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The Impact of Mesoscale Gravity Waves on Homogeneous Ice Nucleation in Cirrus Clouds

28 May 2019-Geophysical Research Letters (John Wiley & Sons, Ltd)-Vol. 46, Iss: 10, pp 5556-5565

Abstract: Effects of a spectrum of mesoscale gravity waves on homogeneous aerosol freezing in midlatitude cirrus are studied by means of parcel model simulations that are driven by random vertical wind speeds constrained by balloon measurements. Stochastic wave forcing with mean updraft speeds of 5–20 cm/s leads to substantial nucleated ice crystal number concentrations (ICNC) of 0.1–1 cm−3 in situations with slow large-scale cooling, which by itself would generate fewer ice crystals. The stochastic nature of wave-driven air parcel temperatures enhances ICNC even further, but the times required to reach freezing conditions unsupported by large-scale cooling may vary widely. In the presence of wave forcing, ice crystals with low ICNC (<1–10 L−1) are also generated by homogeneous freezing, albeit only rarely. Comparisons with aircraft measurements suggest significant influences of heterogeneous ice-nucleating particles and ice crystal sedimentation on ICNC, but quantifying their individual contributions remains elusive. Plain Language Summary Spontaneous freezing of airborne, water-containing particles below −38 ◦C is a fundamental pathway to form ice crystals in high-altitude cirrus clouds. This ice formation process has been well researched and was the first represented in weather forecast and climate models to advance cirrus predictions. One key characteristic is its strong dependence of the number of ice crystals formed on the cooling rate of air. Recent observations show that rapid cooling rates are generated by ubiquitous gravity waves. Here, we explore the rich suite of phenomena taking place during cirrus formation caused by a spectrum of gravity waves. We find that wave effects should be considered in future model simulations, when comparing model results with observations, and in parameterizations of cloud ice crystal formation.
Topics: Nucleation (63%), Cirrus (62%), Ice nucleus (59%), Mesoscale meteorology (56%)

Summary (2 min read)

1. Introduction

  • Mesoscale air motion variability is crucial for the nucleation of ice crystals in cirrus (see Kärcher, 2017a, and references therein).
  • Superpressure balloon (SPB) measurements at altitudes of 18–21 km directly link mesoscale vertical wind speed and the associated temperature variability to gravity waves and quantified spectral properties (Podglajen et al., 2016; Schoeberl et al., 2017).
  • While the attribution of ice nucleation mechanisms in cirrus clouds in global climate models is challenging (Dietlicher et al., 2018; Gasparini et al., 2018) and such models have already begun to parameterize the impact of unresolved gravity waves on cirrus formation (Penner et al., 2018), it is important to explore this issue systematically on the process level as a prerequisite to improving ice nucleation parameterizations (Barahona & Nenes, 2008; Kärcher & Lohmann, 2002).
  • Before enhancing complexity by considering effects of heterogeneous ice-nucleating particles (INPs), which are poorly constrained by field observations at cirrus temperatures (<230–235 K; Hoose & Möhler, 2012; Jensen et al., 2018), the authors focus on the more basic and much better understood homogeneous freezing process.
  • The authors evaluate statistically microphysical parcel model simulations forced with a large number of different random realizations of fluctuation time series.

2. Stochastic Simulations

  • The spectral parcel model primeice solves a large set of equations governing the temporal evolution of heat, water vapor, and supercooled/frozen water during ice nucleation and aqueous aerosol particle and ice crystal growth due to uptake of water vapor (Kärcher, 2017b).
  • 2 Geophysical Research Letters 10.1029/2019GL082437 tion between constant updraft and wave-driven vertical wind speed fluctuations, w′ , is somewhat artificial.
  • Individual w′ values are sampled randomly from a Laplacian with prescribed standard deviation 𝜎w, or, in terms of adiabatic cooling rates (𝜅), 𝜎𝜅 = 𝛤𝜎w.
  • The authors note that across all the cases discussed here, T* ≈ 218 K with very little scatter (±0.25 K), corresponding to a narrow range of ice saturation ratios, S⋆ ≈ 1.5 ± 0.02, characteristic for homogeneous freezing events (Kärcher & Jensen, 2017).
  • The data points in Figure 1 exhibit considerable scatter for w0 < 10–20 cm/s, about 15% lie below n = 10−3 cm−3.

3.1. Expectation Values

  • The authors performed two additional sets of simulations halving and doubling the mean vertical wind forcing of 10 cm/s. Figure 2 shows the resulting averaged ICNC, 𝜇n(w0) (expectation values).
  • The authors would expect the nucleated ICNC to approach a constant value for w0 ≪ 𝜇w, if they just looked at the mean ICNC calculated directly from the updraft speed fluctuation statistic without accounting for sink processes of the ICNC.
  • The authors call those values—shown as smooth colored curves in Figure 2—instantaneous ice numbers (equation (S4)).
  • Stronger subsidence will make cirrus formation increasingly unlikely due to the rapidly growing separation between the diminishing ice supersaturation and the homogeneous freezing threshold.
  • Preferential freezing results from the stochastic nature of the temperature fluctuations.

