How High Will Melting Ice Cause Sea Levels To Rise When Temperatures Rise 4°C?

So How High Will The Seas Rises When Temperatures Rise Due To Global Warming?

It’s a trick question.

Temperature does not cause ice to melt.

Temperature is an indication of how much (heat) energy stuff has.  Or in every day language how hot the stuff is.

Most stuff can be in one of at least 3 states, solid, liquid  or gas. For water these states are called

  • Ice
  • Water
  • Water Vapor

My children learned this when they were about 9 at primary school.

So if you start with ice and give it heat it warms up – its temperature rises. But when it begins to melt ice stays at the same temperature (melting point).  As the ice absorbs energy (heat) it changes state (from ice to water) rather than  have a rise in temperature.

Once the ice has all melted its temperature will rise if it absorbs more heat, until it gets to boiling point when the temperature stays at boiling point as heat is absorbed until the water has changed to gas.

UK Environment Agency, DEFRA and Met Office

I started writing about sea level rise a year ago when EA (Environment Agency) wanted to make a hole in the sea wall about 1/2 mile from where I live.  This from the body responsible for flood defense in the UK.

EA’s argument is

  • sea levels are rising
  • the rate of rise is accelerating due to global warming
  • this means it is uneconomic to maintain sea walls
  • so the best thing is to make holes in them now

It proved impossible to have any sensible discussion with EA about the rate of sea level rise, using observations held by as EA claimed they were bound to take DEFRA’s projections.

I have posted about DEFRA 2006 and DEFRA 2009 projections.  Also I have put pages on (outside the blog) for every station in UK that hold data for.

DEFRA obviously didn’t believe their 2006 projections as the 2009 projections were lower.

The 2009 projections came in 3 varieties (high medium and low) and even the low variety was higher than observations.

I guess by now you were expecting some sort of ruse.

Here it is.  There was a fourth extra high projection made (called H++ or High++).  This H++ scenario was described as “extremely unlikely” but “physically possible given known laws of physics”.

For some reason person leading the team that produced these projections, Jason King, works for the Met Office.

Given the Met Office don’t seem to be able to predict the weather tomorrow – what hope have they got of predicting sea levels 100 years from now.

Anyway what this meant was that EA no longer had to bother talking about why they were using projections that were very different from observed rates of sea level rise.  They could simply say

“Yes we know the projections are much higher than observations, but they represent a worst case scenario and we are required by DEFRA (our paymasters) to use the H++ scenario for planning purposes”

This is a bit like saying

“I know my house is extremely unlikely to fall down, but I’m going to knock it down now just in case.”

Read all about the DEFRA climate change projections  (I recommend checking out what they mean by probability) and even EA Shoreline Management Plan.

Introducing Bill Donovan of EA

By December 2011 the local branch of EA had run out of answers to my questions (or just got feed up with them) so they passed me on to Bill Donovan who is

Senior Advisor, Climate Change, Flood and Coastal Risk Management, National Office

Bill sent me several papers including this A Sea Of Uncertainty
If you look at the references to this paper you can see that they’ve used the old advocates trick of only using references that support their case. Who are

  • Nils Axis-Morner
  • PJ Watson
  • James Houston and RG Dean


Nonetheless A Sea Of Uncertainty talks about various possible contributions to sea level rise and concludes that they would add up to less than the expected 2 meters (or 1.9). Then they state this

The semi-empirical methods assume that any difference is due to a missing contribution that will increase with global warming.

Even though it is immediately qualified with this

Though that assumption may be correct, without understanding/identifying the physical processes that may make up this shortfall in sea level, there is little in the way of supporting evidence.

Still leaves me gobsmacked. And actually  Jason, there is NO supporting evidence at all.

People who are paid by UK tax payer are seriously writing papers which talk about “missing contributions” increasing with “global warming”.  Why not write

because we don’t get the result we want when we add up all the possible contributions we will assume that there is a magic ingredient which will give us the result we want AND this magic ingredient will get bigger with global warming (whatever that is).

