No abstract

A porous layer of multi-year snow known as firn covers the Greenland-ice-sheet interior. The firn layer buffers the ice-sheet contribution to sea-level rise by retaining a fraction of summer melt as liquid water and refrozen ice. In this study we quantify the Greenland ice-sheet firn air content (FAC), an indicator of meltwater retention capacity, based on 360 point observations. We quantify FAC in both the uppermost 10 m and the entire firn column before interpolating FAC over the entire ice-sheet firn area as an empirical function of long-term mean air temperature (T a ) and net snow accumulation (ċ). We estimate a total ice-sheet-wide FAC of 26 800 ± 1840 km 3 , of which 6500 ± 450 km 3 resides within the uppermost 10 m of firn, for the 2010-2017 period. In the dry snow area (T a ≤ −19 • C), FAC has not changed significantly since 1953. In the low-accumulation percolation area (T a > −19 • C andċ ≤ 600 mm w.e. yr −1 ), FAC has decreased by 23 ± 16 % between 1998-2008 and 2010-2017. This reflects a loss of firn retention capacity of between 150 ± 100 Gt and 540 ± 440 Gt, respectively, from the top 10 m and entire firn column. The top 10 m FACs simulated by three regional climate models (HIRHAM5, RACMO2.3p2, and MARv3.9) agree within 12 % with observations. However, model biases in the total FAC and marked regional differences highlight the need for caution when using models to quantify the current and future FAC and firn retention capacity.

This paper presents a comparison of solutions of the shallow water (Saint Venant) equations for unsteady one-dimensional/low over a plane and solutions of the diffusion and kinematic wave equations,which are approximate forms of the Saint Venant equations. In the cases studied, the lateral inflow is constant and positive but may cease before a steady state/low is reached. It is shown that for highly subcritical flow, the criterion proposed by Woolhiser and Liggett is necessary but not sufficient to enable a choice between the shallow water equations and the kinematic approximation. An additional criterion is proposed for these cases.

Density profiles in the upper 10-14 m of snow have been measured along a 500 km traverse across the Greenland ice sheet, using a neutron scattering technique. Repeat measurements, over periods ranging from a few days to 5 years, allow strain rates to be determined as a function of depth. Very large strain rates are observed in the surface layer of snow over summer periods. In the underlying multiyear snow, strain rate decreases with decreasing porosity. However, once this effect has been removed, the effect of increasing overburden pressure is counteracted by increasing strength of the material. There are fluctuations in strain rate associated with the annual layering, which indicate that winter and summer snow have different strengths. Based on these observations, we derive a new densification equation which includes the effect of snow density and snow type, and the effect of temperature, described by an Arrhenius expression with activation energy of the order of 110 kJ mol −1 and an exponential prefactor determined simply by the temperature history of the snow. For multiyear snow and meteorological conditions that do not vary from year to year, our equation reduces to a form similar to the Herron and Langway equation for first-stage densification. Using the new equation, we calculate the sensitivity of compaction rate to short-term fluctuations in temperature and accumulation as 0.11-0.20 m a −1 K −1 and 0.33-0.95 m a −1 (meters water equivalent) −1 , respectively, and discuss the consequent uncertainty in satellite measurements of the long-term elevation trend in this area of the Greenland ice sheet.