# Waterlevel increase calculation

So I tried to calculate the rise of waterlevel myself. But the results I have gotten seem to be pretty low: Given the earths radius, I clalculated different Events:

1) If all landice melts there is an increase of the earths radius of ~54m. This number should be a bit higher because only ~70% of earths surface is water. For the ice I also didn't took the change of density into account because its relatively negligible.

2) Then I calculated the new radius given the annual loss of ice 2011-2014. This number was surprisingly low with only ~1mm each year.

3) And for the extreme increase of water temperature globally of 9°C I took the Global Water Volume into account. But the increase of 5.2m is not that big either.

So are my numbers as expected or did I do something wrong? Because these numbers don't explain the predicted massive increase of the sea level in the near future.

• Beside some unnecessary simplifications (like assuming the whole Earth is cover with water) The numbers looks right. Why do you think they are not consistent with sea level rise predictions? What predictions are you talking about? (add source) IPCC predictions are between 0.4 and 1.0 meters by year 2100, I find that consistent with your numbers. You should add your source for annual ice melt. And instead of the cumbersome radius calculation just divide the volume in km$^3$ by the oceans total surface in km$^2$, and you will get sea level rise in km. – Camilo Rada Feb 4 '19 at 16:26
• That's the way to go, do the math yourself! – Roberto Feb 5 '19 at 1:08
• Yes thats what I meant with "This number should be a bit higher because only ~70% of earths surface is water". en.wikipedia.org/wiki/Sea_level_rise states that the yearly increase is 3.2 mm. My number for melting ice is ~1mm (bit higher because not all of earths surface is water). So does that mean that most of the increase in sealevel comes from water getting warmer? – Evator Feb 6 '19 at 15:24

Beside some unnecessary simplifications (like assuming the whole Earth is cover with water) The numbers looks right. IPCC predictions are between 0.3 and 0.8 meters by year 2100 for the most likely scenarios, and I find that perfectly consistent with your numbers.

Your calculation yields about 0.98 mm per year from glaciers, which using the actual surface of the sea (361,132,000 km$$^2$$), gives a more accurate value of 1.39 mm per year.

Look at the IPCC observations and models summarized on table 13.1 of the Chapter "Sea level Rise" of the Assesment Report 5: For the latest period, if you add up all land ice contributions you get that they are between 0.87 and 2.05 mm/yr, totally consistent with your estimation (of ~1 mm).

The largest single contribution is thermal expansion with 0.8 to 1.4 mm/yr.

Also note that the observed contribution don't quite add up to the observed sea level rise, so we are either sub-estimating some contributions or ignoring significant ones.

If you multiply the current 3.2 mm/yr by 80 years you get ~26 cm by year 2100, but the point is that the rate of sea level rise is increasing (see this answer). That is why all predictions are above that value.

For future predictions, thermal expansion is still the leading cause of sea level rise, as you can see on figure 3.10 of the same IPCC report: I find these predictions consistent with your numbers if you consider the current acceleration on the sea level rise rate. Unless you are talking of other predictions, not the IPCC ones. Or maybe you think that half a meter of sea level rise over 80 years is not much. If that's the case, I suggest you to research what would be the impacts in land loss, infrastructure loss and human populations displacements of such sea level rise.