As my basic set of parameters, I will start with an approximation of Earth. With the exception of the guesstimated Latent Heat Energy Factor and the Meridional Heat Transport Coefficient these parameters are readily ascertained. The MHTC, for its part is a multiplier of an assumed Earth value(0.015), but I’m not sure where he got that value, so there is a bit of uncertainty here. In, “Determination of the Heat-Transport Coefficient in Energy-Balance Climate Models by Extremization of Entropy Production,” by P. H. Wyant et al I find estimates for the MHTC of 0.218, 0.238 and 0.16(if we divide by ten, these could correspond to about 1.45, 1.59 and 1.07, so there might be a bit of uncertainty here as well).
The basic parameters I’m using are –
Stellar luminosity: 1.00; Stellar mass: 1.00; Semimajor axis: 1.00; Orbital period: 1.00(?); Orbital eccentricity: 0.017; Orientation: 190°; Diameter: 12,800 km; Mass: 1.00; Density: 5.52(??); Inclination: 23.5°; Hydrosphere: 71%, Surface pressure: 1013 mb; CO2: 0.37; Latent Heat Energy Factor: 0.3; Meridional Heat Transport Coefficient: 1.00 times Earthassumed baseline
Using a 45 year run and a global model
Although, the simulator will give “monthly”(twelfths of a planetary year) temperatures and albedos for several latitude bands I’m just going to record the globally averaged surface temperature(avgTemp) the integrated albedo(intAlb), and the albedo neglecting the polar contribution(nonPAlb).
First I’ll vary the Latent Heat Energy Factor holding all other parameters constant.
LHEF 0.2 – intAlb: 0.308; nonPAlb: 0.292; avgTemp: 15.52° C
LHEF 0.3 – intAlb: 0.308; nonPAlb: 0.292; avgTemp: 15.42° C
LHEF 0.4 – intAlb: 0.308; nonPAlb: 0.292; avgTemp: 15.35° C
LHEF 0.5 – intAlb: 0.309; nonPAlb: 0.293; avgTemp: 15.31° C
Albedo seems fairly insensitive to an increasing LHEF with a very small increase, at least over the measured interval(This is a bit of a surprise, since LHEF was supposed to be an exponent controlling the increase in cloudiness with increasing temperatures). Temperature shows a small increase with increasing LHEF. The assumption of 0.3 for LHEF seems reasonable enough and the small sensitivity makes playing around with this value seem pretty safe. It might be worth testing for a wider range of values in the future…
Now I’ll vary the Meridional Heat Transfer Coefficient from 0.50 to 1.50 in increments of 0.25.
MHTC 0.50 – intAlb: 0.344; nonPAlb: 0.287; avgTemp: 14.37° C
MHTC 0.75 – intAlb: 0.323; nonPAlb: 0.288; avgTemp: 14.54° C
MHTC 1.00 – intAlb: 0.308; nonPAlb: 0.293; avgTemp: 15.42° C
MHTC 1.25 – intAlb: 0.302; nonPAlb: 0.295; avgTemp: 15.95° C
MHTC 1.50 – intAlb: 0.299; nonPAlb: 0.296; avgTemp: 16.03° C
Average surface temperature is pretty sensitive to the MHTC and diverges from the generally accepted value of about 15° C for Earth pretty quickly. From what we see here, the generally accepted value of 0.306* for Earth’s albedo will likely lie somewhere between an MHTC of 1.00 and 1.25, while a temperature fit would lie between 0.75 and 1.00. Given the relatively high sensitivity and the opposing directions of the errors, 1.00(0.015) seems like a good compromise. A more detailed comparison, possibly involving monthly latitudinal values might be in order…
The current MHTC of Earth might be particularly low because the continental arrangement would tend to restrict poleward oceanic heat transport(a large factor in determining overall heat transport) and promote the growth of ice caps. Planets with generally wider seaways leading to the poles might have higher MHTC values. Planets with large continents lying on both poles and more extensive east-west oriented continents might have somewhat lower values.
I decided to look at how the results might vary with hydrospheric fraction and was somewhat surprised by the results.
Hydrosphere 50 – intAlb: 0.326; nonPAlb: 0.274; avgTemp: 11.04° C
Hydrosphere 60 – intAlb: 0.313; nonPAlb: 0.274; avgTemp: 14.34° C
Hydrosphere 70 – intAlb: 0.308; nonPAlb: 0.293; avgTemp: 15.40° C
Hydrosphere 80 – intAlb: 0.305; nonPAlb: 0.296; avgTemp: 16.27° C
Hydrosphere 90 – intAlb: 0.302; nonPAlb: 0.301; avgTemp: 17.58° C
Hydrosphere 100 – intAlb: 0.300; nonPAlb: 0.300; avgTemp: 18.77° C
Big oceans warm planets! I’m not sure exactly why as I haven’t really closely analyzed the code yet. I’ll have to do that since I’d like to try making some minor enhancements to the program(batch processing, narrower latitude bands, some more user control of “constants,” etc.). Certainly, the higher the overall hydrosphere coverage, the less restricted the oceanic heat transport to the poles; that will tend to reduce the prevalence of ice caps and thus reduce the albedo of the planet which will lead to greater absorption of insolation. Also, water vapor is a particularly powerful absorber of outgoing longwave radiation, if that is modeled then a large hydrosphere could lead to a greater greenhouse effect.
My curiosity drove me to try another run with an extreme value of a totally dry surface(close enough, anyway)
Hydrosphere 0 – intAlb: 0.600; nonPAlb: 0.240; avgTemp: -48.92° C
Well. There you go. The pattern definitely continues. Although, I didn’t record the data here, this planet was frozen from pole to pole! The overall albedo of 0.6(!) is the same as the programs hardwired constant for the albedo of ice. The few patches of iceless surface(the Dry Valleys) are pretty dark, with an albedo of 0.24, but there clearly aren’t a lot of them.
It’s interesting to note that some, presumably more rigorous energy-balance model(EBM) simulations I have seen like this one and this one, seem to indicate that reduced effectiveness of meridional heat transfer(particularly due to fast planetary rotation) leads to colder temperatures overall. Given that oceanic heat transport is a big element in the total poleward heat transfer, this seems appropriate. One might thus expect a hot desert planet(say, like Tatooine…) to be very near to its star(or perhaps with one or more other stars illuminating it…). An intriguing development.
It would be interesting to try additional runs with very high hydrospheres to see how much that might extend the outer edge of the ecosphere and low hydrospheres to extend the inner edge of the ecosphere.
That’s an initial not-too-scientific test of the simulation. The results seem plausible. Good enough for science fiction work.
Thank you for reading,