A new model for the CBL growth based on the turbulent kinetic energy equation

Starting from the evolution equation for the turbulent energy density spectrum (EDS), we develop a new model for the growth of the Convective boundary layer (CBL). We apply dimensional analysis to parameterize the unknown inertial transport and convective source term in the dynamic equation for the three-dimensional (3-D) spectrum and solve the 3-D EDS equation. The one-dimensional vertical spectrum is derived from the 3-D spectrum, employing a weight function. This allows us to select the magnitude of the vertical spectral component for the construction of the growing 3-D EDS. Furthermore, we employ the vertical component of the energy spectrum to calculate the eddy diffusivity (required in dispersion models). Currently there are no available experimental data to directly verify our EDS model.