I should say that overall A Sea Of Uncertainty says that there is no evidence for sea level rise of the order of 2 meters, strange that offers any support to the idea especially as it says of semi-empirical methods

“The approach is loosely based on an understanding of physical processes, but the relationship is determined by statistical methods. The general assumption is that the relationship between sea level rise and temperature (or forcing) will hold in the future and for a much greater range of warming than occurred during the period from which it was calibrated.”

Obviously whoever developed this model has no idea that this assumption is valid.

Time For Some School Level Physics

The amount of heat stuff absorbs as it warms is called specific heat.

The amount of heat stuff absorbs as it changes state (e.g. melts) is called latent heat.

There are tables of the values for specific and latent heat, especially for common stuff such as water, for example at

Wikipedia has details of the size of the earth and weight of the atmosphere.

Energy is measured in Joules (symbol j)

Specific heat is the amount of heat need to raise a given weight of stuff by 1°C.

Latent heat is the amount of heat need to change state of a given weight of stuff.

  • We can look up the area of the oceans
  • So we can calculate the volume of water for a 2meter rise
  • We can look up the density of water and hence calculate the weight of water for a 2 meter rise.
  • Then we can calculate the heat required to melt this weight of ice.

If you not familiar with it the little 2 in 102 just tells you the number of zeroes after the 1, so

is 102
as 100 is a 1 followed by 2 zeroes
is 103
as 1000 is a 1 followed by 3 zeroes
is 106
as 1000000 is a 1 followed by 6 zeroes

As we will have 1023, this saves writing out a lot of zeroes.

Energy required to melt enough ice to raise sea level 2 meters

area of oceans
3.61 × 1014
assumed sea level rise
volume of water needed to cause 2m sea level rise
7.22 × 1014
mass of 1m3 water
mass of water needed to cause 2m sea level rise
7.22 × 1020
energy needed to melt 1g water
3.34 × 102
energy needed to melt enough ice to raise sea level 2m
2.41 × 1023


For comparison we can look at the weight of the atmosphere and calculate the energy required to raise the temperature 4°C


mass of atmosphere
5.15 × 1021
specific heat of air
j g-1C-1
energy needed to raise temperature of atmosphere 4°C
2.06 × 1022


So roughly 10 times more energy is required to melt enough ice to raise sea levels by 2 meters as to warm just the atmosphere by 4° C.

How long would it take to melt this amount of ice?

A simplistic estimate might be if it will take about 100 years to warm atmosphere by 4°C, then to melt enough ice to raise sea levels by 2 meters will take 1000 years as it requires 10 times as much energy.

Clearly this argument is way too naive.

Even if this amount of energy was available how is the melting going to take place?
Temperatures in the Arctic and Greenland are well below zero for most of the year. This suggests even if there was increased melting during the ’summer’ there would be freezing in winter.

How will the energy to melt the ice arrive? Presumably by sea.

This implies that water from freshly melted ice will have to move away allowing warmer water to arrive and requiring even more energy.

How long will this take?
What will drive the warmer water to Arctic and Greenland?


And Then?

And then I put this calculation in an email and sent it to Bill.  I’m waiting for a reply.


But there’s more.

It will not be enough to supply 2.41 × 1023 Joules and say ice will melt.  What about the rest of the earth; land oceans and atmosphere.  The heat will be distributed around the whole world (in some fashion).

So if there is going to be ice melting and global warming there has to be enough energy to

  1. melt the ice
  2. warm the earth, oceans and atmosphere

Obviously the second amount of heat is harder to estimate, not least as it depends to what depth the earth and oceans are heated.

