modeling jupiter's atmospheric dynamics - EPIC Atmospheric Model ...

MODELING JUPITER’S ATMOSPHERIC DYNAMICS
WITH AN ACTIVE HYDROLOGICAL CYCLE
By
Csaba Palotai
M.S., Technical University of Budapest, Hungary 2001
A Dissertation
Submitted to the Faculty of the
Graduate School of the University of Louisville
in Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
Department of Mechanical Engineering
University of Louisville
Louisville, Kentucky
August 2006

MODELING JUPITER’S ATMOSPHERIC DYNAMICS
WITH AN ACTIVE HYDROLOGICAL CYCLE
By
Csaba Palotai
M.S., Technical University of Budapest, Hungary 2001
A Dissertation Approved On
Date
by the following Dissertation Committee:
Dissertation Director
ii

ACKNOWLEDGEMENTS
I foremost wish to express gratitude to my parents and grandparents. Sometimes,
as teens or young adults we don’t realize how much people sacrifice for us, and
looking back later we recognize all the great things they have done for us, even if it
was hard for them or they had to give up something for us. They were also letting
me go for this amazing journey in my life far away from them, which must have been
the toughest thing for them to do. I will do my utmost to earn all this.
I would like to thank to my advisor, Professor Tim Dowling for his help, guidance
and constructive criticism, through thick and thin. He was the source of all the
planetary science that I know today. He also helped through a continuous revision of
this dissertation, correcting all the 35,945 grammar errors that I have made. I appreciate
the helpful comments of Adam Showman, Ray LeBeau, Glenn Orton, Gerard
Williger and Aaron Heirrnstein, they were very generous with sharing their time and
expertise. I express my appreciation to NASA, supporting this research through their
EPSCoR, Planetary Atmospheres and Outer Planet Research Programs.
I would like to thank the members of my dissertation committee, Ellen Brehob,
Geoffrey Cobourn, John Kielkopf, and Keith Sharp for their service and support. I
wish to express my appreciation to Dr. Kielkopf for the LaTeX dissertation template
that saved me a great deal of time. Several friends have been helping me along the
way: Tanya, Grace, Harrison, Móni, Tomi, Marjorie, thank you for listening to (and
ignoring) all my whinings and encouraging me when I needed it.
I would like to
iii

acknowledge all my great teachers throughout the years, I have been very fortunate
because there were so many of them. Thank you for all your lessons about life.
And most of all, I would like to thank my family. I have been working for
them, but they had to sacrifice a lot too. Benita, thank you for all your patience and
for accepting me for who I am. You are my Lobstress. Junior, I am so happy that
you have arrived. You are so small yet, but you already have the power to fill our
hearts with happiness. I am looking forward to all the joy and great times that we
will share. And Ben, your energy and love have been so inspiring. Every day is an
adventure with you and I have been having the time of my life. You make me want
to be a better parent and a better person every day. I’m eager to find out where the
next steps in our journey will take us.
iv

ABSTRACT
MODELING JUPITER’S ATMOSPHERIC DYNAMICS WITH AN ACTIVE
HYDROLOGICAL CYCLE
Csaba Palotai
June 1, 2006
An active hydrological cycle has been added to the EPIC general circulation
model (GCM) for planetary applications, with a special emphasis on Jupiter. Scientists
have suspected for decades that clouds, and in particular latent heating, strongly
influence Jupiter’s atmospheric dynamics and this research provides a tool to investigate
this phenomenon. Components of the model have been adapted for the planetary
setting from recently published Earth microphysics schemes.
The behavior of the cloud model is investigated in two steps. First, we explore
in detail the runtime properties of a nominal model, and second, through sensitivity
tests we determine how the full microphysics and selected components of the scheme
affect the formation and evolution of clouds and precipitation.
Results from our
one-dimensional (vertical) simulations match expectations based on thermochemical
models about the vertical positioning of ammonia and water clouds, and the nature of
precipitation. Using meridional-plane (two-dimensional) simulations, we investigate
the latitudinal variation of clouds. We conclude that the the zonal-wind structure
vi

under the visible cloud deck strongly affects the position of the cloud bases.
We
describe in detail an equatorial storm system observed in our 2D simulations. We
also show that simplification of our microphysics scheme would improperly simulate
large scale weather phenomena on Jupiter.
We support future laboratory tests and in-situ measurements that would improve
the cloud parameterization scheme and would also add more constraints on the
global distribution of condensibles and on the zonal wind-structure. The complete
computer program resulting from this research can be downloaded as open-source
software from NASA’s Planetary Data System (PDS) Atmospheres node.
vii

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS
ABSTRACT
LIST OF TABLES
LIST OF FIGURES
iii
vi
xi
xii
CHAPTER
1 BACKGROUND AND MOTIVATION 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The EPIC Model . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Review of Previous Studies . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Published EPIC Simulations . . . . . . . . . . . . . . . . 6
1.3.2 Earth Models . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3 Planetary Atmospheric Models . . . . . . . . . . . . . . . 9
1.4 Logistics for Experiments . . . . . . . . . . . . . . . . . . . . . 10
1.4.1 Simulation Tools . . . . . . . . . . . . . . . . . . . . . . 11
1.4.2 Hardware Tools . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.3 Analysis Tools . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 Scope of Research . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 MICROPHYSICS SCHEME 14
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
viii

2.2 Moisture Equations . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Number Concentration of Ice Crystals . . . . . . . . . . . . . . 17
2.4 Precipitation Size Distribution . . . . . . . . . . . . . . . . . . . 22
2.5 Fall Speed of Particles . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.1 Raindrops . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.2 Terminal Velocity of Snow . . . . . . . . . . . . . . . . . 29
2.6 Microphysical Processes . . . . . . . . . . . . . . . . . . . . . . 33
2.6.1 Condensation of Vapor/Evaporation of Cloud Liquid (P COND ) 34
2.6.2 Initiation of Cloud Ice (P INIT ) . . . . . . . . . . . . . . . 36
2.6.3 Deposition of Vapor/Sublimation of Cloud Ice (P DEPI ) . 38
2.6.4 Melting of Cloud Ice/Freezing of Cloud Liquid and
Melting of Snow/Freezing of Rain (P SMLTI ) . . . . . . . 40
2.6.5 Autoconversion of Cloud Liquid to Rain (P RAUT ) . . . . 41
2.6.6 Collection of Cloud Liquid by Rain (P RACW ) . . . . . . 41
2.6.7 Deposition of Vapor on Rain/Evaporation of Rain (P REVP ) 42
2.6.8 Autoconversion of Cloud Ice to Snow (P SAUT ) . . . . . . 43
2.6.9 Collection of Cloud Ice by Snow (P SACI ) . . . . . . . . . 44
2.6.10 Deposition of Vapor on Snow/Sublimation of Snow (P SEVP ) 44
2.7 Code Implementation . . . . . . . . . . . . . . . . . . . . . . . 45
2.7.1 Positivity adjustment . . . . . . . . . . . . . . . . . . . . 45
2.7.2 Sequence of Process Transfers . . . . . . . . . . . . . . . 46
3 1D SIMULATIONS 48
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Nominal Model Description . . . . . . . . . . . . . . . . . . . . 49
ix

3.2.1 Vertical Structure of Model Environment . . . . . . . . . 49
3.2.2 Vertical Structure of Clouds . . . . . . . . . . . . . . . . 51
3.3 Results of 1D Simulations . . . . . . . . . . . . . . . . . . . . . 54
3.3.1 Sensitivity to abundance . . . . . . . . . . . . . . . . . . 57
3.3.2 Static Stability of the Atmosphere . . . . . . . . . . . . . 61
4 MERIDIONAL PLANE SIMULATIONS 65
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.1 Vertical Structure of Model Environment . . . . . . . . . 66
4.2.2 Vertical Structure of Condensibles . . . . . . . . . . . . . 68
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3.1 Equatorial Storm System . . . . . . . . . . . . . . . . . . 71
4.3.2 Sensitivity tests . . . . . . . . . . . . . . . . . . . . . . . 77
5 CONCLUSIONS 85
REFERENCES 89
CURRICULUM VITAE 99
x

LIST OF TABLES
TABLE
Page
2.1 Saturation vapor pressure coefficients. . . . . . . . . . . . . . . . . . . 18
2.2 Power law coefficients used in the EPIC microphysics code to calculate
N ice for water and ammonia (2.6–2.11). . . . . . . . . . . . . . . . . . 23
3.1 Microphysical components turned on (+) and off (-) in the Brunt-
Väisälä test runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
xi

LIST OF FIGURES
FIGURE
Page
1.1 Jupiter’s Great Red Spot and its turbulent zone to the west. . . . . . 2
1.2 A jovian storm, color-coded to highlight structure. . . . . . . . . . . . 3
1.3 Comparison of visual image of methane clouds on Neptune with EPIC
simulations using a diagnostic (passive) cloud scheme. . . . . . . . . . 7
2.1 Correlation between the Reynolds- and Best-numbers in the Bestnumber
regime of 10 3 to 10 5 . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Comparison of terminal velocities of raindrops and snow. . . . . . . . 30
2.3 Schematic diagram of the eleven phase-change processes included in
the five-phase EPIC microphysics model. . . . . . . . . . . . . . . . . 35
2.4 Comparison of initialized ice mass calculated from (2.5) for water on
Earth (solid line), and from (2.40) for ammonia (dash-dot line) and
water (dotted line) on Jupiter. . . . . . . . . . . . . . . . . . . . . . . 38
3.1 Basic state temperature and mean zonal wind profiles used in the 1D
simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2 Models of the vertical profiles of ammonia and water volume mixing
ratios used in this study. . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3 The time evolution of water and ammonia clouds and precipitation in
the nominal 1D model of Jupiter’s atmosphere. . . . . . . . . . . . . 56
3.4 Cloud and precipitation evolution using various initial deep abundance
values, with initial supersaturation set to 10%. . . . . . . . . . . . . 59
xii

3.5 Sensitivity of cloud and precipitation evolution to various initial supersaturation
values, with the deep abundance values set to the nominal
case of 4.0 and 1.0 times solar for ammonia and water, respectively. . 60
3.6 Brunt-Väisälä frequency of the initial state. . . . . . . . . . . . . . . 62
3.7 Brunt-Väisälä frequency at 2 hours into the simulation with selected
microphysics components turned off. . . . . . . . . . . . . . . . . . . 64
4.1 Initial state temperature and mean zonal wind profiles used in the 2D
simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Vertical structure of clouds in the nominal 2D model. . . . . . . . . . 69
4.3 emporal evolution of the latitudinal variation of cloud density for ammonia
(top) and water (bottom), sampled at the 750 mbar and the
4000 mbar pressure levels, respectively. . . . . . . . . . . . . . . . . . 72
4.4 Time evolution of the equatorial storm in the nominal model. . . . . 73
4.5 40 day difference of zonal mean temperature compared to the initial
state of the active simulation. . . . . . . . . . . . . . . . . . . . . . . 74
4.6 Close up images of the equatorial storm. Panels on the left show clouds
and wind velocity vectors, panels on the right show clouds and precipitation.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.7 Zonal cloud structure with modified initial saturation ratio values. . . 78
4.8 Cloud and zonal wind structure at 30 days into the active simulation
using S = 1.00 initial saturation ratio. . . . . . . . . . . . . . . . . . . 80
4.9 Sensitivity test in the domain of -20 ◦ to 60 ◦ latitude. . . . . . . . . . 80
4.10 Test results with reduced abundance initial condition . . . . . . . . . 81
4.11 Snapshots from a simulation, where water was the only condensible
species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
xiii

4.12 Cloud structure in model runs with selected microphysical components
turned off, at 40 days into the active simulation. . . . . . . . . . . . 83
xiv

CHAPTER 1
BACKGROUND AND MOTIVATION
1.1 Motivation
The well-known features of Jupiter’s atmosphere, the Great Red Spot (GRS,
Fig. 1.1), and the dark and bright bands called belts and zones, have been observed
for several centuries, yet the energy sources that shape the active meteorology on
the planet, forming and maintaining its long lived vortices and jets, are not well understood.
Recent results from the Galileo spacecraft answer several questions about
Jupiter’s energetics, but leave many others unanswered. One of the most promising
candidates for driving the motions is the internal heat source (Gierasch et al. 2000,
Seiff 2000). Observations of lightning (Little et al. 1999) imply precipitation in convective
storms, thus these observations indicate moist convection on Jupiter. These
storms (Fig. 1.2) resemble clusters of thunderstorm cells on Earth called mesoscale
convective complexes (MCCs).
On our planet, the atmosphere and the surface are strongly influenced by the
clouds and precipitation through phenomena like their transport of heat, moisture,
and aerosols, the latent heat from phase changes of water, the alteration of the atmospheric
and surface radiative fluxes, and their effect on surface hydrology. For a more
accurate terrestrial weather and climate simulation one needs to take these effects
into account when using atmospheric models. The software component that handles
1

Figure 1.1. Jupiter’s Great Red Spot and its turbulent zone to the west. The
erupting white clouds northwest of the GRS occur relatively often in this region, as
was shown by Galileo and other data (Image:NASA/Voyager1)
2

Figure 1.2. A jovian storm, color-coded to highlight structure. Light areas indicate
high haze. Deep red in the lower right shows storm clouds. Researchers suspect the
clouds result from condensed water driven by convection. The schematic at right is
a cross-section of the storm showing the cloud structure. This is an example of the
phenomena we wish to begin to capture with the cloud microphysics scheme developed
here. (Image: P. Gierasch/ c○Nature)
the formation and evolution of clouds is usually referred to as the “cloud microphysics
model”.
General circulation models (GCMs) make it possible to simulate an atmosphere
realistically without using any artificial boundary conditions.
GCMs allow
one to investigate idealized or localized processes to improve our knowledge about
the underlying dynamics. They serve as a testing tool for verifying new ideas, also
to make clear what observational input is most sensitive to a particular process. The
GCM developed at University of Louisville is called the Explicit Planetary Isentropic
Coordinate (EPIC) atmospheric model (Dowling et al. 1998, Dowling et al. 2006).
It is specifically designed for comparative-planetology studies, with the potential to
simulate all the dozen or so atmospheres in the Solar System with a single model. It is
the leading software for investigating the atmospheric dynamics and thermodynamics
of gas-giant planets.
One major component missing from the EPIC simulations thus far is the effect
3

of cloud microphysical processes. There has been one EPIC paper involving clouds to
date, a study of methane cloud formation on Neptune (Stratman et al. 2001). They
diagnosed clouds when the relative humidity of methane reached 100% or greater,
assumed non-precipitating clouds, and neglected the effects of latent heating. This
approach can be justified for certain applications when the abundance of the condensible
species is low or the latent heat of phase change is low. In other applications
(e.g. water clouds on Earth or on Jupiter) latent heating plays a significant role and
consequently needs to be accounted for (Ingersoll et al. 2004). The objective of this
research is the addition of a cloud microphysics scheme to the EPIC atmospheric
model, which allows for the simulation of the full hydrological cycle. While the particular
emphasis is on Jupiter, the cloud microphysics scheme is flexible and can be
easily adapted to other planetary atmospheres.
1.2 The EPIC Model
The governing equations of the EPIC model are the hydrostatic primitive equations
in spherical coordinates with a hybrid vertical coordinate, similar to those used
by Konor and Arakawa (1997, hereafter KA97). This vertical coordinate, ζ, uses the
advantages of an isentropic θ-coordinate near the top of the model that transitions
smoothly into a terrain following pressure-based coordinate, σ (Dowling et al. 2006).
In the case of gas giant planets, which do not have solid lower boundaries but have
a nearly constant θ interior, the transition is into a pressure coordinate that allows
one to model the deeper atmosphere. The material time derivative with the hybrid
coordinate can be expressed as
( )
D ∂
Dt = + v · ∇ ζ +
∂t
˙ζ ∂ ∂ζ , (1.1)
ζ
4

where ˙ζ ≡ Dζ/Dt, ∇ ζ is the horizontal gradient on constant ζ surfaces, and v is the
horizontal velocity on the ζ surfaces. One can introduce the variable h, defined by
h ≡ − 1 g
∂p
∂ζ , (1.2)
which for a shallow (hydrostatic) atmosphere plays the role of density in the (x, y, ζ)
space, where p is pressure and g is the gravitational acceleration (assumed constant).
In the case of a dry atmosphere (i.e. no condensible species, only a homogeneous gas
mixture) using the hybrid density h, the continuity equation may be written as
( ) ∂h
+ ∇ ζ · (hv) + ∂ ∂t
∂ζ (h ˙ζ) = SHS h + SZF h , (1.3)
ζ
where SHS h and SZF h represent the rates of change due to the horizontal eight order
smoothing (hyperviscosity) and the high latitude zonal filtering, respectively (Dowling
et al. 2006). In this coordinate system the hydrostatic equation may be written in
the form of
∂Φ
∂ζ
= αgh, (1.4)
where α is the specific volume, and Φ is the geopotential, defined by
where z is the geometric height.
is given by
Φ ≡
∫ z
0
gdz, (1.5)
We assume the model atmosphere to be an ideal gas, thus the equation of state
α = RT
p , (1.6)
where R is the gas constant and T is the temperature. Dowling et al. (1998) define
the mean potential temperature, θ, for Jupiter taking into account for the ortho-para
hydrogen mixture. The 1st Law of thermodynamics can thus be written as
( )
Dθ ∂θ
Dt = ∂θ
+ v · ∇ ζ θ + ˙ζ
∂t
∂ζ = ˙Q
Π + SHS θ + SZF θ + STB θ , (1.7)
ζ
5

where ˙Q is the heating rate per unit mass, STB θ represents the rate of change of θ
due to the turbulent diffusion, and Π is the Exner function, defined by
Π = c pT
θ , (1.8)
where c p is the specific heat at constant pressure. The horizontal momentum equation
may be written as
( )
Dv ∂v
Dt = + v · ∇ ζ v +
∂t
ζ
˙ζ
∂v
∂ζ = −(∇ pΦ) − fk × v + F, (1.9)
where ∇ p is the horizontal gradient on constant pressure surfaces, F is the friction
force, k is the vertical unit vector, f = 2Ω sin λ is the Coriolis parameter, Ω is the
planet’s angular velocity, and λ is the latitude. After combining equations similarly
to KA97, we can express the horizontal pressure gradient force as
−∇ p Φ = −∇ ζ M + Π∇ ζ θ, (1.10)
where M is the Montgomery potential, defined by
M ≡ c p T + Φ. (1.11)
1.3 Review of Previous Studies
1.3.1 Published EPIC Simulations
There are several previously published results using the EPIC model. For example,
simulations of the impact of Comet Shoemaker-Levy 9 (SL9) on Jupiter that
successfully predicted that there would be no long-lasting vortices spawned from that
event (Harrington et al.
1994), followed by simulations of time-dependent, threedimensional
vortices under conditions similar to those on Neptune that showed relation
between the meridional drift of the vortices and the background absolute vorticity
6

