Planetary Atmospheres
The Link Bewteen Cloud Perimeter, Fractal Dimension, and Atmospheric Stability
The geometric properties of clouds visible from space -- perimeter, area, size distribution, and fractal dimension -- provide detail about the underlying thermodynamic properties of theatmosphere. The fractal dimension is a measure of of self-similarity. In clouds it is a measure of how similar the cloud edge appears at different measurement scales. In two dimensions, Euclidean shapes have a fractal dimension of unity, and infinitely self-repeating patterns have a fractal dimension of two. That is, shapes with increasingly complex edges have more perimeter per area, and larger fractal dimensions. An analog to the individual fractal dimension is a representation of the total complexity of all lines within a domain area that contains multiple objects, referred to here as the ensemble fractal dimension.
A straightforward expression that relates cloud perimeters to global atmospheric stability defines the total cloud perimeter in a domain as a function of fractal dimension and measurement resolution. The expression verifies well with Large Eddy Simulations, however, satellite observations follow an unexpected power law. The discrepancy arises when using the canonical value for individual cloud fractal dimension, and instead requires a larger value, suggesting that the two-dimensional perimeter measurement from space is instead more closely tied to the fractal properties of the ensemble. The ensemble fractal dimension is not a well studied phenomenon, and is not a true fractal dimension by definition, but it appears to be more closely tied to generalized expressions for global cloud perimeter viewed from space and the atmospheric stability.
Hadley Circulations on Solar System Planets
Analytical descriptions of the angular width of Earth's Hadley cell show it to be related to the square root of the product of the tropospheric thickness and buoyancy frequency, and to the inverse square root of the angular velocity and planetary radius. Here, the applicability of this formulation is examined for other planetary bodies in the solar system. Generally, good consistency is found between predictions and observations for terrestrial planets provided the pressure scale height rather than the tropopause height is assumed to determine the thickness of the tropospheric circulation. For gas giants, the relevant thickness is deeper than the scale height, possibly due to the internal heat produced by Kelvin-Helmholtz contraction. On Earth, latent heat release within deep convection may play a similar role in deepening and widening the Hadley cell.
(Rees & Garrett 2019)
Exoplanets
We plan to apply these concepts to exoplanets using radiative transfer code to obtain estimated height and temperature profiles. We believe that this simple model can extract robust details about exoplanets, including the determination of exoplanet habitibility, from minimal data.