In the nocturnal boundary layer, under calm and clear-sky conditions, the aerosol-rich surface layer cools radiatively to the upper atmosphere. This cooling significantly impacts the vertical temperature profile, affecting areas several hundred meters above the surface. The cooling process results in a stable nocturnal inversion layer. However, the ground surface, with its higher thermal inertia, cools more slowly. This difference in cooling leads to the development of an air layer about one meter thick, which can be \({2-6}^\circ \) C cooler than the surface. Consequently, an unstable convective layer forms at the surface, capped by a stable inversion layer that extends upwards for hundreds of meters. This situation, where the presence of a convective layer below a stably stratified inversion layer, is a classic example of penetrative convection. Micro-meteorological phenomena near the surface, such as heat and moisture transport from the ground, fog formation and deepening are affected by this convection. This study presents numerical simulations of penetrative convection driven by radiative cooling in the nocturnal boundary layer. The results show that entrainment velocity-governing the growth of the surface convective layer-follows the Deardorff model and is influenced by aerosol number density, bulk Richardson number based on the penetrative length scale, and convective layer height.
