A Stochastic Representation of Temperature Fluctuations Induced by Mesoscale Gravity Waves

Ubiquitous mesoscale gravity waves generate high cooling rates important for cirrus formation. We make use of long-duration balloon observations to devise a probabilistic model describing mesoscale temperature uctuations (MTF) away from strong wave sources. We define background conditions based on observed probability distributions of temperature and underlying vertical wind speed fluctuations. We show theoretically that MTF are subject to damping at a rate near the Coriolis frequency when the vertical wind speed fluctuations are autocorrelated over a fraction of a Brunt-Väisälä period. We find that for background wave activity, a decrease in temperature of 1K translates into cooling rate standard deviations and mean updraft speeds of 4–8Kh⁻¹ and ≈ 10–20 cms⁻¹, respectively, depending on latitude and stratification. We introduce an effective Coriolis frequency to generate cooling rates in equatorial regions consistent with balloon data. Above ice saturation, MTF are large enough to affect ice crystal nucleation. Our results help constrain uncertainty in aerosol-cirrus interactions, provide insights to better meet challenges in comparing measurement data with model simulations, and support the development of cutting-edge ice cloud schemes in global models.