For over a year I have been pondering how to reconcile the near constant rise in sea levels with the accelerating polar ice melt. At the end of September the UNIPCC published the AR5 Working Group II (the Physical Science Basis) Summary for Policymakers which provides some useful evidence.

The following from the UNIPCC gives some estimates of the rate of polar ice melt. In page 9

• The average rate of ice loss from the Greenland ice sheet has very likely substantially increased from 34 [–6 to 74] Gt yr^–1 over the period 1992 to 2001 to 215 [157 to 274] Gt yr^–1 over the period 2002 to 2011.

• The average rate of ice loss from the Antarctic ice sheet has likely increased from 30 [–37 to 97] Gt yr^–1 over the period 1992–2001 to 147 [72 to 221] Gt yr^–1 over the period 2002 to 2011. There is very high confidence that these losses are mainly from the northern Antarctic Peninsula and the Amundsen Sea sector of West Antarctica.

Put in sea level rise terms, the combined average rate of ice loss from the polar ice caps increased from 0.18 mm yr^–1 over the period 1992 to 2001 to 1.00mm yr^–1 over the period 2002 to 2011.

There is a problem with these figures. The melting ice will end up raising sea levels. The satellite data from the University of Colorado shows a near constant rate of rise of 3.2mm yr^–1.

Assuming a one year lag in raising sea levels, the 0.18 mm yr^–1 over the period 1992 to 2001 is equivalent to 5% of the 3.3mm yr^–1 average sea level rise from 1993 to 2002, whilst the 1.00mm yr^–1 over the period 2002 to 2011 is equivalent to 32% of the 3.1mm yr^–1 average sea level rise from 2003 to 2012. Some other component of sea level rise must be decreasing. The estimates of the other components are given on page 11

Since the early 1970s, glacier mass loss and ocean thermal expansion from warming together explain about 75% of the observed global mean sea level rise (high confidence). Over the period 1993 to 2010, global mean sea level rise is, with high confidence, consistent with the sum of the observed contributions from ocean thermal expansion due to warming (1.1 [0.8 to 1.4] mm yr^–1), from changes in glaciers (0.76 [0.39 to 1.13] mm yr^–1), Greenland ice sheet (0.33 [0.25 to 0.41] mm yr^–1), Antarctic ice sheet (0.27 [0.16 to 0.38] mm yr^–1), and land water storage (0.38 [0.26 to 0.49] mm yr^–1). The sum of these contributions is 2.8 [2.3 to 3.4] mm yr^–1.

The biggest component of sea level rise is thermal expansion. The contribution from this element must be decreasing. Ceteris paribus, that suggests the rate of heat accumulation is decreasing. This contradicts the idea that the lack of surface temperature warming is accounted for by this heat accumulation.

The problem is that all things are not equal. Thermal expansion of water varies greatly with temperature of that water. On page 10 there is the following graphic

The heat content of the upper ocean increased by around 10 x 10²² J from 1993 to 2010. For 700m of ocean depth I estimate this would be 0.1^oC. It is a tiny amount that varies greatly with temperature, as shown by the graph below.

As sea temperature varies greatly according to location and depth, it is possible to hypothesise a decline in the thermal expansion with an increase in heat content. This whilst also accepting that both the rate of rise in the heat content of the oceans has accelerated and the contribution to sea level rise due the increase in heat content has decreased. For example one would just have to hypothesise that the increasing heat content had been predominately in the tropics during the 1990s and switched to the Arctic in the 2000s.

Even this switch is not necessary. There is huge variation between areas of the amount of temperature increase over a twenty year period. Consistent with an increase of 0.1 could have been a decrease in average temperatures in an area of ocean as large as the Atlantic and Indian Oceans combined.

But, what makes this less than credible is that this shift almost exactly offset the estimated increase in the ice melt component. Most likely no-one will try to calculate this, as the data is not there. Even with 3,000 Argo Buoys in the oceans, there is still on average just one buoy per 200,000 km³ of ocean, taking about 25 dips a year. The consensus viewpoint appears the less likely than the view that climate models have an exaggerated belief in the impact of greenhouse gases on average temperatures.

There is an opportunity for some further investigation with the data. But a huge amount of work may not yield anything, or may yield conclusion at odds with the “real”, unknown one. However, the first step is to determine how the UNIPCC calculated the figure for thermal expansion. Hopefully it was more substantial than from the difference between the total sea level rise and the estimates for other factors.

Update

At Bishop Hill Unthreaded michael hart Jun 1, 2014 at 4:13 AM refers to some other variables that determines how warming oceans will affect sea level rise through thermal expansion. So now the list includes.

• The quantity of heat. (see above)
• The initial temperature of the water which the heat was applied to. (see above)
• The initial temperature is in turn related to

1. Latitude – at mid latitudes there is a seasonal variation temperature variation down to about 300 metres.
2. Depth
3. Density variation due to salinity (see pdf page 9)

However, there are local variations as well, due to ocean currents that shift over time.

For these reasons, any attempt at estimating thermal expansion will be reliant on assumptions and estimates. The UNIPCC will have simply estimated the difference between estimated “known” factors – ice melt and land water storage – and deducted from the known sea level rise.

In terms of reconciling polar ice melt to sea level rise, there is something that I missed. According to the UNIPCC, glacier melt has a larger contribution to sea level rise than polar ice melt – 0.76 mm yr^–1 against 0.60 mm yr^–1. It is quite conceivable – particularly since temperatures have stopped rising – that have glacier melt has effectively ceased or even gone into reverse. Unlike with thermal expansion, there should be estimates available to confirm this.