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MIXED-PHASE
CLOUDS
Observations and Modeling
Edited by
CONSTANTIN ANDRONACHE

Elsevier
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or mechanical, including photocopying, recording, or any information storage and retrieval system, without
permission in writing from the publisher. Details on how to seek permission, further information about
the Publisher’s permissions policies and our arrangements with organizations such as the Copyright
Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/
permissions.
This book and the individual contributions contained in it are protected under copyright by the
Publisher (other than as may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing. As new research and experience broaden
our understanding, changes in research methods, professional practices, or medical treatment may
become necessary.
Practitioners and researchers must always rely on their own experience and knowledge in evaluating
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negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas
contained in the material herein.
Library of Congress Cataloging-in-Publication Data
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ISBN: 978-0-12-810549-8
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Typeset by SPi Global, India

CONTRIBUTORS
Andrew S. Ackerman
National Aeronautics and Space Administration, Goddard Institute for Space Studies, New York,
NY, United States
Constantin Andronache
Boston College, Chestnut Hill, MA, United States
Joseph Finlon
University of Illinois at Urbana-Champaign, Urbana, IL, United States
Jeffrey French
University of Wyoming, Laramie, WY, United States
Ann M. Fridlind
National Aeronautics and Space Administration, Goddard Institute for Space Studies, New York,
NY, United States
Kalli Furtado
Met Office, Exeter, United Kingdom
Dennis L. Hartmann
University of Washington, Seattle, WA, United States
Robert Jackson
Argonne National Laboratory, Environmental Sciences Division, Lemont, IL, United States
Olivier Jourdan
Universit
e Clermont Auvergne, Clermont-Ferrand; CNRS, Aubière, France
Daniel T. McCoy
University of Leeds, Leeds, United Kingdom
Steven D. Miller
Colorado State University, Fort Collins, CO, United States
Guillaume Mioche
Universit
e Clermont Auvergne, Clermont-Ferrand; CNRS, Aubière, France
Yoo-Jeong Noh
Colorado State University, Fort Collins, CO, United States
Trude Storelvmo
Yale University, New Haven, CT, United States
ix

Ivy Tan
Yale University, New Haven, CT, United States
Thomas F. Whale
Mark D. Zelinka
Lawrence Livermore National Laboratory, Livermore, CA, United States
x Contributors

PREFACE
The objective of this book is to present a series of advanced research topics on mixed-
phase clouds. The motivation of this project is the recognized important role clouds play
in weather and climate. Clouds influence the atmospheric radiative balance and hydro-
logical cycle of the Earth. Reducing uncertainties in weather forecasting and climate pro-
jections requires accurate cloud observations and improved representation in numerical
cloud models. In this effort to better understand the role of cloud systems, the mixed-
phase clouds present particular challenges, which are illustrated in this book.
The book has two parts, covering a wide range of topics. The first part, “Observa-
tions,” contains articles on cloud microphysics, in situ and ground-based observations,
passive and active satellite measurements, and synergistic use of aircraft data with space-
borne measurements. The second part, “Modeling,” covers numerical modeling using
large eddy simulations to analyze Arctic mixed-phase clouds, and global climate models
to address cloud feedbacks and climate sensitivity to mixed-phase cloud characteristics. It
is my hope that this book will give some indication of the enormous power and future
potential of increasing refined observation techniques and numerical modeling at mul-
tiple scales to solve the complex problems of the role of cloud systems in Earth Sciences.
The publication of this book would not have been possible without the help, interest,
and enthusiasm of the contributing authors. I would like to thank all of the authors and
their supporting institutions for making this project possible. I am particularly grateful to
Ann Fridlind, Michael Folmer, Daniel McCoy, Ivy Tan, and Michael Tjernstr€
om who
offered many useful suggestions during the review process. Finally, it is a great pleasure to
acknowledge Candice Janco, Laura Kelleher, Louisa Hutchins, Tasha Frank, Anitha
Sivaraj, and Anita Mercy Vethakkan from Elsevier for their willing, dedicated, and con-
tinuous help during the project.
Boston Massachusetts
xi

CHAPTER 1
Introduction
Boston College, Chestnut Hill, MA, United States
Contents
1. Observations 2
2. Modeling 5
3. Concluding Remarks 7
Acknowledgments 7
References 7
Clouds have a significant influence on the atmospheric radiation balance and hydrolog-
ical cycle. By interacting with incoming shortwave radiation and outgoing longwave
radiation, clouds impact the energy budget of the Earth. They also have an important
role in the Earth’s hydrological cycle by affecting water transport and precipitation
(Gettelman and Sherwood, 2016). The interaction of clouds with atmospheric radiation
depends on hydrometeor phase, size, and shape. Under favorable humidity conditions,
the cloud phase is determined largely by the temperature, condensation nuclei, and ice
nuclei in the atmosphere. When the cloud temperature is above 0°C, clouds are formed
of liquid water droplets. Ice clouds consist of ice crystals and can be found at temperatures
well below 0°C. In some clouds, supercooled liquid droplets coexist with ice crystals,
most frequently at temperatures from 35°C to 0°C. These are mixed-phase clouds,
which are particularly difficult to observe and describe in numerical weather prediction
(NWP) and climate models.
Mixed-phase clouds cover a large area of the Earth’s surface, and are often persistent,
with a liquid layer on top of ice clouds. Many observations have documented the pres-
ence of these clouds in all regions of the world and in all seasons (Shupe et al., 2008).
They tend to be more frequent at mid- and high-latitudes, where temperatures are
favorable to the formation and persistence of supercooled liquid clouds. Global clima-
tology is available from CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Sat-
ellite Observations (CALIPSO) data, accumulated in recent years (Stephens et al., 2002;
Winker et al., 2009; Zhang et al., 2010). Earlier observations, based on aircraft in situ
measurements, detected single layer mixed-phase clouds characterized by a layer of
supercooled liquid droplets at the top of an ice cloud (Rauber and Tokay, 1991). Over
the last decades, in situ observations using instrumented aircraft (Baumgardner et al.,
2011), have provided very detailed insights in cloud microphysics and dynamical
1
Mixed-Phase Clouds © 2018 Elsevier Inc.
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conditions that form and maintain these clouds. Such data are essential for calibration of
ground-based and spaceborne remote sensing instruments, as well as for the validation of
numerical models.
Given the importance of mixed-phase clouds in a number of applications, such as the
prediction and prevention of aircraft icing, weather modification, and improvement of
NWP and climate projections, a series of research programs have contributed to rapid
progress in these areas. Selected results are illustrated in this volume, accompanied by
references to the most recent studies. The chapters of this book present research on var-
ious aspects of mixed-phase clouds, from cloud microphysics to GCM simulations.
Chapters 2–6 focus mainly on observational aspects, while Chapters 7–10 illustrate
modeling work from small scales using LES to a global scale using GCMs. The next sec-
tions give a short description of each chapter.
1. OBSERVATIONS
Chapter 2 discusses the relevance of ice nucleation to mixed-phase clouds, and current
research on ice nuclei particles (INPs) in the atmosphere. The existence of mixed-phase
clouds is possible because liquid water droplets can exist in a supercooled state at tem-
peratures as low as 38°C. For lower temperatures, in the absence of INPs, the process
of homogeneous ice nucleation can start. The coexistence of liquid water droplets and
ice particles in mixed-phase clouds requires specific microphysical and dynamical con-
ditions. When a cloud consisting of supercooled liquid water droplets evolves to a state
containing some ice crystals, the process of ice nucleation is involved. Despite decades of
research, the process of heterogeneous ice nucleation is not sufficiently known (Phillips
et al., 2008, 2013; DeMott et al., 2011; Atkinson et al., 2013). A better characterization of
the heterogeneous ice nucleation process is needed for the understanding of mixed-phase
clouds. This chapter reviews a series of topics relevant for the study of mixed-phase
clouds. First, the modes of heterogeneous ice nucleation are described, with a focus
on deposition ice nucleation and freezing ice nucleation. Second, the ice nucleation
in the atmosphere—particularly in mixed-phase clouds—is summarized and discussed.
Third, the experimental methods for examining ice nucleation are presented with a focus
on wet and dry dispersion methods. Fourth, the nucleation theory is concisely explained
in both homogeneous and heterogeneous cases. Fifth, the properties of good hetero-
geneous ice nucleators are discussed, including the direct measurement of INP concen-
tration in the atmosphere. This information on direct measurements is particularly
important for (a) providing atmospheric model input data, and (b) allowing comparisons
between models and observations, thus contributing to the understanding of the ice
nucleation processes in the atmosphere.
Chapter 3 introduces a method for the detection of liquid-top mixed-phase (LTMP)
clouds from satellite passive radiometer observations. While in situ measurements of
2 Mixed-Phase Clouds

