These lectures, delivered at the Les Houches Summer School on the Fundamental Aspects of Turbulent Flows in Climate Dynamics, introduce simple models for the energetics of the tropical atmosphere. Topics include bulk-plume convection, convective available potential energy, gravity waves, and free-troposphere humidity.
Cloud-resolving models are wonderful tools for exploring the effect of elevated carbon dioxide on a convecting atmosphere, but they are expensive to run. Here a technique is used to accelerate (by 30x) the equilibration of these simulations, allowing us to study how the equilibrium climate sensitivity (ECS) changes with warming.
Two proxies for lightning — CAPExP and ice flux — make two very different predictions for the future of tropical lightning: CAPExP predicts a large increase, while the ice flux predicts a moderate decrease. Here, we use cloud-resolving simulations to query lightning proxies over the United States and the tropics.
Although climate change is arguably the most urgent issue of our time, studies show that the general public knows little about climate science. In a quest to understand why, we investigate how often five basic climate facts are conveyed in The New York Times news articles covering climate change from 1980 to 2018.
The Fixed Anvil Temperature (FAT) hypothesis is widely accepted, but we show that FAT is supported neither theoretically nor empirically. Instead, a Fixed Tropopause Temperature (FiTT) is found: for a 50-K change in sea-surface temperature, the temperature of the tropopause changes by less than 2 K.
In the tropics, the highest frequency of cloudiness is in the upper troposphere. But, why? The conventional wisdom says that the peak in cloudiness occurs where convective detrainment is highest. Here, we argue that this is wrong. Instead, cloudiness is greatest in the cold upper troposphere because the sublimation of ice is so slow there.
CAPE x P has been used to predict changes in lightning with global warming, but how good is this proxy? As it turns out, quite good! As shown here, the CAPE x P proxy correctly predicts the seasonal maps of lightning and its spatially varying diurnal cycle. Shown here is the hour of maximum (top) CAPE x P and (bottom) lightning for JJA.
Why does global precipitation increase at 2% / K? Here, we explain why. The net upwelling radiative flux F is a fixed function of temperature, F = Ft - k (T - Tt)n, where k and n are positive constants and subscript t denotes the tropopause. Since n = 2 and the depth of the troposphere is 100 K, precipitation increases at 2% / K.
Shallow cumulus clouds provide a large and uncertain feedback on global warming, but the 4D observations needed to characterize their lifecycles are nearly impossible to obtain with current instruments. But, here, we describe a new ring of stereo cameras that is now providing the needed 4D data on a 50-meter grid with a 20-second time step.
Convective aggregation is a bizarre phenomenon where, in numerical simulations, rain clouds clump together into a single blob. How relevant is this numerical oddity to the real world? In this study, the feedbacks responsible for convective aggregation are shown to dramatically accelerate the formation of hurricanes, pointing to a real-world impact.
For nearly 200 years, atmospheric scientists have relied on approximations to the height of the lifting condensation level (LCL). Here, the exact, explicit, and analytic expression for the LCL is derived, as is an analagous expression for the lifting deposition level (LDL). These expressions depend only on basic physical parameters.
What happens to convective heating after it is deposited in the troposphere? This question is fundamental to atmospheric dynamics, but the only known solutions have assumed an artifical rigid lid at the tropopause. This paper presents the first Green's function for buoyancy in a troposphere overlain by a realistic stratosphere.
A cloud's size plays an important role in its dynamics, its ability to form rain, and its radiative forcing. But, the distribution of cloud sizes can be difficult to measure. This paper explores ways to calculate the size distribution from linear sampling, e.g., from vertically pointing lidar or from aircraft.
Severe weather is predicted to become more frequent with global warming, but those predictions are based on warming-induced increases in CAPE, for which we have had no theory. This paper presents the first analytical expression for CAPE. It explains the Clausius-Clapeyron (CC) scaling of CAPE, and its divergence from CC scaling at very warm temperatures.
On average, the largest convective buoyancies and vertical velocities occur in the upper troposphere. Common wisdom states that this results from the extra buoyancy provided by the latent heat of fusion. This paper shows that this is a fallacy: the profiles of convective buoyancy and vertical velocity are the same in a world with and without ice.
In global climate models, the poor treatment of "entrainment" (the mixing of clear air into clouds) is the largest source of uncertainty in how much the Earth will warm for a given increase in atmospheric CO2. This paper describes the Stochastic Parcel Model, a convective parameterization that treats entrainment the way it operates in nature and that is also deterministic and fast enough for use in global climate models.
Many aspects of Earth's climate (e.g., cloud cover, precipitation, and radiation fluxes) depend on the sizes and lifetimes of cold pools, which can trigger storm clouds when they collide. Here, we present analytical expressions for the evolution of cold pools, including their maximum sizes and lifetimes. These results are successfully validated with large-eddy simulations.
The energy available to storms, which is measured by CAPE, is predicted to increase dramatically with warming, leading to more severe storms and more frequent lightning. But, why does this increase in CAPE occur? We show that the increases in CAPE are driven by a ballooning of upper-tropospheric buoyancy, which is correctly predicted by the zero-buoyancy plume model.
Stationary buoyant parcels of fluid do not accelerate at a rate equal to their buoyancy. Instead, they accelerate at a smaller rate, which is found by solving a Poisson equation. This paper shows that the proximity of buoyant parcels to the surface greatly impacts their acceleration. This finding has implications for the triggering of new thermals, which originate at the surface.
