Reconciling Chord Length Distributions and Area Distributions for Fields of Fractal Cumulus Clouds

Abstract

While the total cover of broken cloud fields can in principle be obtained from one-dimensional measurements, the cloud size distribution normally differs between two-dimensional (area) and one-dimensional retrieval (chord length) methods. In this study, we use output from high-resolution Large Eddy Simulations to generate a transfer function between the two. We retrieve chord lengths and areas for many clouds, and plot the one as a function of the other, and vice versa. We find that the cloud area distribution conditional on the chord length behaves like a gamma distribution with well-behaved parameters, with a mean μ=1.1L and a shape parameter β=L−0.645. Using this information, we are able to generate a transfer function that can adjust the chord length distribution so that it comes much closer to the cloud area distribution. Our transfer function improves the error in predicting the mean cloud size, and is performs without strong biases for smaller sample sizes. However, we find that the method is still has difficulties in accurately predicting the frequency of occurrence of the largest cloud sizes.

Size dependence in chord characteristics from simulated and observed continental shallow cumulus

“…That chord occurrence decreases strongly with increasing length and duration is hardly surprising given that it has been well-established that the cumuli size density roughly follows a power law of −3 to −2 (e.g., Raga et al, 1990;Benner and Curry, 1998;Neggers et al, 2003;Zhao and Girolamo, 2007;Dawe and Austin, 2012;van Laar et al, 2019). Given that randomly cutting through a cloud with an area of A cre-ates many chords with a length smaller than √ A but only a few larger than √…”

“…One useful paradigm that simplifies representing the effects of sub-grid-scale shallow cumulus on resolved-scale flow is the assumption that various properties of shallow cumulus are size-dependent, which enables the representation of the high variability in cumulus clouds through a limited number of shallow convective plumes of differing size (e.g., Arakawa and Schubert, 1974;Neggers, 2015;Olson et al, 2019). The idea that larger shallow cumulus clouds have stronger updrafts than small shallow cumulus clouds is as intuitive as it is old (e.g., Plank, 1969;Raga et al, 1990;Benner and Curry, 1998;Zhao and Girolamo, 2007;Yuan, 2011). Assuming shallow cumulus clouds are created by buoyant plumes that are slowed via entrainment with the dry surrounding air (Turner, 1962;Simpson and Wiggert, 1969;Warner, 1970a), it follows that larger plumes could rise faster by either being more buoyant, entraining less, or a mix of both.…”

Composited structure of non‐precipitating shallow cumulus clouds

“…In addition, small cumulus clouds can also help to sustain larger clouds by detraining heat and moisture above the cloud base and thus maintaining cloud–subcloud coupling (Neggers, 2015). Another caveat is that intersections taken during flights are not always through the cloud centre, which can cause difficulties in determining size distributions (e.g., Barron et al ., 2020) and may bias the construction of composites.…”

Fitting Cumulus Cloud Size Distributions From Idealized Cloud Resolving Model Simulations

“…Accordingly, the number of clouds n having a certain size l can be described by: $$$n\left(l\right)\propto {l}^{-b},$$$ where ∝ should be read “scales as,” and b is a characteristic power‐law exponent. Since then, power‐laws (or derived forms thereof like power‐laws with exponential cutoff or broken power‐laws) have been universally recognized as the best functions to model cloud size distributions obtained from either satellite imagery (Benner & Curry, 1998; Bley et al., 2017; Koren et al., 2008; Kuo et al., 1993; Mieslinger et al., 2019; Senf et al., 2018; Sengupta et al., 1990; Welch et al., 1988; Wood & Field, 2011; Zhao & Di Girolamo, 2007), aircraft measurements (Benner & Curry, 1998; Jiang et al., 2008; Wood & Field, 2011), or high‐resolution simulations (Barron et al., 2020; Dawe & Austin, 2012; Garrett et al., 2018; Heus & Seifert, 2013; Jiang et al., 2008; Neggers, Jonker, & Siebesma, 2003; Rieck et al., 2014; Senf et al., 2018; van Laar et al., 2019; Xue & Feingold, 2006).…”