You can try to use a very simple analogic model to understand. Let’s take few ice cubes (they are your iceberg!) and put them in a glass (your southern ocean) and ……………wait and see!
This is so disappointed! And a little surprising for anyone who is not a physicist. So I asked to a physist for some help. It took him a least 5 min to understand what I did not understand. Then he told to be (with a little contempt ….): “but my dear, this is basic physics!”.
So let’s go for a short basic physics lesson!
The level of the ice will not change because the volume of the ice and the volume of the water that it will forms are quite the same. I don’t know for you but I need numbers to understand (simple numbers!). Let’s imagine that the ice in the glass is a big cube of 8 cm3 (2cmx2cmx2cm). The density of the ice is 0,92 g/cm3 so the weight of the ice will be 8×0,92 = 7,36 g.
The density of the water is 1g/cm3 so when your ice cubs melt, they will produce 7,36g of water. It’s a simple question of density. For a same weight, the ice takes more volume than the water.
You also can try to put a full bottle of water in the freezer and wait for a few hours. Then, you will see that the ice takes more place than water for the same weight (ok, don’t try this, I don’t want any trouble with your mum…).
So? Ice melting has no influence on the sea level?
Of course not!
Let’s try another simple experience:
Wait a few hours and you will see that the level of the water in your glass has increased. So, the melt of the ice which is already in water will not change the seal level (melting of the sea ice for example) but the sea level will rise if the ice was not initially in the sea. It’s the case for melting of the ice sheet.
It’s a little more complicated for ice shelves because they are the floating part of an ice sheet. A melting ice shelf will not raise sea level by themselves, but ice shelves are important indirectly to sea level, as they slow down glaciers that drain the ice sheets that are onland and above sea level. If an ice shelf melts, the glaciers they were holding back slide into the ocean quicker and this will raise sea levels…..