Figure 1.3. Comparison of visual image of methane clouds on Neptune with EPIC
simulations using a diagnostic (passive) cloud scheme. Isosurfaces of 100% relative
humidity are white and of eddy relative vorticity of 8.0 × 10 −7 s −1 are blue. The
bottom row is a side view looking north (Image: NASA)
(LeBeau and Dowling 1998). The latter study also investigated oscillations in aspect
ratio and orientation angle, and tail formation, and motivated a three-dimensional
simulation of the bright companion clouds associated with Neptune’s Great Dark
Spot that predicted methane clouds at or just below the planet’s tropopause using a
diagnostic cloud scheme (Stratman et al. 2001, Figure 1.3). In addition, Showman
and Dowling (2000) modeled Jupiter’s 5µm hot spots to simulate the dryness and low
cloudiness measured by the Galileo probe, and recently, Garcia-Melendo et al. (2005)
tested various vertical temperature and wind profiles in order to reproduce observed
disturbances in Jupiter’s highest velocity jet at 24 ◦ N latitude. None of the published
EPIC simulations to date include an active hydrological cycle, which is the main new
functionality introduced in this work.
7

1.3.2 Earth Models
Recently, terrestrial-atmosphere GCM modelers have paid more and more attention
to the development of cloud parameterizations and the inclusion of interactions
between the hydrological cycle, cloudiness, and radiation in terms of cloud microphysical
processes and radiative properties. Modeling clouds in large-scale models
is a complex problem. There are several different cloud types, and their precipitation
content, latent heating, optical depth, and some of their microphysical processes vary
from one type to another. They are formed, maintained and dissipated by several different
physical processes, such as convection, large-scale ascent or descent, small-scale
turbulence, and cloud microphysical processes leading to the generation of precipitation
of different forms. Moreover, different cloud types may coexist within the volume
represented by a single GCM scale grid-cell.
Fowler et al.
(1996) gives an overview on how clouds are typically represented
in large-scale models. Early schemes used a diagnostic approach where the
clouds were predicted based on a prescribed threshold value of relative humidity for
saturation, and cloud fraction and optical properties were diagnosed from selected
large-scale variables, such as relative humidity, rate of precipitation, temperature,
etc. A diagnostic, saturation adjustment cloud scheme is a component of the earlier
EPIC version, but its limitations for modeling jovian meteorology were experienced
by Stratman et al. (2001).
Some other prognostic schemes employ a “double-moment” parameterization
in which both number concentration of particles and mass mixing ratio are predicted
at each grid location (e.g. Ferrier 1994). This method allows one to simulate the
evolution of the hydrometeor size spectra more realistically. However, at this point
we have ruled out using this type of modeling because of the lack of knowledge of the
8

number concentration of the various species on Jupiter.
A more widely used approach for representing clouds and precipitation in
GCMs is a bulk parameterization scheme where the number concentrations are diagnosed
instead of being predicted. Nowadays, almost all terrestrial models use prognostic
equations for the various forms of water substance (vapor, cloud liquid, cloud
ice, rain, snow, graupel, etc.), which are coupled together by the cloud microphysics.
Most of the microphysical processes have smaller characteristic length scales than a
typical grid length used in large-scale simulations, and many of the processes are not
completely understood. For these reasons, GCMs and mesoscale models use parameterizations
for most of the cloud processes rather than explicitly resolving them.
1.3.3 Planetary Atmospheric Models
Many numerical cloud models exist for solid-surface planets (e.g.
James et
al. 1997, Forget et al. 1998, Richardson et al. 2002), and most of them use a
simple cloud scheme or adopt a terrestrial scheme with minor modifications. Some
of these atmospheres (e.g. Mars) tend not to precipitate, which results in a major
simplification in the hydrological cycle modeling.
There are some published cloud models for gas-giant planets as well.
The
absence of a solid surface and the lack of in situ measurements make it challenging
to build an accurate model, and also make it necessary to use assumptions and neglect
potentially important effects, like the feedback from the atmospheric circulation.
Early jovian simulations use equilibrium cloud condensation models to study the vertical
structure of clouds or chemical composition, predicting three major cloud layers
for the jovian troposphere formed by particles of NH 3 , NH 4 SH, and H 2 O (Lewis 1969,
Weidenschilling and Lewis 1973). Carlson et al. (1988) estimated the timescales of
9

microphysical processes on Jupiter using a model with no spatial dimensions. Stoker
(1986) simulated jovian equatorial plumes and cumulus cloud formation with a onedimensional
diagnostic model. Her investigation regarding the importance of water
and ammonia condensation produced results suggesting strong convection and high
vertical velocities that extend several scale heights from the water cloud base to above
the top of ammonia clouds. Lunine and Hunten (1987) applied the same model for
narrow, moist convective plumes to simulate the apparent depletion of water vapor
in the 5-µm observations in the lower troposphere without invoking a depletion of
oxygen from solar abundance throughout the interior.
Del Genio and McGratten
(1990) used a GCM cumulus parameterization scheme in one dimension to study
the effects of moist convection on Jupiter’s large scale atmospheric structure. Some
other simulations included detailed microphysics and an axisymmetric cloud model
to study jovian thunderclouds (Yair et al. 1995) or a three-dimensional model with
simplified microphysics to investigate the formation and evolution of moist convective
storms (Hueso and Sánchez-Lavega 2001). These are models on the regional scale
and exclude the interaction with planetary size jets and vortices. There is a need for
three-dimensional GCMs for gas giant planets that includes cloud microphysics to
expand our knowledge on their atmospheres.
1.4 Logistics for Experiments
Here we mention some technical details about the software and hardware tools
available for our project, and briefly describe techniques used for data visualization
and analysis.
10

1.4.1 Simulation Tools
There are some major upgrades for the current EPIC 4.0 version that help us
with this research. The new hybrid vertical coordinate system made it possible to
model clouds in the deeper atmosphere, such as the water clouds on Jupiter with a
cloud base at around 5 bars. Separate continuity equations are invoked for each phase
of each species, with the possibility of turning any species and phases on and off, or
switching the microphysics (i.e. the interaction between the phases) on and off, as
needed. This tool can help to simulate the effect of latent heating on the dynamics,
for example. A species variable structure has been introduced that contains physical
constants and functions for each species, such as the triple-point temperature and
pressure, saturation vapor pressure, enthaply change due to phase change, coefficients
in the power-law form of the terminal velocity, etc.
1.4.2 Hardware Tools
The EPIC model uses the Message Passing Interface (MPI) standard, which
enables the user to run the code on parallel computers, in order to be able to solve all
these equations on a sufficiently fine mesh. For our project we built a dedicated 40-
node parallel computer with employing a Flat Neighborhood Network (FNN) called
the Comparative Planetology Linux Engine, COMPLINE. The server machines use
the cAos Linux operational system and the whole cluster gives a 33.9 Gflop peak
performance, enabling one to run full-globe climate simulations in a reasonable time.
For example, a 30-day simulation, using 20 layers and a 128x256 grid, including two
species with all five phases and active microphysics runs for approximately 24 hrs
using 8 computing nodes.
11

1.4.3 Analysis Tools
Several applications have been used for analyzing the EPIC computer code
and the output data. For runtime analysis, including memory corruption detection,
memory leak detection, cache-miss and performance profiling, we used PurifyPlus,
Valgrind and Cachegrind on the Linux servers, which helped to write faster and more
reliable codes. For data analysis and visualization, we used Macintosh workstations
with IDL 6.0 (Interactive Data Language), Kaleidagraph 3.6, Microsoft Excel and
various Adobe applications for plotting and animation.
1.5 Scope of Research
We have researched several possibilities for representing the clouds and microphysical
processes in the EPIC model and adapted the ones that we found relevant
for our purposes (summarized by Fig. 2.3). Chapter 2 describes the details of the
microphysics scheme used in the EPIC model. Since there is a lack of knowledge
about several physical properties of planetary atmospheres (Rossow 1978), we have
worked on simplifying and fine tuning the parameterization to be suitable for this
research. For example, ammonia clouds form on Jupiter but not on Earth — how
do they behave with regard to cloud fraction, particle size, or precipitation Are the
clouds and precipitation processes the same in Jupiter’s hydrogen atmosphere as in
Earth’s nitrogen atmosphere The answer is very likely no for both questions. If
not, how should one represent the processes to be suitable for the several different
atmospheres in the Solar System We used a simplified, one-dimensional version of
EPIC to test and to improve the parameterizations in the microphysics scheme, and
to carry out sensitivity tests for the most important unknown parameters. We present
12

esults from these simulations in Chapter 3.
Two-dimensional experiments (latitude-height) were used to formulate comparison
between dry and moist simulations, to estimate the position and thickness
of model water and ammonia clouds, and to determine the direction of vertical motion
relative to the zonal-wind (or belt-zone) structure. Findings from these models
are discussed in Chapter 4. Conclusions and a discussion of future work is given in
Chapter 5.
13

CHAPTER 2
MICROPHYSICS SCHEME
2.1 Overview
There are several different approaches to cloud microphysics in the meteorological
literature, and as we have worked to add this functionality to the EPIC model
we have had to make choices at every step, some with greater certainty than others.
Here, we document the most significant decisions in a manner that is intended
to make it easy to revisit them as necessary, which we expect to do periodically as
we gain experience with modeling clouds on gas giants. We started the process by
making a comprehensive survey of published cloud microphysics models, looking for
those that would be most flexible given the multi-planet nature of EPIC. We were
not overly concerned about memory requirements because of the large capacity of
modern computer clusters. So, for example, we tended to favor those models that
treat snow and rain separately rather than having them be combined into a single
‘precip’ variable, since then there are fewer artificial parameters to consider. On the
other hand, given that we do not yet have strong constraints on many aspects of
cloud microphysics such as the sizes and shapes of cloud particles or of snow flakes,
those models that average over a range of sizes were deemed most appropriate.
The net result of our literature searching has been the identification of a set of
papers that we used to guide our model’s development. Most of our code is adapted
14

from models that we found straightforward to accurately modify for planetary applications,
such as the cloud scheme from the National Centers for Environmental Prediction’s
Regional Spectral Model (NCEP RSM), which implements the algorithms of
Rutledge and Hobbs (1983, hereafter RH83) and Dudhia (1989, hereafter D89), and
is described by Hong et al. (2004, hereafter HDC04). We also found the microphysics
scheme of the Colorado State University General Circulation Model (CSU GCM) very
useful, as described by Fowler et al. (1996, hereafter FRR96).
Because the EPIC model is intended to be applied to many different planetary
systems, we need the flexibility of activating either zero, one, or more than one
condensible species. At initialization, the user chooses from a list which to activate,
and for each species chosen, a continuity equation is added to the model for each
corresponding phase. Our model contains five phases for each species: vapor, liquid
cloud, ice cloud, rain, and snow. We recognize that under many conditions cloud ice
and cloud liquid do not coexist, and the same holds for rain and snow. However,
treating them separately will allow for the straightforward modeling of mixed-phase
clouds in the future, which can play an important role on Earth and may prove to be
interesting on Jupiter, for example as a means of improving the modeling of chemical
processes or the prediction of lightning.
The rest of this chapter is organized as follows. The moist continuity equations
are introduced in Section 2.2. The topics of diagnosing cloud-particle number density
and size distribution are addressed in Sections 2.3 and 2.4, respectively. Terminal
velocity equations for precipitation, with particular emphasis on Jupiter, are derived
in Section 2.5. Microphysical interactions among the phases are described in Section
2.6, and some important technical details are included in Section 2.7.
15

2.2 Moisture Equations
We denote the mass mixing ratio as
q s,p = ρ s,p
ρ dry
= h s,p
h dry
, (2.1)
where ρ refers to conventional density in units of kg m −3 , h refers to the hybrid density
in units of kg m −2 K −1 , which is the density associated with the hybrid-coordinate volume
element, the subscripts “s, p” indicate the species and phase, and the subscript
“dry” denotes the dry-air value. In the core EPIC model, the prognostic variable
for moisture content is the hybrid density, h s,p = h dry q s,p , whereas in the cloud microphysics
subroutines we deal primarily with the mixing ratios themselves, q s,p . In
the following discussion, if the species is unambiguous we drop the species subscript
and refer simply to the vapor, liquid cloud, ice cloud, rain, and snow phases as q vap ,
q liq , q ice , q rain and q snow , respectively. Relative humidity is calculated according to the
definition of the World Meteorological Organization as the ratio of the vapor mass
mixing ratio, q vap , to the saturation mixing ratio, q sat (see Bohren and Albrecht 1998
for an interesting discussion concerning this definition)
r = q vap
q sat
=
q vap
ɛe sat /p dry
, (2.2)
where ɛ is the ratio of the dry air and vapor gas constants, p dry is the pressure of dry
air, e sat is the saturation vapor pressure, and the ideal-gas model is assumed. For each
species the saturation vapor pressures over liquid and ice are calculated assuming the
form
log 10 e sat = a + b T , (2.3)
where T is the temperature in degree Kelvin, and the coefficients a and b are taken
from Lodders and Fegley (1998) and listed in Table 2.1.
16

Inclusion of moisture in the model introduces new continuity equations
∂
∂t (h dryq s,p ) + ∇ ζ · (h dry q s,p v) + ∂ ∂ζ (h dryq s,p ˙ζ) = hdry Ŝ s,p , (2.4)
where Ŝs,p represents the net mixing-ratio source/sink rate for each phase of each
species. The heart of a cloud-microphysics scheme is the manner in which it evaluates
its Ŝs,p terms, so we include a detailed discussion of our calculations below.
With clouds come falling snow and rain, and there are various levels of approximation
one can use to account for the relative motion of precipitation. One issue is
geometric—the hybrid-coordinate surfaces are not geopotential surfaces and so there
is in general a horizontal component to the falling velocity of snow and rain. At this
point, we have not taken this effect into account; we argue that it is relatively small
and comparable to the errors in our estimation of the terminal fall speeds. We also
currently do not include any drag on the atmosphere from the falling precipitation,
but we plan to consider this in the future since it may have a small impact on simulations.
To account for the relative fall speed of precipitation, the hybrid vertical
velocity, ˙ζ, in (2.4) is modified by −|Vt |ρ/h, where |V t | is the terminal fall speed in
ms −1 , the calculation of which is described below, and ρ/h = dζ/dz is the ratio of
the full (moist air) densities. The other major change to the model caused by the
inclusion of moisture is the addition of latent heating and cooling to the heating rate,
˙Q, which is straightforward.
2.3 Number Concentration of Ice Crystals
We start with a description of the models and their parameters that are needed
to characterize the ice and liquid particles that make up clouds and precipitation,
given that they are much too small to be explicitly resolved by our GCM grid. In
17

