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Definition:
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The dimension of mass balance is [M] (mass). The dimension of the mass-balance rate is [M T-1] (mass per unit time). When the mass balance is presented per unit area, it is called specific mass balance and its dimension becomes [M L-2], while the dimension of the mass-balance rate becomes [M L-2 T-1]. When water-equivalent units are adopted (see below), the dimension becomes [L3] or [L3T-1], the corresponding specific units being [L] or [L T-1]. The unit for expressing mass or change of mass numerically is the kilogram (kg). When more convenient the petagram (Pg) or gigatonne (Gt; 1 Gt = 1 Pg = 1012 kg) can be substituted. When mass balance is expressed per unit area, its unit is kg m-2. The unit kg m-2 is usually replaced by the millimetre water equivalent, mm w. E. This substitution is convenient because 1 kg of liquid water, of density 1000 kg m-3, has a vertical extent of exactly 1 mm when distributed uniformly over a horizontal area of 1 m2. The units kg m-2 and mm w. E. Are therefore numerically identical. More formally, the metre water equivalent (m w. E.) Is an extension of the SI that is obtained by dividing a particular mass per unit area by the density of water, w: 1 m w. E. = 1000 kg m-2 / w: Because of the risk of confusion with the metre ice equivalent, or with ordinary lengths, it is important that the qualifier 'w. E.' Not be omitted. Mass balances can also be stated in m3 w. E. (1 m3 w. E. = 1 m w. E. Distributed uniformly over 1 m2) or km3 w. E. Note that 1 km3 w. E. Is numerically identical with 1 Gt. For the mass-balance rate, appropriate units are kg a-1 or kg m-2 a-1 (or m3 w. E. A-1 or mm w. E. A-1) when the time span is an integer multiple of 1 year. Over shorter intervals the unit of time should be the second or the day. Mass units (kg or m3 w. E.) Are useful for hydrological and oceanographic purposes, while specific mass units (kg m-2, mm w. E., m w. E.) Are needed when comparing the mass balances of different glaciers and for studying glacier-climate relations. To convert, with sufficient accuracy for many purposes, to the frequently needed sea-level equivalent (SLE), mass balance in kg m-2 is first converted to kg by multiplying by the area of the glacier, and then divided by the product of w and the area of the ocean (362.5 1012 m2). The sign of SLE is opposite to that of glacier mass balance, a loss from the ice being deemed to be an equivalent gain for the ocean.
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