Model Description, Simulation setup and Diagnostics

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The importance of interactive radiation in driving the aggregation has been con rmed by many studies. The radiation related mechanisms include long-wave radiative cooling from clear sky (Wing and Emanuel, 2014; Emanuel et al., 2014) or cloud top (Muller and Held, 2012) as well as shortwave radia-tion (Wing and Cronin, 2016). The importance of each radiation mechanism and how they drive the aggregation di er among the studies. Here we review the main ones.
Tompkins and Craig (1998) nd that replacing the interactive radiation scheme with a horizontally uniform radiation pro le destroys the convective organization in few days. Thus they conclude that the di erential radiative heating rate is necessary for the maintenance of the aggregated cluster by converging into cloudy region.
Using a 3D CRM in a RCE frame work, Bretherton et al. (2005) nd that homogenizing the longwave radiation suppresses the aggregation. They suggests that an enhanced lower tropospheric longwave radiation in dry region compared to moist region drives a shallow circulation which transports low level moist air to the moist region. Consequently the already dry region dries further and cools more e ciently by radiation while the mosit region radiation reduces. Thus the di erential radiative cooling increases as well as shallow cir-culation hence creating a positive feedback, as was rstly presented by Gray and Jacobson (1977). The nding of Muller and Held (2012) further con rms the role of longwave radiation: in their simulation, removing low clouds from the computation of radiation prevents the aggregation. They thus emphasize the importance of cloud top longwave radiation: the boundary layer circula-tion, which transport moisture up-gradient, is driven by downward motion in the dry region which itself is forced by enhanced cloud top longwave radiation.
Wing and Emanuel (2014) nd that the both the di erential shortwave or longwave heating rate due to upper tropospheric moisture di erence between the moist and dry region (clear sky e ects) is necessary for the aggregation. They nd that, for a sea surface temperature in the range of the current tem-perature of the tropical ocean, the shortwave radiation e ect is to favor aggre-gation in its early and middle stage. The shortwave absorption in clear sky region reduces with reduction of moisture, thus the net di erential radiative cooling increases hence results in stronger subsidence and further dryness. The longwave radiation feedbacks though can be positive or negative depending on the relative emissivity of upper and lower troposphere. At the early stage of aggregation, when the upper troposphere is dry compared to the lower tro-posphere, the longwave radiative cooling increases with further dryness and creates a positive feedback. While when aggregation is established, the lower troposphere also has a small amount of moisture thus the longwave radiative cooling decreases and results in a negative feedback. Wing and Cronin (2016) con rm these nding in a channel domain, but they suggest that driving feed-backs are SST dependent so that the shortwave radiative feedbacks remains positive across all SSTs but weaken with increasing the temperature, while the longwave radiative feedback is negative at low SST but then turn positive for warmer SSTs.
Emanuel et al. (2014) used a toy model with two atmospheric layers to show the importance of clear-sky longwave radiation. Above a critical SST, the lower tropospheric longwave radiative cooling becomes very large due to its large amount of water vapor and comparatively a dry free troposphere. The en-hanced low-level clear-sky longwave radiative cooling increases the large scale subsidence and drives the aggregation. The aggregation drives the atmospheric to a dry pro le far from typical RCE approximation. Thus they suggest that « the ordinary RCE state becomes linearly unstable to large-scale overturning circulations » and the aggregation drives the atmosphere towards a new RCE.
The importance of radiative feedbacks have been also investigated in GCM by Coppin and Bony (2015). They show that the low level radiative cooling in dry non convective region drives a circulation which leads to aggregation. They call these dry region « radiatively driven cold pools ». These cold pools can expand as they cool more e ciently thus they become denser than the moist region. They nd that this feedback is more e ective at cold SSTs ( < 300K).

