacier have never been described in the literature, except in connection with an experiment carried out on the Greenland ice sheet [Oerlemans and Vugts, 1993]. The treatment of the individual variables in this paper will generally start by showing the averages during PASTEX as a function of elevation. Thereafter an attempt will be made to Copyright 1997 by the American Geophysical Union. Paper number 97JD /97/97JD explain the observed distributions with elevation. For incoming short- and long-wave radiation this will be done by means of parameterizations so that the relevant processes can be sepa- rated from each other. The variations with elevation, which are discussed here, are interesting not only from a climatological point of view, but they are also useful for studies of the relation between climate and mass balance on glaciers. Such studies are often done by means of numerical surface energy-balance models [e.g., Greuell and Oerlemans, 1986; Oerlemans and Hoogendoorn, 1989; Oerlemans, 1991/1992; Arnold et al., 1996] or degree-day models [e.g., J6hannesson et al., 1995] (GO, OH, Oe, Ar, and J6, hereinafter). Both types of models use input variables that vary in time and space. In both cases these are atmospheric temperatures, but in the case of energy-balance models, other input variables such as wind speed, cloud amount, and humidity can be used. In the energy-balance models the fluxes of incoming short- and long-wave radiation are then most often computed by means of parameterizations which use the above mentioned input variables as input. This paper may contribute to the further development of such models since elevational distributions of temperature, wind speed, and humidity are analyzed, parameterizations for the fluxes of incoming shortand long-wave radiation are developed, and the temporal and spatial variation of the surface albedo during PASTEX are described. 25,941

2 25,942 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER 12o40 ' 12o50 ' 3200 j u3 u2 47ø0(Y 12o40 ' 12o50 ' Figure 1. Map of the Pasterze. White surfaces are areas that were glaciated in The energy-balance stations were located at U1, A1, U2, U3, U4, and U5. The dashed line represents the flow line that is used to analyze the variation in the 2 m temperature along the glacier. It may be useful to review briefly how elevational changes in the variables discussed in this paper are prescribed in the existing mass-balance models. Ar and GO use a wind speed and relative humidity that are constant with elevation. GO, J6, Oe, Ar, and OH all assume a constant lapse rate in order to describe how the 2 m temperature varies with elevation. In the energy-balance models of GO, OH, and Oe the incoming flux of short-wave radiation is obtained with parameterizations that compute the zenith angle, the transmissivity associated with scattering and absorption by air molecules, water vapor and aerosols, as well as cloud transmissivity. Since these transmissivities depend on elevation, the resulting flux varies with elevation. In none of these models are multiple scattering, reflections by the surrounding terrain and horizon obstruction considered. However, the latter two processes are taken into account by Ar. In all the energy-balance models the influence of the surrounding slopes is also neglected during the calculation of the incoming flux of long-wave radiation. This flux is calculated as a function of the 2 m temperature, the 2 m humidity, cloud amount, and cloud-base temperature only. The locality dependent coefficients in the parameterization of the incoming long-wave radiative flux are assumed to be uniform along the glacier. Changes in the albedo with time and elevation are modeled as follows: GO have an ice albedo that is constant in time and which varies slightly with elevation via the melt rate. In OH the ice albedo decreases exponentially with time but is constant with elevation, whereas in Oe and Ar, it depends on the distance from the equilibrium line. In Oe the ice albedo does not vary during the melt season, while it decreases linearly with cumulative melt in Ar. In all the energybalance models the snow albedo decreases with time if the melt rate remains constant with time, whereas a systematic change with elevation is modeled through a dependence on melt rate in GO and cumulative melt in Oe and Ar. The data analysis performed in this paper will show how the description of the elevational distributions of the model input variables and the parameterizations of the radiative fluxes can be refined. 2. Experimental Setup The Pasterze (47ø06'N and 12ø43'E) is Austria's largest glacier with a surface area of 19.8 km 2 and a length of 9.2 km (in 1969 according to Rott [1993]). Its general exposure is southeast. A map of the glacier is shown in Figure 1. Six energy-balance stations were established along the center flow line of the glacier, two on the upper part of the glacier (U4 and U5), three on the tongue (A1, U2, and U3), and one on the end moraine just about 10 m from the front (U1). Table 1 gives elevations and distances along the flow line of the stations and the variables that were measured. The profile of the glacier along the center flow line is shown in Figure 2.

3 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER 25,943 Table 1. Information About the Setup of the Experiment Elevation, Distance Along Station m asl Center Flow Line, m Variables Measured Period U G, R, Q, Q ' [u, T, U]o.5and 2, d2, rs (four depths) June 17 to Aug. 12 A G, R, L, L ', Q [u, T, U]o.25,o.5,1,2,4,6,8,13 d2. 5 and 13, E, p, m June 18 to Aug. 9 U G, R, L, Q, Q ' [u, T, U]o.5and 2, d2, m June 19 to Aug. 12 U G, R, [/,t, T,]o. 5 and 2, S2, d2, m June 19 to Aug. 12 U G, R, [u, T,]o.5 and 2, U2, d2, m June 15 to Aug. 14 U G, R, L $, [u, T, U]o.5 and 2, d2, m June 15 to Aug. 16 d, wind direction; E, eddy-correlation measurements; G, incoming short-wave radiative flux; L, incoming long-wave radiative flux; L?, outgoing long-wave radiative flux; m, mass balance;p, precipitation; Q, net total radiative flux; Q, incoming total radiative flux; Q?, outgoing total radiative flux; R, outgoing short-wave radiative flux; T, air temperature; T s, soil temperature; u, wind speed; U, relative humidity. Subscripts give nominal heights above the surface in meters. The main station was located at A1, where radiative fluxes were measured for all short- and long-wave components and as net radiation. Profile measurements of wind speed, temperature, and humidity were made at eight levels on a 13 m mast, and turbulent fluxes were measured directly by eddy correlation at 4 (or 2.5) and 10 m on two separate masts. Wind direction was measured at 13 and 2 m. At the other locations (U1, U2, U3, U4, and U5 (the "U stations")), fewer variables were measured. With respecto the radiative fluxes, the short-wave components were registered at all the U stations, whereas incoming long-wave radiation was measured only at U2 and U5. Wind speed, temperature, and humidity were measured at 0.5 and 2 m (but at U3 and U4, humidity was not measured at 0.5 m) and wind direction at 2m. The heights of the wind, temperature, and humidity sensors above the surface (e.g., 50 and 200 cm) are nominal. Ninety percent of the measurements on the glacier were made between 13 and 71 cm and 146 and 221 cm. In the present study, wind speed and direction, temperature, and humidity are analyzed only at the "2 m level." The radiation sensors varied in height between 100 and 170 cm. Before the expedition, in April 1994, many sensors were calibrated, and just before (June 1-5) and after (August 23 to September 5) the expedition, all instruments used during PAS- TEX were set up for comparative measurements. This was done in Cabauw, located km southwest of Utrecht, Netherlands. In order to complete the surface energy balance, the mass balance was determined by stake and density measurements at the stations on the glacier and subsurface temperature measurements at U1. Precipitation was recorded at A1. Cloud observations were made every 3 hours, except during the night, mostly at A1 or at the Karl-Volkert-Haus (see Figure 1). A more detailed description of the experimental setup is given by Greuell et al. [1995]. In this paper, data from the meteorological station on the top of Hoher Sonnblick (3106 m asl) will also be used. This station is located some 20 km east of the Pasterze. Apart from the energy-balance stations the PASTEX setup consisted of two other parts. Firstly, three stations equipped with radiation instruments were established on and near the glacier (at U2, S1, and S2) in order to improve techniques for the retrieval of ice albedo from satellite images. Secondly, at A1, upper air soundings were performed with a tethered balloon. The resulting data, together with data from the energy-balance stations, were used by van den Broeke [1996] to describe the horizontal and vertical structure of the atmospheric boundary layer above the melting glacier as well as its diurnal variation during a period of fair weather. On the basis of the same data sets, van den Broeke [1997] analyzed the momentum, heat, and moisture budgets of the katabatic wind layer U5,, i,,, i,,,,,!, ,...! i... i L.u...2. m I m [ m I, [ m m I I I I I I I Distance from head (km) Figure 2. Profile of the Pasterze along the center flow line with mast locations. The curve represents the glacier surface in Between 1985 and 1994, when PASTEX took place, the surface lowered. Therefore most stations seem to be located below the surface. 