Lets look at the Gulf Stream, Wikipedia says that it is  at least 800 meters deep. This paper    Deep-Ocean Heat Uptake inTransient Climate Change  claims there is equal heat between

  • The surface to 200m
  • 200 to 700m
  • 700m down

Now with the aid of some drastic simplifying assumptions I will attempt to estimate the energy needed over the next century to

  1. raise the temperature of the earth 4°C
  2. melt enough ice to raise sea levels 2m (done this already)

Assumptions are

  1. The world is all water.  70% is, within a factor of 2 the multiple of specific heat and density for clay and granite is the same as water.
  2. Consider a 2°C rise, i.e. 4°C at surface falling linearly to 0.  No idea if this is realistic.
  3. Consider a warming to 400m depth, this is less than gulf stream. This will help counteract any bias in assumption 1.  Obviously going twice as deep will require twice the power.
area of earth
5.10 × 1014
assumed depth for temperature rise
4 x 102
average temperature rise
mass of 1m3 water
approx specific heat of water
j g-1C-1
mass of water (and land to be warmed)
2.04 × 1023
energy needed to warm surface of earth 4°C
1.71 × 1024
energy needed to melt ice to raise sea level 2m
2.41 × 1023
energy needed to melt ice to raise sea level 2m and warm earth surface 4°C
1.95 × 1024
seconds in century (approx)
3.15 × 109
continuous average power required
6.19 × 1014
continuous average power required per square meter
w m-2


Apparently Wetherald et al and Hansen et al  believe the earth energy balance is approximately 0.9 w m-2 roughly 3/4 of this “back of envelope” estimate of the power required to raise the temperature of the earth 4C and raise sea levels 2m.  So Hansen and Wetherald are in the right ball park, though a bit low.  Wikipedia states that the gulf stream transports 1.4 x 1015w  which is nearly ten times this estimate of power required.  So it’s not a totally unrealistic amount.

But this amount of power must be supplied continuously for 100 years.

There are two related problems

  1. Why aren’t sea levels rising – we might expect at least 200mm more than usual by now. But recent satellite measurements show a 10mm fall.
  2. Recent earth energy balance meaurements show it is now negative, which is not surprising given falling sea levels.

This graph from JPL/NASA via University of Colorado shows satellite measurements of global sea levels have fallen about 10mm below trend since 2010.
This graph of sea level rise around UK since 1900, by Prof Phil Woodworth, shows that there was an increase in the rate of sea level rise between 1993 and 2000, but this followed a very sharp fall around 1990/1.

Between about 1993 and 1998 sea levels did rise faster than the 1.4mm/year trend.

  • Mount Pinatubo erupted in 1991 and lowered temperatures and sea levels  for a few years.
  • There was a very strong El Nino in 1997/8 which raised temperatures and sea levels

And looking over the whole period since 1900 nothing out of the ordinary happened, this pattern of sharp rises and falls has happened several times and the long term trend is 1.4mm/year.

Does Anyone Look Out The Window?

I wonder what was going through the mind of whoever decided that working out and average energy balance in watts per square meter (w m-2)  over the whole earth’s surface over a year let alone a century, was a sensible or reasonable thing to do.

Had they looked out of the window they might have noticed things change.

  • Day and Night
  • Winter and Summer

If they travel or watch tv or look at the internet they might have discovered that some parts of the world are hotter and some parts are colder.

When it’s summer in the northern hemisphere it’s winter in the south and vice versa.

Moreover within arctic circles night lasts all winter and temperatures are well below freezing.  If the temperature is below freezing then water will turn to ice (to point out the bleedin obvious).

In Summary

The amount of energy required to warm earth 4°C and melt sufficient ice to raise sea levels 2 meters is not large compared with existing processes on earth such as gulf stream.

The warming, melting ice and raising of sea levels  (at least to give 2m rise in 100 years) is not happening.

Whoever came up with this idea assumed this new process would continue unchanged for  100 years.

In making this assumption they ignored the most striking of patterns on earth, cycles. They also seem not to have heard of winter and certainly arctic winter.


What do you think?


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