mixed-phase clouds provide detailed information for these clouds, such observations are
limited and insufficient for many applications. Satellite remote-sensing techniques are
efficient for the continuous monitoring and characterization of mixed-phase clouds.
Active satellite sensor measurements, such as CloudSat and CALIPSO have the capability
to observe detailed vertical structures of mixed-phase clouds. Nevertheless, they are lim-
ited to a spatial domain along the satellite path (Stephens et al., 2002; Winker et al., 2009)
and have limited applicability for some short-term purposes. Thus, there is great interest
in developing methods for mixed-phase clouds detection using passive radiometry. If
adequate methods are developed, satellite remote sensing will provide an ideal venue
for observing the global distribution of mixed-phase clouds and the detailed structures
such as LTMP clouds. This chapter introduces a method of daytime detection of LTMP
clouds from passive radiometer observations, which utilizes reflected sunlight in narrow
bands at 1.6 and 2.25 μm to probe below liquid-topped clouds. The basis of the algorithm
is established on differential absorption properties of liquid and ice particles and accounts
for varying sun/sensor geometry and cloud optical properties (Miller et al., 2014). The
algorithm has been applied to the Visible/Infrared Imaging Radiometer Suite (VIIRS) on
the Suomi National Polar-orbiting Partnership VIIRS/S-NPP and Himawari-8
Advanced Himawari Imager (Himawari-8 AHI). The measurements with the active sen-
sors from CloudSat and CALIPSO were used for evaluation. The results showed that the
algorithm has potential to distinguish LTMP clouds under a wide range of conditions,
with possible practical applications for the aviation community.
Chapter 4 illustrates some of the problems associated with the microphysical proper-
ties of convectively forced mixed-phase clouds. Field experiments are conducted using
aircraft with particle measurement probes to obtain direct observations of the microphys-
ical properties of clouds. Such experiments have been carried out to study various types of
cloud systems, including supercooled clouds and mixed-phase clouds. One particular
subset of these clouds is the convectively forced mixed-phase clouds. Analysis of obser-
vations based on retrievals from CloudSat, CALIPSO, and Moderate Resolution Imag-
ing Spectroradiometer (MODIS) show that about 30%–60% of precipitating clouds in
the mid- and high-latitudes contain mixed-phase (M€
ulmenst€
adt et al., 2015). In this
chapter, authors describe in detail the methodology used in aircraft campaigns, what
quantities are typically measured, the importance of particle size distribution (PSD) of
hydrometeors, and its moments. The primary in situ measurement methods reviewed
include bulk measurements, single particle probes, and imaging probes, with references
to recent field campaigns ( Jackson et al., 2012, 2014; Jackson and McFarquhar, 2014).
Examples of observations made during the COnvective Precipitation Experiment
(COPE) in southwest England during summer 2013 are presented, with a detailed anal-
ysis of liquid water content (LWC), ice water content (IWC), and PSD characterization.
In general, the microphysical properties of convective clouds can be widely variable due
to numerous factors that include temperature, position in the cloud, vertical velocity,
3
Introduction

strength of entrainment, and the amount of cloud condensation nuclei loaded into the
cloud. The study illustrates that determining IWC from the airborne measurement is
much more challenging than determining LWC. Therefore, reducing the uncertainty
in IWC from airborne cloud microphysical measurements remains an important research
priority.
Chapter 5 provides an overview of the characterization of mixed-phase clouds from
field campaigns and ground-based networks. Earlier field campaigns focused on measure-
ments of the microphysical and dynamical conditions of mixed-phase cloud formation
and evolution (Rauber and Tokay, 1991; Heymsfield et al., 1991; Heymsfield and
Miloshevich, 1993). These studies contributed to solving problems such as aircraft icing
and cloud seeding for weather modification. In situ aircraft measurements documented
the presence of mixed-phase clouds with a layer of supercooled liquid water on the top of
an ice cloud. The US Department of Energy (DOE) Atmospheric Radiation Measure-
ment (ARM) program and its focus on the role of clouds in the climate system facilitated
many field missions. Some were directed to observations in Arctic regions, aiming to
establish a permanent observational station in Barrow, Alaska (Verlinde et al., 2016).
Advances in ground-based remote sensing capabilities developed by the ARM program,
aided by field campaigns, produced accurate methods to observe atmospheric processes
related to water vapor, aerosol, clouds, and radiation. The ability to detect and charac-
terize mixed-phase clouds at ARM sites provided the basis for developing additional
observation stations in other parts of the world. One significant development in Europe
was the Cloudnet program, which established a standard set of ground-based remote
sensing instruments capable of providing cloud parameters that can be compared with
current operational NWP models (Illingworth et al., 2007). Developments following
the Cloudnet program and the expansion of ARM capabilities and collaborations have
resulted in a more comprehensive approach for monitoring cloud systems— including
mixed-phase clouds—at a variety of sites, enabling the evaluation and improvement
of high-resolution numerical models (Haeffelin et al., 2016).
Chapter 6 focuses on the characterization of mixed-phase clouds in the Arctic region,
using aircraft in situ measurements and satellite observations. Data from the CALIPSO
and CloudSat satellites are used to determine the frequency of mixed-phase clouds.
Results show that mixed-phase clouds exhibit a frequent and nearly constant presence
in the Atlantic side of the Arctic region. In contrast, the Pacific side of the Arctic region
has a distinct seasonal variability, with mixed-phase clouds less frequent in winter and
spring and more frequent in summer and fall. The vertical distribution of mixed-phase
clouds showed that generally, they are present below 3 km, except in summer when these
clouds are frequently observed at mid-altitudes (3–6 km). Results indicate that the North
Atlantic Ocean and the melting of sea ice influence the spatial, vertical, and seasonal var-
iability of mixed-phase clouds (Mioche et al., 2015, 2017). The microphysical and optical
properties of the ice crystals and liquid droplets within mixed-phase clouds and the

