Snow Cover and Glacier Variations (Proceedings of the Baltimore Symposium, Maryland, May 1989) 19 IAHS Publ. no. 183, 1989. HOUR-TO-HOUR SNOWMELT RATES AND LYSIMETER OUTFLOW DURING AN ENTIRE ABLATION PERIOD J. MARTINEC Federal Institute for Snow and Avalanche Research, WeissfluhjochDavos, Switzerland ABSTRACT At the test site of Weissfluhjoch in the Swiss Alps, 254 m a.s.l, hourly snowmelt rates were computed for an entire snowmelt season, which lasted from 9 May to 15 July 1985. Snowpack discharge was continuously measured using a snow lysimeter. The liquid water content in the snow cover was estimated from the difference between the total snowmelt and the lysimeter outflow. Computations were checked by the water balance from measurements of the water equivalent of the snowpack and precipitation. INTRODUCTION For studies of water movement in a snow cover, the melt rates at the snow surface are required not only daily, but for shorter intervals. This input into the snow cover can be compared with the outflow measured by a snow lysimeter. In the present study, periodic measurements of the water equivalent of the snowpack and continuous measurements of precipitation were used to verify the computed snowmelt amounts from the start to the end of the ablation period. MEASUREMENT OF THE LYSIMETER OUTFLOW The placement of the snow lysimeter, which has a surface area of 5 m 2, is shown in Fig. 1. As described in more detail elsewhere (Martinec, 1987), the outflow from the snow cover is intercepted by a steel vessel and continuously recorded by a tipping bucket. An example of a recording chart is shown in Fig. 2. Each step signifies 11 of water. The number of steps in each hourly interval indicates the outflow in litres per hour. Thus the recording can be converted into a hydrograph, with a typical daily peak in the early afternoon or later, depending on the velocity of percolation and the snow depth. Figure 2 shows that the minimum flow of this 24-h period occurred about at 12 h (summer time) and amounted to 1.41 h _1. The peak flow of 11 lr 1 occurred at about 18 h. Apart from the travel time of meltwater in the snow, a time lag occurs in the saturated layer at the bottom of the lysimeter and in the pipe leading from the steel vessel to the tipping bucket. According to computations (Stauffer, 1985, personal communication), the lysimeter time lag is approximately in the range from 6 minutes for a flow of 21 h -1 to 55 minutes for a flow of.5 1 lr 1.
2. Martinec FIG. 1 Snow lysimeter at Weissfluhjoch, 254 m a.s.l, on 1 July 1985, six days before the disappearance of the seasonal snow cover. FIG. 2 Recording chart of the lysimeter outflow from 27 May 1985,8 h, to 28 May, 8 h. Each step corresponds to 11 of water. In 1985, the outflow from the snow lysimeter started on 16 May. From then on, the hourly values (Q) were determined until 16 July, when the last snow was melted. Data for the initial and final phase of outflow are listed in Table 1, with values converted from litres per hour into centimetres per hour. The runoff from snowmelt was actually finished at 16 h on 15 July. The subsequent values from 2 to 23 h resulted from rainfall.