Atmospheric Moisture

While convective moistening of the free troposphere has a stabilising e ect on the large scale, the local moistening by convective clouds favors succes-sive convection (Grabowski and Moncrie , 2004). This is known as moisture-convection feedback (Held et al., 1993; Tompkins, 2001b; Craig and Mack, 2013). The free tropospheric moisture-convection feedback has been rstly mentioned by Held et al. (1993) in a two dimensional setup. In their simula-tion with no imposed wind shear, convection becomes organized in a small part of the domain. Adding even a weak wind shear to an already organized sim-ulation, homogenizes moisture over the domain followed by convection being activated outside the organized cluster. However, before losing its organiza-tion, convection follows the region with moist low level free troposphere which is advected by wind shear. They suggests that, as in moist region the enter-tained air into the cloud is also moist, it doesn’t have a negative impact on the buoyancy of convective updraft, convection is more successful thus favored. The reduced entrainment of dry air mentioned above is then the key for the organisation of convection.
In 3D cloud-resolving simulations, Tompkins (2001b) suggests that con-vection moistens its local environment and a moist environment favors more convection thus moisture-convection feedback is important for aggregation. . This study further examines this hypothesis in two sensitivity tests in which the free tropospheric and upper free tropospheric moisture is reduced by 70 percent in the convective area. The consequence is a cut o of the convective activities especially for the case in which the lower free tropospheric water vapor has been reduced. The drier free troposphere enhances the strength of downdraft and also weakens the convective updrafts due to the entrainment of dry air. In a recent study, Tompkins and Semie (2017) shows that a higher entrainment rate (represented by the sub-grid mixing parameterization in nu-merical simulations) favors aggregation. A higher entrainment rate increases the interaction between the convective plume and its local environment’s mois-ture thus it enhances convection-moisture memory Beside the role of free tropospheric moisture, the boundary layer moisture can also play a role in aggregation. Yang (2018), using a boundary layer frame-work shows that a negative boundary layer water vapor anomaly is necessary for the formation of the dry regions thus for the aggregation. A negative mois-ture anomaly creates a locally higher density thus a pressure gradient that is necessary for the horizontal mass transport between non-convective and con-vective regions. He argues that cold pools formed by the evaporation of rain disfavor aggregation by homogenizing the boundary layer moisture. This im-pact of cold pools on the aggregation has been con rmed rstly by Nakajima and Matsuno (1988) in a simple 2D simulation in which they show that sup-pressing the evaporation of rain – thus suppressing the cold pools – leads to clustering of convection. Further, Jeevanjee and Romps (2013) show that the aggregation can occur even in small domains when they prevents the formation of cold pools. They reinforce the idea that cold pools transport moisture to dry region and homogenize water vapor in the boundary layer. This redistribution of moisture is even more e ective over small domains.

Surface uxes

The surface uxes (latent heat and sensible heat uxes) are functions of wind speed, air-sea moisture and temperature disequilibrium. The spatial variation of surface uxes arises from variation in surface wind speed or air-sea disequi-librium. The wind-speed surface ux feedback which is often referred to as WISHE (wind-induced surface heat exchange) is a positive feedback mecha- nism in which a stronger wind enhances surface uxes and the enhanced surface uxes favors stronger atmospheric circulation (wind speed). On the one hand, the interaction of convection and the surface results in a locally enhanced heat and moisture uxes due to increased surface wind, which in return can feed the convection and favor aggregation. On the other hand, the surface uxes are enhanced in a dry non-convective area due to an increased moisture dise-quilibrium at the surface, and thus disfavor aggregation. Tompkins and Craig (1998); Bretherton et al. (2005) show that homogenizing the surface uxes can destroy the aggregation. However Muller and Held (2012) show that the surface uxes are not necessary but helpful for the aggregation and conclude that the aggregation proceeds even with homogenized surface uxes as long as radiative feedbacks are strong and the domain is large.
Wing and Emanuel (2014) show that the surface uxes create a positive feedbacks with aggregation at the early stage, when the aggregation is proceed-ing, but when well established, the surface uxes feedback becomes negative. This change of sing is due to the fact at the early stage the wind e ect domi-nates (WISHE e ect), while at a longer times it is the evaporative demand of dry regions that dominates. In other words, at early stage, the surface uxes are stronger in convective regions (positive feedback) while when aggregation is established, surface uxes become stronger in dry regions due to enhanced air-sea moisture disequilibrium.
Another surface ux related mechanism that can play a role in aggregation of convection is wind-induced surface heat exchange (WISHE, Emanuel et al. (1994)).
Coppin and Bony (2015), using a GCM, show that the surface ux are necessary at warm SSTs (> 305K).They suggest that a WISHE mechanism initiates and develops aggregation at high SST as the deep convection enhances surface uxes and the convection becomes more likely in a region with high surface uxes.

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Objective and Outline of the thesis

