Interior Temperature T related to Snow Temperature To in Clouds

Jennings (2021) [1] wrote a paper where the dew point is the nucleation limit in a cloud. He came up with this equation for onset of rain.

T – To = (3 k To2 / σo ao) (P*H2O / Pair) RH

Where T = temperature Kelvin inside the cloud and To = temperaure Kelvin at onset of rain. In this paper, I assume that onset of snow is described by.

To – T = (3 k To2 / σo ao) (P*H2O / Pair) RH

Where the T and To are flipped because of undercooling and T is still the interior undercooling temperature with To being the snow temperature in the cloud. In another paper, Jennings (2023) [2] derives an equation for snow formation with To – T = ΔT.

T = D (7.15 x 107) /(k a ns ΔT 0.69)

Then, in a bath experiment, based on Hillig (1958) [3], To is the melting point and T is the temperature of the bath. It is valuable to calculate To, so that has to be done by iteration on a computer, as some variables depend on T and others on To.