3.2. Comparison With Observations

  • Normalized probability density functions, dP∕dn, represent the fraction of n values that fall into a given number density bin.
  • The authors expect differences between these distributions, since the MACPEX data contain ICNCs sampled at various stages of the cirrus cloud, while the parcel simulations only consider nucleated ice crystals.
  • Regarding differences in shape, the authors note that the left (low-n) wing of the observed distribution might be affected by sample volume limitations of the measurements.
  • If the authors compute the total ICNC directly from instantaneous expectation values, they obtain 𝜇n = 0.09–0.7 cm−3 from equation (S8) for the range of mean updraft speeds prevailing during MACPEX.
  • The authors offer two explanations to account for the discrepancy in total nucleated ICNC, which is not entirely unexpected.

4. Conclusions and Outlook

  • 7 Geophysical Research Letters 10.1029/2019GL082437 freezing in midlatitude cirrus.
  • The authors find that high updraft speed fluctuations increase total nucleated ICNC to much larger values than those calculated deterministically based solely on the probability of occurrence of the fluctuations.
  • The overall similarity of the shapes of simulated and analytical statistics suggests that wave-driven dynamical forcing and homogeneous freezing play important roles in in situ cirrus formation, inasmuch as ICNC values >10 cm−3 have been measured in cirrus.
  • When including the effects of waves, geographical, seasonal, and topographic variability in updraft speeds should be accounted for.

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The Impact of Mesoscale Gravity Waves on Homogeneous
Ice Nucleation in Cirrus Clouds
B. Kärcher
1
, E. J. Jensen
2
, and U. Lohmann
3
1
DLR Oberpfaffenhofen, Institut für Physik der Atmosphäre, Wessling, Germany,
2
National Aeronautics and Space
Administration, Ames Research Center, Mountain View, CA, USA,
3
ETH Zürich, Institute of Atmospheric and Climate
Science, Zurich, Switzerland
Abstract Effects of a spectrum of mesoscale gravity waves on homogeneous aerosol freezing in
midlatitude cirrus are studied by means of parcel model simulations that are driven by random vertical
wind speeds constrained by balloon measurements. Stochastic wave forcing with mean updraft speeds of
5–20 cm/s leads to substantial nucleated ice crystal number concentrations (ICNC) of 0.1–1 cm
3
in
situations with slow large-scale cooling, which by itself would generate fewer ice crystals. The stochastic
nature of wave-driven air parcel temperatures enhances ICNC even further, but the times required to reach
freezing conditions unsupported by large-scale cooling may vary widely. In the presence of wave forcing,
ice crystals with low ICNC (<1–10 L
1
) are also generated by homogeneous freezing, albeit only rarely.
Comparisons with aircraft measurements suggest significant influences of heterogeneous ice-nucleating
particles and ice crystal sedimentation on ICNC, but quantifying their individual contributions remains
elusive.
Plain Language Summary Spontaneous freezing of airborne, water-containing particles below
38
C is a fundamental pathway to form ice crystals in high-altitude cirrus clouds. This ice formation
process has been well researched and was the first represented in weather forecast and climate models to
advance cirrus predictions. One key characteristic is its strong dependence of the number of ice crystals
formed on the cooling rate of air. Recent observations show that rapid cooling rates are generated by ubiq-
uitous gravity waves. Here, we explore the rich suite of phenomena taking place during cirrus formation
caused by a spectrum of gravity waves. We find that wave effects should be considered in future model sim-
ulations, when comparing model results with observations, and in parameterizations of cloud ice crystal
formation.
1. Introduction
Mesoscale air motion variability is crucial for the nucleation of ice crystals in cirrus (see Kärcher, 2017a,
and references therein). We refer to cirrus as upper tropospheric ice clouds that form in situ, for exam-
ple, in frontal systems. Superpressure balloon (SPB) measurements at altitudes of 18–21 km directly link
mesoscale vertical wind speed and the associated temperature variability to gravity waves and quantified
spectral properties (Podglajen et al., 2016; Schoeberl et al., 2017). Since these airborne measurement plat-
forms are advected by the wind field, properties of fluctuations derived from them are highly useful for
Lagrangian cloud studies. Dinh et al. (2016) and Jensen et al. (2016) used SPB temperature time series to
drive detailed ice nucleation simulations, focussing on the tropical tropopause layer. Kienast-Sjögren et al.
(2015)—using a Lagrangian microphysical aerosol-cloud model—investigated cirrus over a midlatitude site
combining small-scale vertical wind speeds and temperature fluctuations inferred from radiosonde sound-
ings and a high-resolution weather prediction model. Haag and Kärcher (2004) used results from a global
weather prediction model with superimposed fluctuations to study hemispheric properties of midlatitude
cirrus.
Mesoscale gravity waves are ubiquitous in the upper troposphere and lower stratosphere. SPB measure-
ments show that power spectra of their properties versus intrinsic wave frequency are typically broad and
continuous, consistent with a superposition of many waves. A spectrum of mesoscale gravity waves gener-
ates broad frequency distributions of ice crystal number concentrations (ICNC) via homogeneous freezing
of supercooled aqueous solution particles (Hoyle et al., 2005; Jensen & Pfister, 2004; Kärcher & Ström, 2003).
RESEARCH LETTER
10.1029/2019GL082437
Key Points:
We present a systematic process
study of effects of a spectrum of
gravity waves on homogeneous
ice nucleation in cirrus through
ensemble simulations
High cooling rates have
disproportionately large impact
on nucleated ice crystal number
concentrations at low background
updraft speeds
Analysis of midlatitude continental
cirrus measurements suggests impact
of heterogeneous nucleation and
sedimentation on total ice numbers
Supporting Information:
Supporting Information S1
Correspondence to:
B. rcher,
bernd.kaercher@dlr.de
Citation:
Kärcher, B., Jensen, E. J., & Lohmann,
U. (2019). The impact of mesoscale
gravity waves on homogeneous ice
nucleation in cirrus clouds.
Geophysical Research Letters, 46.
https://doi.org/10.1029/2019GL082437
Received 12 FEB 2019
Accepted 22 APR 2019
©2019. American Geophysical Union.
All Rights Reserved.
KÄRCHER ET AL. 1

