# Is global warming being moderated by latent heat of melting polar ice?

I've only had a secondary education in physics, so bear with me, but with the greenhouse effect and all, wouldn't we be much hotter already if the ice melt-rate wasn't increasing, since more (heat) energy goes toward changing state, rather than changing temperature? My understanding of latent heat is that it is the applied heat that does not result in a dramatic temperature increase, rather it is used to change state (i.e. solid ice to liquid water).

The obvious issue would be that once the ice is all melted, or it doesn't melt quick enough, we'll have proper heat problems (not just the 2 or 4 or 6 deg changes being discussed now).

Are there numbers available on this? Or is this effect nonsense? Or am I looking towards a time a few orders of magnitude beyond my years?

• A 2 Kelvin change really is a proper heat problem for human civilisation. – EnergyNumbers Sep 13 '15 at 10:58
• Yes, but not as much as you suggest. The oceans are actually a much bigger factor (think about how the oceans can warm or cool an entire coastline - it's our biggest heat sink). skepticalscience.com/Where-is-global-warming-going.html If there was no ice, climate change might happen a bit faster but there would also be no albedo-ice feedback effect, so melting ice in the long run, adds to climate change, though it might have a temporary slowdown as ice melts, it also acts as a positive feedback mechanism. I could try to expand on this if you like. – userLTK Sep 16 '15 at 8:23

Latent heat is a factor, but is completely eclipsed by the rate of global warming.

For example, since 1978 the April (maximum) Arctic sea ice has decreased in volume by about $11,000$ cubic km. The latent heat absorbed by the ice to achieve this is about $3.7(10)^{18}$ Joules. Compare this to the amount of excess heat, which has been absorbed by the oceans, which is about $2.0(10)^{23}$ Joules per decade. That is, some three to four orders of magnitude more heat than the decadal heat required to melt the Arctic ice.

Of course there are complications of the heat absorbed by land (much less than in the oceans), melting of Greenland and Antarctic ice sheets, and uncertainty over the depth of oceanic warming, due to sparsity of measurements, especially in the southern hemisphere.

But however you cut the statistics, the latent heat is minuscule compared to the planetary heat imbalance.

• Could you add sources of the numbers? – Communisty Sep 4 '18 at 11:51

This IPCC graph (discussed here) shows the amounts of heat going into oceans, atmosphere, land and ice melting. Plot of energy accumulation in zettajoules within distinct components of Earth’s climate system relative to 1971 and from 1971–2010 unless otherwise indicated. Ocean warming (heat content change) dominates, with the upper ocean (light blue, above 700 m) contributing more than the deep ocean (dark blue, below 700 m; including below 2000 m estimates starting from 1992). Ice melt (light grey; for glaciers and ice caps, Greenland and Antarctic ice sheet estimates starting from 1992, and Arctic sea ice estimate from 1979–2008); continental (land) warming (orange); and atmospheric warming (purple; estimate starting from 1979) make smaller contributions. Uncertainty in the ocean estimate also dominates the total uncertainty (dot-dashed lines about the error from all five components at 90% confidence intervals).

The assumption that 15,000 km3 is melted in one year is not correct. This is approximately the amount that will melt in the melt-season. In the winter it will grow back again. Check piomas website for the correct values: http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly/

"To melt the additional 280 km3 of sea ice, the amount we have been losing on an annual basis based on PIOMAS calculations, it takes roughly 8.6 x 10^19 J " Thus the imbalance for the sea-ice in the Northern Hemisphere is only 8.6 x 10^19 J

• That makes a lot more sense, great :) – JeopardyTempest Dec 8 '18 at 4:35

The latent heat issue is indeed a big one. The total latent heat from melting $15,000$ cubic km of ice (this $15,000$ is an arbitrary number, but you could take it to mean a very large amount of melting) is $15000 \cdot 997\frac{\rm kg}{\rm m^3}$ (the density of water) $\cdot \, 334\frac{\rm kJ}{\rm kg}\,$ (the enthalpy of fusion) $\cdot \frac {1000 \, \rm J}{1 \, \rm kJ} \cdot \frac{10^9 \, \rm m^3}{1 \, \rm km^3}$ = $4.995\times 10^{21}$ Joules

Compare that to the total energy imbalance for the Earth of $0.58 \frac{\rm Watts}{\rm m^2}$ (You can replace $0.58$ with $1.17$ if you think that is the real imbalance). For the whole surface area, that comes to $2.96 \times 10^{14}$ Watts. Now, over a year, that energy imbalance is $2.96 \times 10^{14} \cdot \frac{365\, \rm days}{1\, \rm yr} \cdot \frac{24\, \rm hrs}{1\, \rm day} \cdot \frac{60\, \rm min}{1\, \rm hr} \cdot \frac{60\, \rm sec}{1\, \rm min}$. That's $9.33 \times 10^{21} J$.

So, one fair ratio of latent heat to energy imbalance is $4.995:9.33$. Of course, this assumes the $15,000$ cubic km of ice is melted in one year. On the other hand, the relevant number for energy imbalance is also overestimated. That's because the amount of heat that is actually available to heat the earth is a tiny fraction of the imbalance (The exact fraction depends on the model you use). Regardless, latent heat is a major problem for further heating...scarily so.

• Could you add sources of the non-trivial numbers? – Communisty Sep 4 '18 at 11:57
• Energy imbalance = 0.58 W/m^2 : giss.nasa.gov/research/briefs/hansen_16 (third paragraph from the bottom). The rest of the numbers could be from any basic physics text. – AniB Sep 4 '18 at 12:30
• (For folks wondering at a relative size of AniB's arbitrary number, looks like the Greenland Ice Sheet is about 2.8 million km$^3$ in volume!?!) – JeopardyTempest Sep 4 '18 at 17:32

The melting polar ice definitely absorbs a significant amount of energy, maybe not as much as the oceans do, but critical here is that the energy absorbed is latent energy HIDDEN heat, and does not show up on the big thermometer, and also exhibits positive feedback, i.e., less reflection and more absorption, Therefore the melting ice is very important and scary.

Another less talked about topic, increasing atmospheric water vapor, another source of latent HEAT, with positive feedback, $H_2O$ is a powerful greenhouse gas, very scary, VERY SCARY indeed.

• I'm interested to know if the total qty of water is known, and what amount is either ice (isolated from geothermal energy), water as liquid or water as vapour. And how these values might be plotting. I suspect ice qty is going down, vapour qty is going up. – Shane Dec 10 '18 at 1:00