Tropical convective clouds evolve over a wide range of temporal and spatial scales, which makes them difficult to simulate numerically. Here we propose that cloud statistical properties can be derived within a simplified time-independent coordinate system of cloud number n, saturated static energy h⋆, and cloud perimeter λ. Under the constraint that circulations around cloud edge compete with each other for total buoyant energy and air, we show that the product of cloud number and cloud perimeter nλ is invariant with λ and that cloud number follows a negative exponential with respect to cloud-edge deviations of h⋆ with respect to the mean. Overall, the summed perimeter of all clouds scales as the square root of the atmospheric static stability. These theoretical results suggest that the complexity of cloud field structures can be viewed statistically as an emergent property of atmospheric bulk thermodynamics. Comparison with a detailed tropical cloud field simulation shows general agreement to within ≤13%. For the sake of developing hypotheses about cloud temporal evolution that are testable in high resolution simulations, the shapes of tropical cloud perimeter distributions are predicted to be invariant as climate warms, although with a modest increase in total cloud amount.