associated formation and growth processes responsible for the cloud life cycle are eval-
uated based on in situ airborne observations. Lastly, the authors show that the coupling of
in situ mixed-phase clouds airborne measurements with the collocated satellite active
remote sensing from CloudSat radar and CALIOP lidar measurements are useful in val-
idating remote sensing observations.
2. MODELING
Chapter 7 provides an overview of numerical simulations of mixed-phase boundary layer
clouds using large eddy simulation (LES) modeling. Atmospheric turbulent mixing
characterizes boundary layer clouds, and the LES modeling has been extensively used
to represent the coupling between dynamical and mixed-phase microphysical processes.
Many detailed LES and intercomparison studies have been based on specific cloud sys-
tems observed during field campaigns (McFarquhar et al., 2007; Fridlind et al., 2007,
2012; Morrison et al., 2011). The focus of this chapter is mainly on modeling results from
the three major field campaigns on which intercomparison studies have been based: the
First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment-
Arctic Cloud Experiment (FIRE-ACE)/Surface Heat Budget in the Arctic (SHEBA)
campaign (Curry et al., 2000), the Mixed-Phase Arctic Cloud Experiment (M-PACE)
(Verlinde et al., 2007), and the Indirect and Semi-Direct Aerosol Campaign (ISDAC)
(McFarquhar et al., 2011). The chapter presents detailed results from each case study
and discusses outstanding questions about fundamental microphysical processes of Arctic
mixed-phase clouds.
Chapter 8 presents efforts toward a parametrization of mixed-phase clouds in general
circulation models. Observations show that mid- and high-latitude mixed-phase clouds
have a prolonged existence, considerably longer than most models predict. A series of
simplified physical models and LES simulations have been applied to data from aircraft
observations to understand the factors that lead to the longevity of mixed-phase clouds.
The results from many case studies indicate that the persistence of mixed-phase condi-
tions is the result of the competition between small-scale turbulent air motions and ice
microphysical processes (Korolev and Field, 2008; Hill et al., 2014; Field et al., 2014;
Furtado et al., 2016). Under certain situations, this competition can sustain a steady state
in which water saturated conditions are maintained for an extended period of time in a
constant fraction of the cloud volume. This chapter examines previous work on under-
standing this mechanism and explains how it can be elaborated into a parametrization of
mixed-phase clouds. The parametrization is constructed on exact, steady state solutions
for the statistics of supersaturation variations in a turbulent cloud layer, from which
expressions for the liquid-cloud properties can be obtained. The chapter reviews the
implementation of the parametrization in a general circulation model. It has been shown
to correct the representation of Arctic stratus, compared to in situ observations, and
5
Introduction

improve the distribution of liquid water at high latitudes. Some important consequences
of these enhancements are the reduction in the recognized radiative biases over the
Southern Ocean and improvement of the sea surface temperatures in fully coupled cli-
mate simulations.
Chapter 9 introduces and examines cloud feedback in the climate system. The
reflected shortwave (SW) radiation by the oceanic boundary layer (BL) clouds leads to
a negative cloud radiative effect (CRE) that strongly affects the Earth’s radiative balance.
The response of the BL clouds to climate warming represents a cloud feedback that is
highly uncertain in current global climate models. This situation impacts the uncertainty
in the estimation of equilibrium climate sensitivity (ECS), defined as the change in the
equilibrated surface temperature response to a doubling of atmospheric CO2 concentra-
tions. This chapter considers cloud feedback, with a focus on the mid- and high-latitudes
where cloud albedo increases with warming, as simulated by global climate models. In
these regions, the increase in cloud albedo appears to be caused by mixed-phase clouds
transitioning from a more ice-dominated to a more liquid-dominated state (McCoy et al.,
2014, 2015, 2016). The chapter discusses problems in constraining mixed-phase clouds in
global climate models due to: (a) uncertainties in ice nucleation—a fundamental micro-
physical process in mixed-phase clouds formation, and (b) current difficulties in measur-
ing the cloud ice mass. Another feature of global climate models is that they use a
parameterization of mixed-phase clouds. A frequent approach is to use a phase partition
with temperature based on aircraft measurements. One serious limitation of this method
is that it cannot account for the regional variability of ice nuclei (IN) (DeMott et al.,
2011). Comparisons with satellite data suggest that this behavior appears to be, at least
to some extent, due to an inability to maintain supercooled liquid water at sufficiently
low temperatures in current global climate models.
Chapter 10 addresses the impact of mixed-phase clouds’ supercooled liquid fraction
(SLF) on ECS. The ECS is a measure of the ultimate response of the climate system to
doubled atmospheric CO2 concentrations. Recent work involving GCM simulations
aimed to determine ECS due to changes in the cloud system in a warming climate. This
chapter examines the impact of mixed-phase clouds SLF on ECS using a series of
coupled climate simulations constrained by satellite observations. It follows a series of
recent studies on mixed-phase cloud feedback as determined by GCM simulations
(Storelvmo et al., 2015; Tan and Storelvmo, 2016; Tan et al., 2016; Zelinka et al.,
2012a,b). This study presents non-cloud feedbacks (Planck, water vapor, lapse rate,
and albedo) and cloud feedbacks (cloud optical depth, height, and amount). The cloud
phase feedback is a subcategory within the cloud optical depth feedback. It relates to how
the repartitioning of cloud liquid droplets and ice crystals affects the reflectivity of
mixed-phase clouds. Results suggest that cloud thermodynamic phase plays a significant
role in the SW optical depth feedback in the extratropical regions, and ultimately influ-
ences climate change.

