Scale Height and Adiabatic Lapse Rate in Ice-Giant Tropospheres

This paper examines the vertical thermal structure of the ice-giant tropospheres. Using only published input values and transparent formulae, the calculation addresses what pressure scale heights and dry adiabatic lapse rates follow from the measured tropopause and one-bar temperatures, gravities and mean molecular weights of the two atmospheres. The headline results are: scale_height_km_tropopause_uranus = 18.8; scale_height_km_tropopause_neptune = 14.1; dry_adiabatic_lapse_K_per_km_uranus = 0.68. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. The central finding is that despite similar temperatures, Neptune scale heights are roughly twenty percent smaller than those of Uranus because of its stronger gravity, so a cloud deck at a given pressure interval occupies a thinner geometric shell on Neptune. Agreement and disagreement with independent published estimates are reported at their actual size, and the conclusions are limited to what the budget arithmetic supports.