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I mean rewriting the entire model such that temperature uses ˚C instead of Kelvin. I expect everything to work very similar, instead of probably radiation, where somewhere the Stefan-Boltzmann ~T^4 should appear. We could then convert from ˚C to Kelvin therein. But from a precision point-of-view using Kelvin is awful as you'll hit massive rounding errors in the time integration, e.g. T = 300K, tendency dT = 0.1K
In Kelvin you can't resolve the increment, but in ˚C you can.
Having said that, we obviously do the time stepping in spectral space, meaning that we'd only have that problem on the l=m=0 mode which we could also solve with compensated summation, but I think in general, we should try to use ˚C if possible. If it turns out that ˚C is a bad idea then we can still revert back.
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With #123 this should become much easier as we can define tempC and tempK for a given column and use both within the parametrizations. Given that the tendencies in ˚C and Kelvin are the same, we then are left with the question whether we can carry temperature in ˚C around in the dynamics...
Most parts in the dynamical core now use the temperature anomaly anyway, so maybe less of an issue. Hoskins and Burridge 1975 normalise temperature by $a^2\Omega^2/R$ ($a$ radius, $R$ gas constant) which might be another option
Copying @milankl's comment from PR #82:
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