While a lot has been done identifying the mechanisms triggering and governing the aggregation of convective clouds, there is still a need to better understand how these mechanisms are a ected by SST. More speci cally, the majority of these studies use idealized simulation designs that exclude any SST hetero-geneity which potentially impacts surface uxes, atmospheric circulation, and convective activities. This study works towards achieving a better understand-ing of the physics of aggregation and how it is a ected by SST heterogeneities. The key questions to address are:
How does the aggregation of convective clouds depend on the surface temperature, when SST is xed in time and space?
How does the presence of a spatiotemporally xed SST anomaly impact the aggregation, and what role do the amplitude and the fractional cov-erage of the SST anomaly play?
How does an interactive surface temperature feedback on convection its aggregation?
Does including a diurnal cycle a ect the progress of aggregation when the surface temperature is interactive?
To that end, we will use radiative-convective equilibrium simulations per-formed with the cloud-resolving model SAM. Chapter 2 describes this cloud-resolving model in more detail, as well as the simulation settings, and the diagnostics used to quantify the aggregation of convective clouds in our simu-lations.
In chapter 3, we rst investigate the range of xed SST that favors the ag-gregation in SAM, as this range is model and setup dependent. Then for SST = 300 K, we impose a spatially and temporally constant warm SST anomaly at the center of the domain (but keeping the domain-mean SST constant by reducing the SST outside of the warm anomaly) to investigate how fast the ag-gregation progresses, and how its progress depends on the size and magnitude of the warm anomaly. One of the interesting questions is whether a simulation with homogeneous SST which does not aggregate, does with a hot spot, and in that case whether removing the warm anomaly after reaching the aggregation leads to disaggregation. In other words, does this forced aggregation drive the system to a new stable equilibrium? The chapter continues by exploring the importance of radiative feedbacks for the aggregation when a warm anomaly is present. To do so, we spatially homogenize the radiation pro le for simulations with di erent warm anomalies. These results are published in Shamekh et al. (2019).
In chapter 4, we investigate the feedbacks between the SST and the aggre-gation when the SST is interactive. To allow the SST to interact, a slab ocean with xed mean SST is implemented. Thus the domain-mean SST is held xed, but the local SST can evolve according to the surface energy budget. When SST is interactive, reaching equilibrium can take signi cantly longer (Cronin et al., 2015), but keeping the domain mean SST constant excludes this problem. Using this setup, we investigate the sensitivity to the slab depth and to mean SST. As the radiation feedbacks are known to be necessary for ag-gregation, we further investigate separately the role of free tropospheric versus boundary layer radiation, in order to determine which part is more important to drive the aggregation. These results are submitted in Shamekh et al. (2020).
Chapter 5 is devoted to the importance of the diurnal cycle for the ag-gregation. Indeed, the previous chapters neglected the diurnal cycle for sim-plicity, and used constant incoming solar radiation. But the diurnal cycle can modify the SST anomalies by intensifying them spatially but damping them temporally. We therefore use the same setup but adding a diurnal cycle to the simulations with interactive surface temperatures. We nd that the diur-nal cycle can signi cantly accelerate the aggregation, particularly for shallow ocean slab depths. We believe that this is linked to a new onset mechanism for aggregation, namely cold pools serving as seeds for the expanding dry regions. The results are being written for publication (in preparation).
In chapter 6, we present a summary of the key results from the 3 research chapters, a discussion of their implications, and potential directions for further research.

Table of contents :

1 Introduction 
1.1 Motivation
1.2 Tropical convective clouds
1.3 Aggregation in numerical simulations
1.4 Surface temperature dependency
1.5 The aggregation mechanisms
1.5.1 Radiation
1.5.2 Atmospheric Moisture
1.5.3 Surface
1.6 Objective and Outline of the thesis
2 Model Description, Simulation setup and Diagnostics 
2.1 Introduction
2.2 Model Description
2.2.1 Governing Equations
2.2.2 Radiation
2.2.3 Cloud Microphysics and water partitioning
2.2.4 Surface Fluxes
2.2.5 Sub-grid Scale Model
2.3 Simulation Setup
2.3.1 SST
2.4 Diagnostics
2.4.1 Dry patch and Aggregation Index
2.4.2 Moist Static Energy
2.4.3 Stream Function and Circulation
3 How do ocean warm anomalies favor the aggregation of deep convective clouds
3.1 Introduction
3.2 Model description and simulation design
3.2.1 Cloud-resolving model
3.2.2 Experimental setup
3.2.3 Aggregation metrics
3.3 Hot-spot impact on aggregation of deep convection
3.3.1 Results without and with hot-spot at dierent SSTs
3.3.2 Development of a large-scale circulation
3.4 Convective aggregation without radiative feedbacks
3.4.1 Hot-spots with or without radiative feedbacks
3.4.2 Two-box model: Pulled or pushed aggregation?
3.4.3 The aggregation onset phase
3.5 Equilibrium phase
3.6 Conclusions
4 Self-aggregation of convective clouds with interactive sea sur- face temperature 
4.1 abstract
4.2 Introduction
4.3 Method
4.3.1 Cloud-resolving model
4.3.2 Experimental setup
4.3.3 Slab ocean
4.3.4 Analysis Framework
4.4 The impact of interactive SST on the aggregation of convective clouds
4.4.1 Overview of results
4.4.2 SST anomalies
4.4.3 Surface pressure anomaly
4.4.4 Divergent
4.5 The impact of slab depth and SST on self-aggregation
4.5.1 Delayed aggregation with shallow mixed layer and cold SST
4.5.2 Link with the strength of the shallow circulation compared to the deep circulation
4.6 Conclusions
4.A Impact of interactive SST with constant deep ocean sink
4.B Surface pressure computation
4.C Sensitivity simulations and low-level radiative cooling
5 Impact of the diurnal cycle on the aggregation of convective clouds with interactive surface temperature 
5.1 Introduction
5.2 Experimental setup
5.3 Results
5.3.1 The diurnal cycle in aggregating simulation
5.3.2 Diurnal cycle vs constant solar radiation
5.4 Conclusion
5.A Sensitivity to relaxation time
6 Conclusions and Future Research Directions 
6.1 Conclusions
6.2 Future Research Directions
6.2.1 Ocean Eddies
6.2.2 Boundary Layer Divergent Flow
6.2.3 Dry patch triggering
6.2.4 Shallow Circulation
6.2.5 Interactive SST with adjusted mean energy removal


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