söndag 8 april 2012

The outer boundary

In a previous post I attempted to build an elementary atmospheric model based on the heat equation. By assuming that the heat absorbing capability of the gas depended monotonically on the mass one could predict a stratosphere, (or a tropopause), at a point where the density had decreased below a certain value. Here we will not focus so much on the stratosphere as such but instead assume that there is some tropopause somewhere and give it a temperature. Following the heat equation reasoning one could speculate on a boundary condition of the form:

Where the first term on the right hand side is simply the temperature of "outer space". If we assume that this is zero we obtain the missing boundary condition:

Upon inspection of the planetary data this seems to be a reasonable way forward.


Upon more careful inspection it appears as if you get a better fit by assuming

F_s = T^4/constant

Thus bringing us back to the "blackbody" law.