Geophysical Research Letters 10.1029/2019GL082437
The random nature of wave perturbations motivates the use of probabilistic methods to describe them. Pro-
cess models have studied aspects of homogeneous freezing using randomized small-scale dynamical forcing
(Dinh et al., 2016; Hoyle et al., 2005; Murphy, 2014; Shi & Liu, 2016).
Faithful applications of cirrus parameterizations in cloud schemes of large-scale models require sound rep-
resentations of unresolved cooling rates (Lohmann & Kärcher, 2002). While the attribution of ice nucleation
mechanisms in cirrus clouds in global climate models is challenging (Dietlicher et al., 2018; Gasparini et al.,
2018) and such models have already begun to parameterize the impact of unresolved gravity waves on cirrus
formation (Penner et al., 2018), it is important to explore this issue systematically on the process level as a
prerequisite to improving ice nucleation parameterizations (Barahona & Nenes, 2008; Kärcher & Lohmann,
2002).
Before enhancing complexity by considering effects of heterogeneous ice-nucleating particles (INPs), which
are poorly constrained by field observations at cirrus temperatures (<230–235 K; Hoose & Möhler, 2012;
Jensen et al., 2018), we focus on the more basic and much better understood homogeneous freezing process.
Field measurements leave little doubt that homogeneous freezing of supercooled aerosol particles is active
in cirrus and responsible for at least the generation of the rightmost tail (
>0.5 cm
3
) of probability distribu-
tions of ICNC. The main factor limiting INP effects is their low upper tropospheric number concentration
(
<0.1 cm
3
; DeMott et al., 2010), which makes them inefficient in suppressing homogeneous freezing in
the presence of sufficiently large vertical wind speeds (DeMott et al., 1997). Nonetheless, potent INPs are
capable of modulating or, if sufficiently abundant, dominating cirrus properties according to global model
simulations (Gettelman et al., 2012; Kuebbeler et al., 2014; Penner et al., 2018; Shi & Liu, 2016; Zhou &
Penner, 2014).
We explore systematically the homogeneous freezing process in midlatitude cirrus clouds due to gravity
wave-driven fluctuations of vertical wind speed consistent with Lagrangian SPB measurements. The pre-
scribed wave perturbations represent conditions away from strong local wave sources such as elevated
mountain ridges or deep convective clouds. We evaluate statistically microphysical parcel model simula-
tions forced with a large number of different random realizations of fluctuation time series. We compare our
results with data taken during an extensive airborne field campaign, allowing us to extend previous findings
on factors controlling midlatitude cirrus cloud formation (Jensen et al., 2013). We describe the stochastic
ice nucleation simulations in section 2, analyze the results of tens of thousands of them and compare them
to aircraft observations in section 3, and conclude our work in section 4.
2. Stochastic Simulations
The spectral parcel model prime solves a large set of equations governing the temporal evolution of heat,
water vapor, and supercooled/frozen water during ice nucleation and aqueous aerosol particle and ice crystal
growth due to uptake of water vapor (Kärcher, 2017b). We consider ambient conditions above ice but below
water saturation, where ice crystals can form homogeneously by freezing of liquid solution droplets.
Air parcel temperature, T, is adiabatically perturbed by random vertical wind speed fluctuations, w
. These
fluctuations are superimposed onto a constant updraft speed, w
0
0, driving ice microphysics in the
absence of wave-driven variability. Its prescribed value may be thought of as representative for synoptic
conditions (w
0
< 10 cm/s), orographic forcing (10–100 cm/s and sometimes exceeding 1 m/s), or pertur-
bations induced by convection (
>1 m/s). Values of w
0
greater than 1–10 m/s are found in the detrainment
zones of deep convective clouds, where homogeneous ice formation involves aerosol particles that have
been activated into cloud droplets prior to or along with freezing at temperatures 233–238 K. Presumably,
at these conditions, vertical wind speed fluctuations have different statistical properties (e.g., mean values,
variances, and power spectral densities) than those caused by gravity waves, so the findings reported here
are not directly applicable to such cases. Background wind speeds of (fractions of) millimeters per second
are found in the tropical tropopause layer, where T is lower (<200 K) than in midlatitudes studied here.
A decomposition of updraft speeds has also been employed by Spichtinger and Krämer (2013), represent-
ing fluctuations by a monochromatic sinusodial wave. Investigating the impact of wave phase at which ice
nucleation sets in, Jensen et al. (2010) showed that a spectrum of waves with random phases leads to broad
ICNC distributions. Since the constant updraft w
0
introduced here refers to the large-scale vertical wind
speeds resolved in global models, only the range w
0
< 1–10 c/s is relevant. For higher w
0
values, the separa-
KÄRCHER ET AL. 2

