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Cloud
Kwang Hee Ko
September, 27, 2012
This material has been prepared by Y. W. Seo.
Introduction
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Clouds are a ubiquitous feature of our world
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Provide a fascinating dynamic backdrop, creating
an endless array of formations and patterns.
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Integral factor in the behavior of Earth’s weather
systems
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Important area of study for meteorologists,
physicists, and even artists
Introduction

Clouds play an important role when making
images for flight simulators or outdoor scenes.

Clouds’ color and shapes change depending on the
position of the sun and the observer.
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The density distribution of clouds should be defined
in three-dimensional space to create realistic
images.
Introduction

The complexity of cloud formation, dynamics,
and light interaction makes cloud simulation
and rendering difficult in real time.

Ideally, simulated clouds would grow and disperse
as real clouds do.
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Simulated clouds should be realistically illuminated
by direct sunlight, internal scattering, and
reflections.
Cloud Dynamics Simulation

Clouds are the visible manifestation of
complex and invisible atmospheric processes.
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Fluid dynamics governs the motion of the air, and
as a result, of clouds.
Clouds are composed of small particles of liquid
water carried by currents in the air.
The balance of evaporation and condensation is
called water continuity.
The convective currents are caused by
temperature variations in the atmosphere, and can
be described using thermodynamics.
Cloud Dynamics Simulation

Fluid dynamics, thermodynamics, and water
continuity are the major processes.

The physics of clouds are complex.

By breaking them down into simple components,
accurate models are achievable.
Cloud Radiometry Simulation
Clouds absorb very little light energy.
 Instead, each water droplet reflects, or scatters
nearly all incident light.
 Clouds are composed of millions of these tiny
water droplets.
 The light exiting the cloud reaches your eyes,
and is therefore responsible for the cloud’s
appearance.

Cloud Radiometry Simulation
Accurate generation of images of clouds
requires simulation of the multiple light
scattering.
 The complexity of the scattering makes
exhaustive simulation impossible .
 Instead, approximations must be used to
reduce the cost of the simulation.

Efficient Cloud Rendering

After efficiently computing the dynamics and
illumination of clouds, there remains the task
of generating a cloud image.
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A volumetric representation must be used to
capture the variations in density within the cloud.
Rendering such volumetric models requires much
computation at each pixel of the image.
The rendering computation can result in excessive
rendering times for each frame.
Efficient Cloud Rendering

The concept of dynamically-generated
impostors
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A dynamically-generated impostor is an image of
an object.
The image is generated at a given viewpoint, and
then rendered in place of the object.
The result is that the cost of rendering the image
is spread over many fames.
Useful for accelerating cloud rendering
Physically-based Simulation on
GPUs

Using the GPU for simulation does more than just free
the CPU for other computations.
 It results in an overall faster simulation.

GPU implementations of a variety of physically-based
simulations outperform implementations.

General-purpose computation on GPUs has recently
become an active research area in computer graphics.
Cloud Dynamics

The dynamics of cloud formation, growth,
motion and dissipation are complex.

To understand the dynamics is important.

To choose good approximations allows
efficient implementation.
The Equations of Motion
Assume that air in the atmosphere is and
incompressible, homogeneous fluid.
 Incompressible if the volume of any sub-region
of the fluid is constant over time.
 Homogeneous if its density is constant in space.
 These assumptions do not decrease the
applicability of the resulting mathematics to the
simulation of clouds.

The Equations of Motion

The motion of air in the atmosphere can be
described by the incompressible Euler
equations of fluid motion
where ρ is the density of the fluid. B is
buoyant acceleration, and f is acceleration
due to other forces.
Parcels and Potential
Temperature
A conceptual tool used in the study of
atmospheric dynamics is the air parcel.
 The parcel approximation is useful in developing
the mathematics.
 When a parcel changes altitude without a
change in heat, it is said to move adiabatically.
 We can account for adiabatic changes of
temperature.

