# Climate Warming, From Ice to Flood?

# Why we don’t actually know what the sea rise due to melting ice-caps is going to be.

There appears much confusion and misinformation over what effect the Ice-Caps melting into the sea will have on sea level around the world.

When we look to examples of accepted reference sources, we see no shortage of information, which possibly adds to confusion.

Further, these sources may avoid discussions around quantification of rising sea-levels, as we can see, it appears very easily politicised by either side.

This article shows by calculation why there is so much uncertainty.

Cutting to the chase:

From the reference above, there are around 321 million cubic miles of water in the oceans, and around 5.8 million cubic miles of water in the ice-caps.

The volume of the oceans are added to the volume of the Earth as a sphere.

Initially, to obtain an outrageously worst case, we will consider the ice-caps as being separate from the rest of Earth, i.e. they are not yet added to the volume of Earth.

Further, we will consider the sea level as approximately equal to the mean radius of the sphere of the earth.

The volume of water in the separate ice-caps, added to the volume of Earth, would result in an increase in the volume of Earth, thus a corresponding rise in the mean radius of Earth, the sea level.

The volume of Earth is 360,000,000,000 cubic miles.

Using the figures given in the source above, we calculate the volume of water in the ice-caps is 0.0016% of the volume of Earth.

This concept of having the volume of water in the ice-caps separate from the volume of Earth, we’ll name as “scenario A”.

The water in the ice-caps in ice-caps added to the volume of Earth will increase the volume of Earth by 0.0016%. We’ll name this as “scenario B”.

The radius of Earth related to its volume is given by the standard equation for the volume of a sphere:

V = 4/3 x pi x (radius cubed)

Rearranging for radius:

radius = cube root(V/(4/3 x pi))

The sea rise corresponds to the change in Earth’s radius from scenario A to scenario B:

radius A = cube root(360e9/(4/3 x pi)) = 4413.041015

radius B = cube root((360e9+5.8e6)/(4/3 x pi)) =4413.064715

More astute readers might notice a difference between the values computed above, and the value of Earth’s radius given in some references.

However, we are not interested in the actual absolute value of the radius, it is the same ball-park, and we are interested only in the difference from A to B, to obtain the rise in sea level from what it is now, to what it will be in the future.

Subtracting A from B gives us the change in radius, which corresponds to sea rise:

radius B -radius A = 0.0237

This initial worst case estimate is in miles.

There are 5280 feet in a mile, so to obtain the sea rise estimate in feet, we multiply this by 0.0237 to obtain 125.136 feet.

This looks alarmingly high!

We must look at where there might be errors in our logic.

The initial assumption that the ice-caps can be considered separately is incorrect, as much of that ice is already floating in the ocean, supported by the ocean.

Ice already floating in the ocean will have no effect on sea rise whether it melts or not. The volume of water in the floating ice remains the same, with no change in weight whether or not the ice thaws to liquid.

So the question is, how much of the ice is not already floating, still supported by land?

We know that ice is less dense than water, with the effect that ice floats with around 92% of its bulk submerged.

So only ice supported by land, with more than 8% of its bulk above sea-level will make a positive contribution to sea rise.

In Antartica, we can see ice elevations above sea level of up to 4000m (4km).

For that ice to be floating, we would need eight or nine times as much draft under sea level, to provide clearance for the undersea part of the ice to float off the ocean bed. This seems pretty obviously highly unlikely, as it would require an ocean depth of some 36km. Thus this ice melting would contribute to sea level rise.

Only detailed surveys of the ice and sea bed in the ice-caps can reveal the information of how much ice is floating, and how much is not.

This uncertainty is undoubtedly one of the primary drivers of scientific expeditions to the ice-caps, and until comprehensive detailed information from those is obtained, including from the undersides of the ice, we will never really know what the sea level rise is likely to be, despite what may be claimed by either side in the argument.

All we know is it *will* rise, assuming further that it keeps melting.