3. CONCLUDING REMARKS
The recent research on mixed-phase clouds presented in this volume, as well as the
selected references for each chapter, provide an overview of current efforts to appreciate
cloud systems and their role in weather and climate. Understanding the role of clouds in
the atmosphere is increasingly imperative for applications such as short-term weather
forecast, prediction and prevention of aircraft icing, weather modification, assessment
of the effects of cloud phase partition on climate models, and accurate climate projections.
In response to these challenges, there is a constant need to refine atmospheric observation
techniques and numerical models. These efforts are sustained by many evolving research
programs and by a vibrant community of scientists. The book “Mixed-phase Clouds:
Observations and Modeling” provides the essential information to help readers under-
stand the current status of observations, simulations, and applications of mixed-phase
clouds, and their implications for weather and climate.
ACKNOWLEDGMENTS
I want to express my sincere gratitude to all of the authors and reviewers who contributed to this volume.
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9
Introduction

CHAPTER 2
Ice Nucleation in Mixed-Phase Clouds
Thomas F. Whale
Contents
1. The Relevance of Ice Nucleation to Mixed-Phase Clouds 13
1.1 Modes of Heterogeneous Ice Nucleation 14
1.2 Ice Nucleation in the Atmosphere 14
1.3 Ice Nucleation in Mixed-Phase Clouds 15
2. Experimental Methods for Examining Ice Nucleation 16
2.1 Wet Dispersion Methods 17
2.2 Dry Dispersion Methods 17
3. Nucleation Theory 18
3.1 Homogeneous Ice Nucleation 18
3.2 Heterogeneous Ice Nucleation 21
4. Properties of Good Heterogeneous Ice Nucleators 26
4.1 The Traditional View of Heterogeneous Ice Nucleation 26
5. What Nucleates Ice in Mixed-Phase Clouds? 30
6. Field Measurements of Ice Nucleating Particles 34
7. Summary 34
Acknowledgments 35
References 35
1. THE RELEVANCE OF ICE NUCLEATION TO MIXED-PHASE CLOUDS
At atmospheric pressure ice Ih is the thermodynamically stable form of water below 0°C.
Pure water does not freeze at 0°C because the stable phase must nucleate before
crystal growth can occur. Liquid water can supercool to temperatures below 35°C
(Herbert et al., 2015; Koop and Murray, 2016; Riechers et al., 2013) before ice nucle-
ation occurs homogenously. On some level, this fact must be responsible for the exis-
tence of mixed-phase clouds. If liquid water supercooled only slightly, much of the
variability and interest caused by the coexistence liquid water droplets and ice particles
would not occur. The progress of a cloud from consisting entirely of supercooled liquid
water to a state also containing ice must at some point involve an ice nucleation process.
Despite decades of research, heterogeneous ice nucleation remains poorly understood.
Improved insight into the process is of great importance for understanding of mixed-
phase clouds.
13
Mixed-Phase Clouds © 2018 Elsevier Inc.
https://doi.org/10.1016/B978-0-12-810549-8.00002-7 All rights reserved.

1.1 Modes of Heterogeneous Ice Nucleation
There are several pathways by which ice can form on a heterogeneous ice nucleating
particle (INP). These are known as modes. Historically, several different sets of defini-
tions have been used for these modes. Notably, the definitions of Vali (1985) and
Pruppacher and Klett (1997) are a little different. Recently, Vali et al. (2014) led an online
discussion by the ice nucleation community on terminology and published a document
outlining new definitions (Vali et al., 2015). These definitions that are described here are
used throughout this chapter.
The two principle modes of ice nucleation are deposition and freezing. Deposition ice
nucleation is defined as ice nucleation from supersaturated vapor on an INP or equivalent
without prior formation of liquid (a phase transition from gas to solid). Freezing ice
nucleation is defined as ice nucleation within a body of supercooled liquid ascribed to
the presence of an INP, or equivalent (a phase transition from liquid to solid). Freezing
nucleation is subdivided into immersion freezing, where the entire INP is covered in
liquid water, contact freezing, where freezing is initiated at the air-water interface as
the INP comes into contact with supercooled liquid water and condensation freezing,
where freezing occurs concurrently with formation of liquid water. It is challenging
to differentiate condensation freezing from both deposition nucleation and immersion
freezing in a strict physical sense, as the microscopic mechanism of ice formation is
not known in most cases. It is entirely plausible that many, most, or all cases of deposition
nucleation are preceded by formation of microscopic quantities of water which then
freezes, followed by depositional growth (Christenson, 2013; Marcolli, 2014). Mecha-
nisms of this sort are known to occur for organic vapors (e.g., Campbell et al., 2013;
Kovács et al., 2012). Similarly, it is not clear how condensation freezing differs from
immersion freezing in cases where liquid water does form prior to freezing (which
may be most or all cases). Happily, it is thought that immersion mode freezing is likely
to be the dominant freezing mode in most mixed-phase clouds (Cui et al., 2006; de Boer
et al., 2011) so we need not concern ourselves with nucleation of ice below water sat-
uration. The remainder of this chapter is therefore solely concerned with immersion
mode ice nucleation, where particles are clearly immersed in water. The following sec-
tion briefly describes the relevance of immersion mode ice nucleation to the atmosphere
in general, to determine the role of ice nucleation in mixed-phase clouds within the
broader field of ice nucleation studies.
1.2 Ice Nucleation in the Atmosphere
Clouds are made up of water droplets or ice crystals, or a mixture of thereof, suspended in
the atmosphere. By interacting with incoming shortwave radiation and outgoing long-
wave radiation, they can impact the energy budget of the earth and thereby play a key role
in the earth’s climate. They also strongly influence the earth’s hydrological cycle by

controlling water transport and precipitation (Hartmann et al., 1992). The magnitude of
the impact of clouds on the global energy budget remains highly uncertain despite
decades of research (Lohmann and Feichter, 2005). The latest Intergovernmental
Panel on Climate Change (IPCC) report suggests a net cooling effect from clouds of
20 Wm2
(Boucher et al., 2013).
Much of this uncertainty stems from the poorly understood nature of interactions
between atmospheric aerosol and clouds (Field et al., 2014). Atmospheric aerosol consists
of solid or liquid particles suspended in the air. There are many different types of aerosol
in the atmosphere. Primary aerosol is emitted directly from both natural and anthropo-
genic sources as particles, and includes mineral dust, sea salt, black carbon, and primary
biological particles. Secondary aerosol forms from gaseous precursors that are often
emitted by plants and oceanic processes. Clouds form when moist air rises through
the atmosphere and cools down. Typically, water droplets form on aerosol particles called
cloud condensation nuclei (CCN)(Pruppacher and Klett, 1997).
As the majority of clouds are formed via processes involving aerosol particles, cloud
properties such as lifetime, composition, and size are highly dependent on the properties
of the aerosol particles with which the cloud interacts. These effects are known as aerosol
indirect effects (Denman et al., 2007). Cloud glaciation, which is dependent on the ice
nucleation properties of the aerosol in clouds, (Denman et al., 2007) is one of these
effects. In the latest IPCC report, these effects have been grouped together, and confi-
dence in the assessment of the impact of aerosol-cloud interactions is rated as low. The
potential scale of the impact ranges from a very slight warming effect to a relatively sub-
stantial cooling of 2 Wm2
(Field et al., 2014).
There are two overarching categories of tropospheric clouds in which ice nucleation
is most relevant. These are cirrus clouds and mixed-phase clouds. Cirrus clouds form in
the upper troposphere at temperatures below 38°C, and consist of concentrated
solution droplets, which can be frozen via immersion mode ice nucleation, or ice formed
by deposition nucleation. Mixed-phase clouds form lower down in the troposphere
between 0°C and about 38°C (the approximate temperature of homogeneous ice
nucleation). Ice formation in these clouds is generally thought to be controlled by
immersion mode ice nucleation (Cui et al., 2006; de Boer et al., 2011) although the con-
tact mode may also play a role (Ansmann et al., 2005).
1.3 Ice Nucleation in Mixed-Phase Clouds
Ice nucleation processes have the potential to alter mixed-phase cloud properties in sev-
eral ways. Liquid water clouds may occasionally supercool to temperatures where
homogenous freezing is important before any ice is formed, below about 35°C
(Herbert et al., 2015), but generally glaciate at warmer temperatures (Ansmann et al.,
2009; Kanitz et al., 2011). This indicates heterogeneous ice nucleation controls
15

