The change of mass per unit of time as the interval of mass change approaches zero, obtained in practice by dividing the mass balance by the duration over which it is measured or modelled. See mass-ba
lance units. The qualifiers 'instantaneous' and 'average' can be used to distinguish between the rate in the mathematical sense and the rate as obtained in practice. For example, the average mass-balance rate
The ratio of the mass-balance gradient in the ablation zone to the mass-balance gradient in the accumulation zone, each of these gradients being assumed constant and that in the accumulation zone also
being assumed non-zero.
The change in mass balance due to a change in a climatic variable such as air temperature or precipitation. Sensitivities to temperature and precipitation are often expressed as changes in response to
a 1 K warming or a 10% precipitation increase, resulting in a negative sensitivity to temperature and a positive sensitivity to precipitation. Sensitivities are generally derived from mass-balance modelling, that is, from the difference in mass balance between model runs with and without climate perturbation, but they have also been estimated from mass-balance and climate observations. Mass balance does not vary linearly with the climate in general. That is, d: B/d: T and d: B/d: P are not constant, but they may be assumed constant as a good approximation for small changes of the climatic variable. The 'dynamic' mass-balance sensitivity changes as the extent and area-altitude distribution of the glacier or glacierized region evolve. In contrast, the 'static' sensitivity neglects these geometric changes, although it may still vary with, for example, components of the surface energy balance.
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 balanc
e 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.
The time span, equal or approximately equal in duration to one calendar year, to which the Annual mass balance in any time system refers. In the stratigraphic system the Annual mass balance is the cha
nge of mass during the period between formation of two successive minima in the sequence of Annual cycles of mass growth and decline. These minima are usually reached at different times in successive years, and the duration of the mass-balance year may therefore vary irregularly and substantially in duration from year to year. Point mass balances can be determined unambiguously in the stratigraphic system, but glacier-wide determinations require the assumption that the diachronous character of the summer surface can be neglected. In the fixed-date system the first day of the mass-balance year is always on the same calendar date, which is typically chosen to coincide with the start of the local hydrological year, for example 1 October in the mid-latitudes of the Northern Hemisphere or 1 April in the mid-latitudes of the Northern Hemisphere, or sometimes with the average date of minimum Annual mass. The mass-balance year is 365 (or 366) days long. In the floating-date system the mass-balance year is defined by the calendar dates of the two successive surveys, which may vary from year to year and may or may not be 365 (or 366) days apart.
A synonym of mass balance. Mass budget is a more correct term than mass balance, but is used less often. While water balance and energy balance refer to equations in which the change in storage is onl
y one of the terms, common glaciological usage equates mass balance with the change in storage (in other words, with the mass imbalance). It is unlikely that this usage will change.
1 The horizontal rate of flow of mass through a plane normal to the direction of the horizontal velocity vector. Depending on the context, the flux may be through an element of area at a given positio
n in the vertical plane, through a unit of width extending from the glacier bed to the surface, or through an entire glacier cross section. 2 The vertical rate of flow of mass at the glacier surface or bed. In sense 2, the flux at the surface is equal to the sum of surface accumulation and surface ablation, or in other words to the surface mass balance. Equivalently the flux at the bed is equal to the basal mass balance.