Probability law of turbulent kinetic energy in the atmospheric surface layer

We investigate the significance of turbulent kinetic energy (TKE, $k$) and its variability in the atmospheric surface layer (ASL), needed in many applications. The statistics of $k$ around its mean state is studied using the probability density function $p(k)$ for ASL flows with significant buoyancy forcing. A nonlinear Langevin equation that preserves $p(k)$ but allows linear relaxation of $k$ to its mean state is suggested and tested using multiple ASL data sets that span various stabilities and surface roughness conditions. Model parameters for the proposed Langevin equation are derived from similarity theory, reproducing measured $p(k)$ with minimal Kullback-Leibler divergence.