mixed-phase cloud glaciation in many cases. Satellite observations have indicated that at
20°C about half of mixed-phase clouds globally are glaciated (Choi et al., 2010).
The presence of ice crystals in a cloud can change its radiative properties significantly
compared to a liquid cloud and the size and concentration of ice crystals are also impor-
tant (Lohmann and Feichter, 2005). Cloud thickness, spatial extent, and lifetime can also
alter radiative forcing and can potentially depend on INP concentration. Precipitation
processes are closely linked to ice formation as ice I is more stable than liquid water below
0°C. As such, ice particles in mixed-phase clouds tend to grow at the expense of super-
cooled liquid water droplets. This process is known as the Wegener-Bergeron-Findeisen
process and is thought to be the most important route for precipitation from mixed-phase
clouds as larger particles will fall faster than smaller ones (Pruppacher and Klett, 1997).
Clouds which contain relatively small ice crystal concentrations and more supercooled
water are more likely to precipitate as the ice crystals can grow to larger sizes than they
might have if ice crystal concentrations were higher. As a result, lifetime of these clouds
might be shorter than it would otherwise have been. Additionally, ice multiplication
processes can result from the fragmentation of ice formed through primary ice nucleation
processes and increase the concentration of ice crystals in clouds by several orders of mag-
nitude (Phillips et al., 2003). The best understood of these is the Hallett-Mossop process
which occurs from 3°C to 8°C (Hallett and Mossop, 1974) although other processes
have also been posited (Yano and Phillips, 2011). These various processes, and others,
interact in complex and generally poorly understood ways, contributing to the large
uncertainty on the radiative forcing due to aerosol-cloud interactions (Field et al.,
2014). These interactions between aerosol, clouds, and liquid in mixed-phase clouds
need to be understood quantitatively to properly understand and assess the impact of
clouds on climate and weather. This chapter focuses on experimental methods for quan-
tifying concentrations of INPs, ways of describing the efficiency of INPs, what is known
about the identity of INPs in the atmosphere, and the progress of studies into fundamental
understanding of why certain substances nucleate ice efficiently.
2. EXPERIMENTAL METHODS FOR EXAMINING ICE NUCLEATION
The majority of quantitative studies of how efficiently a particular material nucleates ice
have been conducted with the goal of determining what species nucleate ice in the atmo-
sphere. The atmospheric science community has employed a wide variety of techniques.
There are two overarching families of techniques for determining the immersion mode
ice nucleating efficiency of nucleators. These are wet dispersion methods and dry disper-
sion methods (Hiranuma et al., 2015). Wet dispersion methods involve dispersion of
INPs into water, which is then frozen. Dry dispersion methods involve the dispersion
of aerosol particles into air, where they are then activated into water droplets before
freezing. Techniques have also been divided into those which use droplets supported

on the surface or suspended in oil, and those which use droplets suspended in gas (Murray
et al., 2012) which are largely synonymous with wet and dry dispersion techniques,
respectively. Almost invariably, raw ice nucleation data takes the form of a fraction of
droplets frozen under a given set of conditions. Typical variables are temperature, cooling
rate, droplet size, and nucleator identity and concentration of the nucleator in droplets.
2.1 Wet Dispersion Methods
Most wet dispersion techniques are droplet freezing experiments, also known as droplet
freezing assays. These involve dividing a sample of water into multiple sub-samples and
cooling these individual samples down until they freeze. For studies of heterogeneous ice
nucleation a nucleator is suspended in the water prior to sub-division, or pure water
droplets are placed onto a nucleating surface. The temperature at which droplets freeze
is recorded, typically by simultaneous video and temperature logging. Different droplet
volumes have been used, ranging from milliliters to picoliters (Murray et al., 2012; Vali,
1995). Droplets are typically either placed on hydrophobic surfaces (e.g., Lindow et al.,
1982; Murray et al., 2010) or in wells or vials (e.g., Hill et al., 2014). In these cases, freez-
ing is usually observed visually, often through a microscope. Emulsions of water droplets
in oil can also be frozen, and freezing events recorded via microscope (e.g., Zolles et al.,
2015) or by using a calorimeter (Michelmore and Franks, 1982). Recently, microfluidic
devices have been used to create mono-disperse droplets for studying ice nucleation
(Riechers et al., 2013; Stan et al., 2009).
Droplet freezing techniques typically use linear cooling rates, although isothermal
experiments have also been conducted (Broadley et al., 2012; Herbert et al., 2014;
Sear, 2014). Larger droplets up to milliliter volumes have typically been used for investi-
gations of biological ice nucleators while the smallest droplets have been used for studies of
homogeneous ice nucleation. The majority of studies of atmospherically relevant INPs
have been conducted using smaller, nano- to picoliter-sized droplets (Murray et al., 2012).
Other techniques that use wet dispersion to produce droplets include those that freeze
single droplets repeatedly many times in order to establish the variation in freezing tem-
perature in that single droplet (Barlow and Haymet, 1995; Fu et al., 2015). Wind tunnels
are similar in that they support single suspended droplets in an upward flow of air of
known temperature (Diehl et al., 2002; Pitter and Pruppacher, 1973). Freezing pro-
babilities are determined by conducting multiple experiments. Droplets are typically pre-
pared by wet dispersion then introduced into the airflow but could also be dry dispersed.
Similarly, droplets can be suspended by electrodynamic levitation (Kr€
amer et al., 1999).
2.2 Dry Dispersion Methods
Cloud expansion chambers are large vessels in which temperature, humidity, and aerosol
contents are controlled, usually with the goal of simulating clouds (Connolly et al., 2009;
17