TABLE 2.1
Saturation vapor pressure coefficients used in (2.3). The subscripts “ice” and “liq”
refer to whether the saturation is over solid or liquid material, as determined by the
temperature. Values are from Table 1.20 of Lodders and Fegley (1998), with 5 added
to the a columns to yield e sat in Pa instead of bar.
Species a ice b ice a liq b liq
H 2 O 12.610 -2681.18 11.079 -2261.1
NH 3 11.900 -1588.00 10.201 -1248.0
H 2 S 10.610 -1171.20 9.780 -1015.5
CH 4 9.283 -475.60 9.092 -459.8
CO 2 12.025 -1336.00 11.045 -1201.0
NH 4 SH 12.600 -2411.20 n/a n/a
O 3 n/a n/a 8.912 -632.4
N 2 9.798 -360.20 8.944 -305.0
this project we consider both water (H 2 O) and ammonia (NH 3 ), but for simplicity we
exclude H 2 S and its corresponding NH 4 SH cloud, which is thought to form between
Jupiter’s water and ammonia clouds, to avoid for now the additional complication
of active chemistry. Some characteristics of individual particles are sensitive to the
details, but if we average over an appropriate range of possibilities we can expect
to get useful estimates of the average behavior. As mentioned above, some models
employ separate continuity equations for mass and number, called double-moment
schemes, which gives them added flexibility in matching observations, but there are
numerical issues associated with advecting these separately that we would like to
avoid at this time, and so we follow papers such as HDC04 and treat number density
as a diagnostic variable, called the single-moment approach.
We begin with ice crystals, which make up the bulk of clouds in our Jupiter
model. Single-moment bulk microphysics models usually parameterize the number
18

concentration of ice particles, N ice , in terms of local thermodynamic variables. Many
of the existing schemes calculate it from cloud temperature, using the formula given
by Fletcher (1962)
N ice = 0.01e 0.6(T −T0) , (2.5)
where T is the temperature and T 0 is the freezing point. In the EPIC model we use
the triple-point temperature, T tp , in equations that call for a freezing point. For the
case of water on Earth, HDC04 note that (2.5) has no physical basis for temperatures
lower than −35 ◦ C and that it often overpredicts the number of small ice crystals in
the upper troposphere. This parameterization increases the number concentration by
an order of magnitude for about every 4 ◦ C temperature drop, so a common practice
is to put an upper bound on the calculated value, e.g. 10 9 m −3 is used in the MM5
model (Grell et al. 1994). On Earth, mid-latitude cirrus clouds often have cloud-top
temperatures colder than −50 ◦ C, and there is a similar problem on Jupiter, where
ammonia clouds typically have temperatures below the ammonia freezing point by
about 50–70 ◦ C. In addition, Galileo Orbiter observations (Gierasch et al. 2000) show
that the strongest convective water clouds on Jupiter can rise above the ammonia
cloud level where the temperature drops below the water freezing point by about
150 ◦ C. Thus, we cannot use (2.5) for either water or ammonia, because it would
produce too many ice crystals in these clouds, causing a bias in the microphysical
functions that use number concentration as a parameter. There are alternatives to
(2.5) that formulate N ice in terms of other variables in addition to temperature, such
as relative humidity or supersaturation (e.g. Rotstayn et al. 2000), but because many
of the coefficients used in these methods are fits to Earth observational data, and the
correlations are not always consistent from case to case (Ryan 2000), we found them
hard to adapt.
19

Instead, to determine N ice we follow HDC04, who obtained reasonable results
by diagnosing ice crystal number concentration from ice mass. Although they also
used several coefficients that are fixed for application to Earth, we find that their
approach is easier to adapt because the parameters are more closely tied to physical
processes. HDC04 proceed by combining two power-law equations for the terminal
velocity, one in terms of diameter and one in terms of mass, a power-law equation for
mass in terms of diameter, and the definition of the mean mass
V t,ice = xD y ice , (2.6)
V t,ice = a(ρ dry q ice ) b , (2.7)
m ice = αD β ice , (2.8)
m ice = ρ dryq ice
N ice
, (2.9)
where y, b, and β are nondimensional exponents, x [m 1−y s −1 ], a [kg −b m 1−3b s −1 ] and
α [kg m −β ] are the corresponding multipliers, and D ice [m] is the diameter of an ice
crystal. To complete the set of equations, we need the number concentration of ice
crystals. In the diagnostic equation the terminal velocity, V t,ice , is equated in (2.6)
and (2.7), and then (2.8) and (2.9) are used to get
N ice = c (ρ dry q ice ) d , (2.10)
where c [kg −d m 3(d−1) ] and d are given by
c = 1 α
( x
a
) β/y
, d = 1 − βb
y . (2.11)
An advantage of this formulation of the single-moment approach is that the microphysical
processes and the advection that affect ice mass will likewise affect the
number concentration (HDC04). HDC04 list values of the coefficients used in the
20

above equations for application to Earth; our task is to estimate appropriate values
for application to Jupiter.
Equation (2.9) does not contain empirical parameters, but equations (2.6),
(2.7), and (2.8) contain a total of 6 parameters that must be fit to observations.
To estimate x and y in (2.6), we apply to cloud-ice crystals the same technique we
use for estimating the terminal fall speed of snow, which involves the correlation of
Reynolds and Davies nondimensional numbers to observations and is described in
Section 2.5.2 below. Equation (2.8) relates mass to diameter and the coefficients can
be calculated based on crystal geometry and species ice-density data. The geometry
a crystal favors is called its habit, and HDC04 tested the effect of crystal habit on
N ice by comparing several different shapes. They found that the choice of ice-crystal
habit does not result in significant differences in N ice and has a small overall impact
on the microphysical behavior. Therefore, for simplicity we follow HDC04 who used
single-bullet crystals, and we adopt their mass- size correlation for water. For other
species, we calculate the coefficients using (2.31).
To calculate the remaining coefficients in the set of equations, at first it appears
that we can proceed either of two ways. In the first, we make assumptions for the
terminal velocity vs. cloud mass equation.
Estimating a and b in (2.7) is rather
difficult because the correlation is more empirical than (2.6). We are not aware of
any fall-speed vs. cloud mass data taken under Jupiter conditions, thus we adopted
the value of b in (2.7) from Earth observations.
The magnitude parameter, a, is
likely to be significantly larger for Jupiter than Earth, judging from various terminal
velocity estimates. In our preliminary calculations we found for cloud-base conditions
that water-cloud particles typically fell about four times faster on Jupiter than Earth,
and that ammonia-cloud particles fell roughly 25% faster than water-cloud particles.
21

Thus, for Jupiter we increased a by a factor of 4 and 5 over its terrestrial value for
water and ammonia, respectively, and we calculated the remaining coefficients, c and
d, for both species using (2.11). However, during our test runs we found that the
threshold mixing ratio for snow autoconversion (described in detail below, see Eq.
2.58) yields a very low value, resulting in too strong and unrealistic snow formation
even for low-density clouds. We conclude that the terminal velocity as a function of
cloud mass on Jupiter is not linearly proportional to its Earth value as it nearly is
for individual particles, thus the method above cannot be used in the current form
in our parameterization. This is an area where laboratory measurements and further
parameterization sensitivity tests are needed.
The other way we can proceed for determining the remaining coefficients is to
assume that the number concentration of particles in the jovian clouds are similar to
those on Earth, and hence to adopt the value of c and d in (2.10) from HDC04. In
the absence of laboratory or in situ data, the terrestrial values of these coefficients
provide at least a reasonable first estimate, but this issue will need to be re-examined
when new data become available. Since coefficients a and b in (2.7) are not part of any
microphysical functions, we do not need to calculate them when using this method.
This method prevailed in the 1D tests described in the next chapter, values of the
cloud densities, the microphysical transfer rates and their time scales are qualitatively
reasonable. The values of the coefficients we used in our simulations are listed in Table
2.2.
2.4 Precipitation Size Distribution
The next task is to account for the wide distribution of sizes of raindrops and
snowflakes. We assume the number density for raindrops follows the exponential form
22

TABLE 2.2
Power law coefficients used in the EPIC microphysics code to calculate N ice for water
and ammonia (2.6–2.11). Values needed for the terminal-velocity of rain and snow in
equation (2.21) and (2.29), respectively, are included. Units are MKS.
Coefficient H 2 O NH 3
α ice 7.06165e-3
3
7.06165e-3·ρNH
ρ H2 O
β ice 2.0 2.0
c ice 5.38e+7 5.38e+7
d ice 0.75 0.75
x ice 735.5 702.46
y ice 0.86273 0.8695
x rain 2615.1 2479.0
y rain 0.74245 0.76217
x snow 54..96 53.065
y snow 0.45254 0.46179
ρ liquid 1000.0 733.0
ρ bulk ice 917.0 786.8
23

given by Marshall and Palmer (1948)
n rain (D) dD = N 0rain e −λ rainD dD , (2.12)
where D is the raindrop diameter, n rain dD is the number of raindrops per volume
with diameters in the range D to D + dD, λ rain is the slope parameter [1/m] and
N 0rain is the intercept parameter. Multiplying (2.12) by the mass of each raindrop,
assuming spherical shape and constant density ρ liq , and integrating over all diameters
yields
λ rain =
(
πρliq N 0rain
ρ dry q rain
) 1/4
. (2.13)
Following Earth models (e.g. RH83, D89, FRR96) we use the value of 8 × 10 6 m −4
for the intercept parameter N 0rain for water, and we currently apply the same value
to other species (for lack of better values).
Although snow is more complicated than rain in terms of shape, Gunn and
Marshall (1958) showed that the same functional form for size distribution (2.12) can
be applied to snow if the diameter, D, is interpreted as the melted-snow spherical
diameter. Houze et al. (1979) went further and showed that for precipitation particles
bigger than 1.5 mm in diameter, frozen or otherwise, the exponential size distribution
is quite accurate when the diameter is defined assuming spherical shape and the
density is taken to be the actual rather than melted value.
It has since become
common practice to not convert to melted diameter when applying (2.12) to frozen
hydrometeors in GCM applications, and we follow this practice and use
n snow (D) dD = N 0snow e −λsnowD dD , (2.14)
with
λ snow =
(
πρsnow N 0snow
ρ dry q snow
) 1/4
. (2.15)
24

Ryan (1996) showed that using a constant for the intercept parameter N 0snow (e.g.
RH83, D89) does not approximate well the strong temperature dependence that has
been observed. An error in the number density will lead to inaccuracies in the calculated
rates of sublimation, deposition, accretion of cloud ice by snow, and sedimentation
velocity. Thus, we follow HDC04 and use a temperature-dependent expression
for N 0snow for water that is based on observations by Houze et al. (1979)
N 0snow = (2 × 10 8 m −4 ) min { 0.01 e −0.12(T−Ttp) , 1 } , (2.16)
and we currently apply (2.16) to other species as well (for lack of better functions).
2.5 Fall Speed of Particles
We turn now from number and size distributions to precipitation terminal velocities.
Values for the parameters x and y in the power-law formulation (2.6) have
been determined for rain and snow for different particle sizes and shapes under terrestrial
conditions (Pruppacher and Klett 1997, Rogers and Yau 1989). To generalize to
planetary conditions in the absence of empirical data, we refer to aerodynamic-drag
calculations that are couched in terms of nondimensional numbers. The aerodynamicdrag
force acting on a free-falling particle is defined in terms of the drag coefficient,
C D , as
F D = 1 2 ρ airV 2
t AC D , (2.17)
where A is the area of the particle projected normal to the flow and ρ air is the density
of the gas through which it is falling.
Once the terminal velocity is reached, this
force is exactly balanced by the gravitational force, F G = mg, where m is the mass of
the particle. For strongly viscous flow, meaning low Reynolds number (low-Re) flow,
Stokes’ law provides an analytical expression for C D and hence V t . However, falling
25

precipitation averaged over the complete size range is not a low-Re phenomenon,
therefore we proceed by adapting the methods developed for raindrops and snowflakes
described by Pruppacher and Klett (1997).
2.5.1 Raindrops
The definition of the Reynolds number, Re, may be rewritten in this context
as an expression for the fall speed
where µ air
V t = 1 D
µ air
ρ air
Re , (2.18)
is the dynamic viscosity and Re is defined using diameter (instead of
radius), hence a calculation of Re yields V t . The range of Re that corresponds to fall
speeds that are fast enough for inertial effects to be important, which are neglected
in Stokes’ flow, but slow enough to avoid breakup of a liquid drop is approximately
0.01 ≤ Re ≤ 300, for which raindrops fall like rigid spheres (Pruppacher and Klett
1997). We assume that this range is sufficient to model the fall speed of raindrops for
our purposes. Drop shape and stability are active areas of research, for which surface
tension effects enter in through the nondimensional Weber number.
A discussion
of the current understanding of this complex problem can be found in Chap. 10
of Pruppacher and Klett (1997). Our model is most sensitive to this issue in our
estimate of the maximum drop size (see below), we therefore tested a set of values in
1-D sensitivity tests. Doubling and halving the value of maximum raindrop diameter
in the terminal velocity calculation resulted in less than 5% difference overall between
the times required for the complete rainout in the nominal case (see Chap. 3 below),
thus we conclude that our Jupiter cloud model is insensitive to this parameter.
Given spherical raindrops, the net buoyancy is πD 3 (ρ liq − ρ air )g/6, and when
this is equated to the drag force in terms of C D (2.17), with V t written in terms of
26

Re using (2.18), one obtains
C D Re 2 = 4D3 ρ air g(ρ liq − ρ air )
3µ 2 air
. (2.19)
The new nondimensional number X ≡ C D Re 2 that arises in (2.19) is known as the
Davies number or the Best number. It is significant in the theory of falling precipitation
because, unlike C D or Re, it can be easily evaluated without reference to the
quantity in question, V t , thereby avoiding iteration, while on the other hand, it is a
nondimensional expression of the drag force and hence must have a functional correspondence
with Re. Therefore, the strategy is to find an empirical formula for Re
in terms of X, which will then directly yield V t via (2.18). Clift et al. (1978) determined
empirical correlations for a wide range of Re and X, in which the mass of the
raindrops was converted into diameter assuming rigid sphere geometry. Introducing
W ≡ log 10 X, they found
log 10 Re ≈ −1.81391 + 1.34671W − 0.12427W 2 + 0.006344W 3 , (2.20)
for the interval 12.2 < Re ≤ 6.35 × 10 3 . This range of validity is broad enough to
cover all the raindrop sizes and atmospheric conditions we expect for Jupiter. Panel
A) of Fig. 2.1 shows the Reynolds number – Best number correlation.
The next step is to cast V t into the power-law form as a function of raindrop
diameter for Jupiter conditions, V t = xD y . To do this, we calculate the fall speed
of drops in the diameter range 200µm to 5mm (Re of 3.268 to 5260.0 and 1.785 to
4449.0 for water and ammonia, respectively, at the reference pressure level, see below),
and solve for the best-fit x and y (Table 2.2). The lower limit is a typical value
for raindrops, and we do not consider larger drops than the upper limit because they
are likely to break up (Rogers and Yau 1989, Pruppacher and Klett 1997). Such calculations
for Earth usually include a factor that accounts for the change of fallspeed
27

with altitude, for example Foote and DuToit (1969) included the factor (p 0 /p) γ from
empirical correlations, where p 0 = 1000 mbar and γ = 0.4. Their research was limited
to raindrops, but most models use these values to describe the variation of terminal
velocity with height for solid precipitation as well (e.g. RH83, D89). In our calculations
we found the exponent is different for liquid and solid particles and we denote
them with γ liq and γ ice , respectively. On Jupiter, water drops form near the 5 bar
pressure level and ammonia drops are not likely to form at all, but for consistency we
keep p 0 = 1000 mbar and calculate reference theoretical fall speeds at this level. Our
results for Jupiter show γ liq = 0.33 provides a consistently good fit to the altitude
dependence for both water and ammonia raindrops, thus we write the fall speed as
V t = x rain D y rain
(p 0 /p) γ liq
, (2.21)
with γ liq = 0.33 for Jupiter. In panel A) of Fig. 2.2 we compare our results for the
terminal velocity of water raindrops on Jupiter to previously published results for
water raindrops on Earth and methane raindrops on Titan. As expected, the speeds
are larger on Jupiter, which implies that processes such as accretion will be relatively
stronger. Also, the implied rapid vertical transfer of water and other soluble gases
downward are expected to deplete the local abundance of these substances above
Jupiter’s rain evaporation level (Rossow 1978).
The final step is to calculate an average fall speed for rain in an EPIC-model
gridbox, which ties this section into the preceding discussion on size distribution. We
follow Srivastava (1967) and express the mass-weighted mean terminal velocity as
V t =
∫ ∞
∫0
∞
0
V t mn dD
, (2.22)
mn dD
where V t (D) is the terminal fall speed, m(D) = πρ liq D 3 /6 is the mass of a raindrop of
diameter D, and ndD is the number density in the diameter range D to D + dD, as
28

Figure 2.1. A) Correlation between the Reynolds- and Best-numbers in the Bestnumber
regime of 10 3 to 10 5 . Solid line represents the function for rain calculated
using (2.20), dashed line shows the correlation for snow calculated using (2.26). B)
Power law curve fit of H 2 O snow terminal velocities at the reference pressure level.
The correlation coefficient of the curve is R = 0.99561.
discussed above. Substituting (2.21) and the distribution function (2.12) into (2.22)
yields the formula we use in the model
V t,rain = (p 0 /p) γ
x rain
(λ rain ) y rain
Γ(y rain + 4)
6
, (2.23)
where Γ(n) = ∫ ∞
0 e −t t n−1 dt is the Gamma function.
2.5.2 Terminal Velocity of Snow
Most of the precipitation in our Jupiter model turns out to be in the form of
snow. As we have already mentioned, snow can be treated in a similar fashion to rain
with slightly less accurate but still satisfactory results. We follow Böhm (1989), who
developed a method for predicting terminal velocities of solid hydrometeors based on
boundary-layer theory with an error ≤ 10% for a wide variety of particles, including
various planar and columnar crystals, rimed and unrimed aggregates, graupel, and
hail. Böhm’s approach readily adapts to planetary situations because of its explicit
29

