Eddy diffusivities derived from a numerical model of the convective planetary boundary layer

Abstract

Functional forms for the vertical eddy diffusivity K_z (z) are sought that optimize the performance of the K-theory diffusion equation. The method developed to determine the optimal diffusivity is first tested by applying it to analytic solution of the diffusion equation in which the functional form of the diffusivity is known precisely. In all test cases performed, the technique yields the correct K_z profile regardless of the initial estimate of K_z from which the technique’s search procedure begins. When applied to “observed” mean, cross-wind-integrated point source concentration fields derived from Lagrangian diffusion theory and data from a numerical turbulence model jointly, the technique yields optimal diffusivities that make the solution of the diffusion equation agree within ±20% of the “observed” values within the core of point source plumes. Expressed in terms of the convective-velocity scale w* and the mixed-layer depth z_i, the optimal diffusivity has a quasiuniversal form for atmospheric stabilities in the range z_i/L ⪯ -10 where L is the Monin-Obukhov length. The optimal diffusivity is found to be strongly dependent on the source hight. The K_z profiles derived for the two source heights z_s ∼ -0.025 z_i and z_s ∼ -0.25 z_i are of opposite shape, but they have comparable maximum values of K_z ∼ -0.25 w*z_i