Hour-to-hour snowmelt rates 21 TABLE 1 Hourly outflows from the snow cover measured by the snow lysimeter Time (h) 16--17 May 1985 Q (cm-rr 1 ) Q Time (h) 15 Tuly 1985 Q (cm-lr 1 ) Q 15-16 16-17 17-18 18-19 19-2 2-21 21-22 22-23 23-24 -1 1-2 2-3 3-4 4-5 5-6 6-7 7-8.28.28.28.28.28.28.28.46.12.18.18.18.16.16.15.14.28.56.84.112.14.168.196.242.362.542.722.92.162.1222.1372.1512 7-8 8-9 9-1 1-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-2 2-21 21-22 22-23 23-24.8.122.146.66.88.9.56.22.14.73.184.22 16.23 16.352 16.498 16.564 16.652 16.742 16.798 16.82 16.834 16.834 16.834 16.834 16.834 17.564 17.748 17.77 17.77 COMPUTATION OF THE HOURLY MELT RATES In detailed computations of snowmelt, air temperature is not an adequate indicator because the short term variations and peak melt rates are caused, for the most part, by global radiation. Since there are seldom data available for a complete energy balance, Bengtsson (1984) used the following simplified equation: M = «T T + M R (l-r) (1) where M = hourly snowmelt depth a T = coefficient (cm C _1 Ir 1 ), not to be confused with the overall degreeday factor T = temperature integrated over time ( C h) M R = global radiation converted to hourly meltwater depth r = albedo as a decimal fraction. In conditions with nightly refreezing of the surface snow layer, it is also necessary to take into account the longwave radiation balance as proposed by de Quervain (Martinec & de Quervain, 1975): M = a T T + M R (1-r) - G (2) where G is the net outgoing longwave radiation converted to hourly meltwater depth. The uncertainty concerning the values of a T can be reduced by substituting snow lysimeter measurements in the following equation:
22. Martinec [M -M B (l-r) + GJT (3) where a T,, = 24 a T T24 T M * 24 = snowmelt depth in 24 h measured as lysimeter outflow R24 - global shortwave radiation converted to a meltwater depth in 24 h G 24 = net outgoing longwave radiation converted to the meltwater depth in 24 hours r = albedo as a decimal fraction. This computation is only possible in equilibrium conditions, when the snowmelt depth equals the lysimeter outflow. This occurs during a sequence of days with approximately equal daily snowmelt depths, as illustrated in Fig. 3. If the 24-h period of the lysimeter outflow ends at 8 h, a certain amount of meltwater is cut off, which is still leaving the snow cover at a receding rate. However, it is replaced by a similar recession outflow from the previous 24-h period. By this assessment of a T and with the albedo values estimated according to the state of the snow cover surface, the hourly melt rates were computed in the initial phase of the snowmelt period, when the snow lysimeter was of no help since there was no outflow. In the later stage, it was possible to compare the computed snowmelt depths with lysimeter measurements and, if necessary, reassess the values of a r, and r and G. The temperatures as hourly means and the global shortwave radiation were measured at the automatic meteorological station of the Swiss Meteorological Office situated nearby at 1693 m a.s.l. The temperatures were extrapolated for the lysimeter site by a lapse rate of.65 C per 1 m. Precipitation was recorded each 1 minutes, and whenever it occurred as rain, it was added to the computed snowmelt. Since the computations comprise over 16 hourly intervals, it is only possible to show in this paper the results for the first 16 days in Fig. 4. It appears that in the first week, meltwater was retained in the snow cover and the liquid water content was gradually built up. During the night and on an occasional cold day, this liquid water was refrozen in the surface snow layer, according ÏM (5 45-2l 45 )- 3,517 cm Refreezing- -,73cm Q(8-8 ) ZNo.3-658 VMmmmmmmtvmrfm S^SS3RSm\<im\TW^ 8 1 12 14 16 18 2 22 24 2 4 6 8 1 12 14 16 18 2 22 24 2 4 6 8 I JUNE 1985 SUMMER TIME 2 JUNE FIG. 3 Daily hydrographs of the lysimeter outflow with the recession flows in equilibrium.
Hour-to-hour snowmelt rates 23 FIG. 4 Computed hourly snowmelt depths, measured hourly flow depths and amounts of refreezing from the start of the snowmelt season, 1985. to computations, as well as by site inspections. The frozen water depth could only be estimated from the temperature profile of snow in the morning and from the assumed liquid water content of the snow layer in question before it was frozen. Only uniform hourly rates evaluated from the total for each refreezing period are shown in Fig. 4. The values offl T24 during the whole ablation period were assessed mostly in the range of.2-.25 cm "C" 1 day- 1. Lower values were assumed on days with little wind and a low air humidity. On 4 July, with the average wind speed of 3.1 m s" 1 and humidity of 46%, a T24 went as low as.12 cm C day" 1. Otherwise the computed daily meltwater depth would have been much higher than the resulting lysimeter outflow. The albedo was in the range of.9-.6. High values were assumed after each snowfall (the latest occurred on 25 June), low values towards the end of the
