The seasonal and spatial variation of downward longwave radiation (L↓) at the surface of the Antarctic ice sheet is studied using data from four stations. L↓ is found to depend on the fourth power of the surface temperature but on the sixth power of the temperature at the top of the surface inversion layer. The former result is shown to be a consequence of the dominance of longwave radiation in the surface energy balance while the latter raises some questions concerning the radiative properties of Antarctic clouds. Simple parametrizations of L↓ as a function of temperature are suggested; these may find application in validating General Circulation Model radiation calculations over Antarctica.

Classically, in order to resolve an equation u ≈ v over a free monoid X*, we reduce it by a suitable family $\cal F$ of substitutions to a family of equations uf ≈ vf, $f\in\cal F$, each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get $\cal F$ in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u ≈ v. We carry out such a parametrization in the case the prime equations in the graph involve at most three variables.