Parcels and Potential
Temperature

The potential temperature, Θ, of a parcel of
air can be defined as the final temperature
∏ is called the Exner function, Rd is the gas
constant.
Buoyant Force
Change in the density of a parcel of air relative
to its surroundings result in a buoyant force on
the parcel.
 If the parcel’s density is less than the
surrounding air, this force will be upward.
 If the parcel’s density is greater, the buoyant
force will be downward.
 The density of an ideal gas is related to its
temperature and pressure.
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Buoyant Force
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A common simplification in cloud modeling is
to regard the effects of local pressure
changes on density as negligible
where g is the acceleration due to gravity and
qH is the mass mixing ratio of hydrometeors.
Environmental Lapse Rate
The Earth’s atmosphere is in static equilibrium.
 The hydrostatic balance of the opposing
forces of gravity and air pressure results in an
exponential decrease of pressure with altitude

Here, z is altitude, and P0 and T0 are the
pressure and temperature at the base altitude.
Saturation Mixing Ratio
Cloud water continuously changes from liquid
to vapor and vice versa.
 The water vapor mixing ratio at saturation is
called the saturation mixing ratio, denoted by
qVS(T,p)

with T in Celsius and p in Pa.
Environmental Lapse Rate
The water mixing ratios at a given location are
affected both by advection and by phase
changes.
 The rates of evaporation and condensation
must be balanced, resulting in the water
continuity equation
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Where C is the rate of condensation.
Thermodynamic Equation

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The potential temperature of saturated air cannot be
assumed to be constant.
If latent heating and cooling due to condensation and
evaporation are the only non-adiabatic heat sources,
then the first law of thermodynamics results in
where L is the latent heat of vaporization of water.
Vorticity Confinement

Vorticity confinement works by first
computing the vorticity
, from
which a normalized vorticity vector field
is computed.
 From these vectors we can compute a force
that can be used to replace dissipated
vorticity back in
Vorticity Concept


In fluid dynamics, the vorticity is a vector that
describes the local spinning motion of a fluid near
some point, as would be seen by an observer
located at that point and traveling along with the fluid.
One way to visualize vorticity is this: consider a fluid
flowing. Imagine that some tiny part of the fluid is
instantaneously rendered solid, and the rest of the
flow removed. If that tiny new solid particle would be
rotating, rather than just moving with the flow, then
there is vorticity in the flow.
From wikipedia
Solving the Equations
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Fluid Flow
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Water Continuity
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Thermodynamics
Solving the Equations
(Fluid Flow)
The cloud model is based on the equations of
fluid flow.
 The simulator is built on top of a standard fluid
simulator.
 Solve the equations of motion using the stable
two step technique described .
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First, use the semi-Lagrangian advection technique
Second, the intermediate field is made.
incompressible using a projection method based on
the Helmholtz-Hodge decomposition .
Solving the Equations
(Fluid Flow)
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The projection is performed by solving for the
pressure using the Poisson equation
with pure Neumann boundary conditions

Subtract the pressure gradient from u’
Solving the Equations
(Water Continuity)
The changes in qV and qC are governed by
advection of the quantities as well as by the
amount of condensation and evaporation.
 Solve equations in two steps
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First, advect each using the semi-Lagrangian
technique mentioned.
Second, at each cell, compute the new mixing ratio
as follows
Solving the Equations
(Thermodynamics)
Potential temperature is advected by the
velocity field.
 The temperature increases by an amount
proportional to the amount of condensation,
and is able to update it as follows.
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Implementation
Solve the equations on a grid of voxels.
 Use a staggered grid discretization of the
velocity and pressure equation.
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This means that pressure, temperature, and water
content are defined at the center of voxels.
This method reduces numerical dissipation.
It prevents possible pressure oscillations that can
arise with collocated grids.
Interactive Applications
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Cloud simulation is a very computationally
intensive process.
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It is usually done offline.
Simulations of phenomena such as clouds
have the potential to provide rich dynamic
content for interactive applications.
Interactive Applications
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Integrate the cloud simulation into SkyWorks
cloud rendering engine.
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“Simulation of Cloud Dynamics on Graphics
Hardware”
SkyWorks was designed to render scenes full of
static cloud very fast.
It recomputes the illumination of the clouds, and
then uses this illumination to render the clouds at
runtime.
Cloud Rendering
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Convert the simulation’s current cloud water
texture into a true 3D texture, which is then
used to render the cloud for multiple frames.
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Rendering directly from the flat 3D texture is too
expensive.
The conversion is overall much faster.
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A simulation time step dose not complete every
frame.
The generation of the 3D texture is included in the
simulation amortization.
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It doesn’t affect our interactive frame rates.
Cloud Illumination

To create realistic images of clouds, we must
account for the complex nature of their
interaction with light.
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Light has been scattered many times by the tiny
water droplets in the cloud.
This is what gives clouds their soft, diffuse
appearance.
A full simulation of multiple scattering requires the
solution of a double-integral equation.
Cloud Illumination
A full simulation of multiple scattering
requires the solution of a double-integral
equation.
 Cloud water droplets scatter most strongly in
the direction of travel of the incident light, or
forward direction.
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Example