A prototype stochastic parameterization of regime behaviour in the stably stratified atmospheric boundary layer

Recent research has demonstrated that hidden Markov model (HMM) analysis is an effective tool to classify atmospheric observations of the stably stratified nocturnal boundary layer (SBL) into weakly stable (wSBL) and very stable (vSBL) regimes. Here we consider the development of explicitly stochastic representations of SBL regime dynamics. First, we analyze whether HMM-based SBL regime statistics (the occurrence of regime transitions, subsequent transitions after the first, and very persistent nights) can be accurately represented by “freely running” stationary Markov chains (FSMCs). Our results show that despite the HMM-estimated regime statistics being relatively insensitive to the HMM transition probabilities, these statistics cannot all simultaneously be captured by a FSMC. Furthermore, by construction a FSMC cannot capture the observed non-Markov regime duration distributions. Using the HMM classification of data into wSBL and vSBL regimes, state-dependent transition probabilities conditioned on the bulk Richardson number (RiB) or the stratification are investigated. We find that conditioning on stratification produces more robust results than conditioning on RiB. A prototype explicitly stochastic parameterization is developed based on stratification-dependent transition probabilities, in which turbulence pulses (representing intermittent turbulence events) are added during vSBL conditions. Experiments using an idealized single-column model demonstrate that such an approach can simulate realistic-looking SBL regime dynamics.