3. Results The following results are all based on half-hourly means. Unless stated otherwise, only those half-hourly means were analyzed which coincided with simultaneous measurements of the same variables at all other stations. Temperatures during PASTEX were extremely high. On Sonnblick the mean summer temperature (JJA) in 1994 was 3.0øC. This is equal to the highest value during the period , when the mean summer temperature was 0.6øC [B6hrn, 1992]. The summer (JJA) was further characterized by a relatively long total sunshine duration (640 hours; the mean for was 482 hours) and an almost average total amount of precipitation (420 mm; the mean for was 430 mm). A typical day consisted of a morning with clear skies, followed by the appearance of clouds and sometimes rain and thunderstorms during the afternoon Wind Field In principle, three systems determine the wind field near the surface' (1) the synoptic-scale gradient wind; (2) mountain and

4 25,944 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER valley winds, and slope winds, which are due to radiational cooling or heating of sloping surfaces; and (3) the glacier wind. constancy on the glacier tongue are a result of specific conditions during the experiment. Note that the fact that during The last develops over slopes with melting snow or ice when 77% of the time at A1 the wind maximum was found below the adjacent air has a temperature higher than 0øC. Under such conditions, owing to the exchange of sensible heat with the surface, the lowest part of the atmosphere cools and starts to flow down the glacier under the influence of gravity. During PASTEX the wind regime was dominated by the glacier wind. At all stations, mean wind vectors pointed downward along the local slope and directional constancies (see Table 2) were high, except at U5, located near the crest. The directional constancy, defined as the ratio of the magnitude of the time-averaged wind vector and the time-averaged wind speed, reached a maximum at the upper end of the tongue (0.97 at U3). It decreased toward the lower end of the tongue 13 m demonstrates that during most of the time the downward directed wind was indeed the glacier wind. In the context of this section about the wind it might be useful to have a rough idea of the vertical extent of the glacier wind. This is given by the height above the surface of the maximum in the mean wind speed profile, which was typically between 4 and 8 m at A1, and by the fact that the direct cooling effect of the glacier, associated with the glacier wind, extended to some 20 m above the surface at A1, on average [van den Broeke, 1997]. Mean wind speed hardly varied with elevation and was around 4 m/s (Table 2). This lack of variation may have been (0.93 at U1) because occasional erosion of the glacier-wind caused by two factors (see also the treatment of the directional layer by the valley wind started at the lower end of the tongue and then moved gradually upward. Such events were visible in constancy above): (1) the glacier wind is more developed at lower elevations, whereas (2) because of the relatively open the wind direction data. The wind first turned from a down- landscape, large-scale wind systems penetrate more easily to the surface at higher elevations. It is likely that the lack of elevational variation in the mean wind speed is due to specific conditions during PASTEX (in terms of, for example, the temperature of the free atmosphere and strength of the gra- ward to an upward direction at U1, sometime later at A1, then at U2, etc. At the end of the event the reversal to the "usual" direction moved gradually down the glacier. The directional constancy also decreased toward the glacier head (0.81 at U4 and 0.07 at U5). This may be explained by (1) the smaller temperature contrast between the melting glacier surface and the ambient atmosphere at higher elevations leading to smaller katabatic forces (but steeper slopes at those elevations, see Figure 2, lead to larger katabatic forces!); (2) the smaller fetch of the glacier wind at U4 and U5; and (3) the fact that because of the relatively open landscape, large-scale winds penetrate more easily to the surface at U4 and U5. The values for the directional constancy found on the glacier tongue are comparable dient wind) and to the topography of this specific glacier. An attempt was made to relate the 2 m wind speed to the 2 m temperature (according to the analysis made by Ohata [1989] the speed of the glacier wind should increase with temperature) and/or the wind vector on Sonnblick (indicative of the gradient wind). No conclusive relations were found. Wind speed frequency distributions on the glacier tongue were quite different from the distribution at U5, located near the crest (see Figure 3). Whereas at A1 a normal distribution to the highest annual values (up to was approached, a much more skewed distribution was found 0.97) found in the coastal zones of Antarctica [Schwerdtfeger, at U5. Furthermore, at U5 the variance was much larger than 1984] and summertime values ( ) found in the abla- at A1. Wind speeds of less than 2 m/s occurred during 15% of tion area of the Greenland ice sheet [van den Broeke et al., the time at U5 and during only 8% of the time at A1. This low 1994]. One might ask whether values found during PASTEX frequency of small wind speeds on the tongue is almost cerwere abnormally high due to the extremely high temperatures tainly due to the almost continuous katabatic forcing there. On or to the large-scale circulation. These suppositions are not supported by the data. Daily values of the down-valley directivity, defined here as the ratio of the mean down-valley component of the wind and the mean wind speed, were not correlated with the temperature on Sonnblick. Furthermore, at the stations on the glacier tongue the down-valley directivity never became negative (which means that the resulting daily wind vector always had a down-valley component), even when the up-valley component of the geostrophic wind exceeded 10 m/s. So it seems unlikely that the high values of the directional the other hand, probably due to shielding effects of the surrounding mountains, the wind speed never exceeded 9 m/s at A1, whereas at U5, this occurred during 9% of the time. The distributions at the other stations on the tongue (U1, U2, and U3) resembled that at A1, while the distribution at U4 was intermediate between the two distributions plotted here. Wind speed is often used as an input variable in surface energy-balance models designed to simulate the mass balance on glaciers [e.g., Greuell and Oerlemans, 1986]. Since during PASTEX wind speed hardly varied with elevation and no re- Table 2. Average Values for Some Meteorological Variables During PASTEX Number of Half-Hourly Means U1 A1 U2 U3 U4 U5 2075m 2205m 2310m 2420m 2945m 3225m Directional constancy 2 m wind speed, m/s 2 m temperature, øc 2 m relative humidity, % 2 m humidity mixing ratio, g/kg 2 m water vapor pressure, Pa * * * * * * 612 Only those half-hourly means were analyzed which coincided with simultaneous measurements of the same variables at all other stations. Asterisk, no value is given since too many data are missing and/or the existing data are not accurate enough.

