Groundwater feedbacks on ice sheets and subglacial hydrology

Abstract

The dynamics of many of Antarctica's glaciers are modulated by a hydrological system at the base of the ice. Sedimentary basins beneath the ice bed contribute to the water budget in this hydrological system by discharging or taking up water. However, sedimentary basins are not included in most current models of ice dynamics, and little is known about their effect. In this paper we develop an idealised model of a glacier whose sliding is coupled to a subglacial hydrological system, which includes a sedimentary basin. We find that groundwater discharge (exfiltration) and recharge (infiltration) are controlled by the shape of the ice sheet and of the sedimentary basin, and that exfiltration promotes sliding whereas infiltration hinders it. Overall, the presence of a sedimentary basin leads to thicker and slower-flowing ice in the steady state. We also find that, when the ice sheet is undergoing retreating, groundwater exfiltration can lead to a positive feedback which accelerates this retreat. Our results shed light on the potential role and importance of Antarctic sedimentary basins, and how these might be incorporated into existing models of ice and subglacial hydrology.

Figures (8)

• Figure 1: Schematic of the model, featuring an ice sheet with thickness $H(x,t)$ and hydrological system with effective thickness $h(x,t)$, above the bed elevation $b(x,t)$, with a sedimentary basin of thickness $H_{sb}(x)$ beneath. The grounded portion of the ice occupies $0<x<x_g(t)$. Melting of the ice supplies a flux of water $m(x,t)$ to the hydrological system, and exfiltration (or infiltration if $q_E<0$) from the sedimentary basin provides a flux $q_E(x,t)$.
• Figure 2: (i) Ice sheet profile and groundwater streamlines, and (ii) effective pressure $N$ for (a) $m=10$ mm yr$^{-1}$ (dimensionless $m=1$) and (b) $m=80$ mm yr$^{-1}$ (dimensionless $m=8$), and for $K \ll 1$, with uniform sedimentary basin thickness $H_{sb}=2000$ m. The effective pressure is compared to the $\mathcal{E}=0$ and $\psi=0$ approximations given by Equation \ref{['eq:NE0']} and \ref{['eq:Npsi0']} respectively.
• Figure 3: (a) Ice sheet profile and sedimentary basins, and (b) effective pressure for a relatively low melt rate $m=10$ mm yr$^{-1}$ (dimensionless $m=1$), as in Figure \ref{['fig:SS_K0']}(a), but with various values of $k_{sb}$ corresponding to $K\ll1$ and $K=2,4,6$ respectively, and a uniform sedimentary basin depth $H_{sb} = 2000$ m. The streamlines are only plotted for $k_{sb} =0$ m$^2$ and the maximum value of $k_{sb}$.
• Figure 4: (a) Ice sheet profile and sedimentary basin streamlines, (b) exfiltration $q_E$, (c) effective pressure, and (d) ice velocity for a higher melt rate $m=80$ mm yr$^{-1}$ (dimensionless $m=8$), as in Figure \ref{['fig:SS_K0']}(b). The various values of $k_{sb}$, the sedimentary basin depth $H_{sb}$, and the plotted streamlines are as in Figure \ref{['fig:SS_varyK_m1']}.
• Figure 5: (a) Ice sheet profile and sedimentary basin streamlines and (b) effective pressure for a nonuniform sedimentary basin depth $H_{sb} = 750 - 500 \cos(2\pi x / 250 \text{ km})$ m. The various values of $k_{sb}$ and the plotted streamlines are as in Figures \ref{['fig:SS_varyK_m1']} and \ref{['fig:SS_varyK_m8']}. (Note that in (a), as elsewhere, the aspect ratio is exaggerated for illustrative purposes.)