Figure 2.2. A) Comparison of terminal velocities of raindrops on Earth, Jupiter,
and Titan. The dotted and dashed curves show the calculated fall speed of methane
drops on Titan at 40km altitude and water drops on Earth at the surface, respectively
(Lorenz 1993). The solid curve shows the fall speed of water raindrops on Jupiter at
p = 5.5 bar calculated in this work. B) Comparison of terminal velocities for ammonia
and water snow. The dashed line is H 2 O snow at the surface of Earth from the model
by Dudhia (1989), the dotted line is NH 3 snow at p = 700 mbar from this work, and
the solid line is H 2 O snow on Jupiter at p = 4500 mbar from this work.
30

use of environmental parameters such as density, viscosity, and gravitational acceleration
and of particle parameters such as mass and crystal geometry via a unified
Davies number.
Locatelli and Hobbs (1974) collected data on the mass-size relationship
of solid precipitation particles and we use their correlations in our terminal
velocity calculation. We assume snowflakes to be graupellike snow of hexagonal type,
with density ρ snow , such that the mass may be expressed as
m = 0.333 ρ snow D 2.4 . (2.24)
Locatelli and Hobbs (1974), however, do not list density values for this habit. For
other geometries they found a large variation of density ranging from 20 kg m −3 to
450 kg m −3 . We have no information on density values under Jupiter-like conditions
and for other species, but to take into account the porous nature of snow particles in
this study we use ρ snow = 0.5 ρ bulk ice . We chose this value to take into account for the
graupellike nature of this habit, but future sensitivity tests need to be carried out to
investigate the importance of this parameter.
Böhm (1989) points out that the drag coefficient is much more sensitive to the
holes and irregularities near the edge of an object than to its circumscribed shape,
and that the former can be represented by an effective projected area, A e . He handles
the variety of solid hydrometeor shapes by defining a unified Davies number in terms
of a particle’s mass, effective projected area, and projected area A, which is the area
of the smallest circle or ellipse that completely contains A e ,
X = 8mgρ air
πµ 2 air
( A
A e
) 1/4
. (2.25)
The value of A/A e depends on the crystal type and we have no direct information
on that for planetary applications. From our assumption of hexagonal-shaped snow
particles (A/A e ) 1/4 ≈ 1.05. Böhm inverts X(Re) from his drag-coefficient curve fit to
31

solid precipitation particles to obtain
Re = 8.5
[ (1
+ 0.1519X
1/2 ) 1/2
− 1
] 2
. (2.26)
Panel A) of Fig. 2.1 shows the correlation between the Reynolds number and the
Best number. The fall speed for snowflakes is then obtained as in (2.18), but with
the length scale now generalized in terms of the projected area, A
V t =
( ) π 1/2
µ air
Re , (2.27)
4A ρ air
where Re is defined in terms of the characteristic length. Given the spherical diameter
D, this is simply
V t (D) = 1 D
µ air
ρ air
Re . (2.28)
The next step is to express this V t for snowflakes in a power-law format, as
was done for raindrops above. Based on values found in Pruppacher and Klett (1997)
we calculate the fall speeds of snowflakes in the size range D = .5 to 5 mm (500 to
5000 µm). The lower value is our threshold value for autoconversion of ice crystals
into snow, and with the upper value we take into account the breakup of large solid
precipitation particles. This procedure is done at various pressure levels and then fit
to
V t (D) = x snow D ysnow (p 0 /p) γ ice
, (2.29)
to yield x snow and y snow as given in Table 2.2, with γ ice = 0.47 for both species
and for both ice and snow. As an example, the accuracy of the curve fitting water
snow terminal velocity data is shown in panel B) of Fig. 2.1. Panel B) of Fig. 2.2
compares the terminal velocity of water snow on Earth and Jupiter, and ammonia
snow on Jupiter. As expected, snow falls faster on Jupiter. Interestingly, although
water snowflakes are heavier, they fall much slower than ammonia snowflakes because
the air they encounter is significantly denser.
32

The final step is to calculate the mass-weighted average fall speed for snow in
a gridbox (2.22). One obtains the same form (2.23) as for rain
V t,snow =
x snow Γ(y snow + 4)
(p 0 /p) γ ice
, (2.30)
(λ snow ) ysnow 6
but with the physical differences expressed through the different x, y and λ parameters.
Turning back to the clouds themselves, it is important to distinguish between
the cloud-ice crystals and the much larger snow particles. Following HDC04, in Section
2.4 we derived an equation for the cloud-ice number concentration that requires
the terminal velocity of ice crystals in power-law format. We proceed in the same
manner as for snow, but we find it is best to treat them separately and to fit a different
power law for ice crystals. Following HDC04 we use single-bullet shaped crystals
that have density of the bulk ice, and their value of (A/A e ) 1/4 ≈ 1. We consider
diameters in the range D = 1 to 500µm, and use the diameter-mass relation from
HDC04, which is D = 11.9 m 1/2 , in MKS units. For species other than water, we
scale this by the density such that
D ≈ 11.9
(
ρwater ice
ρ ice
) 1/2
m . (2.31)
The resulting power-law coefficients for ice crystals are included in Table 2.2.
2.6 Microphysical Processes
We next consider the processes that govern phase changes. These affect the
model dynamics via the mixing-ratio source/sink terms, Ŝs,p, in the continuity equations
(2.4) and latent heating/cooling terms in the energy equation. Figure 2.3 provides
a graphical overview of the interplay between the phases for a given species like
33

water or ammonia. There are a total of eleven processes that we presently consider.
Dropping the species index, the explicit source terms for phase index p = vap, liq,
ice, rain, and snow are:
Ŝ vap = −P COND − P INT − P DEPI − P REVP − P SEVP , (2.32)
Ŝ liq = P COND + P SMLTI − P RAUT − P RACW , (2.33)
Ŝ ice = P INT + P DEPI − P SMLTI − P SACI − P SAUT , (2.34)
Ŝ rain = P REVP + P RAUT + P RACW + P SMLTS , (2.35)
Ŝ snow = P SEVP + P SACI + P SAUT − P SMLTS . (2.36)
These terms all have units s −1 and the processes corresponding to the abbreviated
subscripts are explained in the caption to Fig. (2.3). The modification to the heating
rate, ˙Q, is
˙Q lat = L evap (P COND + P REVP )
+ L sub (P INT + P DEPI + P SEVP )
+ L fus (P SMLTI + P SMLTS ) , (2.37)
where L evap , L sub , and L fus
are the latent heats of evaporation, sublimation, and
fusion.
2.6.1 Condensation of Vapor/Evaporation of Cloud Liquid (P COND )
The process labeled P COND on the upper-left of Fig. 2.3 represents the condensation
of vapor to form cloud liquid when the vapor mixing ratio exceeds its saturation
value with respect to liquid and the temperature is above the triple point, T ≥ T tp .
Conversely, when the ambient air is subsaturated and T ≥ T tp , then evaporation of
the cloud-liquid phase into vapor takes place. Some cloud microphysical processes
34

Figure 2.3. Schematic diagram of the eleven phase-change processes included in the
five-phase EPIC microphysics model. These are P COND : condensation of vapor to
cloud liquid and evaporation of liquid cloud, P INIT : initiation of ice crystals, P DEPI :
deposition of vapor onto ice crystals and sublimation of cloud ice to vapor, P SMLTI :
melting of cloud ice to form cloud liquid, P RACW : collection of cloud liquid droplets by
rain, P RAUT : autoconversion of cloud liquid droplets to rain, P REVP : evaporation of
rain, P SEVP : sublimation and depositional growth of snow, P SMLTS : melting of snow to
form rain, P SACI : collection of cloud ice crystals by snow, and P SAUT : autoconversion
of cloud ice crystals to snow.
35

can be modeled as instantaneous, while others are more accurately treated with a
finite-rate approach. FRR96 represented condensation as a finite-rate process using
P COND = (q satl − q vap )/τ, where q satl is the saturation mixing ratio over liquid and
τ = 100s is the relaxation time for condensation. Since the time constants used in
Earth modeling are not necessarily match those on other planets, we found it more
suitable to adapt the formula used in RH83:
⎧
⎨q satl − q vap
P COND = − min
⎩ ∆t
(
) ⎫
−1
1 + L2 vapq satl
, q ⎬
liq
c p R vap T 2 ∆t ⎭ , (2.38)
where L vap is the latent heat of evaporation, c p is the specific heat of air at constant
pressure, R vap is the ideal gas constant of vapor, and ∆t is the timestep used in the
numerical integration. Evaporation is limited by the term q liq /∆t to prevent negative
overshooting of q liq . The latent heat associated with this process in either direction
modifies the saturation mixing ratio, which is taken into account by the correction
factor in parentheses (Teixeira and Miranda 1997).
2.6.2 Initiation of Cloud Ice (P INIT )
The next process is the nucleation of cloud-ice particles from vapor, P INIT .
This is a complicated process and there are many questions that arise in the gasgiant
context that may ultimately require in situ probes to provide the necessary
data for high accuracy. Yair et al. (1995) point out that a key unknown is the nature
of condensation nuclei on Jupiter, and they develop a complete parameterization
to address the problem. At this point, we have opted to use a somewhat simpler
approach for the initialization of cloud ice that fits within our framework, but we
recognize that the importance of this topic will require us and other groups to revisit
the question periodically as new information becomes available.
36

The process of cloud-ice initiation in this study follows that described by
HDC04.
It is a one-way process in which cloud ice is initiated from vapor when
T < T tp , the air is supersaturated with respect to ice (q vap − q sati > 0) and q ice = 0,
where q sati is the saturation mixing ratio over ice. We calculate the rate of initiation
as
{ qice0
P INIT = min
∆t , q }
vap − q sati
, (2.39)
∆t
where q ice0 is the initiated mixing ratio value of cloud ice, and the second term prevents
shooting into ice subsaturation in one time step. Recall that in the algorithm we have
adopted, q ice may be related to the number concentration of ice particles, N ice , via
the powerlaw (2.10) with coefficients c and d. Thus, we may find q ice0 by calculating
the corresponding number concentration N ice0 (which is not to be confused with the
precipitation number-intercept parameters N 0rain or N 0snow used in (2.12), (2.14),
(2.16)), such that
q ice0 = 1
ρ dry
min
{ (Nice0
c
) 1/d
, 1.5 × 10 −3 kg m −3 }
. (2.40)
The upper limit reins in the power law when subject to Jupiter’s temperature range,
which is broader than Earth’s. HDC04 make a point of considering a different formulation
for N ice0 than for N ice in general. For N ice0 , they use Fletcher’s (1962)
temperature-dependent equation to insure that colder temperatures produce more
ice nuclei, but with different coefficients that are specifically chosen to model the
cloud-ice initiation process itself.
We found that the formula given by HDC04 is
more appropriate for our application than Fletcher’s original coefficients (2.5). In
particular, Fletcher’s coefficients produce negligible initiation unless temperatures
are colder than about 30 ◦ C below the freezing point, which on Jupiter translates into
weak water-ice cloud formation below the 2.5 bar level. In contrast, Galileo spacecraft
37

Figure 2.4. Comparison of initialized ice mass calculated from (2.5) for water on
Earth (solid line), and from (2.40) for ammonia (dash-dot line) and water (dotted
line) on Jupiter.
data reveal deep clouds at p ≥ 4 bar (Banfield et al. 1998) and the correlation given
by HDC04 affords such clouds. Yair et al (1995) suggested that the number of ice
nuclei should be on the order of 10 5 m −3 , and to take into account for their suggestion
we have increased the multiplier in HDC04’s equation and we write
N ice0 = max { 10000 e −0.1(T −Ttp) , 1.0 × 10 8 m −3} . (2.41)
In our sensitivity tests (Chaps. 3 and 4 below) we found that varying the value of
the multiplier does not affect the overall results in long time simulations. The upper
limit is for safety such that N ice0 would never grow too large at colder temperatures.
The resulting initialized cloud ice, q ice0 , calculated from (2.40) and (2.41) is shown in
Figure 2.4 .
2.6.3 Deposition of Vapor/Sublimation of Cloud Ice (P DEPI )
Cloud-ice crystals grow by deposition, P DEPI , when the air is supersaturated
with respect to ice, and shrink by sublimation when the air is subsaturated. Given a
38

value of supersaturation, S ice − 1, where S ice = q vap /q sati is the saturation ratio with
respect to ice (also the WMO’s definition of relative humidity), Pruppacher and Klett
(1997) give an expression for the rate of growth of mass by vapor deposition (their
13-76) for a hexagonal-plate ice crystal (their 13-77), which we write in a form similar
to RH83 as
dm
dt ≈ 4D ice(S ice − 1)
A ice + B ice
, (2.42)
where D ice the diameter of the ice crystal, and A ice and B ice are thermodynamic terms
given by
and
A ice = L sub
K air T
B ice =
(
Lsub
R vap T − 1 )
, (2.43)
1
ρ dry q sati χ . (2.44)
Here, K air is the thermal conductivity of air, R vap is the gas constant of vapor, and χ
is the diffusivity of vapor in air. For water vapor in Earth’s atmosphere, RH83 take
χ = 2.26 × 10 −5 m 2 s −1 . However, Pruppacher and Klett (1997) show that assuming
that the transport coefficients K air and χ are constants overestimates the growth rate
of submicron particles.
They cite a size-dependent modification that corrects the
problem (see their 13-14), but then they downgrade the importance of this correction
under natural conditions because it vanishes once the particles grow large enough,
so at the present time we do not include this modification. On the other hand, Yair
et al. (1995) find that the differences between the transport coefficients for Earth
and Jupiter are important to the cloud microphysics, hence we are careful to use
appropriate values. For K air on Jupiter, we use the function given by Hansen (1979).
For χ(T, p), we use the Fuller-Schettler-Giddings correlation with parameters from
Perry’s Chemical Engineers’ Handbook (1997), Tables 5-14 and 5-16, for which the
typical error is less than 5%.
39

Unlike for raindrops and snowflakes, we do not have an expression for the
size distribution of cloud particles, especially not for Jupiter. A common approach
used in Earth models is to assume a monodispersed, average cloud-particle diameter
in each gridbox, D ice , for use in (2.42) and calculate the depositional growth by
P DEPI = N ice dm/dt. We adopt this strategy and calculate D ice using (2.8) and (2.9),
which yields
P DEPI = 4 ¯D i (S ice − 1)N ice
A ice + B ice
= 4 (S ice − 1) α −1/β ice
ice N 1−1/β ice
ice (ρ dry q ice ) 1/β ice
. (2.45)
A ice + B ice
Similarly to the ice initiation process (2.39), we follow the standard practice of limiting
P DEPI such that the deposition rate does not lead to subsaturation in one time step.
In subsaturated conditions, S ice < 1, the right hand side of (2.45) becomes negative
and represents the cloud-ice sublimation rate.
2.6.4 Melting of Cloud Ice/Freezing of Cloud Liquid and
Melting of Snow/Freezing of Rain (P SMLTI )
Next, consider the two processes in Fig. 2.3 that are represented by two-way,
horizontal arrows. As mentioned above, the memory is laid out in the model to handle
mixed-phase situations, but we have decided to wait until the second generation of our
microphysics code before exploring this more complicated option. We currently follow
FRR96 and assume that these melting and freezing processes occur instantaneously
such that no mixed-phase situations arise, in other words that the precipitation in a
gridbox is either rain or snow but not both simultaneously, and the same for cloud
liquid versus cloud ice. Here, cloud ice is completely converted into cloud liquid when
T ≥ T tp and cloud liquid is completely converted into cloud ice when T < T tp
⎧
⎨ q ice /∆T , T ≥ T tp ;
P SMLTI =
⎩
−q liq /∆T , T < T tp ,
(2.46)
40

with a similar conversion between snow and rain
⎧
⎨ q snow /∆T , T ≥ T tp ;
P SMLTS =
⎩
−q rain /∆T , T < T tp .
(2.47)
2.6.5 Autoconversion of Cloud Liquid to Rain (P RAUT )
One of the two processes by which cloud liquid can be converted into rain is
through mutual coalescence, also called autoconversion and labeled P RAUT in Fig. 2.3.
During this process, cloud droplets collide with each other as a result of their nearly
random motion. Similarly to RH83 and FRR96, we have implemented the approach
introduced by Kessler (1969)
P RAUT = max { α RAUT (q liq − q liq0 ), 0 } , (2.48)
where α RAUT is a rate coefficient and q liq0 is a threshold value for autoconversion. Weinstein
(1970) found that this parameterization is sensitive to q liq0 , but fortunately
for planetary applications, is not so sensitive to α RAUT . Since neither parameter is
constrained by observations for planetary atmospheres, we have adopted the terrestrial
values used by FRR96, q liq0 = 0.00025 kg kg −1 and α RAUT = 0.001 s −1 . These
parameters may need to be reexamined before applying them to a planet where rain
is an important component of the hydrological cycle (such as Titan).
2.6.6 Collection of Cloud Liquid by Rain (P RACW )
Cloud droplets are also swept up by falling raindrops, which is the process
labeled P RACW in Fig. 2.3. Similarly to RH83 and FRR96, we calculate the mass
increase of a single raindrop of diameter D due to collection of cloud liquid as
dm
dt = π 4 D2 V t (D) q liq E rl , (2.49)
41