5 , GREUELL ET AL.' METEOROLOGICAL VARIABLES ALONG A GLACIER 25, ! i i!! i i i i i i i i i i i... thickness... i' ][ \ i a: 4.53 rr /s ii'"'11... ii'""i Wind speed (m/s) I i i i! i i i i i i i ] I i i [15 (3225 m) 'i... i ' '"'-"T¾O I i a=4.95rn s Wind speed (m/s) Figure 3. Half-hourly mean 2 m wind speed frequency distributions at A1 and U5. Best fits of the two parameter Weibull distribution function characterized by the parameters kw and a (see equation (1)) are also shown. This can be understood by the following analysis which describes the temperature change of an air parcel traveling down along the glacier within the glacier-wind layer which has a fixed H. It is assumed that wind speed (u) and temperature (T) within this layer do not vary with the height above the surface. Only two processes are taken into account, namely, adiabatic heating and exchange of sensible heat with the underlying surface. Therefore temperature changes due to entrainment, phase changes, radiation divergence, and variation of fluxes in the horizontal direction normal to the flow line are neglected. This two-term balance in the heat budget was indeed found at A1 [van den Broeke, 1997]. Since adiabatic heating does not affect potential temperature, the rate of change of the potential temperature of the parcel ( ) is determined only by the sensible heat flux: do H -= -c,(t- Ts)u (2) where c r is the bulk transfer coefficient for heat. It depends, among other things, on the surface roughness lengths and the stratification, but here, it is assumed to be constant. Further, T s is the surface temperature. During PASTEX the surface was usually melting. Therefore setting Ts = 0øC, substituting dx = u dt (x is the distance along the glacier), and rearranging (2) yields 7.5 lation was found between the local wind speed and any other variable, for example, the local atmospheric temperature or the wind vector on Sonnblick, it might be tempting to prescribe the wind speed as a constant with elevation and in time in the models. However, since the turbulent fluxes are nonlinear in the wind speed, it would be an improvemento impose random variations of the wind speed described by distribution functions. Therefore the PASTEX data were fitted to the two- parameter Weibull distribution function [Justus et al., 1978]: where F(U) is the probability that the wind speed is less than U and a and kw are free parameters. Best fits to the data at A1 and U5 are shown in Figure 3. The distribution functions can also be used for comparison with wind speed frequency distri- butions obtained at other locations. (1) _ o 5.5 o 5 o U5 U4,, I,,, I,,, l,,, l,,, Elevation (m a.s.1.) 3.2. Temperature In the top panel of Figure 4, mean 2 m temperatures are plotted as a function of elevation. First of all, the comparatively high temperature on Sonnblick shows the cooling effect of the melting surface on the 2 m temperatures above the glacier. However, more remarkably, the usually assumed constant decrease of temperature with elevation does not show up. The temperature at U3 is even higher than the temperature 215 m lower at A1, and the temperature at U5 (3225 m) is almost equal to that at U4 (2945 m). However (see bottom panel of Figure 4), potential temperature decreases monotonically and almost constantly with the distance along the flow line (x).,,, I,,, I,,, I, [ [ [ [ [ ] Distance from head (km) Figure 4. Mean 2 m temperature against elevation and mean 2 m potential temperature against distance along the glacier during PASTEX. An estimate of the accuracy in the mean temperature (+_0.15øC) is given by the error bars.

6 25,946 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER T do = -c, dx (3) with T in degrees Celsius. Note that the wind speed no longer appears in the equation. If the ratio T/H is constant in x, potential temperature is linear in x. Since such a linear relation is suggested by the data shown in Figure 4, it is concluded that during PASTEX (1) the temperature of the glacier-wind layer was determined mainly by adiabatic heating and exchange of sensible heat with the surface, and (2) the ratio T/H was approximately constant along the flow line. Support for the latter conclusion is provided by Ohata [1989], who analyzed the glacier wind over melting glaciers with a constant slope by means of a theoretical model and found that both T and H are approximately linear in x [Ohata, 1989, Figure 2]. Many assumptions were made in order to derive (3). Probably convergence and divergence of the flow as well as the fact that the wind was not always a glacier wind have a large influence on the mean 2 m temperature distribution. Possibly, the neglect of such processes compensates for each other to some extent. It is beyond the scope of this paper to treat such effects in detail, but the spatial temperature distribution found during PASTEX will be treated more thoroughly in a separate paper. With the foregoing analysis in mind, one can explain the observed temperature profile as follows: following a downward traveling parcel, adiabatic heating dominates cooling due to the exchange of sensible heat with the underlying surface over steeper parts of the glacier, whereas the inverse is true for gentle slopes. Hence net heating occurs in the ice fall between U4 and U3, but no temperature increase or even cooling occurs over more gentle slopes, namely, in the accumulation basin between U5 and U4 and along the tongue between U3 and A1. In conclusion, a linear function of potential temperature with distance gives a much better description of the observed 2 m temperature variation along the melting glacier than a constant decrease of the temperature with elevation. A linear fit to the data of T(z) in Figure 4 leads to a residual standard deviation of 0.53øC, whereas a linear fit to the corresponding data of O(x) gives a residual standard deviation of 0.31øC. One might ask whether this improvement in fit is a result of the extremely high temperatures or specific geostrophic winds during PASTEX. This supposition was tested by making the linear fits T(z) and O(x) to the data of the individual days. It appeared that the difference in the performance of the two models was not correlated to the temperature on Sonnblick, nor to the down-valley component of the geostrophic wind. So there is no indication that the conclusion that a linear function O(x) describes the distribution of the 2 m temperature above a melting glacier better than a linear function T(z) is due to specific conditions during PASTEX. A linear relation between O and x was also found in the melting zone of the Greenland ice sheet [Oerlemans and Vugts, 1993, Figure 2]. This finding is relevant for the extrapolation or interpolation of measured temperatures, especially along flow lines of glaciers with considerable variations in slope angle Humidity During PASTEX the mean humidity mixing ratio at the 2 m level did not change with elevation (see Table 2). Note that this statement is based on the data from four stations only since the humidity data from U3 and U4 are considered to be too inaccurate for this comparison. A constant humidity mixing ratio implies that the water vapor content of an air parcel traveling along the glacier does not change. However, because of the change of pressure with elevation the water vapor pressure of a parcel with a constant humidity mixing ratio increases, while the parcel moves downward (see Table 2). At U5 the measured mean water vapor pressure (612 Pa) is almost equal to the saturation water vapor pressure of melting snow and ice (611 Pa). This does not necessarily lead to a negligible mean water vapor transport between the 2 m level and the surface, because the transport also depends on factors such as the wind speed and therefore on the correlation between temperature and wind speed fluctuations, but energy-balance calculations do show indeed a very small mean latent heat flux (1 W/m2). Because of higher atmospheric pressure, 2 m water vapor pressures are larger than 611 Pa on the tongue, resulting in a mean latent heat flux of 10 W/m 2 toward the surface as calculated with the energybalance approach. Since the water vapor content of a parcel traveling along the