## Saturday, 11 August 2018

### A Simple Estimate of Global Mean Sea Level Rise due to Increase in Global Temperatures

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During the 20th century, mean sea-level rose by about 10 cm and is expected to rise at a much faster rate in future. Rising sea-level increases the intensity of severe stroms and  tides causing serious flooding.  Cities and infrastructure near coastlines are vulnerable to damage. Rising sea-level also increases the risk of coastal erosion and shoreline retreat.

Climate change is given as the reason for the accelerated rise in global mean sea-level and under current scenarios, we should expect a further rise of 60 to 100 cm by the year 2100.  For a lay person, it is difficult to relate a warming climate to a sea-level rise, and how the estimates are made might appear confusing.

In this blog, I shall calculate sea-level rise due to melting of ice on land and thermal expansion of water. Both estimates may be reliably made using school level arithmatic.  I shall use  numbers rounded to two decimal places to make the calculations look tidy.

Thermal Expansion of water:  Water expands with rising temperature. For each degree centigrade rise in temperature, the volume of water increases by a factor equal to 2.14 x 10-4.   The average sea surface temperature is 17oand during the 20th century the surface water temperature  increased by ~ 0.5oC

The interesting part of this calculation is to appreciate that the water temperature in the sea drops steadily with depth and reaches 4oC
at about 700 m.  At 4oC, water has the highest density and sea water below 700 m does not change much in temperature - hence does not expand in volume and does not contribute to sea-level rise.

When the sea warms, it is mainly the layers up to 700 m depth that warm and expand.  We can calculate the increase v in the volume V of water  when the temperature changes by dT.  Since the surface area A of the sea may be assumed constant, the increase h for dT = 0.5oC
is

v = 2.14 x 10-4 x 0.5 x V
or               h A = 2.14 x 10-4 x 0.5 x 700 A
or               h = 0.075 metres = 7.5 cm in 100 years

Over the past 20 years, the global warming rate has accelerated and it is estmated (IPCC 2013 Report) that in the next 100 years the sea level will rise by at least 20 cm due to thermal expansion of water (IPCC Senario RCP4.5).

Melting of Ice on Land:  At present, glaciers cover 10% of the land area and store about 75% of world's fresh water (of all the water on Earth, only about 2.5% is fresh water).  Twenty thousand years ago, at the peak of the last ice age, glaciers covered ~32% of the total land area!
Ice is also present in the sea in the Arctic Ocean; but the  melting of ocean ice, as in the Arctic Ocean, does not change the sea-level.  It is only the land ice that can add additional water to the seas and cause its level to rise.
Ice on land is present in inland glaciers and ice sheets - the Greenland Ice Sheet (GIS) and Antarctic Ice Sheet (AIS). So far, the inland glaciers have contributed the largest amount of  melt-water; IPCC estimate (5th asssessment report 2013, chapter 13) that melting inland glaciers will contribute 12 ± 6 cm sea-level rise by the year 2100.

The Greenland Ice Sheet, GIS covers 80% of Greenland surface and has an area equal to 1.7 million km2, its thickness on average is 2 km.  GIS is losing ice quite rapidly; during the decade 2002 to 2011, the average ice loss was 215 billion tons per year!

Antarctic Ice Sheet, AIS is much bigger.  It covers 98% of Antarctic continent and has an area 14 million km2, and is up to 4 km thick at some places.  It contains 26 million billion tons of ice.  While most parts of the ice sheet are considered reasonably stable, over the past few years, loss of ice from West AIS has been increasing and is currently about 80 billion tons per year.

Before we calculate the rise in sea level due to melting of the ice-sheets, let us note that the Earth has a surface area of 510 million km2. Of this about 71% is ocean - 360 million kmand the land is 150 million km2.

GIS is losing 215 billion tons or 215 x 1012 kg of ice per year (1 ton is equal to 103 kg).  The density of ice is 917 kg m-3Therefore, volume of water produced per year =  215 x 1012/917 or 2.35 x 1011m3.
This water will raise the level of sea by 2.35 x1011m3360 x 1012m2  = 0.653 mm per year
In 100 years GIS will increase the sea level by 6.5 cm.
However, it is expected that the rate of ice loss will increase significantly due to continued warming of the planet resulting in a much greater rise of global mean sea level due to GIS ice loss.

The amount of ice lost per year by the Antarctic Ice Sheet is about 80 billion tons per year and will contribute only 2 cm to the rise of sea level over the next 100 years. This might be a gross underestimate of what could happen if our planet continues to heat up.  AIS has large areas of ice plates (shelves) projecting over the sea with their base in contact with the sea water (the grounding line). Warmer sea water is already melting the underside of these plates and adding extra water to the oceans. See slide.

The grounding line also moves inland increasing  the probability of thinned ice shelves breaking and falling in the ocean to raise sea levels. IPCC 2013 report estimates that, by the year 2100,  this (Ice Sheet Rapid Dynamics) can add 10 cm to the sea level rise.

But what happens if all of the GIS and AIS melt over the next few hundred years.  How much the sea level rise be?

Considering that GIS is on average 2 km thick and covers an area 80% of 1.71 million km2; the volume of water that the ice in GIS will generate is 2.5 million km3; The resulting sea level rise will be 7 metres.  At 250 billion tons of ice lost per year, it will take GIS 10000 years to melt completely; however, the melting rates are expected to increase and many scientists think that GIS might melt away within the next 1000 years. The 7 meter sea-level rise will be catastrophic for our civilisation.