Geophysical Research Letters 10.1029/2019GL082437
tion between constant updraft and wave-driven vertical wind speed fluctuations, w
, is somewhat artificial.
Outside of convection, waves are the only source of updraft speeds in excess of
10 cm/s and even smaller
values associated with synoptic and planetary waves.
The wave forcing employed here accounts for the observed, double exponential (Laplacian) shape of the
vertical wind speed statistic, L(w
)=exp(−|w
|𝜇
w
)∕(2𝜇
w
). This distribution has zero mean, and 𝜇
w
is
the mean value taken over the one-sided (updraft) statistic, relating to the standard deviation,
𝜎
w
, via
𝜇
w
2
0
w
L(w
)dw
= 𝜎
w
2. The Laplacian approximately fits Lagrangian measurements (Podglajen
et al., 2016) and is used to generate fluctuation time series, w
(t), one for each nucleation simulation. The
vertical wind speed fluctuations are autocorrelated over a time t
c
= 2.8 min. Therefore, they are defined
only at discrete times (multiples of t
c
) and were approximated by stair steps for numerical integration. The
power spectrum of w
is flat (Figure 1 in Podglajen et al., 2016), meaning that all wave frequencies up to
the Brunt-Väisälä frequency—an upper limit constraining gravity wave propagation—are included in the
forcing with equal weight.
The temperature fluctuations, T
, that result from the wind forcing are obtained by advancing the stochastic
differential equation DT
Dt =−𝛤 w
, where DDt denotes the Lagrangian (material) time derivative and
𝛤 0.01 K/m is the dry adiabatic lapse rate. Individual w
values are sampled randomly from a Laplacian
with prescribed standard deviation
𝜎
w
, or, in terms of adiabatic cooling rates (𝜅), 𝜎
𝜅
= 𝛤𝜎
w
. This approach
replicates the first-order autoregressive model to represent T
(t) as proposed by Podglajen et al. (2016) based
on the underlying w
measurements. In prime, DT
Dt is added to adiabatic and diabatic temperature
tendencies, related to w
0
and latent heat exchange, respectively. Based on previous observational evidence,
we choose a cooling rate standard deviation 𝜎
𝜅
= 5 K/hr as a baseline value at cirrus levels. Cooling rate
fluctuations do not vary significantly with altitude within few kilometers around the tropopause (Podglajen
et al., 2016).
Figure 1 shows results from parcel model simulations, each initialized at T
0
= 221 K (air pressure 300 hPa)
and ice saturation ratio S
0
= 1.3. These values are slightly above (3 K for T
0
) and below (0.2 for S
0
) the
values at freezing and were chosen such that mesoscale temperature variations are capable of triggering
homogeneous freezing and within reasonable time scales (few hours). The initial total number density, mean
dry radius, and geometric standard deviation of lognormally distributed aerosol particles were 500 cm
3
,
20 nm, and 1.5, respectively. We do not vary aerosol parameters, because the dependence of n on them is
much weaker than on w (Kärcher & Lohmann, 2002; Kay & Wood, 2008; Liu & Shi, 2018). Time steps used in
the simulations are variable, 𝛿t [s]=1∕(w
0
+ |w
|)[cms], resolving individual freezing events. In addition,
we imposed t
c
as an upper limit time step to capture each vertical wind speed fluctuation.
With n indicating the number concentration of nucleated ice crystals, the circles in Figure 1 represent all
{n, w
0
} data points resulting from an ensemble of 10, 000 simulations. Each simulation was started with a
random choice for w
0
and a different w
(t)-realization (given 𝜎
𝜅
= 5 K/hr or 𝜇
w
10 cm/s) and terminated
once the nucleated ice crystal number mixing ratio assumed a constant value after the first freezing event.
The quenching of supersaturation right after freezing makes subsequent nucleation events unlikely, except
in cases with very low n; therefore, the restriction of our analysis to first nucleation events is not problematic.
Statistics of first freezing times are presented in the supporting information.
The simulations capture the dependence of nucleated ICNC on the homogeneous freezing temperature, T
,
which is, however, very weak. We note that across all the cases discussed here, T
*
218 K with very little
scatter (
±0.25 K), corresponding to a narrow range of ice saturation ratios, S
1.5 ± 0.02, characteristic for
homogeneous freezing events (Kärcher & Jensen, 2017). Examining the full upper tropospheric temperature
range would reveal significant variations of T
and nucleated ICNC.
The data points in Figure 1 exhibit considerable scatter for w
0
< 10–20 cm/s, about 15% lie below n =
10
3
cm
3
. These nonpersistent cooling events have been termed temperature limited by Dinh et al. (2016).
Most of these low-n events are generated when w
changes its sign before the freezing event is completed.
They happen to occur since the wave-driven vertical wind speed fluctuations contain high-frequency con-
tributions associated with time scales of 5–10 min, comparable to the duration of homogeneous freezing
events (minutes; Jensen et al., 2016). The fraction of nonpersistent cooling events would be lower without
restricting the analysis to first freezing times.
KÄRCHER ET AL. 3

