USGS Logo 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



Most ice-balance data for glaciers are obtained by the use of stakes, pits, or probes, referenced to or from a marker horizon that is usually a summer surface. This is termed the stratigraphic system of measurement (UNESCO/IASH, 1970). However, summer surfaces may be transgressive with time so that a comparison of stratigraphic ice-balance data with water-balance data is difficult. This difficulty may be circumvented by use of the annual system, which references all measurements to values taken at two instants in time, normally the beginning and end of a hydrologic year. The annual system, however, is not convenient in regard to field measurement. Some scheme is needed to relate these two systems and take advantage of the best qualities of each.

We use a combined system that relates the annual and stratigraphic systems on the basis of identification of the material involved—snow and frozen water of the year under consideration, previously deposited ice and firn, and new snow deposited after the summer of the year in question. This system also relates changes in these materials to hydrologic and meteorologic quantities.

The terms used in this report are illustrated on a graph (fig. 6) showing ice-balance quantities, reported in millimeters or meters of water equivalent, averaged over the glacier as a whole. Symbols for these terms use the following conventions: A bar over the letter symbol indicates an average taken over the whole glacier or drainage basin; a letter in parentheses following a symbol indicates that only the material snow (s), ice and old firn (i), or new firn (f) is considered; if no parentheses follow a symbol, the total mass (undifferentiated) is considered; the subscript 0 refers to measurements made on or about the beginning of the hydrologic year, which runs from t0 (Oct. 1) to t1 (Oct. 1); the subscript a refers to quantities measured over one hydrologic year; the subscript 1 refers to measurements made only at the end of a hydrologic year; and the subscript n refers to measurements made close to but not at the end of the hydrologic year. At t0, the amount of snow (including superimposed ice) above a summer surface overlying older ice and firn is the initial snow balance b0(s). At t1, the amount of newer snow overlying a new summer surface is the final snow balance, b1(s).

FIGURE 6.—The combined system for ice-balance terms. This diagram portrays the ice-mass changes with time, averaged over a whole glacier. See text for description of terms. (click on image for an enlargement in a new window)

The amount of the old ice and firn lost during the hydrologic year as measured from t0 to t1 is the annual ice balance,ba(i). The net change in glacier mass from t0 to t1 is the annual balance, ba. The glacier actually reaches a minimum mass at times t0' and t1', generally close to but not the same as t0 and t1. The net change in glacier mass from t0' to t1' is the total mass net balance bn. An initial balance increment, b0, relates the balance at t0' to that at t0. At some time t0'', after t0', ablation generally ceases for a considerable length of time during the winter. The change in mass of old ice and firn from t0 to t0'' is the initial ice balance, b0(i). As new snow accumulates near the end of the hydrologic year, the older snow becomes firn. At some time t1'', after t1', ablation again ceases for a period during the ensuing winter.

The term "net balance" has been used in the past to describe the difference between the amount of ice lost and the amount of snow added to storage as firn. This concept can be defined more exactly in two ways. The change in mass of old firn and ice at t0'' to new firn at t1'' is the firn and ice net balance, bn(fi); the amount of new firn accumulated at t1'' is the net firnification, bn(f). Alternatively, the change in mass of old firn and ice at t0 to new firn at t1 is the firn and ice annual balance, ba(fi); the amount of new firn accumulated at t1 is the annual firnification, ba(f). This alternate scheme should not be used on glaciers, such as South Cascade, in which appreciable changes in the amount of new firn may occur after the end of a hydrologic year.

Other useful parameters are the maximum balance during the hydrologic year, bx (generally estimated or computed from other data), and the measured late-winter snow balance, bm(s). Not all these terms are measured, computed, or even needed for all glaciers in this program, but all must be defined to relate the results from different glaciers properly. Other terms relating to accumulation, ablation, balance, exchange, and glacier areas are used as given in UNESCO/IASH (1970).


Errors arising from measurements of ice, snow, and water balances are difficult to treat analytically owing to the inherent difficulty of measuring large masses of moving and compacting snow and ice and to sampling problems. Reliable measurements of standard errors of balance values at a single stake have been made. But even these error measurements may be subject to large unknown influences if there are long time periods when no observations are made or if there are unexplained vertical movements of ablation stakes; in addition there are always difficulties and unknown errors in making continuous and accurate density measurements. Interpolating between widely separated points over large areas of glacier ice and snow is normally done using snowline information as a guide. This improves the result but also drastically increases the difficulties of assigning meaningful error values to each measurement. The standard errors given in this report should be considered as little more than approximations; they represent a combination of error measurements at points and subjective error estimates for interpolations or values not susceptible to error measurement, We have used the rule that the error of an indirectly measured quantity (which is the sum or product of two or more directly measured quantities) is equal to the square root of the sum of the squares of the errors of the directly measured quantities. Standard error values are given in the same dimensions as the balance values to which they apply (meters of water equivalent).

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Last Updated: 28-Mar-2006