glacier does not change, this water vapor flux must be compensated for by entrainment of water vapor into the glacier-wind layer [see also van den Broeke, 1997] Global Radiation During PASTEX the incoming short-wave radiative flux at the top of the atmosphere was virtually the same at all locations because differences in the latitude of the locations were very small. However, the mean incoming short-wave radiative flux at the surface (also called global radiation when surfaces are horizontal) differed considerably from site to site (Figure 5 (top)) due to several processes. In this section these processes will be quantified. For interpretation it is useful to distinguish three categories of processes: (1) absorption and scattering by aerosols, water vapor, and other gases in the atmosphere; these processes cause loss of energy and are relevant at any location; (2) multiple reflections between the atmosphere and the surface and reflection by the surrounding terrain, which both lead to energy gain, and horizon obstruction, which leads to energy loss; these processes are only relevant in terrain with high albedos and/or substantial relief; and (3) absorption and scattering by clouds, causing energy loss. The effect of each of these processes during PASTEX was quantified by means of a parameterization scheme described by Meyers and Dale [1983], but since this scheme does not include the factors relating to albedo and relief, these have been added here. The equations and the method of analysis are treated in Appendix A. The mean effect of each process is depicted in the bottom panel of Figure 5, and values are given in Table A1 in Appendix A. Note that all factors are valid for clear-sky conditions only, except for the cloud factor, of course. Differences in global radiation from station to station can be explained as follows: the stations U2 and U3 received more short-wave radiation than A1, mainly because of less horizon obstruction and increasing terrain reflections from tributary glaciers. Global radiation reached a maximum at U4, located in the accumulation basin, where the albedo was high and the horizon-obstructing slopes were largely covered by snow fields with a similarly high albedo. Therefore the factors relating to multiple scattering and terrain reflections were relatively large (1.03 and 1.07, respectively). At the same time, horizon obstruction was sharply reduced in the relatively open accumu-

7 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER 25,947 lation basin as compared to the tongue. At the crest (U5), only a very small part of the upper hemisphere was occupied by the surrounding slopes, so horizon obstruction was very small and terrain reflections had a smaller effect than at U4. Despite an almost equal local albedo, multiple reflection at U5 was also reduced with respect to U4 since a smaller part of the surrounding terrain was covered by snow (there was a steep nonglaciated slope to the west of U5). In summary, differences in the clear-sky radiation at the various stations were hardly due to differences in absorption and scattering by aerosols, water vapor, and other gases in the I rn....}.... i.j:.... [ atmosphere. They were caused mainly by differences in terrain -" rn... [... reflections, multiple reflection, and horizon obstruction and therefore by differences in local albedo and relief. Differences 0, I,,, I,,, I,,,,,, [,,, I, between stations would have been an order of magnitude smaller if the stations had been located on horizontal planes Cloud amount having different elevations but the same albedo. Figure 6. Mean transmission for clouds as a function of The effect of clouds on global radiation is taken into account cloud amount according to the data collected at A1 and acby the cloud factor. Its mean value was taken as the ratio of the cording to data from Austrian climate stations at elevations of mean measured global radiation and the mean computed 2000 and 3000 m asl [from Sauberer, 1955]. The standard declear-sky radiation for the period from June 22 to August 7. Therefore the cloud factor represents not only the direct effect viations of the A1 data are also shown. of the clouds on the short-wave radiation but also the indirect effects of the clouds, for example, enhancement of multiple at U4. From there, extinction increased slowly with decreasing scattering. Of all factors depicted in Figure 5, the cloud factor elevation and increased also toward U5. The latter increase is is the most effective. Extinction by clouds reached a minimum presumably due to relatively high cloud amounts around the ridge at U5. The three-hourly cloud observations were used to study the I I ' I I relation between the cloud factor (Tc) and the cloud amount.,- o 300 (n). The observations (208, in total), mostly made at At, were.,- linked to the ratio of half-hourly means of measured and computed clear-sky global radiation at At. The result is depicted in 250 Figure 6. The following fit was made: 0.1 -o o U1 A1 U2 U3 U4 U5 2075m 2205m 2310m 2420m 2945m 3225m I Horizon obstruction k-xq Clouds [m[ Water vapor [-] Aerosols k ] Rayleigh scattering and permanent gas absorption [] Multiple reflection [7 Terrain reflections Tc = t n //2 (4) This equation explains 98% of the variance in the cloud factors, if averages of the cloud factors are computed per category of cloud amount (the circles shown in Figure 6). However, because the optical thickness may vary considerably depending on cloud type, the equation explains only 55% of the variance in the 204 individual "observed" cloud factors. Sauberer [1955] published tables with monthly values for the cloud factor for different elevations based on data from Austrian climate sta- tions. Polynomial fits through his data for July at elevations of 2000 and 3000 m are also shown in Figure 6. The difference between 2000 m fit and (4) is less than 0.04 along the entire range of cloud amount. In view of this small difference we conclude that the PASTEX data are in line with the data presented by Sauberer Albedo -0.4 Daily values for the albedos at the energy-balance stations are plotted in Figure 7. The surface at the stations in the upper part of the glacier (U4 and U5) was snow covered during the I I I entire experiment. Therefore the albedo was relatively high U1 A1 U2 U3 U4 U5 and showed a typical decreasing trend with time [e.g., Dirmhirn 2075m 2205m 2310m 2420m 2945m 3225m and Eaton, 1975]. Superimposed on this trend were some peaks caused by fresh snow. Figure 5. Mean measured global radiation between June and August on the Pasterze (top). The heights of During the measurement period the surface at the stations the columns in the bottom panel correspond to the gain (pos- on the tongue (At, U2, and U3) consisted of ice, except at the itive) or loss (negative) of energy due to different processes beginning of the measurements at U3, when the surface was and are scaled by the extraterrestrial flux. All values are valid snow covered. The disappearance of this snow pack led to a for clear skies, except for the cloud factor, of course. sharp decline in albedo. After that, the albedo at U3 (upper

