Physical Processes Controlling the Organization of Shallow Cumulus as Assessed Using Simple Cloud Models

October 30, 2025

Michelle Kanipe

Committee: Peter Jan van Leeuwen (Advisor); Susan van den Heever; Christine Chiu; Iuliana Oprea (Mathematics)

Abstract

Shallow cumulus are ubiquitous throughout the maritime tropics and commonly self-organize into distinguishable patterns. These patterns have widely varied radiative effects and thus induce a large source of uncertainty in climate modeling. Four such patterns have gained particular attention in the past decade as identified in a study by Stevens et al (2019); these patterns are colloquially termed sugar, gravel, flowers, and fish. Sugar are small, non-precipitating cumulus with little vertical extent randomly distributed about the domain. Gravel are medium-sized cumulus organized into lines or arcs and are typically associated with precipitation and cold pools. Flowers are large clusters of cloud formed within shallow mesoscale circulations that clear out their immediate surroundings. Fish are open-cell cumulus organized along a gust front or other boundary and resemble a fishbone-like structure. Typically, shallow cumulus are studied using Large Eddy Simulations (LES), which allow a comprehensive tracking of moisture content through its dynamical and thermodynamical transformations, but are also computationally expensive and do not allow the isolation of individual processes. To that end, we look to the use of a simple warm-cloud-rain model, developed around the idea of predator-prey-type relationships, to aid in our understanding of these patterns and which internal and external processes, such as latent heating effects or turbulence, are critical to their formation.

In part I, we develop a 0-dimensional box model composed of four nonlinear differential equations describing the evolution of cloud water concentration, rain water concentration, cloud drop number concentration, and vertical velocity. We then couple this model across a 2D grid to describe the manner in which momentum and condensate advect about the domain. Using the same set of initial conditions and simply varying the parameter settings that describe the environment, this model shows itself capable of producing three distinct patterns emulating sugar, gravel, and flowers, with the first two patterns aligning well with real-world observations (fish, dependent on synoptic scale forcings, will not be included in this study). We find that there are a set of minimum processes necessary for inclusion in a simple model to produce each pattern, and that the manner of coupling determines the way in which clouds self-organize.

In part II, we assess the shortcomings of the first model surrounding the formation of appropriately sized flowers and reconceptualize the way in which moisture is coupled. In order to represent shallow mesoscale circulations in a model with no vertical coordinate, we replace the equation for cloud drop number concentration with one for water vapor concentration and couple the model through advection of water vapor at cloud base and cloud water at cloud top. These changes allow us to produce flowers of realistic size while still being able to model sugar and gravel. We find that our conclusions from part I hold true for both models in terms of the necessary processes to form each of the three patterns, while also demonstrating a way in which such a simple model can be coupled in order to adequately simulate the vertical circulations that drive self-organization.

We conclude part III by applying our second simple model to a case study of a sugar-to-flowers transition observed during the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC4A) field campaign and analyzed by an LES. We find that the simple model is able to produce clouds of comparative size to the LES results when varying the domain-mean vertical velocity. Both models were then used to test the sensitivity of the system to the strength of the vertical circulations and the peak moisture content in controlling the cloud size. We find some evidence that cloud water is a stronger predictor of cloud size than water vapor while circulation strength correlates well with cloud size overall, but we are unable to conclusively conclude whether one predictor supersedes another. Additionally, we find that both cloud water and water vapor in the mid to upper portions of the cloud correlate most strongly with cloud size with a lag time of up to 1 hour, with the level of the moisture relating to the strength of the boundary layer decoupling. Overall, this work shows that a simple model is capable of producing vastly different patterns of tropical shallow cumulus using a minimum set of physical processes and can be applied to real-world analysis in conjunction with an LES to further our understanding of shallow cumulus self-organization.