where E rl is the cloud-liquid collection efficiency for rain, which we take to be unity
as is usually done. We substitute the fallspeed of the raindrop V t (D) from (2.21),
multiply the equation with the Marshall-Palmer distribution (2.12), and integrate
over all diameters to get an expression similar to that in D89
P RACW = π ( ) γliq
4 x p0 Γ (y rain + 3)
rainq liq E rl N 0rain
p λ y . (2.50)
rain+3
rain
2.6.7 Deposition of Vapor on Rain/Evaporation of Rain (P REVP )
In addition to the two processes just discussed, raindrops also grow by deposition
of vapor when they pass through a supersaturated environment, and conversely
shrink by evaporation when they fall into a subsaturated environment. This is the
process labeled P REVP in Fig. 2.3. The growth rate of a single raindrop may be expressed
with an equation analogous to (2.42) for the deposition of vapor on cloud
ice, P DEPI (see Byers 1965; Pruppacher and Klett 1997, p. 547), but for the spherical
shape of the raindrop, and with a ventilation factor F that accounts for the drop’s
motion
dm
dt = 2πDF (S liq − 1)
A rain + B rain
, (2.51)
where S liq = q vap /q satl is the saturation ratio over liquid. Analogous to (2.43) and
(2.44), we have
and
A rain = L vap
K air T
B rain =
(
Lvap
R vap T − 1 )
, (2.52)
1
ρ dry q satl χ . (2.53)
We use the ventilation factor given by Beard and Pruppacher (1971)
F = f 1r + f 2r Sc 1/3 Re 1/2 , (2.54)
42

where Sc = (µ air /ρ dry )/χ is the Schimdt number, µ air is the dynamic viscosity, and
the empirically determined parameters are f 1r = 0.78 and f 2r = 0.308. Integrating
(2.51) over all drop sizes using the Marshall-Palmer distribution, with Re in terms of
the diameter power-law formulation for the terminal velocity (2.21)
Re = ρ air
DV t = ρ ( ) γliq
air p0
x rain D 1+y rain
, (2.55)
µ air µ air p
yields an expression similar to that in D89
P REVP = 2π(S [ ( ) 1/2 (
liq − 1)N 0rain f1r
+ f
A rain + B rain λ 2 2r Sc 1/3 xrain ρ air p0
rain
µ air p
) γliq /2 ]
Γ(c r )
, (2.56)
λ cr
rain
where c r = (y rain + 5)/2. In case of subsaturation, S liq < 1, the right hand side of
(2.56) is negative and is the evaporation rate.
2.6.8 Autoconversion of Cloud Ice to Snow (P SAUT )
The final three processes in Fig. 2.3 involve snow and have forms similar to the
analogous processes involving rain. First, the autoconversion of cloud ice to snow,
P SAUT , occurs when the mixing ratio for cloud ice exceeds a threshold q ice0
P SAUT = max { α SAUT (q ice − q ice0 ), 0 } . (2.57)
Even though the threshold concept is the same, having two liquid drops merge into
one is quite a different process from having two solid crystals stick together, and so it
is common to treat the autoconversion rate coefficients for rain and snow differently.
For snow, RH83 and HDC04 simply use α SAUT = 1/∆t such that it is treated as an
instantaneous process, and we currently do the same. Since we do not yet know the
maximum size of cloud-ice particles in planetary settings, we follow these papers and
assume D ice0 = 500 µm, above which autoconversion to snow occurs. Substituting
43

this value into (2.8), and combining it with (2.9) and (2.10) yields the threshold
q ice0 = 1
ρ dry
(
cice α ice D β ice
ice0
) 1/(1−dice )
. (2.58)
2.6.9 Collection of Cloud Ice by Snow (P SACI )
Falling snow collects cloud ice just as falling rain collects cloud liquid, and the
form of the mass equation is the same
dm
dt = π 4 D2 V t (D)q ice E si , (2.59)
where E si is the cloud-ice collection efficiency for snow. Since the accretion of cloud
ice by snow is a stronger process at higher temperatures (Lin et al. 1983), we have
adopted the temperature-dependent ice-collection efficiency function used by HDC04
E si = e 0.05(T −Ttp) . (2.60)
Given the terminal velocity (2.29) and number distribution (2.14), integrating over
all particle sizes generates an equation analogous to (2.50) for rain
P SACI = π ( ) γice
4 x p0 Γ (y snow + 3)
snowq ice E si N 0snow
p λsnow
ysnow+3 . (2.61)
2.6.10 Deposition of Vapor on Snow/Sublimation of Snow (P SEVP )
The final microphysical process we consider is the interaction between snow
and vapor, P SEVP . This is similar to the interaction between cloud ice and vapor,
except that snow experiences a ventilation effect because of its motion and has an
exponential size distribution. As is standard, we model the ventilation effect using
(2.54) with f 1s = 0.65 and f 2s = 0.44 (Thorpe and Mason 1966). After accounting for
the size distribution, the process equation resembles (2.56) for rain with a geometry
44

factor of 4 as in (2.42) instead of 2π
P SEVP = 4(S [ ( ) 1/2 (
ice − 1)N 0snow f1s
+f
A snow + B snow λ 2 2s Sc 1/3 xsnow ρ air p0
snow
µ air p
) γice /2 ]
Γ(c s )
, (2.62)
λ cs
snow
where c s = (y snow + 5)/2. In case of subsaturation, S ice < 1, the right hand side of
(2.62) is negative and it represents the sublimation rate.
2.7 Code Implementation
We end this chapter with some details concerning the implementation of the
microphysics scheme in the EPIC model. The following chapters detail our initial
results from application of this model to Jupiter using one- and two-dimensional
configurations.
2.7.1 Positivity adjustment
It is important for physical and computational reasons that all mass-related
variables, including all five phases of each active species, remain positive definite everywhere
(Ooyama 2001). For this reason, we use a positive-definite advection scheme
in the dynamical core and a robust conditional-branching function for floating point
numbers in the microphysics code (Belding, 2000). Truncation errors throughout the
model may still lead to the occasional incidence of negative mass, and so we take the
standard precaution of performing an adjustment step to make the masses positive
definite. There are various ways to do this, for example borrowing from nearby gridboxes,
but after trying various schemes in the end we have decided to simply reset
negative values to zero. The main drawback of this simple approach is a lack of strict
mass conservation, but we note that the algorithms we use are designed to conserve
total energy and enstrophy on the grid rather than total mass. In practice, for any
45

easonable resolution the total mass in the model does not drift in an appreciable
manner and we have not encountered any problems with this issue.
2.7.2 Sequence of Process Transfers
Implementing cloud microphysics in a GCM is an inherently complicated task,
and in addition to establishing good algorithms for each process, the order in which
these processes are applied to the model variables (the timesplitting) usually affects
the outcome, primarily because more than one process competes for the same material.
There is little agreement yet among research groups as to what order microphysical
processes should applied. For example, FRR96 apply freezing and melting
processes first and Morrison et al. (2003) apply them last. Therefore, no model description
is complete without a description of its process sequencing, which we include
here. Similarly to FRR96, we calculate the freezing and melting processes first, which
we treat as instantaneous, and we update the mixing ratios accordingly, but do not
update the temperature at this point. As mentioned above, in our current implementation
“warm” and “cold” processes do not take place simultaneously in a given
grid box. For the case T > T tp , we calculate P COND first, followed by P RAUT , P RACW
and P REVAP , in this order. For the case T < T tp , we calculate P INT or P DEPI first,
depending on whether cloud ice has previously existed or not at the grid location,
and then P SAUT , P SACI and P SEVP . We update the mixing ratios and the temperature
via the heat equation after all these transfer rates are calculated. As has been described
above, care is taken to avoid unnatural flip-flopping between supersaturation
and subsaturation from one timestep to the next, and to avoid negative mass. After
the microphysical processes have been applied, in the dynamical core we advect each
phase of each active species, including the relative fall speeds of snow and rain. The
46

next chapter describes tests and results of the model when configured for the vertical
dimension only.
47

CHAPTER 3
1D SIMULATIONS
3.1 Introduction
Before using the microphysics scheme in a full GCM model it is useful to
test its functions in simplified simulations, where we examine the robustness of the
processes, modify or fine-tune the parameterizations, and evaluate the importance of
individual elements of the scheme. The Earth atmospheric modeling community uses
single column models for this purpose (Randall and Cripe, 1999). We have tested the
microphysics scheme in a simplified, one-dimensional version of EPIC, the setup and
results of which are described in this chapter.
We have tested our cloud scheme in two steps. First, we have established a
nominal model and investigated its runtime properties. In the absence of dynamics
we perturb the model with a high initial supersaturation that generates a thermodynamically
unbalanced state, which triggers the various processes into action. The
description of the column model and the results from these simulations are discussed
in Section 3.2 and 3.3, respectively. Second, we have explored the sensitivity of the
model using a suite of initial abundance and relative humidity values. These details
are given in Section 3.3.1. Section 3.3.2 describes the effect of clouds on the static
stability of the atmosphere.
48

3.2 Nominal Model Description
The one-dimensional model is built with 155 layers, which is much higher
vertical resolution than we can typically employ in full three-dimensional simulations.
The base of the model is located at the 10 bar pressure level and the top of the model
is at 10 mbar. When vertical layers were spaced proportional to the logarithm of
pressure, which corresponds to approximately even spacing in height, or when they
were evenly spaced in pressure, the vertical resolution was not fine enough within the
saturation range of at least one of the species, thus we have opted for a custom spacing
that provides sufficient number of layers in the expected cloud and precipitation
region and a coarser resolution at the top and bottom of the model for computational
efficiency. Figure 3.3 shows the position of the layers. The top five layers of the
model are used as a sponge to damp the reflection of vertically propagating waves.
In the hybrid vertical coordinate system (Dowling et al. 2006) a σ-to-θ coordinate
transition pressure of p σ
= 120 mbar (for the undisturbed model) was chosen for
all the 1D simulations (Fig. 3.1). For this vertical resolution we use a time step of
∆t = 30 s for all of the simulation in this chapter. This value was determined by
decreasing the time step until it was the largest possible that did not introduce any
numerical instability.
3.2.1 Vertical Structure of Model Environment
The initial temperature profile above the visible cloud deck at about the 700
mbar level was taken from Voyager radio occultation data published by Lindal et al.
(1981). Below this pressure level our temperature profile followed a dry adiabatic
extrapolation of the Voyager data. Figure 3.1 shows the mean temperature profile
49

Figure 3.1. (Left) The solid line represents the basic-state temperature profile used
in our simulations. Data were given by Lindal et al. (1981) with a dry adaiabtic
extrapolation towards the bottom. The dotted line shows the variation of potential
temperature in the model, the dashed line is the hybrid vertical coordinate, ζ, with a
transition to a pressure based coordinate below p σ = 120 mbar. (Right) Mean zonal
wind profile of the basic-state, as described in the text.
50

used in our calculations.
The only in situ measurement of the zonal wind profile below the cloud level
comes from the Galileo probe doppler-wind measurement data. The probe entered
one of Jupiter’s singular regions, a so-called 5µm hot spot (Orton et al. 1998), a
phenomenon in Jupiter’s equatorial region that is thought to be caused by the dry
downdraft of an equatorially trapped wave (Ortiz et al. 1998, Showman and Dowling
2000). Such a downdraft modifies the local thermal and wind profiles, thus the data
should probably not be generalized for the whole planet.
In our test simulations,
we found that the model is sensitive to the deep wind profile, causing numerical
instability for cases of too much vertical shear in regions of low static stability. In
this study we have reduced the vertical wind shear to 20% of the value measured by
the Galileo probe. Above the cloud deck the magnitude of the zonal wind is set to
follow the thermal-wind decay determined by Gierasch et al. (1986) from Voyager
IRIS data. The resulting zonal wind, u, as a function of pressure can be written as:
⎧
0, p ≤ p 0 · e −cs ,
(
⎪⎨ u(p
u(p) = 0 ) 1 − 1 ln p )
0
, p 0 · e −cs < p < p 0 ,
c s p
( [ ] )
u(p)probe
⎪⎩ u(p 0 ) du vert − 1 + 1 , p 0 ≤ p,
u(p 0 )
(3.1)
where p 0 = 680 mbar, c s = 2.4 is the mean value of the scale height of the wind shear
for the planet (Gierasch et al. 1986), u(p) probe is the wind profile measured by the
Galieo probe (Atkinson et al. 1997), and du vert = 0.2. This profile used is shown in
Figure 3.1.
3.2.2 Vertical Structure of Clouds
The first experiments to simulate the vertical structure of Jupiter’s atmosphere
used one-dimensional thermochemical equilibrium models (Lewis 1969, Wei-
51

denschilling and Lewis 1973). These models assumed solar-based compositions. It is
widely used and convenient to compare the abundance of elements to a solar value,
which represents the ratio of the number of the species atoms to hydrogen atoms in
the Sun. In this study we have adopted the standard solar values published by Anders
and Gravesse (1989). The Galileo probe in situ measurements and ground based observations
both question the validity of the solar composition of the planet. A recent
review of Jupiter’s composition is given by Taylor et al. (2004). The analyses of the
probe radio signal attenuation data suggests a deep ammonia abundance of 4.0 ± 0.5
times the solar abundance (Folkner et al. 1998). Updated Galileo probe mass spectrometer
(GPMS) measurement analysis provides a 2.96 ± 1.13 solar enrichment for
the 8.9-11.7 bar pressure region (Wong et al. 2004). The probe could not identify
the deep value of water abundance, and based on the dry nature of hot spots, the
measured sub-solar value serves only as a lower limit.
The condensible volatiles we include in this study are ammonia and water.
Although Rossow (1978) has argued that ammonia and water will form a single condensing
vapor solution and its saturation vapor pressure can be a more complicated
function of temperature, following Stoker (1986) and Yair et al. (1995) we have represented
water as a pure substance in these simulations. Sulfur is also important and
is thought to produce an NH 4 SH cloud that lies between the NH 3 cloud above and
the H 2 O cloud below. However, the chemistry involved represents an added level of
complexity, and we have decided to delay the treatment of sulfur to a future paper.
The volume molar mixing ratios generated by the EPIC model for solar abundance
are 0.000187 and 0.00142 for NH 3 and H 2 O, respectively. In the nominal model we
used a 4.0 times solar deep ammonia abundance and, in the absence of indisputable
evidence, a solar deep water abundance. In the EPIC model, species are initialized
52

Figure 3.2. Models of the vertical profiles of ammonia (top) and water (bottom) volume
mixing ratios (v.m.r.’s) used in this study. The solid lines indicate deep v.m.r.’s
of 4.0 bounded by the saturation curve and the cold trap (see text). The v.m.r.’s
corresponding to solar values of 0.5 and 1.0 are indicated with finely dotted and
dashed-triple dotted lines, respectively. Saturation curves of 120% (supersaturated)
and 80% (subsaturated) are represented by the coarsely dotted and dashed parallel
curves, respectively.
53

starting in the abyssal layer and working up. Based on the temperature of the layer, a
saturation mole fraction value is calculated and limited by the user-defined maximum
allowed saturation factor (e.g. 1.1 in our nominal 1D case). The final mole fraction of
the species in the layer is the minimum of this value and the deep abundance value.
Proceeding upwards, once we pass the tropopause the temperature begins to increase,
and in this case, instead of increasing the abundance according to the temperature,
we use the value of the previous layer (the “cold trap” model). Figure 3.2 shows the
resulting initial vapor profile.
3.3 Results of 1D Simulations
The nominal 1D model was used to test the formation and evolution of clouds
and precipitation as governed by the microphysical processes described in the previous
chapter. As expected, the cloud initialization starts at the first time step as a direct
result of our 10% supersaturation. Ammonia-ice cloud forms at and above the 820
mb pressure level, while water-ice cloud forms at and above the 4700 mb pressure
level. Interestingly, a single layer of liquid-water cloud forms at the 4750 mb pressure
level, which has a slightly higher temperature than the triple point of water. These
results show good agreement with published thermochemical models. Atreya el al.
(1999) predicted an ammonia ice cloud with a base at about 720 mb and a waterammonia
solution cloud at 5690 mb assuming solar abundance for each species. The
difference between their predicted cloud base levels and our results comes from the
use of slightly different initial T(p) profiles. The cloud initialization does not remove
all the supersaturation, thus the remaining excess vapor provides a source for fast
and strong crystal growth that can be observed at the lower water-ice cloud region.
Parallel with the growth of the clouds, snow formation starts near the ammonia-ice
54

cloud base and in the midst of the water-ice cloud, and rain forms in the liquid-water
cloud. At about 10 minutes into the model run, snow starts to form near the waterice
cloud base as well, and then melts into rain as it falls through the triple-point
temperature level.
As the falling precipitation reaches the lower cloud levels, the
increasing amount of snow collects more and more ice particles, thus we have the
highest value of snow density at about one hour into the simulation. This occurs near
the water-ice cloud base with a peak value of 3.8 × 10 −4 kg m −3 . The extremum of
water-ice cloud density is 2.57 × 10 −4 kg m −3 and liquid-water cloud has a maximum
density of 6.27×10 −4 kg m −3 . The maximum value of water rain density is 9.7×10 −5
kg m −3 , and it reaches down to about the 5200 mb pressure level before it completely
evaporates. The maximum density for the ammonia-ice cloud and snow is 4.3 × 10 −4
kg m −3 and 8.83×10 −5 kg m −3 , respectively, and the precipitation falls down to about
the 880 mb pressure level before it evaporates. The fallout of ammonia precipitation
is complete at about 100 minutes into the simulation, while all the water rain and
snow fall out and evaporate in about 5 and 8 hours, respectively.
The maximum temperature increase in a single layer due to latent heating is
0.073 K in the ammonia-cloud region and 0.192 K in the water-cloud region. The
cooling caused by the evaporating precipitation is -0.0196 K and -0.458 K below the
ammonia and water cloud base, respectively. For ammonia, the absolute value of the
cooling is smaller than the heating because only a small portion of the cloud turns
into evaporating precipitation. This is in agreement with Carlson et al. (1988), who
suggested that ammonia clouds on Jupiter are non-precipitating or weakly precipitating.
On the other hand, for water the temperature change of cooling in a single layer
is higher than for the heating. Figure 3.3 shows that this is because the water clouds
and precipitation form over a widespread region between about 3.5 and 5 bars (∼14
55