8 25,948 GREUELL ET AL.: METEOROLOGICAL VARIAB'LES ALONG A GLACIER I I o U 1 (2075 m) ß * ] []--A1(2205 m)i i i! ' '". s-i,... x... U2(2310m) 1 l-?... c '!..'.....' i!.--i'? i;i'i' {2 "+':. i... o U3 (2420 m) I--- r¾---- _ I I : ".[ i i :i;., i,' i U4 (2945 m) I.. l :.,,:. : :.:,. ::.,, U5(3225m) I.,. :.:.,,:, :...,, :..'.. - :,,. : +: : : : :... s , -: ** -I:---a-+---.g.a : d '... ' ' '...; Figure 7. Ju 17 Ju 27 Jul/7 Jul/17 Jul/27 Aug/6 Aug/16 Date Ratio of daily means of outgoing and incoming short-wave radiative flux at the surface. part of the tongue) was almost equal to that at A1 (lower part of the tongue) and lower than the albedo at U2 (middle part of the tongue). The reasons for the relatively high value at U2 compared to U3 and A1 are further discussed below. The ice albedos do not show a trend with time, but at U2 and U3, interdaily variations seem to be related to the melt rate as computed with an energy-balance model, in the sense that water reduces the albedo (the computed melt rate explains 48 measurements, which suggest a strong local maximum in the albedo around U2. This maximum is probably caused by albedo variation on a subpixel scale. The TM pixel size is 30 x 30 m 2. The downward facing pyranometer of the albedometer at the glacier surface receives most of the reflected radiation from an area which is of the order of 10 x 10 m 2 (W. Knap et al., Comparison of Landsat-TM-derived and ground-based albedos of Haut Glacier d'arolla, Switzerland, submitted to Inand 40% of the observed variance at U2 and U3, respectively). ternational Journal of Remote Sensing, 1997). The albedo max- The albedo of the moraine at U1 is only slightly lower than the albedo of the ice at A1 (lower part of the tongue). In order to examine the spatial distribution of the albedo over the entire imum at site U2 may be caused by reflection on a relatively bright ice surface directly beneath the pyranometer. The area may be too small to influence the albedo on the scale of the glacier, a Landsat TM scene was processed (July 30, 1994). satellite measurements. This proved to be the only clear-sky Landsat image during the That the ice albedo is almost constant with elevation on the measuring period of PASTEX. The surface albedo was calculated on the basis of radiances in channels 2 ( nm), 4 ( nm), and 7 ( nm). A two stream radiative tongue of the Pasterze contrasts to what is found at, for example, the Hintereisferner [Koelemeijer et al., 1993] and on the Haut Glacier d'arolla (W. Knap et al., submitted manuscript, transfer model was used to calculate a correction for atmo- spheric interference. For further details about the retrieval method the reader is referred to Koelemeijer et al. [1993]. The result is shown in Figure 8. At this stage of the ablation season the transition from ice to snow occurs in the upper part of the ice fall. The snow fields above the ice fall generally have high albedos, whereas the glacier tongue is dominated by low albedos. The dark bands on the glacier tongue are caused by relatively high concentrations of supraglacial material (debris, till, etc.). Figure 9 shows the satellite-derived albedo along the flow line of the glacier. Since there is uncertainty in the geographical coordinates of the pixels and the sites, it is not possible to determine exactly to which pixel a mast location corresponds. Therefore the albedo values were calculated as means of 5 x 5 pixels (150 x 150 m). The albedo range of the 25 pixels is also shown. So that the satellite-derived albedo can be compared with the ground albedo, the albedos at the mast locations on the glacier are shown in the figure as well. Except for the situation at site U2 the ground albedo matches the satellitederived albedo fairly well. The satellite-derived calculations suggest that on the tongue of the glacier the ice albedo is almost constant with elevation. This contrasts with the ground Figure 8. Horizontal distribution of the surface albedo of the Pasterze on July 30, 1994 (1116 LT). The albedo was derived from Landsat TM scene

9 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER 25, ß mean albedo of 5x5 pixels t range of 5x5 pixels " ground measurements U2 U3 "i'" 1 A Distance along the flow line (m) Figure 9. Satellite-derived albedo along the flow line of the Pasterze on July 30, The thick line represents mean albedos of 5 x 5 pixels. The thin lines give the maximum and minimum values for each box of 25 pixels. first, the part of the parameterization that was used to estimate the clear-sky flux from a hemisphere not occupied by slopes (Lcs) will be considered briefly: (5) Lcs= 0.23+b aa trta4 With this expression, L cs is estimated as a function of the 2 m temperature (Ta) and the 2 m water vapor pressure (ea). The coefficient b depends on the location, and its role. is illustrated in Figure 10. Although the two profiles shown have the same 2 m temperature, Lcs is larger in case 2 because the inversion height is larger, so temperatures are higher in the upper part of the profile (it is assumed that there are no differences in the humidity profile). The two different values for L cs can be obtained from (5) by taking different values for b in the two cases. Therefore systematic differences in the shape of the profiles at the various locations can be expressed in different values for b. Best fits of the PASTEX data were obtained by setting b = at U2 and at U5. Over the Greenland ice sheet, Konzelmann et al. [1994] found b = The increases in b 1997). On these glaciers a gradual increase with elevation was from U5 to U2 and from U2 to Greenland may perhaps reflect found. It is possible that this difference is caused by different increases in the mean height of the inversion layer. gradients in the concentrations of morainic material or melt- Factors causing the difference in mean measured L $ bewater at the glacier surface. tween U2 and U5 during the period of 46 days mentioned 3.6. Long-Wave Radiation above were quantified by computing L $ for the same period with the complete parameterization. Results are shown in Fig- In this section the measurements of the incoming long-wave ure 11. Several computations were made by varying the radiative flux (L $ ) at U2 (2310 m asl) and U5 (3225 m asl) amount of slopes and the coefficient b, but in each case, locally will be analyzed. During the period from June LT to measured values for Ta and e a were taken as input. August LT, mean values for this flux amounted to First, L $ was computed for clear skies (n = 0), in the W/m 2 at U2 and 274 W/m 2 at U5. One can expect a larger absence of slopes and on the assumption that characteristics of mean L at U2 relative to U5 for two reasons. Firstly, at U2, the shapes of the temperature and humidity profiles (e.g., temperatures at the same height above the surface are higher inversion height) at U2 were identical to those at U5 (b = than at U5 owing to the difference in elevation and exemplified at both sites). Therefore during this experiment, only T a by the 2 m temperatures (6.8øC at U2 and 3.8øC at U5, on and e a were different at the two sites, leading to a higher L $ average (see Table 2)). The second reason has to do with the at U2 of 13 W/m 2. role of upper hemisphere slopes. Slopes cover a larger part of 2. Secondly, at U2, b was set equal to 0.475, so allowance the upper hemisphere at U2 (29%) than at U5 (5%). Since, on was made for systematic differences in the shape of the temaverage, radiances received from slopes are larger than radiperature and humidity profiles, for example, different inverances received from the sky, the amount of upper hemisphere sion heights. The difference in L $ between U2 and U5 tripled slopes provides a reason for a higher L $ at U2 than at U5. to 39 W/m 2. Moreover, average radiances emitted by upper hemisphere slopes at U2 were probably higher than those at U5, because at U2 the greater part of these slopes (-70%) was free from snow and ice; the opposite was the case at U5 where -80% of the slopes were covered by snow or ice and during PASTEX snowfree and ice-free slopes probably had a higher mean surface temperature than slopes covered by snow and ice. In addition to these factors, which enhance the flux at U2 relative to that at U5, the average effect of clouds is different o at the two sites because there are certainly differences in cloud amount and cloud properties. Clouds enhance the incoming 2m,,,,. long-wave radiative flux, but it is difficult to tell a priori whether the increase is larger at U2 or at U5. In summary, the difference in measured incoming long-wave radiative flux between U2 and U5 may be attributed to (1) 0øC differences in temperature profiles, (2) differences in the Temperature amount and status of the upper hemisphere slopes, and (3) Figure 10. Schematic picture of two temperature profiles. differences in cloud amount and properties. The effect of each Profile 2 results in higher values for the incoming long-wave of these factors was estimated by means of a parameterization radiative flux than profile 1, though 2 m temperatures are which is described in detail in Appendix B, together with the identical (assuming no differences in water vapor content of method of analysis. Here, only the results will be discussed, but the atmosphere).

