Ice-stream response to ocean tides and the form of the basal sliding law

Abstract

Abstract. The response of ice streams to ocean tides is investigated. Numerical modelling experiments are conducted using a two-dimensional flow-line model of coupled ice-stream and ice-shelf flow. The model includes all components of the equilibrium equations, and uses a non-linear viscoelastic constitutive equation for ice. Basal sliding is simulated with a Weertman type sliding law where basal sliding is proportional to some power of the basal shear stress. The response of ice-streams to tidal forcing is found to be profoundly affected by mechanical conditions at the bed. For a non-linear sliding law, a non-linear interaction between the two main semi-diurnal tidal constituents (M2 and S2) can give rise to a significant perturbation in ice-stream flow at the lunisolar synodic fortnightly (MSf) tidal period of 14.76 days. For a linear sliding law, in contrast, no such modulation in flow at the MSf frequency is found. For vertical ocean tides of the type observed on Filchner-Ronne Ice Shelf (FRIS), the amplitude of the horizontal modulation in ice-stream flow at the MSf frequency resulting from a non-linear interaction between the S2 and M2 tidal constitutes can be larger than the direct response at the S2 and the M2 frequencies. In comparison the non-linear interaction between K1 and O1 tidal components is weak. As a consequence, modelled icestream response to mixed oceanic tides of the type found on FRIS is stronger at the MSf period of 14.76 days than at both the semi-diurnal and diurnal frequencies, while at the same time almost absent at the similar Mf period of 13.66 days. The model results compare favourably with measurements of tidally induced flow variations on Rutford Ice Stream (RIS), West Antarctica. On RIS a strong tidal response is found at the MSf frequency with a smaller response at the semidiurnal and diurnal frequencies, and almost no response at the Mf frequency. A non-linear viscous sliding law appears to have the potential to fully explain these observations.

Diurnal and semidiurnal tide‐induced lateral movement of Ronne Ice Shelf, Antarctica

“…For parts of RIS where its length exceeds 600 km and the thickness ranges from 300 m at the ice front, to over 1200 m at the grounding lines, the horizontal elastic stresses could exceed AE20 kPa, which is approaching the stress perturbations caused by the tidally varying height of the water column. The long-term flow of ice streams and therefore the mass balance of ice shelves is already known to be modified by oceanic tides, generating fortnightly variations in flow speed of up to 20% and increasing mean speeds by 5% [Gudmundsson, 2011] to 12% [King et al, 2011a], depending on the basal shear stress of particular ice streams. While visco-elastic model predictions replicate quite well the observed Rutford Ice Stream flow, the lowest speed is not at high tide, as would be assumed if water pressure was the main driver [Gudmundsson, 2011].…”

“…The long-term flow of ice streams and therefore the mass balance of ice shelves is already known to be modified by oceanic tides, generating fortnightly variations in flow speed of up to 20% and increasing mean speeds by 5% [Gudmundsson, 2011] to 12% [King et al, 2011a], depending on the basal shear stress of particular ice streams. While visco-elastic model predictions replicate quite well the observed Rutford Ice Stream flow, the lowest speed is not at high tide, as would be assumed if water pressure was the main driver [Gudmundsson, 2011]. This suggests that the similarly sized additional stress from tidal tilting, which is absent in current models, may contribute to both enhanced ice stream flow and the complicated phase relationship that arises from the nonlinear visco-elastic rheology of ice.…”

“…The complicated non-linear response of ice streams to tidal forcing, which includes stresses from ice shelf tilt, show that if we are to fully understand these systems it is important to identify key processes, their interactions, and develop specific parameterizations, rather than combining multiple and potentially opposing effects into a single parameterizations. Since long-term ice-shelf/ice-stream flow is also modified by oceanic tides [Gudmundsson, 2011;King et al, 2011a], studying the effects of tidal tilting will enable the validation of more comprehensive non-linear visco-elastic ice shelf / ice stream models.…”

“…Ice shelves are now known to play an important role in the dynamics of the entire ice sheet by regulating the inland ice's coastward flow [Dupont and Alley, 2005;Gagliardini et al, 2010]. Ocean tides modify ice shelf back stresses and can significantly affect the large-scale and long-term flow regime of active ice streams [Gudmundsson, 2011;King et al, 2011a] and hence their contribution to sea level change. Prior to Global Positioning System (GPS) observations, ice shelves were usually considered only to rise and fall with the tides and to have a uniform horizontal motion with flow determined by viscous processes [e.g., MacAyeal et al, 1996].…”

Tidal bending of ice shelves as a mechanism for large-scale temporal variations in ice flow

“…In some cases the ice flow responds at a different frequency to the tidal forcing, for example on the Rutford Ice Stream (RIS) the largest response is at a fortnightly (M sf ) frequency (Gudmundsson, 2006). More recent observations have shown that the M sf signal actually increases in strength on the adjoining ice shelf (Minchew et al, 2016;Rosier et al, 2017) and also exists on isolated ice shelves which do not have large ice streams feeding into them (King et al, 2011;20 A multitude of mechanisms have been proposed which could lead to a fortnightly modulation in ice flow: a nonlinear basal sliding law (Gudmundsson, 2007(Gudmundsson, , 2011Rosier et al, 2014), tidal perturbations in subglacial water pressure (Thompson et al, 2014;Rosier et al, 2015), grounding line migration (Rosier et al, 2014) and changes in the effective ice-shelf width (Minchew et al,25 2016). Understanding the root cause of the strong and widespread tidal signals observed on ice shelves and ice streams is not done for its own sake but is a means to an end.…”