24. Martinec TABLE 2 Computed components of the liquid water input into the snow cover Period 1985 La T -T EM p IM Rain Refrozen Input 9-31 May 1-3 June 1-16 July 9.4 11.2 17.1 17.6 2.2 24.2 27. 31.4 41.3 2.6 3.9 9.3-2.5-1.65 -.3 27.1 33.65 5.6 9 May-16. July 37.7 62. 99.7 15.8 -A.Y7 111.35 ablation period. The net longwave radiation was estimated according to the literature (Himmel, 195; Braun, 1985; Schàdler, 1987, personal communication) taking into account cloudiness. It ranged from to about -5 W m~ 2. The snowmelt depths from the shortwave global radiation (M R ) and from other processes represented by temperature (a T T) are summarized for the respective months and for the whole ablation period in Table 2. The rainfall depths and estimated amounts of refreezing are also included to obtain the liquid water input. If refreezing is taken into account, it can be estimated that the all-wave radiation was responsible for about 6% of the effective snowmelt, with 4% remaining for the sensible and latent heat. In a detailed study of snowmelt on a Canadian glacier, 251 m a.s.l. (Fôhn, 1973), the result was 44% for the all-wave radiation, 48% for the sensible heat and 8% for the latent heat. In this case, the average air temperature in the studied period was 7.95 C, while it was only 2.7 C at Weissfluhjoch. Results for the partial periods in Table 2 indicate that the proportion of snowmelt attributable to air temperature increases as the ablation period progresses in accordance with the general rise of the air temperature. In high altitudes, for example in most glacial areas, high temperatures seldom occur, and therefore radiation is the dominant snowmelt component. At low altitudes, temperatures are higher but the shortwave radiation is the same or smaller. Thus the temperature component of snowmelt gains more importance. LIQUID WATER CONTENT IN THE SNOWPACK From the difference between the snowmelt as the liquid input into the snow cover (including rain) and the lysimeter outflow as the liquid output, the current liquid water content of the snow cover was computed also in hourly intervals. The lysimeter outflow started on 16 May 1985, when the total liquid water content of the snow cover reached 5 cm or 2.3% by volume. Figure 5 illustrates the gradual build-up of the liquid water content until this date. In the subsequent period, the liquid water content did not increase any more, apart from daily fluctuations that were caused by the alternating snowmelt and refreezing in the night. The morning minima also fluctuate, partly due to occasional inaccuracies of the snowmelt computations. Figure 6 shows the variations of the minimum liquid water content for each day of the ablation period. These values usually occurred between 6 and 8 h. Having reached about 2.5% by volume, the liquid water content stays in a relatively narrow range until the end of June, when a steep increase sets in. It is possible that in the last stage of the snowmelt season, the nightly outflow from the snowpack cannot
Hour-to-hour snowmelt rates 25 w Vol. %,3 ikâ,2,1 I 3 START LYS. OU SLF ZNo.3-659 1 II 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 28 29 3 31 I MAY 1985 FIG. 5 Computed daily minima and maxima of the liquid water content of the snow cover at Weissfluhjoch, 244 m a.s.l. cm Water f 1 1 If J ^"'"-^.._' i i j s \ ~*\ 2 25 1 2 25 3 MAY JUNE JULY 1985 SLF 2Noi3-66 FIG. 6 Morning values (daily minima) of the liquid water content in the snow cover at Weissfluhjoch in terms of centimetres of water depth (solid line) and in percent by volume (dashed line). w Vol.% further reduce the liquid water content towards an irreducible value, which is 2-3% by volume according to Lemmela (1973). At the same time, the computed values may be too high. A possible error increases as the total snow depth decreases. The steep increase in July could be reduced by adjusting the meltwater computations towards smaller rates, for example by taking into account the evaporation losses. Without pertinent data, the liquid water content, especially in the last weeks of the ablation period, remains uncertain and should be measured directly.