Geophysical Research Letters 10.1029/2019GL082437
Figure 1. Number concentration, n, of homogeneously nucleated ice crystals versus background updraft speed, w
0
,
from ensemble simulations (circles). In each case, gravity wave-induced vertical wind speed fluctuations driving ice
microphysics in the parcel simulations were randomly sampled from a Laplacian distribution with a mean value of
updraft speed (standard deviation of cooling rate) fluctuations
𝜇
w
= 10 cm/s (𝜎
𝜅
5 K/hr) added to the constant w
0
.
The arrow points to an excessively high concentration generated by an exceptionally large updraft fluctuation. The
curve was obtained from simulations without fluctuations.
The scatter of n in a given narrow w
0
-range decreases progressively with increasing w
0
. The curve obtained
from simulations without fluctuations follows a power law dependence, as expected from cloud physical
theory (Kärcher & Lohmann, 2002): n(w)=n
1
[(w
0
+ w
)∕w
1
]
𝛼
, where n
1
is the nucleated ICNC at a given
T and w = w
1
. A good fit at T = 218 K is obtained for n
1
= 0.185 cm
3
, w
1
= 10 cm/s, and 𝛼 = 32
(Figure 1). The data collapse onto this curve beyond w
0
= 1 m/s, showing that w
0
governs ice formation
for w
0
≫𝜇
w
(deterministic regime). By contrast, ice formation is entirely controlled by the fluctuations
for w
0
≪𝜇
w
(fluctuation-dominated regime). In the deterministic regime, nonpersistent cooling events no
longer occur; we do not discuss this regime any further with
𝜇
w
= 5 20 cm/s, as we are concerned with
nonconvective (in situ) ice formation, where values w
0
< 10 cm/s prevail.
The arrow highlights a very rare data point indicating
400 ice crystals per cubic centimeter of air. In this
case, one single freezing event caused by an updraft speed fluctuation of 16.7 m/s (10 𝜎
w
) depleted about
80% of the available aerosol particles. Fluctuation amplitudes of comparable magnitude are captured by the
non-Gaussian statistic, L(w
). The probability of occurrence of such a value is exp(−10
2)≈10
6
. This
means that in a sample of 10, 000 data points, there is a 1% chance of encountering such an event. Filling
the gap between the outlier and the majority of the other data points in Figure 1 requires a much larger
number of simulations.
3. Analysis of Nucleated ICNC
3.1. Expectation Values
We performed two additional sets of simulations halving and doubling the mean vertical wind forcing of
10 cm/s. We calculated in each case moving averages of n over 75 w
0
data points from the full {n, w
0
} data
sets. Figure 2 shows the resulting averaged ICNC,
𝜇
n
(w
0
) (expectation values). As expected from the above,
the nucleated concentrations converge showing decreasing scatter as w
0
enters the deterministic regime.
KÄRCHER ET AL. 4

Geophysical Research Letters 10.1029/2019GL082437
Figure 2. Mean ice crystal number concentration, 𝜇
n
,versusw
0
from ensemble simulations for three cases
𝜎
𝜅
= 2.5, 5, 10 K/hr (red, magenta, and blue), or 𝜇
w
5, 10, 20 cm/s (𝜎
w
7.5, 15, 30 cm/s, respectively. The black
curve is obtained from simulations without fluctuations, where ice forms at w
0
. For comparison, the colored smooth
curves mark the mean nucleated concentrations calculated analytically from the updraft speed statistic. The left panel
highlights the transition of simulated
𝜇
n
to vanishing background cooling (w
0
0).
A surprising feature is the increase of 𝜇
n
for low w
0
that is most pronounced for larger forcing. We would
expect the nucleated ICNC to approach a constant value for w
0
≪𝜇
w
, if we just looked at the mean ICNC
calculated directly from the updraft speed fluctuation statistic without accounting for sink processes of the
ICNC. We call those values—shown as smooth colored curves in Figure 2—instantaneous ice numbers
(equation (S4)).
High cooling rates have a greater chance than low cooling rates to reach freezing thresholds,
{T
, S
}, giving
them a large statistical weight despite their lower abundance in the updraft distribution. For example, at T
already close close to T
, while a small cooling rate might not suffice to reach T
, a high cooling rate might
well trigger freezing. This effect (coined preferential freezing) is stronger the larger
𝜇
w
and significantly
increases
𝜇
n
as w
0
diminishes. With increasing w
0
pushing the parcel faster close to freezing conditions,
low cooling rate fluctuations have an increasing chance to nucleate ice as well. The contribution of the
fluctuations to w is dwarfed by w
0
for w
0
≫𝜇
w
.
This said, we still expect
𝜇
n
to saturate in the limit w
0
0, at which point the air parcels undergo a pure
random temperature (supersaturation) walk unsupported by a constant baseline cooling. The left panel in
Figure 2 extends the simulations to lower w
0
and indeed shows the expected behavior as w
0
0. An imme-
diate implication is that freezing is also possible for slightly negative w
0
causing a background warming.
However, stronger subsidence will make cirrus formation increasingly unlikely due to the rapidly growing
separation between the diminishing ice supersaturation and the homogeneous freezing threshold.
Preferential freezing results from the stochastic nature of the temperature fluctuations. It is absent in esti-
mates of instantaneous values of nucleated ICNC (colored curves), or when the updraft statistic is equal to, or
approaches, a monodisperse distribution. Apart from this, preferential freezing does not depend on the exact
functional form of w
statistic, as long as it has a finite second moment. Times at which freezing conditions
are met along a stochastic air parcel trajectory vary widely depending on the actual mesoscale temperature
evolution and hence on how far initial conditions {S
0
, T
0
} are away from {S
, T
} (Figure S3). These times
KÄRCHER ET AL. 5

Figures (3)
Citations
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Daniel J. Cziczo1, Karl D. Froyd2, Karl D. Froyd3, Corinna Hoose4  +6 moreInstitutions (8)
01 May 2013-
Abstract: Formation of cirrus clouds depends on the availability of ice nuclei to begin condensation of atmospheric water vapor. Although it is known that only a small fraction of atmospheric aerosols are efficient ice nuclei, the critical ingredients that make those aerosols so effective have not been established. We have determined in situ the composition of the residual particles within cirrus crystals after the ice was sublimated. Our results demonstrate that mineral dust and metallic particles are the dominant source of residual particles, whereas sulfate and organic particles are underrepresented, and elemental carbon and biological materials are essentially absent. Further, composition analysis combined with relative humidity measurements suggests that heterogeneous freezing was the dominant formation mechanism of these clouds.

