Geological Survey Professional Paper 715—A Combined Ice and Water Balances of Gulkana and Wolverine Glaciers, Alaska, and South Cascade Glacier, Washington, 1965 and 1966 Hydrologic Years

SOUTH CASCADE GLACIER

Field Program

Most of the instrumentation needed for measurements of ice and water balance had been installed by January 1, 1965, the beginning of the IHD. As a consequence, nearly complete records of streamflow at the outlet of the drainage basin, air temperature at two locations, and precipitation catch in a gage at one location were obtained for the 1965 hydrologic year (table 1). Ice-balance, wind-speed, and additional precipitation data were obtained during the summer months.

TABLE 1.—Instrumentation at South Cascade Glacier during the 1965 hydrologic year

Instrument locations together with selected snowline positions are shown on plate 3A. The distribution of snow cover over the basin and the late-winter snow balance, _m(s), were measured on May 12, 1965 (pl. 3B), just 15 days before the time of maximum balance. The minimum-balance condition was reached on November 2, 1965 (t₁'; pl. 3C).

Climate

The weather in the North Cascades during the 1965 hydrologic year was marked by slightly above average winter snowfall, a cool spring, and a warm autumn (pl. 3D, 1st and 2d graphs). Except for part of June the summer was cloudier but had less precipitation than average. The accumulation season at South Cascade Glacier continued until almost the end of May, and short periods of snow accumulation occurred every month except July (pl. 3D, 1st graph). The mean winter air temperature was -2.97°C, the mean summer temperature +7.3°C, and annual mean temperature +1.3°C.

Ice Balance

Unusually small basin-storage changes occurred during October and November of 1964, as shown by the hydrologic-balance curve (pl. 3D, 3d graph). The near zero balance until November 22 was due to the mild temperatures and low snow accumulation during these two months. Such subtle, seemingly minor climatic aberrancies during the normal accumulation period can significantly alter the ultimate glacier balance.

Table 2 gives snow, ice, and water balances and related values for the South Cascade Glacier during the 1965 hydrologic and balance years. The standard error for each measurement is shown adjacent to each parameter value and is based on calculations of the reliability of the field measurement. For some parameters the standard error is estimated. For example, runoff, _a, is measured only for the entire drainage basin, but a value for the glacier alone can be derived on the basis of annual ablation, _a, and measured precipitation as rain, p_a(r). The much larger standard error for glacier runoff is then estimated in accordance with ablation errors and errors arising from an approximation of liquid precipitation runoff from the glacier.

TABLE 2—Snow, ice, and water balances, South Cascade Glacier, 1965 hydrologic and balance years

[Parameter values and errors in meters except where indicated, Date: Hydrologic year, Oct. 1, 1965 (t₀), to Sept. 30, 1966 (t₁)]

	Glacier		Basin		Date	Term	Explanation
	Value	Error	Value	Error
Parameters for annual mass balance
a	0.07	0.10	0.04	0.18	Hydrologic year	Annual balance	Net change in glacier mass from t0 to t1; approximately equal to the difference between precipitation as snow and melt-water runoff for one hydrologic year.
n	-.17	.12	-.09	.10	Nov. 1, 1965 (t0') to Nov. 2, 1965 (t1').	Total mass net balance	Net change in mass from (t0') to (t1'); change in mass during one balance year.
n(fi)	-.19	.13	-.10	.10	Nov. 22, 1964 (t0'') to Nov. 22, 1965 (t1'').	Firn and ice net balance	Change in mass of old firn and ice during a single melt season; the mass between two consecutive summer surfaces.
Parameters relating annual and net mass balance
0	0.03	0.01	0.02	0.01	Oct. 1 to Nov. 1, 1964	Initial balance increment	Balance change between first time of minimum balance (t0') and t0; relates balance-year quantities to hydrologic-year quantities.
0(s)	.03		.02		Oct. 1, 1964	Initial snow balance	New snow accumulated on summer surface (ss0) at t0.
0(i)	-.08	.05	-.04	.05	Oct. 1 to Nov. 21, 1964	Initial ice balance	Ice melt in the ablation area after t0 and before ice melt begins the following spring; measured by ablation stakes.
1(s)	0		0			Final snow balance	New snow accumulated on summer surface (ss1) at t1.
a(i)	-.60	.05	-.30	.10	Hydrologic year	Annual ice balance	Ice and firn melt in the ablation area for the hydrologic year.
n(f)	.60	.08	.30	.15	Nov. 22, 1965	Net firnification	The increment of new firn in the accumulation area at t1''; measured after ablation ceases in the autumn.
Parameters for snow accumulation and ablation
x	3.67	0.18	2.48	0.20	May 27, 1965	Maximum balance	Maximum value of the balance (in relation to balance at t0) for the hydrologic year, similar to the "winter balance" or the "apparent accumulation."
m(s)	3.48	.15	2.40	.20	May 12, 1965	Later-winter snow balance	Balance measured to the summer surface (ss0) in late winter or spring; measured in pits or by probing.
a	4.00	.18	2.66	.25	Hydrologic year	Annual accumulation	Accumulation of snow between t0 and t1.
a	-3.93	.20	-2.62	.20	do	Annual ablation	Ablation of snow, ice, and firn between t0 and t1.
Parameters for glacier dimensions
S	12.90	0.04	6.11	0.02		Area
AAR	2.53	2.03	2.30	2.05	Sept. 30, 1965	Accumulation-area ratio	A rough index of annual balance, measured at time t1, neglecting new snow overlying ss1.
ELA	1880	20			do	Equilibrium-line altitude	Do.
δL	-12	3			Hydrologic year	Advance or retreat	Average horizontal-distance change of terminus in direction of glacier flow.
Parameters for water balances
pa			2.06	0.50	Hydrologic year	Measured annual precipitation	Value measured with a gage at one point.
pa(r)			.33	.05	do	Measured annual precipitation as rain	Do.
pa*	4.25	0.30	3.43	.30	do	Calculated annual precipitation	Calculated average for glacier or basin, using annual basin runoff and balance.
a	4.32	.28	3.39	.10	do	Measured annual runoff
1Glacier area in km2, is larger than previously published value because small connected snow and ice areas are included with the trunk glacier in this report. 2Dimensionless.

