Tropical Meteorology

12.811

Problem Set 1

February 2003

1. Begin with the simple radiative equilibrium model discussed in class and in the lecture notes. At the top of the model atmosphere, add a thin layer of atmosphere with vanishingly small emissivity (and absorptivity). Calculate its temperature as well as the temperature of the two main layers.

2. Now start with the simple radiative-convective equilibrium model described in class and in the lecture notes. Modify this model by taking the emissivity (and absorptivity) of the upper layer to be ε₂, not necessarily equal to unity. Solve for the temperatures and turbulent enthalpy fluxes and comment on how they compare to the case ε₂ = 1 discussed in the notes. (Note: you may not be able to find closed-form solutions.)