44 citations


01 Dec 2013-
Abstract: The indirect effect of aircraft soot on cirrus clouds is subject to large uncertainties due to uncertainty in the effectiveness of aircraft soot acting as heterogeneous ice nuclei (IN) and the complexity caused by background ice nucleation, which introduces two major competing ice nucleation mechanisms: homogeneous freezing that generally produces more abundant ice particles and heterogeneous nucleation that generally produces fewer ice particles. In this paper, we used the coupled Community Atmosphere Model version 5.2 (CAM5)/IMPACT model to estimate the climate impacts of aircraft soot acting as IN in large-scale cirrus clouds. We assume that only the aircraft soot particles that are preactivated in persistent contrail cirrus clouds are efficient IN. Further, we assume that these particles lose their ability to act as efficient IN when they become coated with three monolayers of sulfate. We varied the background number concentration of sulfate aerosols allowed to act as homogeneous ice nucleation sites as well as the dust concentrations that act as heterogeneous ice nuclei to examine the sensitivity of the forcing by aircraft soot to the background atmosphere. The global average effect can range from a high negative (cooling) rate, −0.35 W m−2, for the high sulfate/low dust case to a positive (warming) rate, +0.09 W m−2, for the low sulfate/low dust case (default CAM5 setup) when approximately 0.6% of total aviation soot acts as IN. The net negative forcing is caused by the addition of IN to a background atmosphere that is dominated by homogeneous nucleation (mainly in the tropic Indian Ocean, Central America, and North Atlantic Ocean). The forcings can be all positive, about +0.11 to +0.21 W m−2, when the background atmosphere is dominated by pure heterogeneous ice nucleation.

10 citations


Journal ArticleDOI
Abstract: Ubiquitous mesoscale gravity waves generate high cooling rates important for cirrus formation. We make use of long‐duration balloon observations to devise a probabilistic model describing mesoscale temperature uctuations (MTF) away from strong wave sources. We define background conditions based on observed probability distributions of temperature and underlying vertical wind speed fluctuations. We show theoretically that MTF are subject to damping at a rate near the Coriolis frequency when the vertical wind speed fluctuations are autocorrelated over a fraction of a Brunt‐Väisälä period. We find that for background wave activity, a decrease in temperature of 1K translates into cooling rate standard deviations and mean updraft speeds of 4–8Kh and ≈ 10–20 cms, respectively, depending on latitude and stratification. We introduce an effective Coriolis frequency to generate cooling rates in equatorial regions consistent with balloon data. Above ice saturation, MTF are large enough to affect ice crystal nucleation. Our results help constrain uncertainty in aerosol‐cirrus interactions, provide insights to better meet challenges in comparing measurement data with model simulations, and support the development of cutting‐edge ice cloud schemes in global models. Plain Language Summary: The limited scientific understanding of pure ice clouds (cirrus)—and therefore the difficulty to account for them inmodels—causes substantial uncertainty in climate projections. Two research issues important for cirrus formation continue to form a roadblock on the path of scientific progress: the dynamical forcing driving cirrus ice crystal formation and the ice‐forming properties of solid atmospheric particles. Long‐duration balloons floating in the high atmosphere have quantified key properties of gravity waves that generate vertical air motions (cooling rates) crucial for ice formation in cirrus. Only when occurrence and magnitude of cooling rates are well understood can effects of different solid and liquid ice‐forming particles during cirrus formation be predicted with confidence. Blending insights obtained from the research balloon measurements with theoretical methods developed in statistical physics, our study elaborates on the dynamical forcing issue by devising a model that represents air parcel cooling rates on a probabilistic basis. We thereby hope to contribute significantly to a comprehensive process understanding and, ultimately, to removing one of the roadblocks in cloud research.

10 citations


Cites background from "The Impact of Mesoscale Gravity Wav..."

  • ...important ramifications for ice crystal nucleation in cirrus (Kärcher et al., 2019)....

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  • ...The short autocorrelation time is responsible for the high frequency variability in CHR influencing ice crystal formation (Kärcher et al., 2019)....

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  • ...Kärcher et al. (2019) report a first attempt to tackle this issue....

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Journal ArticleDOI
Ulrich Schumann1Institutions (1)
Abstract: Vertical motions are fundamental for atmospheric dynamics. Compared to horizontal motions, the horizontal spectrum of vertical velocity w is less well known. Here, w spectra are related to ...

9 citations


Journal ArticleDOI
17 Jun 2021-
Abstract: Fully accounting for the climate impact of aviation requires a process-level understanding of the impact of aircraft soot particle emissions on the formation of ice clouds. Assessing this impact with the help of global climate models remains elusive and direct observations are lacking. Here we use a high-resolution cirrus column model to investigate how aircraft-emitted soot particles, released after ice crystals sublimate at the end of the lifetime of contrails and contrail cirrus, perturb the formation of cirrus. By allying cloud simulations with a measurement-based description of soot-induced ice formation, we find that only a small fraction (<1%) of the soot particles succeeds in forming cloud ice alongside homogeneous freezing of liquid aerosol droplets. Thus, soot-perturbed and homogeneously-formed cirrus fundamentally do not differ in optical depth. Our results imply that climate model estimates of global radiative forcing from interactions between aircraft soot and large-scale cirrus may be overestimates. The improved scientific understanding reported here provides a process-based underpinning for improved climate model parametrizations and targeted field observations. Only a small part of aircraft-soot–cirrus interactions succeeds in forming cloud ice, according to simulations with a numerical cirrus cloud model. This suggests that radiative forcing from aircraft soot may have been overestimated.

