In the modern era of scientific computing, high fidelity simulations of physical systems combined with advanced data visualization allow us to control space and time and to perceive complicated dynamical systems in ways not possible only decades go. Below are some examples of how we have performed Large Eddy Simulations using PyCLES to visualize turbulent boundary layers and clouds.

The movies are best viewed in full screen mode by clicking on the title text in the movie thumbnails.

Dry Convective Boundary Layer

The dry convective boundary layer, or DCBL for short, consists of a planar heated surface and overlying atmosphere. Heat from the surface is transferred to the overlying atmosphere through a constant sensible heat flux. This sensible heat flux drives buoyant convective motions which redistribute heat vertically though a turbulent boundary layer. The DCBL most closely resembles the daytime boundary layer that would occur over a flat, arid region, for example a large, dry lake bed. We study this boundary layer because it avoids many complexities associated with phase changes of water, while at the same time being a fully turbulent, three-dimensional boundary layer with essentially direct analogs in nature.

Two movies of a PyCLES simulation of a DCBL are shown here. This simulation is performed at 5m isotropic resolution. The first shows a vertical cross section through the simulated boundary layer. The variable depicted is a diagnostic tracer that is injected at the surface and undergoes exponential (radioactive) decay, and is used by Colleen Kaul to investigate coherent plumes in the boundary layer that are responsible for a large part of the vertical turbulent transport. The simulation is an initial value problem, and the movie shows the growth of turbulent structures from an initially quiescent state with small random perturbations to a fully developed dry convective boundary layer.

The second movie shows the time evolution of the specific entropy on a horizontal surface at a height of roughly 25% of the boundary layer depth. If the movie is viewed in high definition and in full screen mode, towards the end of the move intensely rotating vortices appear. The vortices are dust devils that are resolved by the LES.

More of the the technical details of the simulations are given at Vimeo.


Stratocumulus are Earth's predominant boundary layer cloud type (Wood, 2012). At any single time they cover a significant fraction of the planet's oceans, where they strongly reflect solar radiation relative to the underlying ocean and only modestly reduce the outgoing thermal radiation. Thus reductions in the area coverage of stratocumulus clouds with climate change could constitute a strong positive climate feedback.

Like the DCBL, the primary motive force in stratocumulus boundary layers is buoyancy. But unlike the DCBL, the buoyancy comes not just from surface heat fluxes but also from strong cloud-top radiative cooling. The dynamics of stratocumulus clouds are highly non-linear. For example, the amount of cloud top radiative cooling, which determines the strength of boundary layer turbulence, depends strongly on cloud properties. In turn, the cloud properties are largely determined by the availability of water vapor, which is determined by the strength of the boundary layer turbulence. These strong non-linearities make high fidelity simulation of stratocumulus challenging (e.g. Stevens et al., 2005)

The video on the left is a visualization of stratocumulus clouds simulated at 5 meter resolution using PyCLES, and shows the development of the clouds from an initially uniform state. The view is from the top as if the viewer were in a helicopter looking down. The liquid water path is the rendered variable as it is closely related to the radiative processes that determine how we see clouds with the eye. The clouds grow from instabilities in the cloud layer that arise from non-local effects of velocity fluctuations. Notice how the the scales of the clouds grow in time but with striking self-similarity. More of the the technical details of the simulation are given at Vimeo.

Shallow Cumulus

Shallow cumulus clouds extend over wide swaths of the Earth's tropical and subtropical oceans. They play an important role in moistening the lower free troposphere and conditioning the atmosphere for deeper convection. Shallow cumulus form atop a well-mixed layer, not unlike the dry convective boundary shown above, with the clouds forming the saturated extension of the buoyancy-driven, dry convective plumes within the mixed layer.

The image at right shows a volume rendering of non-precipitating shallow cumulus clouds. The colored contours at the surface show variations in entropy, which is closely rated to the surface buoyancy. Below that is a movie of precipitating shallow convection. Here as before the surface contours show entropy and the blue coloration is falling rain.

Shallow cumulus set in stone

In collaboration with artist Karen LaMonte, data from an LES produced by PyCLES has been used to render a shallow cumulus cloud three-dimensionally in marble. This work, called Cumulus, has been on display during the 2017 Venice Biennale. The simulated cloud upon which the Cumulus is based is shown at right. To render the cloud in marble, we provided the artist with a triangulation of the cloud's surface. The final sculpture, which was carved using robots, stands 7ft tall and weighs about 2.5 tons, is shown below at right.

You can read more about this collaboration in the Caltech magazine here, and more pictures of the sculpture are available on Karen LaMonte's website here.