# Model for ice sheet thickness [closed]

How should I proceed to find a formula $$\lambda(t)$$ for the thickness of and ice sheet in terms of

1. The diference $$T_{a}(t)-T_w(t)$$ of the temperatures of air above the sheet and water below
2. Thermal conductivity ($$k$$) and entalphy of fusion ($$h$$) of ice

Im new to "modelling" this stuff so I haven't made any real progress. All the equations I find online make sense for an ice sheet of area $$A$$ or take into account the depth of the river/lake or some other factor, but I want to assume that the ice sheet is infinite in extension: an infinite plane with some thickness dividing the space into "water region" and "air region". I wouldn't mind if $$T_a$$ and $$T_w$$ are constant (they are regions so huge that their temperatures do not really change).

Please consider explaining some steps that may be obvious in physics. I'm looking for a line of reasoning like "by conservation of energy we should have the following equation _______ which, combined with ______ gives us ______" or something similar. Nothing fancy, only an equation $$\lambda(t)=$$expression in terms of $$k$$, $$h$$ and the temperature difference

Thanks!

• I think you'd also need relative humidity. May 9, 2020 at 20:19
• @zonksoft No you don’t May 9, 2020 at 20:47
• Are you familiar with Fourier's law of heat conduction? May 9, 2020 at 23:16
• I don't know why this thread was closed. It makes perfect sense to me. May 9, 2020 at 23:27
• @ChetMiller No, but I am now. I understand the formula and it makes perfect sense May 10, 2020 at 14:06