10 25,950 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER Such a relation could be expected if the gradient wind affects clear sky, b=0.407, local b, no no slopes the wind on the glacier. On the glacier tongue the wind speed frequency distribution approached a normal distribution with a [ clear with clouds, sky, local b, with slopes (measured) relatively small standard deviation, but at U5, located near the l l l l l l ll lll l l 4 crest, the distribution was more skewed, and extreme values u2 3 ' were more frequent. The distribution of the mean 2 m temperature along the 2310m 12 glacier could not be described by the usually assumed constant m IIIIIIIIIlllllllll 4 decrease with elevation. On the contrary, the temperature at u5 3! U3 was higher than the temperature 215 m lower at A1, and 3225m 2 the temperature at U5 (3225 m) was almost equal to that at U4 1 (2945 m). A much better description is given by a linear rela Incoming long-wave radiative flux (W/m 2 ) Figure 11. Mean incoming long-wave radiative flux between June 22 and August 7, 1994, at U2 and U5. Bars marked 1, 2, and 3 represent clear-sky calculations with the parameterization discussed in Appendix B, while the measurements are given by bar 4. Differences between 1, 2, and 3 are explained in the text. 3. Next, the role of slopes was taken into account. This led to an increase in L $ of 9 W/m 2 at U2 and 1 W/m 2 at U5. The values for L $ obtained after this calculation are best estimates of the mean L $ if clouds had been absent during the entire period. 4. Finally, the mean increase in L $ because of clouds was computed by subtracting L $ as found after step 3 from the measured L $. Increases of 26 and 49 W/m 2 were found at U2 and U5, respectively. Apparently, systematic variations in the shape of the temperature and humidity profile as expressed in variations in b (see experiment 2) are important for our understanding of the variations in mean L $ along the glacier. Variations in 2 m temperature and humidity (experiment 1) and the amount and status of the slopes (experiment 3) are of less importance. In total, during PASTEX the clear-sky L $ at U2 would have been larger than that at U5 by 48 W/m 2, but this is compensated for to some extent by clouds which contribute more to L $ at U5 than at U2. The latter may well be due to higher cloud amounts at U5, located near the crest, than at U2, located in the valley. This trend in cloud amount was also indicated by the analysis of the global radiation data. 4. Conclusions In this paper, 2 months of meteorological measurements obtained at six energy-balance stations ( m asl) along an Austrian glacier, the Pasterze, have been analyzed. Changes with elevation have been emphasized. The wind regime was dominated by the glacier wind, espe- cially in the lower part of the glacier. This resulted in extremely high values for the directional constancy (from 0.94 to 0.97 on the glacier tongue). An analysis of the data of individual days indicates that these high values are not due to specific conditions during PASTEX. The mean 2 m wind speed hardly varied with elevation and was 4 m/s. For glacier winds the 2 m wind speed might be expected to increase with the 2 m temperature, but this relation was not confirmed by the PASTEX data. Moreover, the data did not reveal any relation between the local wind and the wind on a nearby mountain top (Sonnblick). tion between potential temperature and the distance along the flow line. This can be understood from a simple thermodynamic analysis of the glacier wind. An analysis of the data of individual days indicates that the superiority of the linear relation between potential temperature and distance along the glacier is not due to specific conditions during PASTEX. During PASTEX 2 m specific humidity was on average almost constant along the glacier. Fluxes of incoming short- and long-wave radiation were analyzed by means of parameterizations which describe the relevant processeseparately. It was shown that changes in clear-sky global radiation with elevation were due mainly to changes in multiple scattering between the atmosphere and the surface, changes in reflections by the surrounding terrain and changes in horizon obstruction, and therefore to changes in local albedo and relief with elevation. Changes in scattering and absorption by air molecules, water vapor, and aerosols were less important by 1 order of magnitude. According to calculations for a period of 46 days, during clear-sky conditions the mean incoming long-wave radiative flux at U2 (2310 m asl, 273 W/m 2) was much larger than at U5 (3225 m asl, 225 W/m2). A small part of the difference (8 W/m 2) can be ascribed to differences in the amount and the status of upper hemisphere slopes, but the difference was due mainly to higher atmospheric temperatures at U2. The difference in temperature between U2 and U5 at the 2 m level was 3øC, on average, but the analysis of the long-wave radiation data suggests that the temperature difference increased with the height above the surface. These systematic differences in the shape of the temperature profile at the two sites explain a large part of the difference in the clear-sky long-wave radiative flux. The albedo was relatively high (between 0.44 and 0.92 for daily values) at U4 and U5, which were both located in the upper part of the glacier, because at these sites, the surface was covered by snow during the entire experiment. During most of the experiment the ice surfaced at the mast locations on the tongue (A1, U2, and U3), leading to relatively low albedos (between 0.18 and 0.33 for daily values). At U2, located on the middle part of the tongue, the albedo was higher than at A1 and U3, which were located on the lower and higher part of the tongue, respectively. However, a satellite image did not reveal such a local maximum, so the relatively high albedo at U2 must be a small-scale feature. The distributions of the meteorological variables and the parameterizations described in this paper might be incorporated in surface energy-balance models designed to simulate the surface mass balance. This might improve especially the computation of elevational gradient of the mass balance. It is difficult to say to what extent the distributions and parameter-

11 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER 25,951 izations presented here are generally valid. Experiments on other glaciers might shed some light on this question. Table A1. Mean Values (June 22 to August 8, 1994) of Input and Output Quantities in the Analysis of Global Radiation Appendix A: Computation of Factors That Deplete or Enhance the Incoming Short- Wave Radiative Flux Clear-sky global radiation (Gcs) was computed by means of the following equation: Gca = Io cos ( z) rrrarwraf mf rf ho (ml) where I o is the flux at the top of the atmosphere on a surface normal to the incident radiation, and z is the solar zenith angle. The factors TR, T a, and T w are transmission coefficients for Rayleigh scattering (R), absorption by gases other than water vapor (g), and water vapor (w). The way these variables were computed is the same as described by Greuell and Oerlemans [1986] and is based on Meyers and Dale [1983]. The factor Tas accounts for aerosol extinction and is given by Meyers and Dale [1983] as ras = k rn (15t2) with k an empirical constant and m optical air mass. Energy gain by multiple scattering (Fms) was computed as [see also Konzelmann et al., 1994]: f 1-je = --+ (A3) Fms 1 - a acs 1 -- OlrOlcs Here acx (=0.064) is the albedo of the clear sky, a is the locally measured surface albedo, and f is the fraction of the surrounding terrain covered by snow and/or ice with an albedo a. The fraction (1 - f ) of the surrounding terrain is not covered by snow and ice and has an albedo Ot r (= 0.10). Here surrounding terrain means that part of the terrain which contributes significantly to global radiation through multiple scattering. This is the terrain within a radius of a few kilometers around the measurement site. For the present calculation, f was subjectively estimated from maps and knowledge of local conditions. Values can be found in Table A1. The factor Frs describes the impact of radiation that is reflected by the surrounding, upper hemisphere, terrain, and subsequently reaches the measurement site directly: where Frs = 1 + F}[(1 - fr)a + frozr] sin d rb (A4) (A5) U1 A1 U2 U3 U4 U5 2075m 2205m 2310m 2420m 2945m 3225m f Frøs fr k a TR T a Tw Tas Fms Frs Fho T c Gm, W/m Symbols are explained in the text. The constant k was found after tuning at the different sites. During the calculations for the entire period the same value (0.96) was used at all sites. face. A fraction 1 - fr of the surrounding, directly visible, terrain is covered by material with an albedo a; the rest (fr) is covered by material with an albedo ot r ( = 0.10). Note that 1 - fr may differ from f because slopes that are invisible from the measurement site may contribute to global radiation by multiple scattering but do not contribute through direct reflections. Values for fr were estimated subjectively from maps and knowledge of local conditions and are listed in Table A1. Finally, Fho accounts for horizon obstruction: Fho = 1 - Frøsfda if z < 90 ø - (A6) Fho = fdb if z >- 90 ø - (A7) where fd, (--0.10) is the average ratio of diffuse to total short-wave incoming radiation during clear-sky conditions, and fdb (=0.15) is the same ratio for zenith angles approximating 90 ø. Thus if the Sun is above the horizon (z < 90 ø - ), the surrounding upper hemisphere slopes shield the measurement site from part of the diffuse sky radiation. If the Sun is below the horizon (z >- 90 ø - ), only diffuse sky radiation impinges on the instrument. Before calculations for the entire period were made with (A1)-(A7), the value for the only tuning parameter, namely the constant k in (A2), was determined. Note that f and fr were set a priori. For the tuning procedure those data were selected for which the strongest indications of clear-sky conditions existed, namely an observed cloud amount less or equal to 1 okta and an undisturbed time series of measured global radiation. This resulted in a total of half-hourly means per station. For each station, k was then varied until the ratio of calculated and measured global radiation was equal to 1.00, on average. Standard deviations of this ratio at the individual stations were around Values found for k are shown in Here rb is the azimuth angle, and is the angle between the vector pointing toward the horizon and the horizontal plane through the measurement site. The quantity Frøs is the fraction of the radiation reflected by a horizontal surface at the measurement site which subsequently hits the surrounding terrain. Table A1. Their small range is an indication of a high relative The amount of energy contained in this fraction is the same as accuracy of the measurements, the validity of the equations, the amount of energy reflected by the surrounding terrain and the reasonableness of the subjectively assigned values for which subsequently reaches the measurement site directly. f and fr- There is no trend in k with elevation, and therefore Here two assumptions are made, namely (1) isotropy of the the mean value (0.96) for all stations was employed during the reflected radiation and (2) the incoming short-wave radiative subsequent calculations. This value is somewhat larger than flux on the surrounding slopes equals the global radiation at the value (0.94) used by Gueymard [1993] for Weissfluhjoch the measurement site, the latter referring to a horizontal sur- (Switzerland, 2667 m).

