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. Plain Language Summary: The limited scientific understanding of pure ice clouds (cirrus)—and therefore the difficulty to account for them in models—causes substantial uncertainty in climate projections. Two research issues important for cirrus formation continue to form a roadblock on the path of scientific progress: the dynamical forcing driving cirrus ice crystal formation and the ice‐forming properties of solid atmospheric particles. Long‐duration balloons floating in the high atmosphere have quantified key properties of gravity waves that generate vertical air motions (cooling rates) crucial for ice formation in cirrus. Only when occurrence and magnitude of cooling rates are well understood can effects of different solid and liquid ice‐forming particles during cirrus formation be predicted with confidence. Blending insights obtained from the research balloon measurements with theoretical methods developed in statistical physics, our study elaborates on the dynamical forcing issue by devising a model that represents air parcel cooling rates on a probabilistic basis. We thereby hope to contribute significantly to a comprehensive process understanding and, ultimately, to removing one of the roadblocks in