No coincidence ! The calculation of Ts = -63.06 °C made with albedo = 0.250, cloudiness = 0, emissivity = 1 and solar constant = 589.2 seems to be very correct. But in the case of Mars the atmosphere is mainly CO2. My hidden suggestion is that, if this Mars atmosphere was mainly made of, let us say, N2 and/or O2 (without CO2), would the resulting temperature Ts have been the same, i.e. -63.06 °C, as you calculate Ts = +13.8 °C for Earth (with its atmosphere of N2/O2) ? Is it only important that an atmosphere does exist ? It is also interesting to compare the Ttoa of Mars -96.48 °C and this of Earth -36.83 °C, i.e. out of the atmosphere. The difference is 50.63 on Earth and only 33.42 on Mars, why ? Is that due to the atmosphere of pure CO2 ? Reply
The simplistic 2-Layers model reduces the atmosphere to a virtual IR emitting layer of zero thickness and transparent to UV/Vis. The beauty of models is that they may remain unrealistic but still are helpful for discussions (not for predictions…). An atmosphere has also a heat capacity, even if it is not absorbing and irradiating in the Infrared. The atmospheric temperature will result from the complex interactions between solar radiative heating of the ground, convective heating of the neutral atmosphere (e.g. only O2, N2 and Ar, no CO2, no H2O), and the day-night alternation. Such hypothetical case will not result with -33°C for the Earth with average 341,5 W/m2 (as many claim) but at a much higher level that I’m not able to calculate. Without atmosphere though, the concept of atmospheric temperature at the surface gets lost! Then it is a case of a one layer system, as for the Moon with quite long nights. Reply
Ttoa question: The Ttoa formula (Stefan Boltzman) gives the surface temperature of a black body that emits back into the space the irradiation that has not been reflected by albedo: Ttoa is lower on Mars because the inbound irradiation (589.2 W/m2) is lower than for the Earth.(1366 W/m2). Far far away from the Sun, everything approaches the space background temperature of 2.7K Reply
One more chilling piece of news ! The present concentration of CO2 in the Earth atmosphere is 415 ppm in volume, but 630 ppm in mass. On the planet Mars, the concentration of CO2 is 95-97%, let us say 96% (here there is no difference between volume and mass concentrations). But one must compare the absolute quantities. The mass of the Earth atmosphere being 5.15 10^18 kg, the mass of CO2 is 3.24 10^15 kg. On Mars, the total mass of atmosphere is only 2.5 10^16 kg (0.5%), but the mass of CO2 is 2.4 10^16 kg, i.e. 7.4 times that on Earth ! On the other side, the solar irradiance on Earth is 1361 W/m^2 (standard mean value at 1 AU, but 1420 W/m^2 at perihelion and 1325 W/m^2 at aphelion, the eccentricity of Earth orbit being only 0.0167) and on Mars 589.2 W/m^2 (mean value at 1.523 AU, but 712.6 W/m^2 at perihelion and 490.3 W/m^2 at aphelion, the eccentricity of Mars orbit being very high, 0.0934). The mean figure on Earth is 2.3 times more than on Mars. With 43% of the solar energy but 7.4 times the amount of CO2, the mean temperature on Mars is only -63 °C and on Earth +15°C, even if a mean temperature has no founded signification. Finally one must calculate the absolute solar energy received by the two planets : 173.4 PW on Earth and only 21.3 PW on Mars. The Earth receives 8.1 times more energy than Mars, but has 7.4 times less CO2. Would that not be a kind of compensation ? Where is the “green house effect” due to CO2 on Mars ? Reply
Intereseting! You may play with a simple 2-layers model on my site climate.mr-int.ch. With an albedo and an emissivity similar to that of the Earth, no clouds, and a solar irradiation of 589.2 W/m2, it calculates a surface temperature of -62.8 °C. Not bad isn’t it? or a simple coincidence. The wrongly called “green house effect” would result from an additional CO2 quantity, or the addition of a different “greenhouse gas” such as methane or a chlorofluorocarbon (not water for these temperatures) Reply