12 ,. 25,952 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER After this tuning procedure, mean values for the factors in (A1) were calculated for the period of simultaneous measurements of global radiation at all stations, namely June 22, 0000 LT to August 7, 0000 LT. The time step used was 3 min. The horizon angle is a function of the azimuth and was discretized in azimuth steps of 10 ø and linearly interpolated. Finally, the cloud factor Tc was computed from measured global radiation (Gin) and calculated clear-sky radiation o data U2 x data U5 o io%ø% o - fit U2.. o o8 o oo ß "i... i... o -: oc> >... fit US.. '_ o o x Tc = (A8) Appendix B: Development of a Parameteriz' 0..n for the Computation of the Incoming Long-Wav Radiative Flux The long-wave incoming radiative flux (L, ) is a function of the vertical profiles of atmospheric temperature and greenhouse gases, including water vapor, of the distribution of clouds and their properties and of the temperature and emissivity of slopes that cover the upper hemisphere. In order to obtain some insight into these relationships during PASTEX, we made a fit of the data from U2 and U5 to the following parameterization: L = L sky -Jr L slopes (B]) 0.6 ' ure Vapour pressure / temperature (Pa/K) B1. Half-hourly means of the clear-sky emittance [=(L $ - Lslope)/(fso-ra4)] against the ratio of the 2 m water vapor pressure and the 2 m temperature. The irradiance received from the slopes was estimated with equations (B4)- (B6)). parameterization developed by Konzelmann et al. [1994] for the Greenland ice sheet could be made. As far as the slopes are concerned, it is assumed that they msky--fs[ecs(1 -l lp)- 8ocl lp]o'ra 4 (B2) emit radiation as blackbodies and that the atmosphere between the slopes and the instrument does not affect the radiance. This leads to (B4), where fr is the fraction of the slopes ecs = b (B3) (ea) 1,8 covered by rocks with a temperature T r (in Kelvin), while the rest is covered by snow and/or ice with a temperature Ti (in Lslopes = (l -- fs)[fro-rr 4 + (l - fr) ri 4] (B4) Kelvin). During the night the rock temperature is set equal to r r = r a + cg (B5) Ta, but during daytime, it is higher than Ta by an amount c G (c is a constant and G is global radiation in W/m2). The Ti = minimum (Ta, K) (B6) snow/ice temperature is set equal to T a but cannot exceed K, of course. Here L (in W/m 2) is the sum of the flux received from the sky (Lsky) and the flux received from the slopes (mslopes). The first term is treated as by Konzelmann et al. [1994]. Only the factor fs was added, which is the ratio of the irradiance from the sky (that part of the upper hemisphere not covered by slopes) and the irradiance that would have been received from On the glacier tongue, most often the cloud base was at or above the elevation of the surrounding crests. This justifies the absence of a cloud effect in the term describing the irradiance received from the slopes. In summary, L $ can be estimated with this parameterization from Ta, ea, n, and G, provided values for the parameters the entire upper hemisphere in the absence of the surrounding fs, fr, P, eoc, b, and c are known. At U2 and US, values for fs slopes. The magnitude of fs depends on the local topography (see above) and fr (see Table A1) were set a priori and the as well as on the zenith-angle dependence of the radiance. Under clear-sky conditions it is estimated to be 0.89 at U2 and 0.99 at U5. As in most other parameterizations of this kind, L s is written as the product of the radiation emitted by a blackbody with the temperature Ta (the 2 m temperature in K) and the emittance. Here the latter varies between ecs for clear skies (n = 0) and oc for totally overcast skies (n = 1), with values for p, e oc, b, and c were determined as follows: the unknowns p and eoc do not affect the calculated L under clear-sky conditions. Therefore first b and c were determined from the "clear-sky data." These data were selected by comparing measured half-hourly means of the global radiation (Gm) to values computed for clear skies (Gcs; see Appendix A). Values for Gm/Gcs between and were considthe variation linear in n p, where p is a constant. The expression ered as indicative of clear skies. In this way, 254 samples (L, for cs (ea is the 2 m water vapor pressure in pascal, b is a constant) is an expression from Konzelmann et al. [1994], which was based on an expression derived by Brutsaert [1975]. Many other equations for cs are proposed in the literature. Here (B3) was preferred because (1) it has a better physical basis than many other equations, (2) by means of calculations with Ta, e a, and G) were selected for U2 and 265 for U5. The disadvantage of this procedure is that only daytime measurements become available. However, the alternative, namely to select on the basis of the cloud observations at A1, was less successful, probably due to differences in cloud amount at U5 and A1. LOWTRAN7, a numerical radiative narrowband model, on It appeared that variations in c hardly affected the quality of test profiles for a location on the Greenland ice sheet, Konzel- the fit between measured and calculated clear-sky L $, a result mann et al. [1994] demonstrated that (B3) is more successful of the relatively small contribution by the slopes to the total than many other equations, and (3) a comparison with the flux. Therefore c was determined from an independent data

13 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER 25, U2 (2310 m) provided G is also calculated from these input variables. In summary, for the Pasterze it was found that p = 2, oc = 0.976, b = at U2 (2310 m), b = at U5 (3225 m), and c = 0.01 m Measured (W/m 2 ) Figure B2. Measured values for the hourly mean long-wave References incoming radiative flux at U2 as compared to values calculated Arnold, N. S., I. C. Willis, M. J. Sharp, K. S. Richards, and W. J. with equations (B1)-(B6)). Values used for p, oc, b, and c Lawson, A distributed surface energy-balance model for a small are mentioned in the text. valley glacier, I, Development and testing for Haut Glacier d'arolla, Valais, Switzerland, J. Glaciol., 42(140), , B6hm, R., Lufttemperaturschwankungen in Osterreich seit 1775, Publ. source, namely measurements of the slope temperature by means of a Heymann IR sensor. Relating these measurements 341, Zentralanst. ffir Meteorol. und Geodyn., Wien, Brutsaert, W., On a derivable formula for long-wave radiation from clear skies, Water Resour. Res., 11(5), , to simultaneous values for the global radiation yielded c = Dirmhirn, I., and