Figure 3.3. The time evolution of water and ammonia clouds and precipitation in
the nominal 1D model of Jupiter’s atmosphere. Blue represents the water-ice cloud,
green the liquid-water cloud (too thin to be seen here, but clearly visible on Fig. 3.4c),
and tan the ammonia-ice cloud. Yellow would indicate a liquid-ammonia cloud, but as
expected, this phase does not form in the model. Snow is marked with black outlines,
and red outlines are rain. The initial abundance of ammonia and water vapor is 1.0
and 4.0 times solar, respectively, with 10% initial supersaturation. The lowest values
plotted for both the filled contours and the outlines correspond to mass mixing ratios
of 10 −6 kg m −3 and are incremented by 0.33 kg m −3 . Black ticks on the right hand
side indicate model layer-interface positions.
56

km in height) such that the amount of heat generated by condensation is distributed
vertically, whereas the evaporation of precipitation from all of those layers mostly
takes place in a relatively narrow region at about 5 bars.
EPIC is a hydrostatic model such that the vertical velocity is a diagnostic
variable. Scaling the hybrid vertical velocity, ˙ζ, into m/s shows that the maximum
updraft and downdraft velocities (gridbox average) caused by the latent heat are 1.77
mm s −1 and -0.94 mm s −1 , occurring at the 3770 mb and at the 5020 mb pressure
level, respectively.
3.3.1 Sensitivity to abundance
While the dryness observed by the Galileo probe can be explained by the
unique nature of the 5 µm hot spots, other observations also contradict the idea that
the abundance of condensible species in the cloudy region is similar to the deep abundances,
in fact there appear to be a range of abundance values at different altitudes.
From Voyager radio occultation measurements, Lindal et al. (1981) reported a volume
mixing ratio of 2.21 × 10 −4 at the 1 bar pressure level, which is slightly higher
than the solar value. From Voyager IRIS spectra, Carlson et al. (1993) suggested
an ammonia vapor profile that decreases with height and is sub-saturated above the
condensation level, based on a fit to data at all wavelengths. Analysis of Jupiter’s microwave
emission indicates depleted ammonia on a global scale, with ammonia mixing
ratios decreasing with altitude at p < 4 bar, and with about 0.5 times solar ammonia
at p ≤ 2 bar (de Pater et al. 2001). There are fewer observational constraints on the
water clouds, since they are below the visible cloud deck and there is a wide range
of suggested abundance values, varying from subsolar to ten times solar. For more
complete listings of various observational data see Sromovsky et al. (1998) and Taylor
57

et al. (2004).
We have carried out experiments to explore the effect of variation of the deep
vapor abundance and the initial supersaturation on the cloud structure. Results for
0.5, 1.0, and 4.0 times solar abundance for both ammonia and water are summarized
here (see Fig.3.2). Figure 3.4 shows the cloud evolution for these three deep abundance
values, each initialized with 10% supersaturation. As expected, the location of the
cloud bases is controlled by this parameter. Water-snow sublimates instead of first
melting into rain when we reduce the water abundance to 0.5 times solar.
The
presence of supercooled liquid is probably required for the lightning activity on Jupiter
observed by Voyager 1 (Smith et al. 1979) and by Galileo (Little et al. 1999),
in analogy with Earth. Based on our tests we estimate that at the latitudes that
exhibit lightning on Jupiter a minimum value of approximately solar local abundance
is needed. The 4.0 times solar abundance results in a thick liquid cloud under the
water-ice cloud (Fig. 3.4c). Large raindrops can form in this dense precipitation field,
which collects liquid cloud drops very effectively. Figure 3.4c shows that the accretion
process is so strong that the liquid portion of the water cloud almost vanishes on the
order of 1 hour, thus we expect any such dense clouds on Jupiter to be local and very
short lived. Ammonia clouds do not precipitate in our simulations when the deep
abundance is only solar or subsolar.
Figure 3.5 illustrates the effect of varying the initial supersaturation, with the
deep mixing ratios held to the nominal-model values. This parameter controls how
dense a cloud becomes. Below 3% initial supersaturation level we found that neither
species precipitates. At 3%, rain forms in the liquid (warm) region of the water cloud
and it falls out completely in about half an hour. In the ice cloud, at first crystals
grow by collecting vapor particles, until around 50 minutes into the simulation they
58

Figure 3.4. Cloud and precipitation evolution using various initial deep abundance
values, with initial supersaturation set to 10%. Panel A) has a deep abundance value
of 0.5 solar for both ammonia and water, panels B) and C) have deep abundances for
both species of 1.0 solar and 4.0 solar, respectively. Color coding is as in Fig. 3.3.
The lowest values plotted for both the filled contours and the outlines correspond to
mass mixing ratios of 10 −6 kg m −3 and are incremented by 0.5 kg m −3 .
59

Figure 3.5. Sensitivity of cloud and precipitation evolution to various initial supersaturation
values, with the deep abundance values set to the nominal case of 4.0 and
1.0 times solar for ammonia and water, respectively. Panel A) has a supersaturation
level of 3% for both ammonia and water, panels B) and C) have supersaturation levels
of 6% and 12%, respectively. Color coding is as in Fig. 3.3. Contours are as in Fig.
3.4.
60

grow big enough to form snow. Increasing the initial supersaturation reduces this
time, and for sufficiently high initial values precipitation forms instantly (Fig. 3.5b
and c). The time required for complete fallout of rain and snow also increases with
the supersaturation.
The ammonia cloud requires a high supersaturation level to
form precipitation, consistent with expectations.
3.3.2 Static Stability of the Atmosphere
The stratification of Jupiter’s atmosphere plays a significant role in controlling
its dynamics.
Stratification can be expressed in terms of the buoyancy or Brunt-
Väisäla frequency, N, or its square. Because of the generalized definition of potential
temperature used in the EPIC model, the Brunt-Väisäla frequency does not satisfy the
classic meteorological relation N 2 = (g/θ)dθ/dz, and so we use the formula derived
in the appendix of Dowling et al. (2006)
N 2 = g 2 [
−ρβ + α2 T
c p
+ dρ ]
env
, (3.2)
dp
where where α ≡ −ρ −1 (∂ρ/∂T ) p = ρ(∂v/∂T ) p is the isobaric volume thermal expansivity,
v ≡ 1/ρ is the specific volume, and β ≡ ρ −1 (∂ρ/∂p) T
is the isothermal
compressibility. When N 2 is positive the atmosphere is statically stable, when it is
zero the atmosphere is neutral and the temperature profile is dry adiabatic, while
negative N 2 is the characteristic of an unstable atmosphere.
We have turned on and off various components of the microphysics scheme in
order to test their contribution to the effects of the active moisture in the atmosphere.
Table 3.1 summarizes which phases and their microphysical processes were used in
the simulations. Figure 3.6 shows the comparison between an initial state with no
condensibles (i.e.
dry model, Case 1) and the nominal model prior to any latent
61

TABLE 3.1
Microphysical components turned on and off in the Brunt-Väisälä test runs (see text
for details).
Vapor Clouds Precipitation Latent heat
Case 1 - - - -
Case 2 + - - -
Case 3 + + + -
Case 4 + + - +
Case 5 + + + +
Figure 3.6. Brunt-Väisälä frequency of the initial state. The solid line represents
an initial state with no moisture added (Case 1 in Table 3.1) and the dashed line
corresponds to the initial state of the nominal model (Case 2), for which the deep
volume mixing ratios are 4.0 and 1.0 times solar for ammonia and water, respectively.
The dotted line shows the variation of the molar mass of moist air with height in the
nominal model.
62

heating or precipitation effect (Case 2). Below each cloud base, at about 800 mb
and 5000 mb for ammonia and water, respectively, the contribution of the added
mass to the stratification is negligible, but above in each cloud condensation region
there is a significant increase in N 2 from the increased molar mass. We found a
similar but smaller stabilizing effect in the low abundance cases, and as previously
mentioned the cloud bases move somewhat higher in the atmosphere. Figure 3.7
compares the static stability of the atmosphere at 2 hours into the nominal model
simulation. In the case of non-precipitating clouds (Case 4) the effect of the latent heat
of condensation increases the stability in the region where clouds form, but the change
is less significant than from just the molar mass effect.
The case of precipitation
without including latent heating (Case 3) moves the stable region downwards as the
snow and rain falls, and introduces a slight instability in the deeper zone where the
precipitation evaporates. Using the full microphysics (Case 5) has the same effect as
the precipitation-only case but the magnitudes of both the stability and instability
are increased by the added effect of latent heating. In the ammonia cloud region,
the sensitivity of the static stability to turning on and off any of the components of
the microphyisics is found to be negligible compared to the molar mass effect. Based
on these tests we confirm that water effects Jupiter’s atmospheric dynamics not only
through the latent heating, but also significantly from the redistribution of mass by
precipitation. Next, we examine how the cloud microphysics interacts with Jupiter’s
belts and zones in a two-dimensional, meridional-plane version of the model.
63

Figure 3.7. Brunt-Väisälä frequency at 2 hours into the simulation with selected
microphysics components turned off. The dotted line represents a model with the
microphysics turned off (Case 2 in Table 3.1), moisture plays the role of a tracer
with mass that is otherwise passive in this simulation. The dashed line shows the
effect of the latent heating turned off in the model (Case 3), while the dot-dashed
line indicates the effect of no precipitation (Case 4). The solid line represents the full
EPIC microphysics scheme (Case 5).
64

CHAPTER 4
MERIDIONAL PLANE SIMULATIONS
4.1 Introduction
In terrestrial meteorology, moist thermodynamics leads to fascinating but complicated
phenomena, from simple precipitation to supercell thunderstorms to hurricanes
to global wave patterns like the Madden-Julien oscillation. The rich set of observations
we have for Jupiter’s atmosphere imply that jovian moist thermodynamics
is equally as interesting, and equally as complicated. With the cloud-microphysics
scheme we have developed and tested in 1D, it is now possible to follow many new
lines of inquiry, for example the interactions of jovian anticyclones and cyclones with
moisture, and the effects of moist thermodyamics on the acceleration of jet streams.
However, our present goal is to test the processes in the new cloud microphysics package
in as simple and controlled a manner as possible, thus we leave for future work
the full-scale investigations just mentioned.
In this chapter we set up experiments in a two-dimensional model to observe
the latitudinal variation of the cloud structure. Having a full 2D meridional plane
opens up the possibility of many interesting flow patterns that cannot be realized
with the 1D model. We describe cases here that illustrate the typical behavior of the
model, with the emphasis placed on stressing the algorithms rather than on achieving
a completely natural state. In our simulations we use the term“storm” to distinguish
65

on the one hand from the ubiquitous, long-lived jovian vortices, and on the other hand
from localized convective thunderstorms that have a shorter time scale and would
require a nonhydrostatic mesoscale or regional-scale model to properly simulate.
4.2 Model Description
In our two-dimensional Jupiter model we use 45 layers. The base of the model
is located at the 8 bar pressure level and the top of the model is at 10 mbar. Similarly
to our 1D simulations, the layers are custom-spaced to give higher resolution in the
cloudy regions. Figure 4.2 shows the position of the layers. We use the top four layers
as sponge layers, and p σ = 120 mbar as the σ-to-θ coordinate transition pressure for
the undisturbed model.
The nominal model is a channel spanning 40 ◦ S to 40 ◦ N
latitude, with 161 evenly spaced grid points (0.5 ◦ resolution). To avoid numerical
instability a time step of ∆t = 120 s is used for all of the 2D simulations in this
chapter. The hyperviscosity coefficient used to damp high-frequency computational
modes is ν 8 = (0.01)[(1/2400)∆y 8 /∆t] m 8 s, and the value of divergence damping is
set to ν div = (0.5)[(1/30)∆y 2 /∆t] m 2 s .
4.2.1 Vertical Structure of Model Environment
Our wind profile is similar to the one described by (3.1) except that it is
expanded by a latitudinal dependence to yield a two dimensional wind field:
⎧
0, p ≤ p 0 · e −cs ,
(
⎪⎨ u(λ, p
u(λ, p) =
0 ) 1 − 1 ln p )
0
, p 0 · e −cs < p < p 0 ,
c s p
( [ ] )
u(p)probe
⎪⎩ u(λ, p 0 ) du vert − 1 + 1 , p 0 ≤ p,
u(p 0 )
(4.1)
where λ is the planetographic latitude, and similarly to the 1D experiments, p 0 = 680
mbar, c s = 2.4, and du vert = 0.2. The velocity profile of the jets as a function of
66

Figure 4.1. (Top) Zonal wind profile of the initial state. Solid and dashed contours
represent eastward and westward jets, respectively. The plotted contours are u =
[−50, −30, −10, 10, 30, 50, 70, 100, 130] m s −1 , with the positive values corresponding
to eastward winds. (Bottom) Mean zonal temperature profile of the basic state, units
are K.
67

latitude at the p 0 pressure level is the standard Limaye (1986) profile from Voyager
cloud-tracking observations. We kept the unknown vertical wind shear at the 20%
value used in Chapter 3, thus du vert = 0.2.
In our 2D simulations we start with the same vertical temperature profile that
was used in the 1D case (Section 3.2). This sounding profile is applied at the equator,
and gradient wind balance dictates the thermal profile in the rest of the model. The
resulting zonal temperature and wind profiles are shown in Fig. 4.2
4.2.2 Vertical Structure of Condensibles
Similarly to the 1D simulations, we have established a nominal abundance
model and through sensitivity tests have investigated how different values of the
species abundances and initial saturation ratios affect the structure of clouds. To
be consistent with our 1D case, in the 2D nominal model the ammonia and water
abundances are set to 4.0 times and 1.0 times solar, respectively.
4.3 Results
First, we investigated the cloud formation and evolution in the meridional
plane. In the first 200 days of our simulations we ran the model with the microphysics
turned off. The mass of the water and ammonia vapor fields is present and
gets advected with the winds, but otherwise these condensibles are passive. In this
geostrophic-adjustment phase the temperature and meridional velocity values differ
significantly from the quasi steady-state values, and since most of the microphysics
functions are a strong function of temperature (e.g. saturation vapor pressure), if we
allowed cloud formation during this adjustment period, the resulting cloud structure
would contain unwanted spurious clouds that are produced on a non-physical basis.
68

Figure 4.2. Vertical structure of clouds in the nominal 2D model at 1 day into the
active microphysics simulation. Color coding and contours are as in Fig. 3.3. Black
ticks on the right hand side indicate layer-interface positions.
At the end of this 200 days period, the model reaches a sufficiently balanced state
that we can turn the cloud microphysics on without triggering unrealistic structure.
Although it is an option in the EPIC model, in these simulations we choose not to
re-initialize the vapor field at the end of this adjustment phase. During the sensitivity
experiments we have tested the re-initialized vapor field case too, and the results are
similar, except that a few days time delay is experienced.
In the nominal model, we use a 10% initial supersaturation level that ensures
rapid cloud growth and precipitation formation. A snapshot of the clouds at day 1 of
69

the active microphysics simulation is shown in Figure 4.2. At this time, the maximum
densities of the ammonia and water ice clouds are 0.044 kg m −3 and 0.076 kg m −3 ,
respectively.
The cloud and precipitation fields for water start out more uniform
than for ammonia, but cloudy and cloud free regions develop for both species. The
meridional structure reflects the vapor redistribution during the first 200 days of
passive advection and geostrophic adjustment. The cloud base of the water-ice clouds
is at about the 4500 mbar pressure level, while the ammonia cloud base is at about
the 800 mbar level, consistent with the 1D simulation results of Chapter 3. Figure 4.3
shows the latitudinal variation of cloud density for water and ammonia, sampled at
4000 mbar and 750 mbar, respectively, for 1 and 30 days into the active simulation.
While the median value of cloud density is about 0.02 g m −3 for both species, the
deviations of the ammonia values are significantly larger, such that cloudy and cloud
free regions alternate frequently.
One conspicuous difference between the 2D and 1D simulations is the location
of the ammonia clouds near the northern edge of the domain. This phenomenon is
caused by the high velocity jet in the vicinity of 24 ◦ N, coupled with our assumptions
about the vertical shear given by (4.1). The gradient balance of the high velocity jet
creates a “shift” in the temperature field at about the ammonia cloud level that can
be seen on the bottom panel of Figure 4.1. The temperature is 5-15 ◦ K higher than at
other latitudes at the same pressure level, which raises the saturation vapor pressure
such that the cloud base gets shifted upwards by about 200 mbar, resulting in nonuniform
bases and tops for the ammonia clouds in the meridional plane. This clearly
illustrates that the zonal-wind structure strongly affects the vertical position and the
overall structure of the clouds. Regarding precipitation, the ammonia snow falls out
in about 10 hrs, while the water snow/rain precipitates out everywhere except in the
70

equatorial region in about 2 days. This is longer than the time we observed in the
1D case. In those simulations the lack of horizontal motion prevented air flows to
feed the cloudy regions with moist air, while in 2D we have seen circulations to form
(for example, two closed circulations on top left panel of Fig. 4.6) that increased the
moisture level in certain regions, causing a longer time for the complete fallout of
precipitation in those areas.
A detailed look at the nominal model reveals an interesting result. Panel A) of
Figure 4.4 shows that at about 6 days into the active simulation a storm starts to form
at the equator, while the rest of the domain stays in a rather steady state No other
dynamic weather events of a similar magnitude were observed in these tests, consistent
with low velocities outside the equatorial region. However, these weak winds do make
the clouds more homogeneous over time throughout the whole domain (Fig. 4.3).
Figure 4.5 shows the temperature change at day 40 into the active simulation
compared to the beginning of the active simulation. In general, where cloud formation
occurred we can see a net positive change, while below the cloud bases, where the precipitation
evaporated, the atmosphere has cooled down as expected. The maximum
value of heating and cooling are 0.66 ◦ K and −0.67 ◦ K, respectively, located near the
base of the rising cloud at about 3000 mbar and below the liquid water layer-clouds of
the equatorial storm at about 5500 mbar, respectively. This equatorial storm system
is one of the more interesting features that has come out of our model testing, and
so we take a closer look at it next.
4.3.1 Equatorial Storm System
Figure 4.6 shows details of the equatorial storm. Near the 5000 mbar level
the meridional winds move air towards the equator in both hemispheres, which re-
71

