# Instantaneous variance scaling of AIRS thermodynamic profiles using a circular area Monte Carlo approach

Satellite observations are used to obtain vertical profiles of variance scaling of temperature (inline-formulaT) and specific humidity (inline-formulaq) in the atmosphere. A higher spatial resolution nadir retrieval at 13.5 km complements previous Atmospheric Infrared Sounder (AIRS) investigations with 45 km resolution retrievals and enables the derivation of power law scaling exponents to length scales as small as 55 km. We introduce a variable-sized circular-area Monte Carlo methodology to compute exponents instantaneously within the swath of AIRS that yields additional insight into scaling behavior. While this method is approximate and some biases are likely to exist within non-Gaussian portions of the satellite observational swaths of inline-formulaT and inline-formulaq, this method enables the estimation of scale-dependent behavior within instantaneous swaths for individual tropical and extratropical systems of interest. Scaling exponents are shown to fluctuate between inline-formula $M5inlinescrollmathml\mathrm{italic \beta }=-normal 1$ 36pt12ptsvg-formulamathimg337b7eabb4326eb5bac8b424c334a8c8 amt-11-2717-2018-ie00001.svg36pt12ptamt-11-2717-2018-ie00001.png and inline-formula−3 at scales inline-formula≥500 km, while at scales inline-formula≤500 km they are typically near inline-formula $M9inlinescrollmathml\mathrm{italic \beta }\approx -normal 2$ 36pt12ptsvg-formulamathimg5037da84e31ca912b8c19dcfa12ff0b7 amt-11-2717-2018-ie00002.svg36pt12ptamt-11-2717-2018-ie00002.png , with inline-formulaq slightly lower than inline-formulaT at the smallest scales observed. In the extratropics, the large-scale inline-formulaβ is near inline-formula−3. Within the tropics, however, the large-scale inline-formulaβ for inline-formulaT is closer to inline-formula−1 as small-scale moist convective processes dominate. In the tropics, inline-formulaq exhibits large-scale inline-formulaβ between inline-formula−2 and inline-formula−3. The values of inline-formulaβ are generally consistent with previous works of either time-averaged spatial variance estimates, or aircraft observations that require averaging over numerous flight observational segments. The instantaneous variance scaling methodology is relevant for cloud parameterization development and the assessment of time variability of scaling exponents.

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Dorrestijn, Jesse / Kahn, Brian H. / Teixeira, João / et al: Instantaneous variance scaling of AIRS thermodynamic profiles using a circular area Monte Carlo approach. 2018. Copernicus Publications.

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