Physical processes controlling the organization of shallow cumulus as assessed using simple cloud models

Abstract

Shallow cumulus clouds are ubiquitous throughout the maritime trade wind region and have a large and varied radiative effect that presents a problem for modeling our future climate Seinfeld and Pandis (2016); Benner and Curry (1998); Bony and Dufresne (2005). How these cloud fields will change in response to a warming planet is not fully understood and modeling the small scales of shallow cumulus explicitly with a climate model is prohibitively expensive, making these changes one of the largest sources of uncertainty in climate models Forster et al. (2021). Further complicating this problem is the manner in which shallow cumulus are seen to frequently self-organize into distinct patterns, each with their own unique impact on the Earth's radiation budget Alinaghi et al. (2024a); Kazil et al. (2024). Understanding shallow cumulus development and organization normally requires a large-eddy simulation (LES) to track the numerous forms of moisture through their dynamical and thermodynamical changes, another method with a very large computational cost. The goal of this thesis is therefore to build a simple cloud model, based on the concept of predator-prey population dynamics and uncomplicated enough to run without the aid of a supercomputer, to simulate a series of distinct shallow cumulus patterns commonly seen in the maritime trades, and to understand what are the drivers of these patterns. Additionally, the results of the simple model are compared to LES results to gain a better understanding of what drives the largest of these patterns, the so-called flowers. This thesis is organized as follows. Chapter 1 gives an overview of the domain of interest: the maritime trades. The structure of this region will be dissected, from the synoptic scale down to the subcloud scale, and will include an in-depth discussion on the general properties and driving processes that form shallow cumulus. The patterns of interest in this thesis are those identified by Stevens et al: sugar, gravel, flowers, and fish Stevens et al. (2019). Chapter 1 will summarize the physical properties that define these patterns as well as review the current understanding on what drives these patterns to form. Finally, a brief history of simple cloud models will be provided to show the progression in development, from the first model from Wacker up to the simple models created in this thesis Wacker (1992). Chapter 2 describes the initial development of a 0-dimensional, vertically averaged, nonlinear dynamical system (NDS) using prognostic equations for vertical velocity, cloud water concentration, rain water concentration, and cloud drop number concentration. This model is then coupled across a grid using a series of different methods representing the manner in which clouds interact with their neighbors: through advection of condensate, to the horizontal expansion of updraft cores, to the circulations induced by cold pools. Using different sets of parameters derived from observations and LES studies, this model is able to evolve 3 distinct patterns that bear a resemblance to sugar and gravel, while aggregating condensate in the manner of flowers but without the requisite size of the real-world cloud. Sugar in this model is found to be primarily controlled by a balance between environmental instability and the gravitational drag of water drops, with very little interaction between clouds. Gravel had a similar result, with the addition of stronger latent heating in the deeper clouds as well as a cold pool-type coupling resulting in cloud arcs consistent with their real-world structure. Flowers were defined by their strong latent heating and the advection of condensate at cloud top driving the formation of clusters, but this model is not capable of simulating the vertical circulations that grow the flowers to a proper size. In order to resolve the flower size issue, chapter 3 develops a second simple model from the first that replaces the equation for cloud drop number concentration with one for water vapor concentration. This allows for the simulation of vertical circulations despite not having a vertical coordinate, as water vapor is advected at cloud base while cloud water is advected at cloud top. By separating these processes and adjusting the parameter settings, this new model is able to simulate flowers of a realistic size while maintaining the ability to produce both sugar and gravel. An analysis of the advection terms across both flowers and gravel shows that a mesoscale circulation is indeed present through the flower, while gravel continues to be most strongly controlled by the outward expansion of the updraft simulating the leading edge of a gust front. Additional processes to distinguish cloud patterns were necessary in this second model that were not present in the first, such as the uptake of water vapor from the ocean surface and the large-scale subsidence outside of the clouds. The effects of the distance over which grid boxes are coupled were tested and found to have negligible impacts on cloud size. Finally, chapter 3 presents a comparison between both models and observed cloud fields from MODIS data, showing that the second model is accurate enough for use in testing real world problems. Chapter 4 then applies the second model to a study conducted by Narenpitak et al on an observed sugar-to-flowers transition from the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC4A) field campaign Narenpitak et al. (2021). The simple model was able to form flowers of a proportionate size to those observed, and testing the impact of the vertical velocity resulted in a smaller flower size when the domain-mean w was reduced by 50%, comparable to the results from a more complex LES. Sensitivity tests showed that the processes necessary to flower formation were further affected by the reduction in vertical velocity, such as the gravitational drag of liquid water or the precipitation terms causing an increase in cloud size when removed as opposed to the control run's unstable growth. Once the simple model's credibility was established in this scenario, further sensitivity testing was done to measure the importance of cloud moisture concentrations to the flower size and growth rate. Both cloud water and water vapor concentrations were found to correlate most strongly with cloud size in the mid to upper levels of the cloud. When the vertical velocity was reduced, the decreased decoupling of the cloud and surface layers led to water vapor near the surface becoming a strong predictor of cloud size, whereas in the control run the two quantities remained slightly more independent between the separate layers. By comparing changes in moisture versus circulation strength, some evidence suggested that circulation was a stronger driver than cloud water of cloud size in the control run and water vapor in the weak w run, but the variances in circulation and moisture were too high to prove conclusive. Overall, this thesis shows that simple models are indeed capable of simulating patterns of shallow cumulus seen in the real atmosphere. By virtue of dynamically coupling the different prognostic equations of the NDS, the model illustrates the manner in which individual clouds grow, advect, combine, and separate throughout their life cycle. This advances our understanding of why these patterns form, and shows that these mesoscale circulations are possible to depict with minimal computational effort, making them a feasible pursuit in climate modeling.