On the climatological probability of the vertical propagation of stationary planetary waves

We introduce a diagnostic tool to assess a climatological framework of the optimal propagation conditions for stationary planetary waves. Analyzing 50 winters using NCEP/NCAR (National Center for Environmental Prediction/National Center for Atmospheric Research) reanalysis data we derive probability density functions (PDFs) of positive vertical wave number as a function of zonal and meridional wave numbers. We contrast this quantity with classical climatological means of the vertical wave number. Introducing a membership value function (MVF) based on fuzzy logic, we objectively generate a modified set of PDFs (mPDFs) and demonstrate their superior performance compared to the climatological mean of vertical wave number and the original PDFs. We argue that mPDFs allow an even better understanding of how background conditions impact wave propagation in a climatological sense. As expected, probabilities are decreasing with increasing zonal wave numbers. In addition we discuss the meridional wave number dependency of the PDFs which is usually neglected, highlighting the contribution of meridional wave numbers 2 and 3 in the stratosphere. We also describe how mPDFs change in response to strong vortex regime (SVR) and weak vortex regime (WVR) conditions, with increased probabilities of the wave propagation during WVR than SVR in the stratosphere. We conclude that the mPDFs are a convenient way to summarize climatological information about planetary wave propagation in reanalysis and climate model data.