MEASUREMENTS ICE-BALANCE TERMS 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 involvedsnow 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 The amount of the old ice and firn lost during the
hydrologic year as measured from t0 to
t1 is the annual ice balance, 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, Other useful parameters are the maximum balance
during the hydrologic year,
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).
pp/715-A/sec3.htm Last Updated: 28-Mar-2006 |