The maximum balance, _x, was 3.67 m averaged over the glacier, or 2.48 m averaged over the drainage basin (table 2). This is a measure of the maximum water-equivalent depth of seasonal snow reached in late winter or early spring, a quantity which has been referred to as the apparent accumulation (Meier, 1962) or erroneously referred to as just the accumulation. The annual accumulation, _a, on the glacier was 4.00 m. The maximum balance was reached on May 27, 1965, 15 days after detailed measurements were made of the late-winter balance, b_m(s), shown on plate 3B. Balance change between May 12 and May 27, 1965, was estimated on the basis of recorded precipitation, air temperature, and runoff. For May 12, 1965, the measured snowpack density, in megagrams per cubic meter, was 0.495 on the glacier (P-1, alt 1,860 m) and 0.523 off the glacier (site 1, alt 1,610 m).

The late-winter balance, b_m(s), net balance, b_n, and the summer change in storage, b_n—b_m(s), are shown as functions of altitude on plate 3E. Note that all three curves become more negative at the highest altitudes. This is presumably due to wind removal of snow and accounts for the patches of bare ice exposed at high altitudes. The balance curves for the basin are near zero at the altitude of South Cascade Lake because the lake (0.24 km² or 4 percent of the basin area) is incapable of supporting a load of snow except for a small area close to the shore. As snow accumulates on the lake during the winter, it displaces water that runs off directly.

The total mass net balance, _n, or change in ice storage was -0.17 m averaged over the glacier and occurred between the minimum balances on November 1, 1964, and November 2, 1965 (table 2). The equivalent 1958-64 average net balance was -0.60 m. Factors tending to produce a less negative balance were the above-average winter snowpack, the late spring, and the summer snowfalls. The low altitude of the previous year's snowline was a significant factor in reducing ice melt in July. Large areas of ice are usually exposed in July and undergo heavy ablation owing to the low albedo of ice and to the intense midsummer radiation. The high albedo 1964 firn covering much of the ice area significantly reduced the total ice melt during the summer. Ablation continued throughout October and caused a net change in basin storage of -4 mm/day during that month. This was an anomalous condition, since the ablation season usually ends shortly after October 1. The result was a positive annual balance of 0.07 m on September 30 and a negative net balance on November 2 (pl. 3D, 3d graph). On the glacier, the standard error of the net balance was about 0.12 m and the error in the annual balance about 0.10 m.

Precipitation

One recording precipitation gage is in continuous operation in this drainage basin (site 1, alt 1,610 m, pl. 3D, 1st graph). Because of its low altitude and the inherent inaccuracy of precipitation gages in mountainous areas, however, this gage is considered only an index of the average basin precipitation.

An estimate of the total basin precipitation is made by treating the entire basin as a large gage where annual precipitation equals annual runoff plus annual storage changes plus net evaporation, or

_a^* = _a + _a +

where p_a^* = calculated precipitation, _a = measured annual runoff, _a = measured annual balance, and = net evaporation-condensation balance. We assume that is negligible compared to the other terms; measurements with lysimeters on the glacier in past years have shown that evaporation and condensation on snow are nearly equal and tend to cancel each other out. Net evapotranspiration undoubtedly occurs over the small part of the basin which is vegetated or becomes bare of snow for a small part of each year. This water loss is difficult to estimate but must be of the order of a few millimeters averaged over the whole drainage basin for a whole year. Assuming zero net evaporation, the calculated basin precipitation is 3.43 m.

Cumulative basin precipitation, σ^* (pl. 3D, 3d graph), is calculated by multiplying cumulative precipitation recorded at the gage since t₀, σp, by a ratio of the calculated annual basin precipitation, _a^*, divided by the annual gage precipitation, p_a:

Hydrologic Balance

An estimation of the daily basin balance (here designated as the hydrologic balance; see pl. 3D, 3d graph) can be made by subtracting cumulative runoff from cumulative basin precipitation. The standard error of the hydrologic balance curve is large (over 10 percent) because of the large basin-precipitation error. An independent check of the calculated hydrologic balance against the measured maximum late-winter balance on May 27 shows a difference of 7 percent (hydrologic balance = 2.31 m, _x = 2.48 m).