Converting glacier volume to mass: what ice density to use?

Question

The density of ice is 0.9167 g/cm³ at 0 °C (under atmospheric pressure).

I know of two factors that may influence this (are there more?)

1. Pressure

   The glaciology faq (Common Questions and Myths about Glaciers) at the Alaska Science Center of the U.S. Geological Survey (USGS) mentions for glacier depth:

   A good guess is that the ice thickness is about one-half of the surface width of the glacier. Although few glaciers have been measured, the measured thicknesses range from a few tens of meters for small glaciers to about 1,500 meters for the largest glaciers in Alaska.

   Does the density of ice change significantly with depth?

   The Wikipedia article on ice mentions the density of ice increasing slightly with decreasing temperature, and the different phases of ice under pressure, but nothing on density.

2. Inclusion of air

   Googling for pressure ice density the (my) first search finds Density of glacier ice at the International Glaciological Society. This focuses on air in glaciers making the density lower, and concludes that at larger depths we reach that 0.92 limit:

   

What would be a good average to take?

Answer 1

This is a non-trivial issue. When you look at volume change of a glacier, you typically subtract two digital elevation models to obtain the difference between the two. First, you must differentiate between ice sheets where ice berg calving reduces volume and more ordinary glaciers with melt processes. There are of course calving glaciers as well so it is possible to get into great detail for any one specific glacier, so here I will just discuss the most common case which is a smaller glacier with melt-freeze conditions.

The change in elevation differs in magnitude across the glacier surface due to the movement of the glacier and accumulation-melt processes. The surface material can be (1) glacier ice, (2) snow, (3) firn snow that has survived a melt season) or (4) super imposed ice all with more or less differing densities, you need to assess what sort of material has been removed.

Ice can be approximated by a density of 900 kg/m³, firn has a density of about 600 kg/m³ but it must be remembered that the firn is converted to glacier ice by metamorphic processes so that the density changes with depth from 600 to 900 kg/m³. the transition to ice occurs at depths of about 30 m in temperate glaciers although few studies exist on the actual processes that occur. Snow have very differing densities but considering averages, I would say that it would vary between 350 to maybe 500 kg/m³ for winter (cold) conditions and around 550 kg/m³ for a melting snow pack. Super-imposed ice is closer to ice and probably varies in the upper range of 800--900 kg/m³.

To make matters worse, snow superimposes firn which in turn superimposes ice. This means that in the accumulation area, volume change can result from both a reduction in a snow cover and the firn layer. In the zone near the equilibrium line there can be a loss of both firn and ice. this is also where the superimposed ice will play a role.

So there is no simple density to use since the loss you try to estimate will involve varying types of densities spatially as well as vertically. For annual changes, you can largely ignore the vertical distribution, but with volume changes covering larger periods where climate change influences the longer term location of the equilibrium line and the size of the accumulation area, vertical layering also has to be included.

As a first approximation, a surface zonation of ice snow and possibly firn can be used and perhaps lumping snow and firn with a single density of around 600 kg/m³ can be used. I would, however, say that to some extent any choice you make will be wrong, so being aware of complexity and the limitations is the only way forward.

EDIT:

A couple of useful sources relating to the question:

Huss, M., 2013. Density assumptions for converting geodetic glacier volume change to mass change. The Cryosphere [Open Access]

Moholdt, G., (Referee) Interactive comment on “Density assumptions for converting geodetic glacier volume change to mass change” by M. Huss. The Crypshere Discuss. [Open Access]