5. Attempts to quantify the action of water as refrigerant
In this section, we look at where the mechanisms schematized in Figures 2 and 3 can lead on the basis of thermodynamics characteristics typical of the water cycle, namely, the 333.55 KJ/Kg latent heat of ice melting, the 2,447 KJ/Kg latent heat of evaporation at 14°C, the 2.11 KJ/Kg/°C specific heat capacity of solid ice and the 4.184 KJ/Kg/°C specific heat of water, various factors with minor effects like salinity, CO2 dissolution in ocean and cloud liquid water, dusts, etc. being neglected (Engineering Tool Box, 2003).
To estimate and compare rAHR and eAHR in terms of Joules, the following data available for year 2018 were used:
- 14°C, the average temperature of Earth’s surface determined from multiple land and ocean local measurements (NOAA; 2021), a value considered common to low atmosphere and ocean surface water;
- 0.79 W/m2 the average radiative forcing (IPCC, 2022);
- 0.03°C and 3.7 mm, the temperature and ocean level respective changes (IPCC, 2022);
- 1.5 trillion tonnes ice imbalance assumed similar to the estimate of 2017 deduced from Figure 4 in (Slater, 2021);
- 20°C, the average temperature of global ices, a temperature proposed in (Slater, 2021); and
- 13.864 GT of oil equivalent, the global energy consumption (BP, 2019), 60 % of which generated 0.35 ZJ eAHR according to 44 MJ/Kg, the average heat of combustion.
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. Then, the temperatures of ice and formed liquid water remained constant at 0°C during the melting of the whole mass of disappeared ices that required c.a. 0.50 ZJ of thermal energy according to ice latent heat of fusion. The heat energy necessary to melt 1.5 trillion tonnes of ice at -20°C and form 1.5 1015 Kg of liquid water at 0°C required about 0.56 ZJ. In addition, bringing 1.5 trillion tonnes of water from 0 °C up to 14°C, required about 0.09 ZJ according to the specific water heat capacity. In total, the heat energy necessary to turn the disappeared ices at -20°C to water at 14°C was thus about 0.65 ZJ (0.56 + 0.09). In other words, the disappeared 1.5 million tonnes of ices absorbed 0.65 ZJ of heat energy introduced in the low atmosphere, regardless of its origin.
The estimate of eAHR did not take into account the injection of Joules in the atmosphere by mammalians (humans, cattle and animals with hot blood), hydrogen-using rockets, criminal wildfires and volcanoes. Based on 80 W per capita, 7.5 billion humans generate about 0.02 ZJ annually to which a minimum of 0.01 ZJ can be added due to cattle. In 2018, 80 volcanoes were active, the Hawaii eruption being the largest with c.a. 0.76 109 cubic meters of 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 by the Hawaiian volcano after cooling was c.a. 0.002 ZJ. Assuming an average of 0.001 ZJ/volcano, heat released by volcanoes was in the range of 0.08 ZJ. Wildfires could hardly be estimated but like volcanoes, they are very likely negligible relative to the 0.35 ZJ of eARH that finally represent less than 3% of the 12.7 ZJ of radiative forcing deduced from the 0.79 W/m2 annual average rate of heating of the climate system for the period 2006-2018 applied to the surface of the planet (IPCC, 2022). This large difference of magnitude between annual e and rAHRs has already been pointed out in the literature (Chaisson, 2008; Zhang & Caldeira, 2015) but for different systems and under different conditions.
In terms of thermodynamics, the estimate of total anthropogenic heat energy released in the atmosphere in 2018 stored in the climate system was about 13 ZJ (0.35 + 12.7). 0.65 ZJ were absorbed by the lost ices, leaving 11.7 ZJ absorbed by oceans (90% of 12.35 ZJ) and land and atmosphere for the rest based on IPCC’s mechanisms. Basically, the storage of heat energy in liquid raises the temperature of this medium unavoidably. However, when ice is present, melting fights temperature rise like when an ice cube is in a glass of water under summer sun. Therefore, one may ask why the 2018 ice imbalance was not much greater than the 1.5 trillion tonnes estimate (Slater, 2021). There are several possible reasons. Firstly, radiative forcing was largely overestimated, a hypothesis going against the current universal CO2-based claim but defended by some specialists of electromagnetic radiations who goes up to denying CO2-related anthropogenic warming (Sirroco, 2016; Humlum, 2022; Guesken, 2020). In this case, the share of eAHR would become predominant or the only source of anthropogenic heat to be eliminated. Secondly, atmospheric and oceanic streams were far from equilibrium and thus were not efficient enough to dispatch and homogenize the radiative forcing up to the surface. Last but not least, the heat absorbing capacity of evaporation was able to absorb the huge excess of eAHR and justify the absence of more important ice imbalance. Evaporation was mentioned about 200 times in IPCC’s AR5 WG1 report (IPCC, 2014), but only relative to its effect on salinity, pan evaporation, balance of evaporation-precipitation, localization and not in terms of heat absorption and temperature regulation. Secondly, the AR6 2022 report mentions only “it is virtually certain that evaporation will increase over the oceans” with no consideration to associated heat exchanges.
In 2018, the average ocean level rise was about 3.7 mm in rather good agreement with the 4 mm generated by a surplus of 1.5 trillion tonnes of ice-derived liquid water in oceans. In parallel, the annual average global ocean and land temperature rises was estimated about 0.02-0.03 °C (NOAA, 2021). Temperature rising observed when a compound is heated depends on the thermal characteristics and the mass of this compound. Based on the 4.184 KJ/Kg/°C heat capacity of salt-free water, a 1 dm thick layer of ocean surface water (361 1014 dm3 or 361 1014 Kg) is able to absorb about 0.15 ZJ of heat energy for 1° C rise. This means that a minimal layer of more than 200 m would be necessary to absorb 11.7 ZJ with 0.03°C homogeneous temperature rise. In contrast, evaporation, that plays an essential role in a refrigerator, is able to absorb 2,247 KJ/Kg according to the latent heat of water evaporation at 14°C, the temperature of the warmly heated source being maintained constant, basically. The surface of Earth covered by water being about 390 106km2 or 390 1014dm2, the evaporation of 1dm layer of ocean water can absorb 95.5 ZJ without temperature change. Therefore, evaporation is about 600 times more efficient than ocean surface water to absorb global anthropogenic heat energy and fight global temperature change due to warming conditions.