Rings of high-humidity air at the edges of cold pools serve as important precursors for deep convection. But, how do those rings form? The conventional wisdom is that evaporation of precipitation is responsible. Here, we test this idea and find, instead, that enhanced surface fluxes are the true source of the high-humidity rings.
Stereo photogrammetry allows us to make quantitative three-dimensional measurements of cloud sizes and speeds. Here, data on dozens of cloud thermals are used to show that drag -- recently argued to be negligible -- is, to the contrary, a dominant term in their momentum balance, and wave drag is the likely culprit.
What physical process gives birth to convective clouds? There are two possibilities: warm and humid air launches off the surface due to its buoyancy, or that air gets pushed up by colder air that collides with it. Here, we cleanly decompose the forces into those due to buoyancy and inertia to find the answer.
Vertical velocities in clouds are important for many phenomena, including hail, lightning, and stratospheric moistening. But, there is no consensus on the dominant balance of forces giving rise to these velocities. In this paper, we identify, track, and analyze thousands of individual cloud thermals to identify whether clouds are slippery (acceleration equals buoyancy) or sticky (buoyancy equals drag).
GCMs disagree on the answer to the following question: will global warming cause an increase or decrease in summertime severe weather over the United States? In pursuit of a resolution, we test a hypothesis that the models that do a good job of simulating today's severe weather will be in better agreement about the future of summertime severe weather.
For hundreds of millions of years, lightning has shaped the evolution of terrestrial species through its triggering of wildfires, and lightning has altered atmospheric chemistry through its production of NOx. Now, with rapid global warming projected for the 21st century, the frequency of lightning is poised to increase dramatically. In this study, we validate a new proxy for lightning and then use it in global climate models to predict a 50% increase in U.S. lightning strikes over the 21st century.
The relative humidity of the atmosphere depends on the precipitation efficiency (PE) of convective clouds. In this study, we measure precipitation efficiency at a new level of detail using water-molecule-following Lagrangian particles. The results show how the PE of water vapor varies depending on where it enters the cloud.
Water vapor is the dominant greenhouse gas in the atmosphere, but what processes set its concentration? This paper provides a simple set of equations for relative humidity and its changes with global warming. In particular, it predicts that relative humidity will remain a fixed function of temperature as the atmosphere warms.
Using methods from the field of computer vision, this paper details how to reconstruct oceanic clouds in 3D using two digital cameras. These techniques are then applied, and validated, using a pair of stereo cameras in Miami, Florida.
This paper eliminates a spurious gravity-wave resonance in a method used to test convective parameterizations for GCMs. The resonance appears as the dashed-blue spike in the figure, while the solid-red curve shows the new scheme, which matches the solid-black benchmark.
In this work, analytical solutions are found for the descent and damping of vertical features in a moist-convecting atmosphere. It is shown that wind profiles with large wavelengths damp slower and descend slower than those with short wavelengths.
This study finds that cold pools are responsible for the abrupt transition to convective aggregation as domain size increases. In their absence, aggregation occurs at all scales.
How can we reconcile the low entrainment rates obtained from mass-flux budgets with the high values obtained from direct measurement? Using Lagrangian particles in a large-eddy simulation of cumulus congestus, we find that clouds rapidly entrain both environmental air and their own detritus, reconciling the two values.
Global climate models use parameterizations to model the effect of convection on the atmosphere's momentum budget. This paper finds that a very simple scheme, which neglects the horizontal pressure force, performs better than the schemes currently used in GCMs.
Cloud-resolving simulations are used to validate the underlying theory and predictions of the weak pressure gradient (WPG) scheme in this paper. WPG is shown to be able to model the stacked layers of negative buoyancy in regions of steady-state ascent.
The weak pressure gradient (WPG) scheme is an alternative to the weak temperature gradient (WTG) scheme for modeling a column of atmosphere coupled to its environment via gravity waves. This paper uses pencil-and-paper derivations to argue that WPG is more accurate than WTG.
This study provides an explanation for the asymmetrical distribution of lightning in hurricanes. Using data from thousands of dropsondes, condensate loading and entrainment are found to be key mechanisms controlling convective ascent.
This study finds that boundary-layer parcels detrained by clouds in the free troposphere come primarily from within 100 meters of the surface. This has important implications for how convective instability is calculated in the atmosphere.
This is the first study of precipitation extremes in a high-resolution cloud-resolving model. Contrary to results from GCMs, convective updrafts become more vigorous when CO2 is doubled, contributing to higher rain rates.
Here, we report on the first investigation of stratospheric HDO using a steady-state cloud-resolving simulation with isotope microphysics. Simulating a Walker cell over an 8000-km-wide domain, the convective injection of ice and the generation of cirrus by gravity waves are found to be dominant controls on HDO in the stratosphere.
The process of convective entrainment has enormous influence on clouds and the Earth's climate sensitivity, but it has not been possible to measure entrainment directly -- at the grid-cell level -- in large-eddy simulations (LES). This paper reports on the first technique for making this measurement at the native resolution of the simulation.
Tropical cyclones, called hurricanes in the North Atlantic, have some of the most intense convection in the world, capable of reaching up into the stratosphere. In this study, we quantify the fraction of convective excursions into the stratosphere that are caused by tropical cyclones.
Within an ensemble of clouds and even within a single cloud, parcels of cloudy air detrain at a variety of different heights. What causes this spectrum of behavior: differences in the properties of those parcels at the cloud base, or differences in how they entrain above the cloud base? This paper answers that question.