Global Tidal Impacts of Large‐Scale Ice Sheet Collapses

Recent studies show that the glaciers draining both the West Antarctic and the Greenland ice sheets are experiencing an accelerated ice loss, highlighting the possibility of large-scale ice-sheet retreat and sea-level rise in the coming centuries and millennia. These sea-level changes would vary spatially, and could significantly alter global tides as the latter are highly dependent on bathymetry (or water column thickness under ice shelves) and basin shape. This paper investigates how the principal semi-diurnal (M2) tidal amplitudes and energy dissipation respond to the non-uniform sea-level changes induced by complete ice-sheet collapses. The sea-level changes are calculated using gravitationally self-consistent sea-level theory, and the tides are simulated using an established tidal model. Results from the simulations show global and spatially heterogeneous changes in tidal amplitudes. In addition, pronounced changes in tidal energy dissipation occur in both the open ocean and in shelf seas, also altering the location of tidal mixing fronts. These changes have the potential to impact ocean mixing, and hence large-scale currents and climate patterns, and the contribution of shelf-sea to the global carbon cycle. The new results highlight the importance of considering changes in the tides in predictions of future climate and reconstructions of past climate phases such as the Last Interglacial.


Introduction
Tides play an important role in the global Earth system. They provide energy for 21 abyssal mixing through tidal conversion, which is of importance for the climate-controlling fully mixed, nutrient rich waters [Simpson and Pingree, 1978]. The location of tidal 29 mixing fronts is controlled by the balance between heating from the sun and mixing by 30 tidal currents and the wind [Simpson and Hunter , 1974], meaning that changes in tides 31 can modify the location of the fronts. Tidal conversion is responsible for sustaining a 32 vertical nutrient flux controlling primary production at the shelf break and around sea-   shelf sea biogeochemical cycles. The paper concludes with a discussion in Section 4.

Simulations and analysis
To demonstrate how collapses of the WAIS or the GIS would impact the tide, and how 106 these impacts could propagate through to key process and pathways in the global climate  Therefore, additionally, we evaluate the tidal response to a globally uniform sea-level rise.
where: U is the depth integrated volume transport; H is water depth; the tidal current 133 velocity u is u = U/H; f is the Coriolis vector; g denotes the gravitational constant; 134 ζ stands for tidal elevation; ζ SAL denotes the tidal elevation due to self-attraction and 135 loading (SAL); and ζ EQ is the equilibrium tidal elevation. F = F B + F w represents 136 frictional losses due to quadratic bed friction (F B ) and linear tidal conversion (F w ). The 137 former is represented by the standard quadratic law: where C d = 0.003 is a drag coefficient, and u is the total velocity vector for all the tidal and K 1 only to reduce the computational expense with only very minor losses in accuracy 152 [Egbert et al., 2004]. 153 We used a grid spacing of 1/8 • × 1/8 • for our OTIS simulations, the same as in 154 Wilmes and Green [2014]. This is a compromise between computational efficiency and Antarctica on water column thickness by reducing water depth by 0.9×ice thickness from 169 the ETOPO1 database which accounts for the density differences between ice and water.

170
The difference in extent between grounded ice and the total ice extent can be seen in 1. The work done by the tide is the sum of two work terms and their corresponding frictional 212 losses expressed as  The reason for the large differences between the fingerprint and the uniform simulation  Table 1). This effect can also be seen for the No Table 1). The North Atlantic is close to resonance at M 2 frequencies with increasing

Dissipation
Pronounced changes in tidal energy dissipation occur throughout the different ocean 336 basins in response to the changes in tidal processes (see Fig. 7, Fig. 8  the Atlantic in all three simulations (Fig. 7d). This includes decreases on the Amazon

362
The changes in shelf-sea dissipation are predicted to lead to changes in the extent of 363 seasonal stratification in a number of temperate and polar shelf seas (see Table 2 and 364 Fig. 9). Globally, the spatial extent of permanently mixed waters decreases by around  These results are applicable for changes that may occur in a warming world, and also 375 for the LIG which is often considered an analogy for our climate system in the next few In most shelf seas large shifts in the location of the mixing fronts occur for all scenarios.

421
Our results suggest that the tidally driven changes in shelf-sea oceanography could be 422 large enough to significantly impact ecosystems and the cycling of carbon and nutrients 423 via the shelf sea pump in these systems.

424
The increased deep-water dissipation rates seen for the central and northern sheet loss occurs during the LIG affects the sea-level fingerprint of the ice loss. 447 We conclude that past and future changes in sea level have the potential not only to alter 448 sea-level variability (via the tides) but could also lead to important feedbacks in the climate