Re: calculating waves sizes after a large mass of material is dumped into ocean

Hi Martin,

This is a tough question to answer definitively. The size (i.e. height and wavelength) of the wave or—more likely—waves created by a trillion tons of ice and rock falling into the Southern Ocean depends on a number of factors. First, what is the ratio of rock to ice? The densities of rock and ice are very different (ice is 920 kg per m cubed and rock is typically 2000-3000 kg per m cubed). This means that the volume of material is very different for a trillion tons of ice versus a trillion tons of rock. Another factor is how the rock and ice enter the ocean. Is it a waterfall, where a smaller area of the ocean is disturbed over a long time, or does it all enter at once, like a stone lobbed into a pond?

That said; let’s do a quick worst-case scenario calculation. First, we’ll assume that the trillion tons is roughly evenly distributed between ice and rock. This makes the average density around 1750 kg per m cubed and the volume of ice and rock is (volume = mass / density) 600 km cubed. Next, we’ll assume that it all enters the ocean at once (since this will create the largest wave). The shape of the chunk entering the ocean is also important, since the height and length scales of the displaced water (i.e. the height and length scale of the chunk) will determine the largest scales of the waves created. For simplicity, let’s imagine that this is a circular chunk lifted right out of the ice sheet. The typical ice sheet thickness is around 2 km (Ref), so the diameter of the circle would be (volume = pi x diameter^2 x thickness / 4 ) about 19 km. This is a huge disturbance. Typically the initial amplitude (or wave height) will be similar to the height of the disturbance, here 2 km. This will decrease by 1/distance travelled, as the wave spreads out is a circular pattern. The maximum wavelengths created will be a few times the diameter, i.e. 40-60 km. For more detailed calculations, check out some of the literature predicting the tsunamis created by landslides (e.g. Landslide Tsunami or Tsunami Landslide Generation).

It is much more likely that the ice and rock will break off in many chunks over the course of years or even decades, creating much smaller waves that will dissipate before the next bit hits the water.

I hope this helps.
Cheers,
Tetjana