Prediction for cloud spacing confirmed using stereo cameras
Romps, David — Lawrence Berkeley National Laboratory
Area of research
What sets the sizes of clouds and the spacing between them? For shallow cumulus, we can at least offer an order-of-magnitude answer to this question: the natural length scale in a field of shallow cumulus is the depth of the boundary layer. Unfortunately, this hand-waving is a bit uncomfortable. If we think a bit more deeply about the problem, we realize there is at least one other length scale in the problem that we have ignored. Why do the clouds not set their sizes and spacing equal to that instead? Thuburn and Efstathiou (2020) offered an answer to this question. Their theoretical derivation predicts that the wavelength of the most unstable mode, which should manifest as the spacing between clouds, is 2√2 times the lifting condensation level (LCL) height.
We use stereo photogrammetry to test this prediction, and it turns out to work surprisingly well. We generated stereo reconstructions of shallow-cumulus events from 129 days at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility's Southern Great Plains (SGP) observatory in Oklahoma. Compositing those events, we find that, compared to 2√2 ≅ 2.8, the ratio of the cloud spacing to the LCL height tends to hover around 2.7 to 3.1. If we focus exclusively on cloud streets, which are closer analogs to the two-dimensional calculation that leads to 2√2, we again find very good agreement. The size of the clouds must be smaller than their spacing, and we find from the observations that their width is about equal to the LCL height.
It is intuitive that the sizes of clouds and their spacings should be the same order of magnitude as the boundary-layer depth, but only recently did Thuburn and Efstathiou (2020) give a convincing theoretical argument as to why. That explanation makes a testable prediction: that the ratio of the wavelength of the dominant eddies to the depth of the boundary layer should be 2√2. Using stereo photogrammetry, we find that the spacing of shallow cumulus clouds closely equals this ratio.