Emersic et al., 2015; Niemand et al., 2012). Experiments involve pumping the chamber
out to reduce temperature thereby inducing ice nucleation in the chamber. The ice
nucleation efficiency of aerosols in the chamber can be determined from the appearance
of ice crystals. In order to conduct experiments in the immersion mode the INPs must
activate as CCN before ice nucleation occurs.
Continuous Flow Thermal Gradient Diffusion Chambers (CFDCs) flow air-
containing aerosols through a space where temperature and humidity are controlled using
two plates coated in ice (Garimella et al., 2016; Rogers, 1988; Stetzer et al., 2008). Typ-
ically, aerosol size distributions and concentrations are characterized going into the area
of controlled supersaturation with respect to ice and the number of ice crystals coming
out the other end it also determined. In this way a droplet fraction frozen can be deter-
mined. Alternatively, a pre-conditioning section can be used to ensure that all aerosol
particles prior are activated as CCN prior to entry to the ice nucleation section of the
instrument, thereby ensuring that all freezing is immersion mode (L€
u€
ond et al., 2010).
3. NUCLEATION THEORY
While there is no satisfactory overarching theory for nucleation phenomena (Sear, 2012)
there are various theories and descriptions used to describe ice nucleation. This section
describes theories and descriptions used for describing immersion mode ice
nucleation data.
3.1 Homogeneous Ice Nucleation
Homogenous nucleation is nucleation that does not involve a heterogeneous nucleator.
In the atmosphere, cloud water droplets can supercool to temperatures below 35°C.
While heterogeneous ice nucleation is probably more common in most mixed-phase
clouds, homogeneous nucleation is also thought to be a factor (Sassen and Dodd,
1988) and mixed-phase clouds have been observed at sufficiently cold temperatures to
support this (Choi et al., 2010; Kanitz et al., 2011). Many laboratory experiments have
also investigated homogenous nucleation (Murray et al., 2010; Riechers et al., 2013; Stan
et al., 2009) and it has been shown that classical nucleation theory (CNT) can describe
laboratory data for homogenous nucleation well (Riechers et al., 2013).
3.1.1 Classical Description of Homogenous Ice Nucleation
The following is a derivation of CNT adapted from work by Pruppacher and Klett
(1997), Mullin (2001), Debenedetti (1996), Murray et al. (2010), and Vali et al.
(2015). Supercooling occurs because of a kinetic barrier to the formation of solid clusters
large enough for spontaneous growth. This stems from the increasing energy cost of
forming interface between ice and supercooled water as the size of a cluster grows. At
the cluster size where the energy gain of adding a water molecule exceeds the energy

cost of forming an interface between the ice and supercooled water spontaneous growth
will occur. This can be expressed as:
ΔG ¼ ΔGs + ΔGV (1)
Where ΔG is the overall change in Gibbs free energy of the ice cluster, ΔGs is the surface
free energy between surface of the particle and the bulk of the supercooled water, and
ΔGV is volume excess free energy. ΔGs and ΔGV are competing terms, ΔGV being neg-
ative while ΔGs is positive. Gs can be expressed as:
Gs ¼ 4πr2
γ (2)
where r is the radius of the solid cluster and γ is the interfacial energy between ice and
water. Gv can be expressed as:
Gv ¼
4πr3
3v
kBT lnS (3)
where v is the volume of a water molecule in ice, kB is the Boltzmann constant, T is the
temperature, and S is the saturation ratio with respect to ice. Adding Eqs. (2) and (3) gives
the total Gibbs free energy of the barrier to nucleation:
ΔG ¼
4πr3
3v
kBT lnS + 4πr2
γ (4)
The two terms of Eq. (4) are opposing so the free energy of ice formation passes through a
maximum, as shown in Fig. 1. The maximum value corresponds to the size of the critical
nucleus, ri
∗.
Critical nucleus size can be calculated by differentiating Eq. (4) with respect to ri
∗
and setting dΔG/dri ¼ 0 before rearranging for ri yields:
Fig. 1 Schematic of ice germ radius against Gibbs free energy.
19

r∗
i ¼
2γv
kBT lnSΔGv
(5)
Eq. (5) can be used to calculate the temperature dependence of critical radius size. S can
be calculated using parameterizations from Murphy and Koop (2005) along with the
value for γ from Murray et al. (2010). It can be seen that the size of the critical nucleus
increases sharply with rising temperature in Fig. 2.
By substituting back into Eq. (4), ΔG∗ at temperature T can be calculated:
ΔG∗ ¼
16πγ3
v2
3 kbT lnS
ð Þ2 (6)
To determine nucleation rate, the Arrhenius style Eq. (7) can be applied.
Jhom ¼ A exp
ΔG∗ T
ð Þ
kT

(7)
Jhom is the nucleation rate, A is the pre-exponential factor, and k the Boltzmann constant.
Combining Eqs. (6) and (7) Eq. (8) can be written down.
ln Jhom ¼ lnA
16πγ3
v2
3k3T3 lnS
ð Þ2 (8)
Hence, a plot of ln Jhom against T3
(lnS)2
will be linear with an intercept of lnA and,
over a narrow temperature range, slope:
m ¼
16πγ3
v2
3k3
(9)
Since v is known, this allows γ to be determined from experiments determining Jhom.
0
5
10
15
20
25
30
35
40
45
50
–40 –35 –30 –25 –20 –15 –10 –5 0
Critical
nucleus
radius
(nM)
Temperature (°C)
Fig. 2 Critical radius size for Ice Isd as a function of temperature.

Jhom has units of nucleation events cm3
s1
. In larger volumes of water nucleation is
therefore more probable. In an experiment looking at a large number of identical droplets
held a constant temperature where a single nucleation event within a droplet is assumed
to lead to crystallization of that droplet a freezing rate R(t) can be determined. R(t) is a
purely experimental value that has units of events s1
. It can be determined for any
droplet freezing experiment, heterogeneous or homogeneous. Application to heteroge-
neous experiments is discussed in the following section. R(t) can be calculated using:
R t
ð Þ ¼
1
N0 NF
dNF
dt
(10)
where NF is the total number of frozen droplets at time t and N0 is the total number of
droplets present, frozen or unfrozen. If V is the volume of the droplets Eq. (11) can be
written down.
Jv ¼
R t
ð Þ
V
(11)
where Jv is the volume nucleation rate. if the droplets are free of impurities so that
nucleation is via the homogenous mechanism then:
Jhom ¼ Jv ¼
R t
ð Þ
V
(12)
Following on from this, for constant temperature the fraction of droplets NL that remains
unfrozen at time t can therefore be calculated using:
NL ¼ N0 exp JhomVt
ð Þ (13)
In cases where droplets are constantly cooled, rather than being held at a steady temper-
ature to small increments of it is necessary to apply Eq. (13) to small time intervals over
which changes in temperature are small. In this way, Jhom(T) can be determined.
3.2 Heterogeneous Ice Nucleation
Immersion mode heterogeneous ice nucleation takes place when an external entity
lowers the energy barrier preventing ice nucleation. As a result, the probability of a
nucleation event occurring at any given supercooled temperature can be far higher in
the presence of a suitable heterogeneous ice nucleator. The observed outcome is that
heterogeneous ice nucleation takes place at higher temperatures than homogenous
ice nucleation in otherwise equivalent systems. Different nucleators nucleate ice with
varying efficiency (Hoose and M€
ohler, 2012; Murray et al., 2012). The following
sections detail methods for describing immersion mode heterogeneous ice nucleation
efficiency.
21

3.2.1 Application of CNT to Heterogeneous Nucleation
In classical nucleation theory, the temperature dependent heterogeneous nucleation rate
coefficient can be related to the energy difference by:
Jhet T
ð Þ ¼ Ahet exp
ΔG∗φ
kT