Figure 4.3. Temporal evolution of the latitudinal variation of cloud density for
ammonia (top) and water (bottom), sampled at the 750 mbar and the 4000 mbar
pressure levels, respectively. Panels on the left show clouds at 1 day into the active
microphysics simulation, panels on the right show the same at 30 days. The dense
region of the water clouds were lifted by the latent heat and buoyancy effects during
this period causing a depletion at the reference pressure level, so we have included
the dotted line on panel D, which represents the new dense layer of water clouds at
the 3500 mbar level.
72

Figure 4.4. Time evolution of the equatorial storm in the nominal model. Color
coding and contours are as in Fig. 3.3.
73

Figure 4.5. 40 day difference of zonal mean temperature compared to the initial
state of the active simulation. Solid and dashed contours represent increases
and decreases in temperature, respectively. The plotted contours are ∆T =
[−0.25, −0.2, −0.1, −0.05, −0.01, 0.01, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3] ◦ K. Color coding
and contours of clouds are as in Fig. 3.3.
74

sults in the formation of solid and liquid stratus clouds between 1 ◦ and 3 ◦ latitude
in both hemispheres.
The equatorial updraft of the forming circulation produces
a large, dense water-ice cloud at the equator.
As this cloud rises in the updraft,
more condensation occurs that strengthens the updraft, which is qualitative confirmation
that our microphysical processes are functioning appropriately. In addition,
the downdrafts of the storm at about ±2 ◦ latitude drag down drier and less dense air
from about the 3000 mbar pressure level, diluting the lower-level water clouds. This
dilution eventually yields cloud free regions at those latitudes (Fig. 4.6). We can
also see a circulation between the 5000 and 7000 mbar pressure levels, rotating in the
opposite direction. The updrafts of this circulation feed the stratus clouds with extra
moisture, creating a dense and precipitating cloud system. At the ammonia cloud
level the dominant motion is horizontal (the vertical component of the wind vectors
is significantly smaller than those in the water cloud region). The ammonia clouds of
the storm system do not precipitate.
The latent heat from the cloud formation and the buoyancy caused by the
continuous precipitation starts to lift the equatorial storm at about 6 days into the
active cloud simulation. The lifting creates more cloud and precipitation formation
that will yield stronger updraft in the cloudy region and stronger downdraft around
it. The maximum and minimum values of the vertical velocity are 0.138 m s −1 and
-0.063 m s −1 , respectively, both occurring at 17 days into the active simulation. The
center of the rising cloud and the equatorward-side of the stratus clouds both form
snow. In case of the equatorial storm, the snow falls almost a scale height before
melting into rain and finally evaporating at about the 5250 mbar pressure level.
The fallout of precipitation and the rising of the cloud ends at about 30 days
into the active simulation. In the resulting cloud system, the cloud top of the equa-
75

Figure 4.6. Close up images of the equatorial storm. Panels on the left show clouds
and wind velocity vectors, panels on the right show clouds and precipitation. Color
coding and contours are as in Fig. 3.3. The vertical component of the velocity vectors
is exaggerated by a factor of 200 to enhance clarity.
76

torial storm is at about the 1000 mbar level while the cloud base is at about 3000
mbar. There is a cloud-free region around and below this storm, spanning about ±2 ◦
latitude. Near the 5000 mbar pressure level we observe some thin stratus clouds; both
solid and liquid phase clouds are present. A dense ammonia cloud system covers this
equatorial storm throughout the simulation, with a cloud top at about 500 mbar and
the cloud base at about 800 mbar. An ammonia-cloud free region spans from about
5 ◦ to 7 ◦ latitude on both hemispheres at this level.
4.3.2 Sensitivity tests
In general, when the microphysics is fully activated in the model, the response
to tests involving unstable initial conditions (supersaturation) takes the form of largescale
storm systems. The location and evolution of these storms varies depending on
the nature and severity of the initial inbalance. Similarly to the 1D case, experiments
are carried out here to investigate how the model responds to various parameter
settings. These tests are of an engineering nature and meant to stress the system,
but they nevertheless reveal the potential of the model’s new functionality.
Figure 4.7 illustrates how varying the initial saturation ratio affects the model
when the deep abundance values are kept the same as in the nominal case. Results
using saturation ratio values of S = 0.95 , 1.00 , and 1.05 are shown. During the
passive simulation (0-200 days), the equatorial dynamics redistributed enough vapor
to form some ammonia clouds at the beginning of the active simulation, even in the
case of a subsaturated initial condition. The top row of Figure 4.7 illustrates that in
the S = 0.95 case, only a trace of water cloud forms at the later stage of the simulation.
In the case of an exact 100% saturation initial condition, we can see all the familiar
components of the equatorial storm system known from the nominal simulation, which
77

Figure 4.7. Zonal cloud structure with modified initial saturation ratio values.
Arrows indicate traces of water clouds. Color coding and contours are as in Fig. 3.3.
78

has a 110% initial saturation, including the rising cloud with the heavy precipitation,
the stratus clouds on both sides of the equatorial storm at about the 5000 mbar
pressure level, and the continuous ammonia cloud cover. Besides this storm system
four other cloudy regions formed in this simulation, with strong vertical coherence
between the two cloud species. The approximate locations of these ammonia and
water clouds are between -36 ◦ and -33 ◦ , between -26 ◦ and -20 ◦ , between 18 ◦ and
22 ◦ , and a smaller water cloud region between 33 ◦ and 35 ◦ latitude. Interestingly,
if we compare these locations with the zonal wind profile (Fig. 4.8) we see in this
simulation that these cloudy areas coincide with the zones (anticyclonic wind shear
regions). The S = 1.05 case (bottom row of Fig. 4.7) shows a very similar picture to
our nominal model except near the northern edge of our domain, we see more cloud
free areas in the region where the clouds are elevated. As expected based on our 1D
tests, the cases with reduced initial saturation ratio yield less dense clouds.
In all the simulations the equatorial region is the most active. Since this model
domain is symmetric about the equator we pose an obvious test question, which is
whether this activity is indeed tied to the equator or perhaps just to the middle
of the domain. To answer this, we set up experiments where the latitude range is
not centered on the equator. Figure 4.9 shows a simulation between -20 ◦ and 60 ◦
latitude, with everything else the same as the nominal model. In this case, a similar
equatorial storm system formed to that in the nominal model. This suggests that
Jupiter’s equatorial dynamics is distinct from its mid latitude dynamics and plays
an important role in shaping the meridional cloud structure, just as is the case for
Earth.
Figure 4.10 shows a reduced deep abundance simulation. In Section 3.3.1 we
discussed that the deep abundance values of 4.0 times solar and 1.0 times solar for
79

Figure 4.8. Cloud and zonal wind structure at 30 days into the active simulation
using S = 1.00 initial saturation ratio. Color coding and contours of clouds and
precipitation are as in Fig. 3.3. Contours of zonal winds are as in Fig. 4.1
Figure 4.9. Sensitivity test in the domain of -20 ◦ to 60 ◦ latitude. Color coding and
contours are as in Fig. 3.3.
80

Figure 4.10. Results with reduced abundance initial condition. Color coding and
contours are as in Fig. 3.3.
ammonia and water, respectively, are close to the observed upper bounds. Thus, to
set up an abundance test we use a reduced profile of 1.0 times solar and 0.5 times solar
for NH 3 and H 2 O, respectively. We keep the initial saturation ratio at S = 1.10, the
same as in the nominal case. Similarly to the 1D experiments, we find that the deep
abundance value controls the location of the cloud base. The location of the ammonia
cloud base has changed from about 800 mbar to about 600-650 mbar and the base
of the water clouds has changed from about 4500 mbar to about 4000 mbar. The
density of the ammonia clouds has reduced and we observe more cloud free regions.
The equatorial storm develops at a later stage of the simulation, with the main lifting
event beginning at about 50 days into the active microphysics simulation, compared
to about 6 days for the nominal case.
In all the simulations where the equatorial storm appears, the rising cloud
stops with its cloud top near the 1000 mbar region, slightly below the ammonia cloud
base level. Is it the ammonia cloud that stops the rise of the water cloud Figure
4.11 illustrates a test case where we include only water, with everything else the
81

same as in the nominal model. The right panel shows that the storm event is very
similar to that in the nominal case. The location and the time scale of the storm
are the same, also the fact that the cloud does not rise above the 1000 mbar region.
In other words, the increase in static stability in the upper troposphere compared
to the lower troposphere is sufficient to significantly suppress vertical motions, with
or without the presence of active ammonia vapor and clouds. Consistent with this
observation, on the close-up images of the nominal case (Fig. 4.6) we see that in
the upper troposphere the vertical component of the wind vectors is small. We can
conclude that the atmospheric constituents above the 1000 mbar level will in general
have little interaction with the deeper regions. Observations indicate that in certain
localized regions, water clouds penetrate through the ammonia clouds (Ingersoll et al.
2000), as shown in Figure 1.2. Such events are the result of local convective storms
that create updrafts of 50-100 m s −1 , and presumably this high velocity carries the
water clouds through the stable region of the atmosphere. Our large-scale, hydrostatic
model creates updrafts of the order of 0.1 m s −1 , thus in order to model nonhydrostatic
convective clouds, new mesoscale components will eventually need to be added to the
EPIC model.
Finally, as with our 1D experiments, we also test cases where selected components
of the microphysics are turned off. The left panel of Figure 4.12 shows a
model with the latent heating turned off, and the right panel shows a model with
the precipitating phases turned off. The most significant difference from the nominal
model is that the equatorial storm system does not appear in either case. Using a
hot-air balloon analogy, this means that it is not enough just to pull the chain for
fire, or to throw the sandbags out of the basket, we need to do both at the same time
in order for this hot-air balloon to rise. Since one of our goals in this project is to
82

Figure 4.11. Snapshots from the model, where water was the only condensible
species. Color coding and contours are as in Fig. 3.3.
Figure 4.12. Cloud structure in model runs with selected microphysical components
turned off, at 40 days into the active simulation. The left panel shows a model with the
latent heating turned off, while the right panel shows a model with the precipitating
phases turned off. Color coding and contours are as in Fig. 3.3.
83

determine which components of a cloud scheme are needed in jovian simulations, we
conclude that any future Jupiter model that employs only a simple, non-precipitating
cloud scheme, or neglects latent heating, will not be able to reliably simulate even
the large-scale cloud dynamics accurately.
84

CHAPTER 5
CONCLUSIONS
An active hydrological cycle has been added to the EPIC general circulation
atmospheric model (GCM). To date, this research project is the first that has developed
a fully functional cloud microphysics scheme for a global-scale GCM for gas giant
applications, and is particularly significant because it has the capability of modeling
multiple species at the same time. Recently published Earth water-cloud schemes
have been adapted and altered to determine appropriate planetary values for various
microphysical functions and parameters. The new subroutines calculate saturation
vapor pressure, microphysical transfer rates, latent heating and cooling, and massaveraged
terminal velocities. The resulting computer program can be downloaded as
open-source software from NASA’s Planetary Data System (PDS) Atmospheres node.
To verify that our numerical algorithms perform reasonably we have carried
out a set of experiments with an emphasis on Jupiter. During these simulations our
goal has been to explore the behavior of the model and to ensure that it is properly
matching expectations based on previous studies, such as Jupiter’s cloud positions and
the nature of precipitation on gas giants, while providing leads for the more complete
and more realistic investigations now made possible by this new functionality.
Both in 1D and in 2D we have tested our microphysics scheme in two steps.
First, we have established a nominal case and observed its runtime properties. In
the nominal case simulations we have used 4.0 times solar and 1.0 times solar values
85

for the deep abundance for ammonia and water, respectively. We have perturbed
the models with a large initial supersaturation, and the resulting thermodynamically
unbalanced state has triggered various microphysical processes.
Second, we have
tested the behavior of the scheme by setting up a suite of sensitivity tests. During
these experiments we have varied the initial saturation and abundance values, and
turned on and off selected components of our cloud scheme.
In our 1D single column test cases, the ammonia-ice cloud formed at and
above the 820 mbar pressure level, water-ice cloud formed at and above the 4700
mbar pressure level, and a single layer of liquid-water cloud formed at the 4750 mbar
level. These results are in agreement with published thermochemical models. During
the sensitivity tests we have observed that the value of the deep abundance controls
the cloud base level, while the value of the initial supersaturation affects the density
of the cloud, as expected. We have shown how turning selected components off in the
cloud scheme affects the static stability.
Our 2D meridional plane cases have allowed us to test how different configurations
affect the latitudinal variation of the clouds. The bases of the clouds for both
species matched those in the one-dimensional simulations, except at 24 ◦ N latitude,
where the ammonia cloud base was raised by about 200 mbar as a result of gradient
balancing in the vicinity of Jupiter’s high velocity jet. In general, water clouds tended
to be more uniform than the ammonia clouds, for which cloudy and cloud-free regions
alternated frequently. We have seen only a small amount of motion in most parts
of the domain, but this motion was significant in that it made both layers of clouds
more uniform in density. We have observed an interesting storm system as a result of
the equatorial dynamics of the model atmosphere. This heavily precipitating storm
raised the water clouds to about the 3000 mbar level, with the cloud top at about 1000
86

mbar. We have shown that the stability of the upper troposphere tends to stop any
mixing between large air masses below and above this level. This equatorial region
has shown the most activity in all of our sensitivity tests. The time required for the
storm to form was controlled by values of the initial deep abundance and saturation
ratio. Significantly, in the 2D case we have shown that turning major components of
the cloud scheme off results in no equatorial storm.
Important conclusions drawn from these experiments are that the locations of
cloud base and cloud top are sensitive to the underlying zonal-wind structure, and that
the simultaneous inclusion of both latent heat and precipitating phases is necessary
in order to simulate important large-scale weather phenomena. Additional research
opportunities are now made possible by the new microphysics scheme. The model is
ready to be applied for short-term weather simulations where the radiation does not
affect the results significantly, such as analysis of the interaction of jovian vortices
with moisture. The interacting vapor, cloud ice, cloud liquid, rain, and snow phases
are ready to be coupled to new development efforts planned for the EPIC model. In
particular, they allow for the development of a realistic radiation transfer scheme, a
subgrid-scale cumulus parameterization, and the inclusion of non-hydrostatic terms.
Each of these will directly affect and improve the cloud simulations.
Addition of
atmospheric chemistry is straightforward and will make it possible to simulate the
ammonium-hydrosulfide clouds, as well as tackle problems involving stratospheric
photochemistry.
Future work directly related to this dissertation will likely include the extension
of the microphysics code to other planets, including active methane for Uranus,
Neptune, and Titan, sulphuric acid for Venus, and dust for Mars. The analysis of incoming
data from ongoing planetary missions, such as atmospheric measurements of
87

the Cassini-Huygens mission to Saturn and Titan, and the European Space Agency’s
Venus Express mission to Venus, are motivating the continued development of planetary
general circulation atmospheric models with realistic hydrological cycles.
There is much that can be done to make improvements to the cloud microphysics
model developed here. Laboratory experiments are needed to clarify the difference
between certain key properties of terrestrial and jovian clouds. For example,
droplet size spectra and collection efficiencies need to be measured in cloud-chamber
tests that reproduce planetary conditions and include species other than just water
(such as ammonia). The incorporation of data from additional Earth-based and
spacecraft observations and in-situ measurements will add more constraints on the
global distribution of condensibles and on the zonal-wind structure. We support a
multi-probe planetary mission to Jupiter that would add valuable information on the
vertical and latitudinal structure of winds, temperatures, and abundances below the
visible cloud deck.
At this point, we do not claim that the results in this dissertation represent
exact simulations of the clouds on Jupiter. However, this research has demonstrated
that a GCM has the potential to model planetary weather patterns in a reasonable
fashion, and it has laid the groundwork to further explore some of the most fascinating
atmospheric features in the Solar System. Our work represents an important step
towards a better understanding of these phenomena.
88

