The Earth's Thermostat
Dai Davies


In Figure 1, temperatures hit a wall at 30 C° and evaporation shoots up. The obvious question is why such an abrupt transition should exist. My starting point was noting that hurricanes only begin to form when the water surface temperature rises above 24 C°.

Figure 1: Atmospheric water column and Saturated Vapour Pressure against temperature

Liquid water has many anomalous properties. These are thought to come from the formation of transient nanoscale structures of up to a few hundred molecules. An anomaly that seems relevant here is the minimum in specific heat at around 35 C°. It is thought that between 0 and 35 Co the nanostructures break down. Another anomaly is water's high surface tension. Water molecules near the surface are more tightly, packed than in the bulk water. The molecules aren't just densely packed. Picosecond pulsed laser energy dumps show that energy can be carried into the whole layer almost instantly by quantum coherent vibrational states that penetrate the layer. [160822, removed speculation on deep surface layers, EZ-water]

A quick look through some of the literature on bulk water spectroscopy showed interest in water's structure at around 30 Co. I don't claim to have a good grasp of this. I have had some experience in molecular spectroscopy – experimental work and quantum calculations for energy levels and decay rates, but it was in gas phase not liquid, and decades ago when spectroscopically useful lasers were simple DIY constructions and computer models were boxes of punch cards, so I won't risk interpretation, just a few quotes.

Rønne et.al. discuss water's behaviour at 30 C° (1): The two lines intersect near 303 K. ... It is interesting to note that 303 K has proven to be a special temperature in various studies of water. ... Mizoguchi et al. have ... observed a kinklike behavior at ~303 K. In pressure dependent studies of the shear viscosity, water behaves like an abnormal liquid below 303 K and the specific heat capacity of water, Cp, has a minimum at 303 K. ... adding all these observations together we obtain indication of a changes in microscopic structure at ~303 K.

From (2):
The power absorption coefficient and refractive index of water at temperatures of 4, 8.9, 30 and 50 °C have been measured ... . The power absorption coefficient profile is observed to increase with increase in temperatures from 4 to 8.9 and then to 30 °C. This is followed by a decrease in the profile at 50 °C.

From (3):
A clear nose [turning point in the graph] appears around T = 300 K, signalling the onset of the network of hydrogen bonds (HB) [as temperature decreases]. Indeed, strong directional interactions (such as the HB), impose a strong coupling between density and energy.

From (4):
Buchner et.al. used a pulsed laser technique to measure electrical properties of water. Figure 8 shows a drop at 30 C° in permittivity (the ability of a substance to store electrical energy in an electric field) and relaxation time (the time taken to dissipate energy). In attempting to explain the data they refer to: ... a contribution of additional processes in the far infrared region, which cannot be resolved within the frequency range of our data.


Figure 8: Anomalous dielectric behaviour of water (10)

Below 30 Co, the relaxation time has dropped by 33%. It then rises by at least 66%. This looks to me like the kind of transition point needed to explain the uptick in Figure 5.
At 30 Co, air molecules have, on average, 10% of the energy needed to remove a water molecule with some having much more. The rest comes from the thermal energy of the water, particularly those water molecules with higher than average kinetic energy. A 15μm photon can supply 20% of the energy needed, and while it is unlikely to be fully absorbed in a pure water surface, the radiation field at the surface may assist evaporation. Seawater has a fine surface layer of organic surfactants, which are likely to absorb in the infrared, if only briefly.

Ejection of a water molecule from the surface will cool the water while increasing the density of water molecules in the air immediately above the surface, so increasing the emission of photons. This gives the possibility of a runaway radiative gas effect causing the runaway cooling seen in Figure 5. This will be limited by the fact that it is cooling the water, and convection is refreshing the air at the surface.

I try to form some kind of specific physical image, if only to show me how little a theory or mathematical model is actually telling us about the real world. Here, I can imagine the surface layer of the sea weakened by a nanoscale phase transition and with bombardment by air molecules and infrared photons creating small patches where the tightly bound surface layer is disrupted, exposing the more loosely bonded molecules of the bulk water, so increasing evaporation. As the water under the patches cools, the surface layer reforms.

References:

1. Rønne, C. et.al., Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation, J. Chem. Phys. 107 (14), 8 October 1997

2. Vij J.K., et.al., Far infrared spectroscopy of water at different temperatures: GHz to THz dielectric spectroscopy of water, Journal of Molecular Liquids, Volume 112, Issue 3, 30 July 2004, Pages 125–135

3. Smallenburga, Frank, et.al., Phase diagram of the ST2 model of water, arXiv:1502.06502v2 [cond-mat.stat-mech] 24 Feb 2015

4. Buchner R. et.al., The relaxation of water between 0 oC and 35 oC, Chemical Physics Letters 306, June 1999