5. Quantification of the action of water as refrigerant
According to physics and thermodynamics, the thermal fate of heated ices described schematically in Figure 3 can be estimated quantitatively in terms of conductive heat exchanges using the specific heat of ice melting (333.55 KJ/Kg), and the specific heat capacities of solid ice (2.110 KJ/Kg/°C) and of water (4.184 KJ/Kg/°C), the presence of salts in sea water being neglected (Engineering Tool Box, 2003).
Let us take year 2018 as example, 17.2°C being the generally accepted global average temperature common to low atmosphere and ocean surface water. The 2018 global ice imbalance was 1.5 trillion tonnes assumed similar to the estimate of 2017 deduced from Figure 4 in (Slater, 2021). Let us take -20°C as average temperature of global ices according to the value retained to evaluate ice imbalance (Slater, 2021). According to the specific heat capacity of ice, 1.5 trillion tonnes of ice at -20°C required about 0,063 ZJ to reach 0°C, the melting temperature of ice. The temperature of ice and that of the formed liquid water remained constant at 0°C during the melting of the whole mass of ices that required c.a. 0.50 ZJ of thermal energy according to ice latent specific heat of fusion. The melting of 1.5 trillion tonnes of ice yielded 1.5 1015 Kg of liquid water at 0°C that required c.a. 0.108 ZJ to reach 17.2°C according to the specific water heat capacity. The heat energy necessary to turn the disappeared ices at -20°C to water at 17.2°C was thus c.a. 0.67 ZJ. Therefore, 0.346 ZJ eAHR (60% of the 0.576 ZJ heat energy consumed in 2018) was enough to cause 52 % of the 2018 imbalanced ice. This estimation does not take into account the injection of Joules in the atmosphere by mammalians (humans, cattle and animals with hot blood, hydrogen-using rockets, and criminal wildfires. Based on lung volume and on breathing frequency, the contribution of 7.5 billion humans and 1 billion cattle heads to eAHR was less than 0.02 ZJ and thus rather negligible. In addition to eAHR, volcanoes contribute to heat Earth from inside. In 2018, 80 volcanoes were active, the Hawaii eruption being the largest with c.a. 0.76 109 cubic meters of flowing lava. Assuming density, specific heat capacity and difference of temperature of lava being 2.6, 840 J/Kg/°C and 1000°C, respectively, the heat released after cooling was c.a. 0.002 ZJ. Assuming an average of 0.001 ZJ/volcano, heat released by volcanoes was c.a. 0.040 ZJ raising non-radiative heat energy introduced in the atmosphere to c.a. 0.4 ZJ, an amount about 4% smaller than the c.a. 9 ZJ rAHR corresponding to 0.8 W/m2 taken as minimal estimate of the annual mean radiative forcing in the 2000’s applied to the whole surface of the planet. This large difference of magnitude has already been pointed out in the literature (Chaisson, 2008; Zhang & Caldeira, 2015) but for different systems and under different conditions. Anyhow, based on physics and thermodynamics, the dominant 9 ZJ rAHR [(27 ZJ if radiative forcing was 2.3W/m2(IPCC, 2014)] should have caused much greater ice loss than the 1.5 trillion of tonnes estimated for 2018 that required only 0.67 ZJ of heat energy to turn lost ice at -20°C to water at 17.2°C.
Since in 2018, temperature and oceans rises were reported 0.79 °C and 3.7 mm respectively, and according to the 4.184 KJ/Kg/°C water heat capacity, oceans stored about 4.4 ZJ leaving 4.6 ZJ unabsorbed (c.a. 22.6 ZJ in case of 2.3 W/m2 forcing) and thus available to heat the rest of the planet and double the global temperature, something against observations and logic.
Amounts of heat exchanges that involved water and water interphase equilibria were obtained using thermodynamics and physics and can hardly be challenged. In contrast, the radiative forcing may be questioned in terms of overestimation or even inconsistency as pointed out by some scientists (Scirocco, 2018). As an alternative, the refrigerator model suggests evaporation as heat absorber, in addition to ice melting. Evaporation may well explain the absorption of 4.6 ZJ by evaporation. Indeed, the capacity of ocean to absorb heat by a thin layer of evaporated water is approximately 81.2 ZJ/dm/°C using 2.25 KJ/Kg/°C as specific heat of evaporation of water. Therefore, 5 mm of evaporated ocean water are basically able to absorb and compensate the warming effect due to a 4.6 ZJ radiative forcing but this goes against global warming since glace melting and evaporation are physical phenomena that normally should compensate warming globally with locally temperature ups and down and enhanced climatic events in strength and frequency as discussed in the previous sections. In other words, global warming in distant future should be less important than presently predicted.
Evaporation is not the only factor that may affect climate-related predictions in distant future.