REFERENCES
[1] Anders, E. and N. Gravesse, 1989. Abundances of the elements - Meteoritic and
solar. Geochim. Cosmochim. Acta 53, 197–214.
[2] Atkinson, D.H., A.P.Ingersoll, and A. Seiff, 1998. Deep winds on Jupiter as
measured by the Galileo probe. Nature 388, 649–650.
[3] Atreya, S.K., M.H. Wong, T.C. Owen, P.R. Mahaffy, H.B. Niemann, I. de Pater,
and P. Drossart, 1999. A comparison of the atmospheres of Jupiter and Saturn:
deep atmospheric composition, cloud structure, vertical mixing, and origin.
Planet. Space Sci. 47, 1243–1262.
[4] Banfield, D., P.J. Gierasch, M. Bell, E. Ustinov, A.P. Ingersoll, A.R. Vasavada,
R.A. West, and M.J.S. Belton, 1998. Jupiter’s cloud structure from Galileo imaging
data. Icarus 135, 230–250.
[5] Beard, K.V., and H.R. Pruppacher, 1971. A wind tunnel investigation of the
rate of evaporation of small water droplets falling at terminal velocity in air. J.
Atmos. Sci. 28, 1455–1464.
[6] Belding, T.C., 2000. fcmp Homepage. http://fcmp.sourceforge.net/ (12 December
2004).
[7] Böhm, H.E., 1989. A general equation for the terminal fall speed of solid hydrometeors.
J.Atmos.Sci. 46, 2419–2427.
89

[8] Bohren, C.F., and B.A. Albrecht, 1998. Atmospheric thermodynamics. Oxford
University Press, 402 pp.
[9] Byers, H.R., 1965. Elements of cloud physics. University of Chicago Press, 191
pp.
[10] Carlson, B.E., W.B. Rossow, G.S. Orton, 1988. Cloud microphysics of the giant
planets. J.Atmos.Sci. 45, 2066–2081.
[11] Carlson, B.E., A.A. Lacis, and W.B. Rossow 1993. Tropospheric gas composition
and cloud structure of the Jovian North Equatorial Belt. J. Geophys. Res. 98,
5251-5290.
[12] Clift, R., J.R. Grace, and M.E. Weber, 1978. Bubbles, Drops, and Particles.
Academic Press, 380 pp.
[13] Del Genio, A.D., and K.B. McGrattan, 1990. Moist convection and the vertical
structure and water abundance of Jupiter’s atmosphere. Icarus 84, 29–53.
[14] de Pater, I., D. Dunn, P. Romani, and K. Zahnle, 2001. Reconciling Galileo
probe data and ground-based radio observations of ammonia on Jupiter. Icarus
149, 66–78.
[15] Dowling, T.E., A.S. Fischer, P.J. Gierasch, J. Harrington, R.P. LeBeau, Jr.,
and C.M. Santori, 1998. The Explicit Planetary Isentropic-Coordinate (EPIC)
Atmospheric Model. Icarus 132, 221–238.
[16] Dowling, T.E., E. Colon, J. Kramer, R.P. LeBeau, G. C. Lee, R. Morales-
Juberías, Palotai Cs.J., V.K. Parimi and A.P. Showman, 2006. The EPIC at-
90

mospheric model with an isentropic/terrain-following hybrid vertical coordinate.
Icarus 182, 259-273.
[17] Dudhia, J. 1989. Numerical study of convection observed during the winter monsoon
experiment using a mesoscale two-dimensional model. J. Atmos. Sci. 46,
3077–3107.
[18] Ferrier, B.S. 1994. A double-moment multiple-phase four-class bulk ice scheme.
Part I.: Description. J. Atmos.Sci. 51, 249–280.
[19] Fletcher, N.H., 1962. The physics of rainclouds. Cambridge University Press, 386
pp.
[20] Folkner, W.M., R. Woo, and S. Nandi, 1998. Ammonia abundance in Jupiter’s
atmosphere derived from the attenuation of the Galileo probe’s radio signal. J.
Geophys. Res. 103, 22,847–22,855.
[21] Foote, G.B., and P.S. DuToit, 1969. Terminal velocity of raindrops aloft.
J.Appl.Meteor. 8, 249–253.
[22] Forget, F., F. Hourdin, and O. Talagrand, 1998. CO2 snowfall on Mars: simulation
with a general circulation model. Icarus 131, 302–316.
[23] Fowler, L.D., D.A. Randall, and S.A. Rutledge, 1996. Liquid and ice cloud microphysics
in the CSU General Circulation Model, Part I: Model description and
simulated microphysical processes. J. Climate 9, 489–529.
[24] Garcia-Melendo, E., A. Sánchez-Lavega, and T.E. Dowling, 2005. Jupiter’s 24 ◦
N highest speed jet: Vertical structure deduced from nonlinear simulations of a
large-amplitude natural disturbance. Icarus 176, 272–282.
91

[25] Gierasch, P.J., B.J. Conrath, and J.A. Magalhães, 1986. Zonal mean properties
of Jupiter’s upper troposphere from Voyager infrared observations. Icarus 67,
456–483.
[26] Gierasch, P.J., A.P. Ingersoll, D. Banfield, S.P. Ewald, P. Helfenstein, A. Simon-
Miller, A. Vasavada, H.H.Breneman, D.A. Senska, and the Galileo Imaging
Team, 2000. Observation of moist convection in Jupiter’s atmosphere. Nature
403, 628–630.
[27] Grell, G.A., J. Dudhia, and D. Stauffer, 1994. A description of the fifthgeneration
Penn State/NCAR Mesoscale Model (MM5). NCAR Tech. Note
NCAR/TN-398+STR, 117 pp.
[28] Gunn, and J.S.Marshall, 1958. The distribution with size of aggregate snow
flakes. J.Meteor. 15, 452–461.
[29] Hansen, C.F., 1979. Viscosity and thermal conductivity of model Jupiter atmospheres.
NASA Technical Memo 78556.
[30] Harrington, J., R.P. Lebeau, K.A. Backes, and T.E. Dowling, 1994. Dynamic
response of Jupiter’s atmosphere to the impact of comet Shoemaker-Levy 9.
Nature 368, 525–527.
[31] Heymsfield, A.J., and L. J. Donner, 1990. A scheme for parameterizing ice cloud
water content in general circulation models. J. Atmos. Sci. 47, 1865–1877.
[32] Hong, S.-Y., J. Dudhia, S.-H. Chen, 2004. A revised approach to ice microphysical
processes for the bulk parameterization of clouds and precipitation. Mon.
Wea. Rev. 132, 103–120.
92

[33] Houze, Jr., R.A., P.V. Hobbs, P.H. Herzegh, and D.B. Parsons, 1979. Size distributions
of precipitation particles in frontal clouds. J. Atmos. Sci. 36, 156–162.
[34] Hueso, R. and A. Sánchez-Lavega, 2001. A three-dimensional model of moist
convection for the giant planets: the Jupiter case. Icarus 151, 257–274.
[35] Ingersoll, A.P., Gierasch, P.J., D. Banfield, A.R. Vasavada, and the Galileo Imaging
Team, 2000. Moist convection as an energy source for the large-scale motions
in Jupiter’s atmosphere. Nature 403, 630–632.
[36] Ingersoll, A.P., T.E. Dowling, P.J. Gierasch, G.S. Orton, P.L. Read, A. Sánchez-
Lavega, A.P. Showman, A.A. Simon-Miller, A.R. Vasavada, 2004. Dynamics of
Jupiter’s Atmosphere, In: Bagenal, F., T.E. Dowling, W.B. Mckinnon (Eds.).
Jupiter: The planet, Satellites and Magnetosphere, Cambridge Univ. Press, Cambridge,
pp. 105–128.
[37] James, E.P., O.B. Toon, and G. Schubert, 1997. A numerical microphysical model
of the condensational Venus cloud. Icarus 129, 147–171.
[38] Kessler, E. 1969. On the distribution and continuity of water substance in atmospheric
calculations. Meteor. Monogr., No.32, Amer. Meteor. Soc., 84 pp.
[39] Konor, C.S. and A. Arakawa, 1997. Design of an atmospheric model based on a
generalized vertical coordinate. Mon. Wea. Rev. 125, 1649–1673.
[40] LeBeau, R.P. and T.E. Dowling, 1998. EPIC simulations of time-dependent,
three-dimensional vortices with application to Neptune’s Great Dark Spot. Icarus
132, 239–265.
93

[41] Lewis, J.S. 1969. The clouds of Jupiter and the NH3-H2O and NH3-H2S systems.
Icarus 10, 365–378.
[42] Lin, Y.-L., R.D. Farley, and H.D. Orville, 1983. Bulk parametrization of the snow
field in a cloud model. J. Climate Appl. Meteor. 22, 1065–1092.
[43] Lindal, G.F., G.E. Wood, G.S. Levy, J.D. Anderson, D.N. Sweetnam, H.B. Hotz,
B.J. Buckles, D.P. Holmes, P.E. Downs, V.R. Eshelman, G.L. Tyler, and T.A.
Croft, 1981. The atmosphere of Jupiter: an analysis of the Voyager radio occultation
measurements. J.Geophys.Res. 86, 8721–8727.
[44] Limaye, S.S., 1986. Jupiter: new estimates of the mean zonal flow at the cloud
level. Icarus 65, 335-352.
[45] Little, B., C.D. Anger, A.P. Ingersoll, A.R. Vasavada, D.A. Senske, H.H. Breneman,
W.J. Borucki, and the Galileo SSI Team, 1999. Galileo images of Lightning
on Jupiter. Icarus 142, 306–323.
[46] Locatelli, J.D., and P.V. Hobbs, 1974. Fall speeds and masses of solid precipitation
particles. J. Geophys. Res. 79, 2185–2197.
[47] Lodders, K., and B. Fegley, Jr., 1998. The Planetary scientist’s companion. Oxford
University Press, 371 pp.
[48] Lorenz, R.D. 1993. The Life, Death and Afterlife of a Raindrop on Titan. Planet.
Space Sci. 41, 647-655.
[49] Lunine, J.I., and D.A.Hunten, 1987. Moist convection and the abundance of
water in the troposphere of Jupiter. Icarus 69, 566–570.
94

[50] Marshall, J.S., and W. McK. Palmer, 1948. The distribution of raindrops with
size. J. Meteor.5, 165–166.
[51] Morrison, H., M.D. Shupe, and J. A. Curry, 2003. Modeling clouds observed at
SHEBA using a bulk microphysics parameterization implemented into a singlecolumn
model. J. Geophys. Res. 108, 10.1029/2002JD002229
[52] Ooyama, K. V., 2001. A dynamic and thermodynamic foundation for modeling
the moist atmosphere with parameterized microphysics. J. Atmos. Sci. 58, 2073–
2102.
[53] Orton, G.S., and 16 coauthors, 1998. Characteristics of the Galileo probe entry
site from Earth-based remote sensing observations. J. Geophys. Res. 103, 22,791–
22,814.
[54] Ortiz, J.L., G.S. Orton, A.J. Friedson, S.T. Stewart, B.M. Fisher, and J.R.
Spencer, 1998. Evolution and persistence of 5-µm hot spots at the Galileo probe
entry latitude. J. Geophys. Res. 103, 23,051–23,069.
[55] Perry, R.H., and D.W. Green, 1997. Perry’s chemical engineers’ handbook, 7th
ed. McGraw-Hill, 2640 pp.
[56] Pruppacher, H.R., and J.D. Klett, 1997. Microphysics of Clouds and Precipitation.
2nd ed. Kluwer Academic Publishers, 954 pp.
[57] Randall, D.A., and D.G. Cripe, 1999. Alternative methods for specification of
observed forcing in single-column models and cloud system models. J. Geophys.
Res. 104, 24,527–24,546.
95

[58] Richardson, M.I., R.J. Wilson, and A.V. Rodin, 2002. Water ice clouds in the
Martian atmosphere: General circulation model experiments with a simple cloud
scheme. J.Geophys.Res. 107, 1-29.
[59] Rogers, R.R., and M.K. Yau, 1989. A Short Course in Cloud Physics. 3rd ed.
Butterworth-Heinemann, 290 pp.
[60] Rossow, W.B. 1978. Cloud Microphysics: Analysis of the clouds of Earth, Venus,
Mars, and Jupiter. Icarus 36, 1–50.
[61] Rotstayn, L.D., B.F. Ryan, and J.J. Katzfey, 2000. A scheme for calculation of
the cloud liquid fraction in mixed-phase stratiform clouds in large-scale models.
Mon. Wea. Rev. 128, 1070–1088.
[62] Rutledge, S.A., and P.V.Hobbs, 1983. The mesoscale and microscale structure
and organization of clouds and precipitation in mid-latitude cyclones. VIII: A
model for the ”seeder-feeder” process in warm-frontal rainbands. J. Atmos. Sci.
40, 1185–1206.
[63] Ryan, B.F., 1996. On the global variation of precipitating layer clouds. Bull.
Amer. Meteor. Soc. 77 53–70.
[64] Ryan, B.F., 2000. A bulk parameterization of the ice particle size distribution
and the optical properties in ice clouds. J. Atmos. Sci. 57, 1436–1451.
[65] Seiff, A. 2000. Dynamics of Jupiter’s atmosphere. Nature 403, 603–605.
[66] Showman, A.P. and T.E. Dowling, 2000. nonlinear simulations of Jupiter’s 5-
micron hot spots. Science 289, 1737–1740.
96

[67] Smith, B.A., L.A. Soderblom, T.V. Johnson, A.P. Ingersoll, S.A. Collins, E.M.
Shoemaker, G.E. Hunt, H. Masursky, M.H. Carr, M.E. Davies, A.F. Cook, J.M.
Boyce, G.E. Danielson, T.C. Owen, C. Sagan, R.F. Beebe, J. Veverka, R.G.
Strom, J.F. McCauley, D. Morrison, G.A. Briggs, and V.E. Suomi, 1979. The
Jupiter System Through the Eyes of Voyager 1. Science 204, 951-972.
[68] Srivastava, R.C., 1967. A study of the effects of precipitation on cumulus dynamics.
J. Atmos. Sci. 24 36–45.
[69] Sromovsky, L.A., A.D. Collard, P.M. Fry, G.S. Orton, M.T. Lemmon, M.G.
Tomasko, and R.S. Freedman, 1998. Galileo Probe Measurements of Thermal
and Solar Radiation Fluxes in the Jovian Atmosphere. J. Geophys. Res. 103,
22,929–22,977.
[70] Stoker, C.R. 1986. Moist convection: A mechanism for producing the vertical
structure of the Jovian equatorial plumes. Icarus 67, 106–125.
[71] Stratman, P.W., A.P. Showman, T.E. Dowling, and L.A. Sromovsky, 2001. EPIC
simulations of bright companions to Neptune’s Great Dark Spots. Icarus 151,
275–285.
[72] Taylor F.W., S.K. Atreya, Th. Enccrenaz, D.M. Hunten, P.G.J. Irwin, T.C.
Owen, 2004. Composition of Atmosphere of Jupiter, In: Bagenal, F., T.E. Dowling,
W.B. Mckinnon (Eds.). Jupiter: The planet, Satellites and Magnetosphere,
Cambridge Univ. Press, Cambridge, pp. 59–78.
[73] Teixeira, M.A.C., and P.M.A. Miranda, 1997. The introduction of warm rain
microphysics in the NH3D mesoscale model. CGUL Technical Report N.4, 23pp.
97

[74] Thorpe, A.D., and B.J. Mason, 1966. The evaporation of ice spheres and ice
crystals Brit. J. Appl. Phys. 17, 541–548.
[75] Yair, Y., Z. Levin, and S. Tzivion, 1995. Microphysical processes and dynamics
of a Jovian thundercloud. Icarus 114, 278–299.
[76] Weidenschilling, S.J., and J.S. Lewis, 1973. Atmospheric and cloud structures of
the Jovian planets. Icarus 20, 465–476.
[77] Weinstein, A.I., 1970. A numerical model of cumulus dynamics and microphysics.
J. Atmos. Sci. 27, 246–255.
[78] Wong, M.H., P.R. Mahaffy, S.K. Atreya, H.B. niemann, and T.C. Owen, 2004.
Updated Galileo probe mass spectrometer measurements of carbon, oxygen, nitrogen,
and sulfur on Jupiter. Icarus 171, 153–170.
98

CURRICULUM VITAE
NAME:
Csaba Palotai
ADDRESS:
Department of Mechanical Engineering
University of Louisville
EDUCATION
& TRAINING:
Louisville, KY 40292
M.S. Mechanical Engineering
Technical University of Budapest, Hungary, 1992-2001
Future Professors Program
University of Louisville, 2002-2003
NASA Summer School for High Performance
Computational Earth and Space Sciences
RESEARCH
INTEREST:
NASA Goddard Space Flight Center, July 12-30, 2004
Atmospheric dynamics and Cloud Physics
Comparative Planetology
Computational Heat Transfer and Fluid Dynamics
99