An attempt to describe the MRF PBL scheme (Troen and Mahrt, 1986)

1. PBL height : a bulk Richardson number is computed from layer 1 to K successively until it exceeds a critical number (.5). A first estimate of the PBL height is obtained for Ri equals the critical number. For unstable surface condition, a thermal enhancement to the first layer virtual potential temperature is done based on the surface sensible and latent heat flux. A second estimate of the PBL height is obtained based on the enhanced surface temperature.

2. Coefficient of diffusivity in the PBL: A cubic function is constructed based on the PBL height. The magnitude of the K within PBL is scaled to match the surface layer by the use of the convective velocity scale. Prandtl number is used to scale the thermal diffusivity from the momentum diffusivity coefficients. A base value of 1 m**2/sec is added for numerical stability.

3. Coefficient of diffusivity above the PBL: Local Richardson number is used to scale the coefficient with a limiting length scale specified (currently lambda=150 m).

4. Vertical diffusion: Fully implicit time integration scheme is used to calculate the update of prognostic variables due to vertical diffusion.