5 citations


References
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Journal ArticleDOI
TL;DR: It is shown that the concentrations of ice nuclei active in mixed-phase cloud conditions can be related to temperature and the number concentrations of particles larger than 0.5 μm in diameter, which reduces unexplained variability in iceuclei concentrations at a given temperature from ∼103 to less than a factor of 10.
Abstract: Knowledge of cloud and precipitation formation processes remains incomplete, yet global precipitation is predominantly produced by clouds containing the ice phase. Ice first forms in clouds warmer than -36 °C on particles termed ice nuclei. We combine observations from field studies over a 14-year period, from a variety of locations around the globe, to show that the concentrations of ice nuclei active in mixed-phase cloud conditions can be related to temperature and the number concentrations of particles larger than 0.5 μm in diameter. This new relationship reduces unexplained variability in ice nuclei concentrations at a given temperature from ∼103 to less than a factor of 10, with the remaining variability apparently due to variations in aerosol chemical composition or other factors. When implemented in a global climate model, the new parameterization strongly alters cloud liquid and ice water distributions compared to the simple, temperature-only parameterizations currently widely used. The revised treatment indicates a global net cloud radiative forcing increase of ∼1 W m-2 for each order of magnitude increase in ice nuclei concentrations, demonstrating the strong sensitivity of climate simulations to assumptions regarding the initiation of cloud glaciation.

846 citations


"The Impact of Mesoscale Gravity Wav..." refers background in this paper

  • ...The main factor limiting INP effects is their low upper tropospheric number concentration (<0.1 cm−3; DeMott et al., 2010), which makes them inefficient in suppressing homogeneous freezing in the presence of sufficiently large vertical wind speeds (DeMott et al., 1997)....

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  • ...The main factor limiting INP effects is their low upper tropospheric number concentration (<0.1 cm−3; DeMott et al., 2010), which makes them inefficient in suppressing homogeneous freezing in the presence of sufficiently large vertical wind speeds (DeMott et al....

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Journal ArticleDOI
Corinna Hoose1, Ottmar Möhler1Institutions (1)
Abstract: . A small subset of the atmospheric aerosol population has the ability to induce ice formation at conditions under which ice would not form without them (heterogeneous ice nucleation). While no closed theoretical description of this process and the requirements for good ice nuclei is available, numerous studies have attempted to quantify the ice nucleation ability of different particles empirically in laboratory experiments. In this article, an overview of these results is provided. Ice nucleation "onset" conditions for various mineral dust, soot, biological, organic and ammonium sulfate particles are summarized. Typical temperature-supersaturation regions can be identified for the "onset" of ice nucleation of these different particle types, but the various particle sizes and activated fractions reported in different studies have to be taken into account when comparing results obtained with different methodologies. When intercomparing only data obtained under the same conditions, it is found that dust mineralogy is not a consistent predictor of higher or lower ice nucleation ability. However, the broad majority of studies agrees on a reduction of deposition nucleation by various coatings on mineral dust. The ice nucleation active surface site (INAS) density is discussed as a simple and empirical normalized measure for ice nucleation activity. For most immersion and condensation freezing measurements on mineral dust, estimates of the temperature-dependent INAS density agree within about two orders of magnitude. For deposition nucleation on dust, the spread is significantly larger, but a general trend of increasing INAS densities with increasing supersaturation is found. For soot, the presently available results are divergent. Estimated average INAS densities are high for ice-nucleation active bacteria at high subzero temperatures. At the same time, it is shown that INAS densities of some other biological aerosols, like certain pollen grains, fungal spores and diatoms, tend to be similar to those of dust. These particles may owe their high ice nucleation onsets to their large sizes. Surface-area-dependent parameterizations of heterogeneous ice nucleation are discussed. For immersion freezing on mineral dust, fitted INAS densities are available, but should not be used outside the temperature interval of the data they were based on. Classical nucleation theory, if employed with only one fitted contact angle, does not reproduce the observed temperature dependence for immersion nucleation, the temperature and supersaturation dependence for deposition nucleation, and the time dependence of ice nucleation. Formulations of classical nucleation theory with distributions of contact angles offer possibilities to overcome these weaknesses.

796 citations


"The Impact of Mesoscale Gravity Wav..." refers background in this paper

  • ...…complexity by considering effects of heterogeneous ice-nucleating particles (INPs), which are poorly constrained by field observations at cirrus temperatures (<230–235 K; Hoose & Möhler, 2012; Jensen et al., 2018), we focus on the more basic and much better understood homogeneous freezing process....