(14)
where Ahet is a constant and φ the factor by which the heterogeneous energy barrier to
nucleation is lower than the homogenous barrier. This equation is identical to Eq. (7),
except that the height of the energy barrier is lowered by a factor φ calculated using:
φ ¼
2 + cosθ
ð Þ 1 cosθ
ð Þ2
4
(15)
where θ is the contact angle between a spherical ice nucleus and a flat surface of the nucle-
ator. It is possible to calculate contact angles if Jhet(T) is known therefore. It is not clear
what contact angles mean physically although they give an indication of a material’s ice
nucleating ability.
3.2.2 Single Component Stochastic Models
The simplest CNT based models are a type of single component stochastic (SCS) model.
Jhet(T) is usually measured per surface area of nucleator meaning it has units of events
cm2
s1
. These models use a single nucleation rate (Jhet) to describe a nucleator’s behav-
ior. Jhet is in principle calculated in the same way as Jhom from Eq. (10) except that a rate per
surface area of nucleator, Js is used:
Jhet ¼ Js ¼
R t
ð Þ
A
(16)
Jhet can be related to CNT as described as in the above section (e.g., Chen et al., 2008) to
account for temperature dependence of Jhet but a simple linear temperature dependence
can also be used (e.g., Murray et al., 2011).
These models are not usually appropriate as they assume that all droplets in an exper-
iment nucleate ice with the same rate. Although there are examples of nucleators which
show good agreement with a single component model, notably KGa-1b kaolinite
(Herbert et al., 2014; Murray et al., 2011) it is clear that this is not the case for many
materials (Herbert et al., 2014; Vali, 2008, 2014). Jhet often does not equal R/A
(Herbert et al., 2014; Vali, 2008, 2014). As a result, various other models of ice nucleation
have been developed. Multiple component stochastic models are an extension of single
component models.
3.2.3 Multiple Component Stochastic Models
Multiple stochastic models (MCSMs) have been developed to describe the observed var-
iation in nucleation rates between droplets. These models divide a population of droplets,

or sites, into sub-populations with different single component rates. There are a number
of different variations on this theme. Some use distributions of efficiencies described by
CNT (L€
u€
ond et al., 2010; Marcolli et al., 2007; Niedermeier et al., 2014; Niedermeier
et al., 2011), while others use linear dependences (Broadley et al., 2012). All use multiple
different curves, representing different sites, droplets, or particles and sum the freezing
probabilities of all these to generate a total nucleation rate at a given temperature. Such
descriptions therefore retain time dependence and account for variability between
droplets.
3.2.4 Singular Models
Singular models of ice nucleation assume that each droplet in an ice nucleation exper-
iment contains a site that induces it to freeze at a specific characteristic temperature
(Vali and Stansbury, 1966). The justification for this approach is that it is typically
observed that variability in freezing temperature for a single droplet frozen and thawed
multiple times is much smaller than the range in freezing temperature of a population of
droplets with identical nucleator content (Vali, 2008; Vali and Stansbury, 1966). The
concept was originally put forward by Levine (1950). Typically, concentration of sites
is related to either droplet volume or surface area of nucleator. The differential nucleus
spectrum, k(T), which can be calculated from the output of ice nucleation experiments
using:
k T
ð Þ ¼
1
V N0 NF T
ð Þ
ð Þ

dNF T
ð Þ
dT
(17)
where V is the droplet volume used in the experiment, N0 is the total number of
droplets in the experiment, and Nf (T) is the number of droplets frozen at temperature T.
By integrating this expression the cumulative nucleus spectrum, K(T) can be derived:
K T
ð Þ ¼
1
V
ln 1
NF T
ð Þ
N0

(18)
K(T) has dimensions of sites per volume. Recently, it has become common to deter-
mine the surface area of nucleator contained in each droplet in order to calculate the
ice active site density ns(T), which is a measure of the number of sites per unit surface
area of nucleator (Connolly et al., 2009). ns(T) is related to K(T) by:
ns T
ð Þ ¼
K T
ð Þ
A
(19)
where A is the surface area of nucleator per droplet. To calculate ns(T) directly from
droplet experimental data the following expression can be used:
ns T
ð Þ ¼
1
A
ln 1
NF T
ð Þ
N0

(20)
23

Site-specific models of ice nucleation can also conceivably use other units besides nucle-
ator surface area and droplet volume, for instance, the number of nucleation sites per cell
or per particle can be calculated, if the number of these entities per droplet is known.
Singular models ignore time dependence. According to a site-specific model at
constant temperature, no freezing will take place. This is generally not the case but it
is often true that freezing does not follow the sort of exponential decay that would be
predicted by a single component model (Sear, 2014).
3.2.5 The Framework for Reconciling Observable Stochastic
Time-Dependence (FROST)
To overcome the difficulty that simple site-specific models do not account for time
dependence, modified singular models can be used (Vali, 1994; Vali, 2008). If two iden-
tical sets of droplets (identical meaning that the two sets contain the same surface area of
nucleator) are cooled at different rates a greater fraction of the droplets that are cooled
more slowly will be frozen at a given relevant temperature. This is because time depen-
dence of ice nucleation will mean that every droplet has a greater probability of freezing
in the longer time interval allowed to it by the slower cooling rate, compared to the faster
cooling rate. Modified singular models incorporate a factor that accounts for shifts
induced by differing cooling rates into typical site-specific expressions for ice nucleation.
The Framework for Reconciling Observable Stochastic Time-dependence (FROST)
derived by Herbert et al. (2014) is similar to the modified singular approach, which allows
ice nucleation data obtained from experiments conducted at different ramp rates, or in
isothermal conditions to be reconciled. The shift in freezing temperature between two
experiments conducted at cooling rates r1 and r2 can be calculated using:
ΔTf ¼ β ¼
1
λ
ln
r1
r2

(21)
where β is the shift in freezing temperature caused by the change in cooling rate and λ
is the slope, dln(J)/dT, of the individual components in the MCSM of Broadley et al.
(2012) and Herbert et al. (2014). This equation can be used to calculate λ from
experimental fraction frozen data. A similar quantity, ω, is defined as the gradient
–dln(R/A)/dT. Herbert et al. (2014) showed using computer simulations that when
ω ¼ λ a single component stochastic model can be applied. When ω 6¼ λ there is vari-
ation in the nucleating ability of droplets in the experiment and a MCSM must be used to
account for data. λ can be regarded as a fundamental property of a nucleator.
FROST can be used to reconcile ns(T) from experiments conducted at different ramp
rates by substituting fraction frozen values calculated using Eq. (21) into Eq. (20). If a
standard r1 value of 1°C min1
it can be shown that:
NF T, r
ð Þ
N0
¼ 1 exp ns T
lnr
λ

