First, ice is less dense than water which means that if you have 12 oz of ice-water, when the ice melts you should get less than 12 oz if you measure accurately. The density of ice is about 0.9167 g/cm³ whereas the density of water is about 0.997 g/cm³ if you had 12 fluid ounces of ice and let it melt and warm to room temperature, you would be left with 12*0.9167/0.997=11.034 fluid ounces of water.

It is important to note that in this experiment, the total volume of the ice+water is what is measured. If instead you put ice in water and record the height of the water before and after the water melts, you will see that the water level does not change significantly. This is because the ice floats and some of it is above the water line before it melts. This ice is displacing a volume of water corresponding to the mass of the ice. When the ice melts it will then occupy the same volume of water which corresponds to the mass of the water it displaced before it was melted. When this happens you will see no change in volume (neglecting the small change in the density of liquid water on warming from 0 C to room temperature). Therefore, when you conduct an experiment, it is important to be precise about exactly what you are measuring and how you are measuring it. In this experiment, if you are measuring the water level, you will see no change, but if you are measuring the overall volume of water+ice, you will see an overall decrease.

Second, the reason sea levels are expected to rise when ice caps melt during global warming is due to the fact that ice that is not already floating in the oceans is not contributing to the height of the sea (such as glaciers sitting on top of land masses). In other words, the analogous experiment would be to put a bunch of ice in a funnel on top of your glass of water and then let the ice melt and flow into the glass of water. Obviously the water level in the glass will rise.

This is an interesting observation! Perhaps on a very small scale melting ice does not significantly change the volume of liquid water, but certainly on a large scale it does. Consider that when water turns to ice, its density decreases approximately 9% (from about 1 g/cm³ to 0.93 g/cm³).

This reduction in density is why ice floats on top of water unlike most other materials which sink to the bottom when they freeze. If you started with 8 fl. oz. of water and 4 oz. of ice to make 12 oz. total, when the ice melts to water the net increase in water should be 4 oz. x 9% = 0.36 oz. Thus you should have 12.36 oz. of water at the end, where mass is conserved but total volume has increased just slightly. This small change is very significant when it comes to melting polar ice caps—imagine how much water is stored in those structures!

Your question may be made further challenging by recalling that solid water (ice) is *less dense* than liquid water. Therefore, one would expect a net volume *decrease* upon turning glaciers into liquid water.

The problem with this line of thinking is that none of the glaciers in question are currently submerged! The added volume being discussed is the volume which is currently occupying the air - not contributing to the sea level. Take 12 oz of ice cubes from your ice tray and place them in an empty cup, then let them melt. The water level in your cup will rise!

P.S. You may also want to check your measurements. The difference is slight, but you should have observed a net decrease in the total volume of water in your cup after melting (since ice is less dense than liquid water). Controlling for evaporation, this is a reasonable way of calculating the density of ice provided you weigh the cubes before hand.

Not quite, there are unfortunately two problems with this experiment. The first problem is that you probably have some small measurement error. Ice is about 8% less dense than water, so after the ice melted you should should have ended up with about 11.7 oz of water, not 12. But it is a small different so it can be hard to measure, try more ice next time. There is also possibly some small unit confusion, I am assuming you are using fluid ounces instead of weight ounces.

But even still, this would seem to support your hypothesis even more strongly - if the ice melts and then takes up less volume because it is more dense after melting, then should ice caps melting reduce ocean levels? The answer is no. The polar ice caps are floating on top of the water because they are less dense than the water, so when they melt a lot of ice that was floating on top of the ocean and not contributing to the sea level will end up as water in the ocean, which causes the sea level to rise.

Archimedes' law: a floating body displaces its weight, while a sinking body displaces its volume.

The ice cubes were floating in the water, which means that their weight, not their volume, was forcing the water level up to the 12 oz.-mark. When the ice melted, their mass was simply added to the water, leaving it still at the 12 oz.-mark.

Incidentally, this does have applications to ice cap melting: the melting of SEA ICE (e.g. the Antarctic Ross Ice Shelf) does NOT raise global sea levels, because the ice was floating on the surface of the ocean, and therefore displacing its weight and not its volume. The ice that matters as far as sea-level rise is concerned is the ice that is actually sitting on continents and not floating in the ocean. There is quite a lot of ice still on the continents - enough for about 20 meters of sea level rise on Greenland, and another 60 m in Antarctica (the latter of which, thankfully, is unlikely to melt even in extreme global warming scenarios, just due to the positions of the continents and ocean circulation).

This is true - icebergs frozen displace as much water as they would melted. The real contribution to sea-level rise would be the ice on Antarctica, or Greenland. This ice is on land rather than floating (Antarctica has solid ground under all the ice). If all the ice on Antarctica melted and flowed into the ocean, sea levels would rise by about 200 feet. The ice covering the ground on Antarctica is around 7000 feet thick! But, most global warming scenarios suggest the seas will rise much less than 200 feet, but still enough to flood many coastal areas of the world.