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Journal ArticleDOI
Daniel J. Cziczo1, Karl D. Froyd2, Karl D. Froyd3, Corinna Hoose4  +6 moreInstitutions (8)
14 Jun 2013-Science
TL;DR: Results demonstrate that mineral dust and metallic particles are the dominant source of residual particles, whereas sulfate and organic particles are underrepresented, and elemental carbon and biological materials are essentially absent.
Abstract: Formation of cirrus clouds depends on the availability of ice nuclei to begin condensation of atmospheric water vapor. Although it is known that only a small fraction of atmospheric aerosols are efficient ice nuclei, the critical ingredients that make those aerosols so effective have not been established. We have determined in situ the composition of the residual particles within cirrus crystals after the ice was sublimated. Our results demonstrate that mineral dust and metallic particles are the dominant source of residual particles, whereas sulfate and organic particles are underrepresented, and elemental carbon and biological materials are essentially absent. Further, composition analysis combined with relative humidity measurements suggests that heterogeneous freezing was the dominant formation mechanism of these clouds.

382 citations


"The Impact of Mesoscale Gravity Wav..." refers background or methods in this paper

  • ...It is therefore reasonable to assume that INP were available at cirrus levels, consistent with a study that showed that some aerosol types were enhanced in ice residuals compared to ambient (interstitial) aerosols (Cziczo et al., 2013)....

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  • ...DeMott et al. (1997) estimated with parcel model simulations a maximum impact of INP on cirrus formation for updraft speeds <20 cm/s, suggesting the potential importance of INP in wave-driven scenarios....

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Journal ArticleDOI
Bernd Kärcher1, Ulrike Lohmann2Institutions (2)
Abstract: [1] The nucleation and initial growth of ice crystals in cirrus clouds at low (<235 K) temperatures prevailing in the upper troposphere and in the tropopause region is theoretically considered. The analysis explains the dependence of the number density of ice crystals on the vertical velocity and temperature seen in numerical simulations of cirrus formation when the timescale of depositional growth of the pristine ice particles is fast compared to the timescale of the freezing event. In such cases, applicable in many situations, the number of crystals formed via homogeneous freezing of aqueous solution droplets is rather insensitive to details of the aerosol size distribution, but increases rapidly with updraft velocity and decreases with temperature. The derived parameterization is validated with parcel model simulations, and its applicability for use in climate models is discussed. The potential role of aerosol size and heterogeneous freezing processes in altering the predicted cirrus properties is briefly addressed.

254 citations


"The Impact of Mesoscale Gravity Wav..." refers background or methods in this paper

  • ...…begun to parameterize the impact of unresolved gravity waves on cirrus formation (Penner et al., 2018), it is important to explore this issue systematically on the process level as a prerequisite to improving ice nucleation parameterizations (Barahona & Nenes, 2008; Kärcher & Lohmann, 2002)....

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  • ...We do not vary aerosol parameters, because the dependence of n on them is much weaker than on w (Kärcher & Lohmann, 2002; Kay & Wood, 2008; Liu & Shi, 2018)....

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  • ...The curve obtained from simulations without fluctuations follows a power law dependence, as expected from cloud physical theory (Kärcher & Lohmann, 2002): n(w) = n1 [(w0 + w ′ )∕w1]𝛼 , where n1 is the nucleated ICNC at a given T and w = w1....

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  • ...The sizes of simulated ice crystals, and hence their fall speeds, are typically smaller than 15𝜇m after quenching the initially high supersaturation (Kärcher & Lohmann, 2002)....

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Journal ArticleDOI
Eric J. Jensen1, Leonhard Pfister1Institutions (1)
Abstract: [1] We use a Lagrangian, one-dimensional cloud model to simulate ice cloud formation and dehydration along trajectories in the tropical tropopause layer (TTL). Time-height curtains of temperature along the trajectory paths are extracted from meteorological analyses. The temperatures are adjusted near the tropopause such that the spatial average cold point temperature matches tropical radiosonde measurements. Temperature perturbations due to Kelvin waves, Rossby gravity waves, and high-frequency gravity waves are superimposed. The cloud model tracks the growth and sedimentation of individual ice crystals. Ice number densities in the cloud simulations without waves range from 1 cm−3) and smaller crystals (1–10 μm radius), resulting in less sedimentation but still effective dehydration overall. Inclusion of wave-driven temperature oscillations decreases the final TTL H2O mixing ratio somewhat primarily because the wave perturbations decrease the tropical average cold point tropopause temperature by ∼0.75 K. Ultimately, air rising through the TTL is effectively dehydrated with or without wave perturbations. In general, the model results suggest that the final water vapor mixing ratios are primarily controlled by the minimum temperatures encountered by parcels and that they are relatively insensitive to factors such as the wave-driven temperature variability, the supersaturation threshold for ice nucleation, and the rate of ascent through the tropopause layer. However, the frequency and geographical distribution of cloud formation is very sensitive to these parameters. On average, the clouds dehydrate the air along trajectories down to mixing ratios ∼10–40% higher than the temperature minimum saturation mixing ratio. The simulations predict efficient freeze-drying of air by cloud formation within the TTL: For the December–January 1995/1996 period simulated the average final H2O mixing ratios at the tropopause (370–380 K potential temperature) range from 2.5 to 3.2 ppmv. These values are somewhat lower than the estimates of the stratospheric water vapor entry value from satellite and in situ measurements; hence an additional source of water (such as injection by deep convection) may be required to explain the observed tropical tropopause humidity.

229 citations


"The Impact of Mesoscale Gravity Wav..." refers background in this paper

  • ...A spectrum of mesoscale gravity waves generates broad frequency distributions of ice crystal number concentrations (ICNC) via homogeneous freezing of supercooled aqueous solution particles (Hoyle et al., 2005; Jensen & Pfister, 2004; Kärcher & Ström, 2003)....

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