A

(22)

where NF(T,r) is the number of droplets frozen at temperature T for an experiment con-
ducted at ramp rate r. This equation is compatible with the modified singular model of
Vali (1994). Typical modified singular approaches use an empirical shift from experimen-
tal data in temperature instead of λ.
By performing multiple experiments Herbert et al. (2014) showed that FROST could
account for experimental data. Four sets of experiments conducted at four different
ramp rates could be reconciled with single λ value for two different nucleators. For
KGa-1b kaolinite this λ was equal to its ω value while for BCS 376 microcline this
was not the case, meaning that a single-component model could be used to describe
ice nucleation by KGa-1b, but not BCS 376.
3.2.6 Comparison and Summary of Models of Heterogeneous Nucleation
Heterogeneous ice nucleation is, in the majority of cases, a phenomenon with both
site-specific and time dependent characteristics. For most freezing experiments it is likely
that individual droplets contain many sites which nucleate ice more efficiently than the
majority of the nucleator surface area, one of which may nucleate ice more efficiently that
all others sites in the droplet, as assumed by the site-specific model. Ice nucleation at sites
is likely to be stochastic, and may be well described by a single component stochastic
model, possibly by classical nucleation theory with a suitably reduced free energy barrier
height. As the specific mechanism of heterogeneous ice nucleation is not known it cannot
be said that this is the case.
There is little reason to suppose that classical nucleation theory as applied to hetero-
geneous nucleation is valid for the nucleation of ice. It is generally acknowledged that the
contact angle used in Eqs. (14) and (15) has no physical meaning and serves as a proxy for
lowering the height of the free energy barrier calculated by CNT at a given temperature.
Clearly, site-specific models are also unphysical insofar as ice nucleation is to some extent
stochastic. No experiment has found that droplets repeatedly freeze at the exact same
temperature.
Site-specific models account for the strong temperature dependence observed in
nucleation by most nucleators while single component stochastic models account for
the time dependence. They ignore time dependence and droplet to droplet variability
in nucleation efficiency respectively. The various multiple component stochastic models
and time dependent site-specific models seek to add the facet of the problem that the
simple models do not account for.
Ultimately, none of these models of ice nucleation offer real insight into the under-
lying mechanism of ice nucleation (Vali, 2014). Multiple component stochastic models
generally provide the best fit to experimental data, which is not surprising as they have the
most degrees of freedom. They are, in a sense, fitting routines. That said, they are prob-
ably also the most physically realistic models of ice nucleation. Generally, it is convenient
to use site-specific models as temperature dependence is the overriding determinant of
25

freezing rate. Many recent studies have tended to determine ns as a means of comparing
ice nucleating species. Agreement is not universal however. For instance, efforts have
been made to explain the variation in freezing rate between the individual droplets in
experiments as a product of variations in the amount of material between different
droplets (Alpert and Knopf, 2016).
4. PROPERTIES OF GOOD HETEROGENEOUS ICE NUCLEATORS
Ideally, it would be possible to predict the efficiency of a heterogeneous ice nucleator
from knowledge of its physical and chemical properties. For comparison, it is possible
to describe the activity of CCN with a single hygroscopicity parameter (Petters and
Kreidenweis, 2007). At current this sort of description is not possible for ice nucleation.
Indeed, it seems unlikely that it will be so straightforward. In the case of deposition mode
ice nucleation there is a growing body of evidence that pore-condensation freezing is
responsible for ice nucleation in many cases (Campbell et al., 2016; Marcolli, 2014),
which has the potential to simplify the problem there. For the immersion mode ice
nucleation relevant to mixed-phase clouds no consistent theory exists. The difficulty
of understanding what makes a good INP stems from the small size of the ice critical
nucleus (see Fig. 2) and the small spatial extent of the nucleation event. According to
CNT, critical nuclei range in size from a 1 nm radius at 38°C to 10 nm at 4°C. These
critical nuclei are spatially rare. Whatever volume of droplet is frozen, there will usually
only be a single critical nucleus present. Droplets are typically at least picometers across.
No current technique is capable of locating and usefully measuring the physical properties
of an event this small and rare. As a result, properties of ice nucleation have usually been
inferred from experimental data.
4.1 The Traditional View of Heterogeneous Ice Nucleation
Historically, five properties were thought to be important for heterogeneous ice
nucleation. These were listed and discussed by Pruppacher and Klett (1997). While these
have never been regarded as hard and fast rules, discussion of the reasons for them and
where they fall down are instructive. They are:
(1) The insolubility requirement: nucleators must provide an interface with water.
Dissolved substances do not provide an interface and so do not nucleate ice.
(2) The size requirement: observations in the atmosphere indicate that INPs tend to be
large. This requirement is somewhat vague, although it stems from the observation
that larger particles in the atmosphere tend to be the ones that nucleate ice. It is also
assumed that an INP must be larger than a critical nucleus.
(3) The chemical bond requirement: a nucleator must be able to bind to water in order
to cause nucleation. Stronger bonding is likely to improve nucleation efficiency.

(4) The crystallographic requirement: the classic lattice matching idea first put forward
by Vonnegut (1947). Substances with a similar lattice structure and spacing to ice will
provide a template for a critical nucleus.
(5) The active site requirement: based on a combination of the observation that site-
specific descriptions often give the best account of ice nucleation and the fact that
deposition mode ice nucleation tends to occur repeatedly on specific locations on
crystals. It seems likely that this is more related to vapor condensation than ice nucle-
ation (Marcolli, 2014).
The next sections looks at how these requirements have been challenged and revised in
recent years and what is known about the mechanism of heterogeneous ice nucleation
from experimental studies. Computational studies of ice nucleation are then examined
and the outcomes of the two approaches discussed.
4.1.1 Size and Solubility of Heterogeneous INPs
While INPs have traditionally been regarded as large and insoluble (Pruppacher and
Klett, 1997) a number of counter examples are known. In recent times biological mac-
romolecules associated with pollen that have been claimed as soluble have been shown to
nucleate ice efficiently (Pummer et al., 2012, 2015). These molecules weigh from 100 to
860 kDa, which equates to a radius of less than 10 nm. This is only slightly larger than the
critical nuclei they nucleate. They are perhaps 10 times smaller than the particles that
Pruppacher and Klett (1997) envisaged as too small to efficiently nucleate ice on the basis
of older work. Similarly, Ogawa et al. (2009) showed that solutions of poly-vinyl alcohol
could nucleate ice, although only at a few degrees above homogenous nucleation
temperatures.
4.1.2 Lattice Matching
The best known example of inference of ice nucleation properties is the lattice matching
concept of Vonnegut (1947). The idea is that substances that have a similar crystal struc-
ture to ice, with similar lattice constants will pattern the first layer of ice. The amount of
lattice mismatch, or lattice disregistry (Pruppacher and Klett, 1997; Turnbull and
Vonnegut, 1952) can be readily calculated from knowledge of the crystal structure.
On this basis Vonnegut (1947) identified AgI as a potentially excellent nucleator and
all subsequent experimentation has shown that he was correct.
The role of lattice matching in ice nucleation by AgI has been questioned for some
time. Zettlemoyer et al. (1961) argued that water likely adhered to specific sites on the
surface of AgI, which may have been oxidized, rather than forming a layer over the crystal
on the basis of the difference in adsorption of water and nitrogen. More recently,
Finnegan and Chai (2003) postulated an alternative mechanism for ice nucleation by
AgI where clustering of surface charge controls ice nucleation. There is no universal
agreement on the mechanism of ice nucleation by AgI from experimentalists.
27

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