26. Martinec WATER BALANCE DURING THE ABLATION PERIOD In view of uncertainties involved in the snowmelt computations, it is useful to totalize the hourly values and compare the meltwater depths not only with the lysimeter outflow, but also with the changes in the water equivalent of the snowpack from direct measurements. A water balance was established based on measurements that take place twice a month at the Weissfluhjoch test site. Precipitation was also measured on the spot by a heated pulviograph. Water equivalents representative for the snow lysimeter were obtained as follows: H w = H wm (H,H, m ) (4) where H w = water equivalent of snow at the lysimeter H wm = measured water equivalent of snow H s = snow depth at the lysimeter H sm = snow depth at the respective localities of the consecutive measurements. In order to correct the catch deficit for snowfalls, the measured precipitation amounts were replaced by the measured water equivalent of new snow whenever necessary. The data are listed in Table 3. The water equivalent of snow was always measured in the morning hours. P is the precipitation total from 8 to 8 h on the respective dates, IM is total of the computed hourly melt rates (with rain added) at 745 h, XQ is total of the measured lysimeter outflow at 8 h. The evaporation losses can be estimated from the difference between the available water depth (initial water equivalent of the snow cover + precipitation) and the runoff depth. The result, 4.81 cm or 4.3%, is in line with previous attempts to establish a water balance at this site (Stichler et al., 1981). Of course, the evaluation of the available water depth may have been affected by difficulties in the precipitation measurement and by redeposition of snow. As shown in Fig. 7, the lysimeter outflow lags behind the computed input from snowmelt (M) and rain, and the difference should correspond to the liquid water content in the snow cover. The computed input is, however, slightly higher than the outflow so that the liquid water TABLE 3 Water balance of the snow cover, ablation period 1985 Date H W AH W P AH +P w EM AM 2Q AQ 16 May 31 May 14 June ljuly 16 July 88.9 73.95 57.17 48.97 14.14 16.78 8.2 48.97 3.63 6.22 9.16 5.48 17.77 23. 17.36 54.45 3.72 23.26 46.84 6.91 111.34 19.54 23.58 14.7 5.43 18.5 42.42 56.71 17.77 18.5 23.92 14.29 51.6 Totals 88.9 24.49 112.58
Hour-to-hour snowmelt rates 27 1 8 ~ r(m+f AIM) UTFLOW, + P) 6 4 4,< ^^ 2 é SLF ZNo.3-661 14 MAY JUNE JULY 1985 FIG. 7 Water balance of the snow cover at Weissfluhjoch in the ablation period of 1985. content in July is too high, as already mentioned with regard to Fig. 6. Also, there are small discrepancies in the intermediate totals of input and outflow. However, the general agreement, also with the measured water equivalent of snow and precipitation (AH+P), is acceptable. It may be considered as an indirect reassurance that the computed hourly snowmelt depths are realistic. CONCLUSIONS The feasibility of computing hourly snowmelt rates from the net all-wave radiation and air temperature was tested by snow lysimeter measurements and the water balance of an entire ablation period. The computed input rates can be used for studies of the water movement in the snow cover. The nightly refreezing of meltwater appears to be a significant factor in alpine conditions. Direct measurements of the liquid water content in the snow should improve the estimates of it. The total liquid water content of the snow cover can be currently evaluated as the difference between the computed liquid input and the measured outflow. In 1985, the outflow from the snow cover started only after the computed average total liquid water content exceeded 2% by volume. In 1987 and 1988, however, small quantities of water were released from the snowpack before this liquid water content was reached, as indicated by direct measurements of the liquid water content. REFERENCES Bengtsson, L. (1984) Modeling snowmelt induced runoff with short time resolution. In: Proceedings, Third International Conference on Urban Storm Drainage (Goteborg, Sweden, June 4-8), 35-324. Braun, L.N. (1985) Simulation of snowmelt-runoff in lowland and lower alpine regions of Switzerland, 4. Zûrcher Geographische Schriften, ETH Zurich, Nr. 21. Fôhn, P.M.B. (1973) Short-term snowmelt and ablation derived from heat- and massbalance measurements.. Glaciol. 12 (65), 275-289. Himmel, J.M. (195) Radiation heat exchange between the snowpack and its environment. Civil Works Investigation Project CW-171, Central Sierra Snow Laboratory, California.
28. Martinec Lemmela, R. (1973) Measurements of evaporation-condensation and melting from a snow cover. In: The Role of Snow and Ice in Hydrology (Proc. Banff Symp., August 1972), 67-677. UNESCO-WMO-IAHS, Vol. I. Martinec, J. (1987) Meltwater percolation through an alpine snowpack. In: Avalanche Formation, Movement and Effects (Proc. Davos Symp. 1986), 255-264. IAHS Publ. no. 162. Martinec, J. & de Quervain, M.R. (1975) The effect of snow displacement by avalanches on snowmelt and runoff. In: Interdisciplinary Studies of Snow and Ice in Mountain Regions (Proc. Moscow Symp. 1971), 364-377. IAHS Publ, no. 14, Snow and Ice. Stichler, W., Rauert, W., & Martinec, J. (1981) Environmental isotope studies of an alpine snowpack. Nordic Hydrol. 12( 45), 297-38. Munskgaard, Copenhagen.