F. D. Eaton, Some characteristics of the albedo of snow, J. Appl. Meteorol., 14, , m 2 Kf. This means that during maximum insolation Greuell, W., and T. Konzelmann, Numerical modelling of the energy conditions (G W/m 2) the mean temperature of those balance and the englacial temperature of the Greenland Ice Sheet, parts of the slopes not covered by ice or snow is 10øC higher Calculation for the ETH-Camp location (West Greenland, 1155 m than the 2 m temperature above the glacier. a.s.1.), Global Planet. Change, 9, , Best values for b are then at U2 and at U5, with Greuell, W., and J. Oerlemans, Sensitivity studies with a mass balance model including temperature profile calculations inside the glacier, residual standard deviations in L of 9.2 and 6.7 W/m 2, re- Z. Gletscherkd. Glazialgeol., 22(2), , spectively. Figure B1 is a scatterplot of measured values for cs Greuell, W., M. van den Broeke, W. Knap, C. Reijmer, P. Smeets, and [=(L $ - Lslope)/(fsO-ra4)] against ea/r a. Best fits of (B3) are also shown. This equation seems to be adequate at US, which suggests that at this site the standard conditions that were imposed to derive (B3), for example, an exponential decrease of the temperature with height, are more or less valid. However, at U2, (B3) is not really adequate, presumably because the inversion layer was thicker at U2 than at U5. In fact, Meesters and van den Broeke [1996] demonstrated that parameterizations of the clear-sky incoming long-wave radiative flux of the form ecs crt 4 are not suitable over melting snow and ice surfaces, but the only alternative they offered was coupling of a melt model to a model with vertical resolution in the atmo- sphere. Therefore it is advisable to use the parameterization presented here in uncoupled melt models, but one should be aware of the limitations. The unknowns p and e oc were derived from the cloud observations made at A1 and simultaneous measurements at U2, on the assumption that cloud conditions were similar at both sites. In total, 197 observations of total cloud amount were associated with hourly means of L $, T a, ea, and G. The above mentioned values for c and b were substituted and best values for p (=2; only integer values were allowed) and e oc (=0.976) computed. The residual standard deviation is 16 W/m 2, and the correlation coefficient between measured and calculated L is 0.82 (see Figure B2). The resulting set of equations (equations(b1)-(b6)) might be used in energy-balance models, in which Ta, ea, and n are used as input variables [e.g., Greuell and Konzelmann, 1994], Acknowledgments. We are very grateful to all the people involved in the field work, to Richard Bintanja, Hans Oerlemans, Michiel van den Broeke, and Roderik van de Wal, whose comments on an earlier version helped us to improve this paper, to Hans Coops and Jon Wieringa, who made useful suggestions about wind speed frequency distributions, to the Zentralanstalt ffir Meteorologie und Geodynamik in Vienna, which kindly provided the Sonnblick data, and to Sheila McNab, who improved the English. The Pasterze project was financed by the Commission of the European Communities (contract EV5V- CT ), the Dutch National Research Programme on Global Air Pollution and Climate Change (contract 276/91-NOP), and the Netherlands Organisation for Scientific Research (NWO/GOA, contract B). I. Struijk, PASTEX: A glacio-meteorological experiment on the Pasterze (Austria), internal report, Inst. for Mar. and Atmos. Res., Utrecht Univ., Utrecht, Neth., and Fac. of Earth Sci., Vrije Univ. Amsterdam, Gueymard, C., Critical analysis and performance assessment of clear sky solar irradiance models using theoretical and measured data, Sol. Energ., 51(2), , J6hannesson, T., O. Sigurdsson, T. Laumann, and M. Kennett, Degree-day glacier mass-balance modelling with applications to glaciers in Iceland, Norway and Greenland, J. Glaciol., 41(138), , Justus, C. G., W. R. Hargraves, A. Mikhail, and D. Graber, Methods for estimating wind speed frequency distributions, J. Appl. Meteorol., 17, , Koelemeijer, R., J. Oerlemans, and S. Tjemkes, Surface reflectance of Hintereisferner, Austria, from Landsat 5 TM imagery, Ann. Glaciol., 17, 17-22, Konzelmann, T., R. S. W. van de Wal, W. Greuell, R. Bintanja, E. A. C. Henneken, and A. Abe-Ouchi, Parameterization of global and longwave incoming radiation for the Greenland Ice Sheet, Global Planet. Change, 9, , Meesters, A. G. C. A., and M. R. van den Broeke, Response of the longwave radiation over melting snow and ice to atmospheric warming, J. Glaciol., 43(143), 66-70, Meyers, T. P., and R. F. Dale, Predicting daily insolation with hourly cloud height and coverage, J. Clim. Appl. Meteorol., 2, , Oerlemans, J., A model for the surface balance of ice masses, I, Alpine glaciers, Z. Gletscherkd. Glazialgeol., 27/28, 63-83, 1991/1992. Oerlemans, J., and N. C. Hoogendoorn, Mass-balance gradients and climatic change, J. Glaciol., 35(121), , Oerlemans, J., and H. F. Vugts, A meteorological experiment in the melting zone of the Greenland Ice Sheet, Bull. Am. Meteorol. Soc., 74(3), , Ohata, T., Katabatic wind on melting snow and ice surfaces (II),

14 25,954 GREUELL ET AL.: METEOROLOGICAL VARIABLES ALONG A GLACIER Application of a theoretical model, J. Meteorol. Soc. Jpn., 67(1), , Rott, H., The Austrian Alps, in Satellite Image Atlas of Glaciers of the World, E, Europe, edited by R. S. Williams and J. G. Ferrigno, U.S. Govt. Print. Off., Washington, D.C., Sauberer, F., Zur Abschfitzung der Globalstrahlung in verschiedenen H6henstufen der Ostalpen, Wetter Leben, 7, 22-29, Schwerdtfeger, W., Weather and dimate of the Antarctic, in Developments in Atmospheric Science, vol. 15, 261 pp., Elsevier, New York, Van den Broeke, M. R., Atmospheric boundary layer structure over a large midlatitude glacier, Ph.D. thesis, chap. 11, Inst. of Mar. and Atmos. Res., Rijksuniver. Utrecht, Utrecht, Neth., Van den Broeke, M. R., Momentum, heat and moisture budgets of the katabatic wind layer over a midlatitude glacier in summer, J. AppL Meteorol., 36(6), , Van den Broeke, M. R., P. G. Duynkerke, and J. Oerlemans, The observed katabatic flow at the edge of the Greenland ice sheet during GIMEX-91, Global Planet. Change, 9, 3-15, W. Greuell and W. H. Knap, Institute for Marine and Atmospheric Research, Utrecht University, Princetonplein 5, P.O. Box 80005, NL 3584 CC Utrecht, Netherlands. (greuell@fys.ruu.nl) P. C. Smeets, Faculty of Earth Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1085, NL 1081 HV Amsterdam, Netherlands. (Received January 28, 1997; revised May 9, 1997; accepted July 3, 1997.)