- Articles & preprints
- Submission
- Policies
- Peer review
- Editorial board
- About
- EGU publications
- Manuscript tracking

Journal cover
Journal topic
**Atmospheric Chemistry and Physics**
An interactive open-access journal of the European Geosciences Union

Journal topic

- Articles & preprints
- Submission
- Policies
- Peer review
- Editorial board
- About
- EGU publications
- Manuscript tracking

- Articles & preprints
- Submission
- Policies
- Peer review
- Editorial board
- About
- EGU publications
- Manuscript tracking

- Abstract
- Introduction
- Experimental method
- Equilibrium temperature model
- Results and discussion
- Summary and conclusions
- Data availability
- Appendix A: Critical temperatures under the influence of solar radiation
- Appendix B: Equilibrium particle temperature and wet particle radius
- Author contributions
- Competing interests
- Special issue statement
- Acknowledgements
- Review statement
- References

ACP | Articles | Volume 19, issue 7

Atmos. Chem. Phys., 19, 4311–4322, 2019

https://doi.org/10.5194/acp-19-4311-2019

© Author(s) 2019. This work is distributed under

the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/acp-19-4311-2019

© Author(s) 2019. This work is distributed under

the Creative Commons Attribution 4.0 License.

Special issue: Layered phenomena in the mesopause region (ACP/AMT inter-journal...

**Research article**
03 Apr 2019

**Research article** | 03 Apr 2019

The impact of solar radiation on polar mesospheric ice particle formation

^{1}Institute of Meteorology and Climate Research, Karlsruhe Institute of Technology – KIT, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany^{2}Deutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany^{3}School of Chemistry, University of Leeds, Leeds, LS2 9JT, UK^{4}Department of Nuclear Engineering, Kyoto University, Kyoto 615-8540, Japan^{5}Meteorologisches Institut München, Ludwig-Maximilians-Universität München, Munich, Germany^{6}Institute of Environmental Physics, University of Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany

^{1}Institute of Meteorology and Climate Research, Karlsruhe Institute of Technology – KIT, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany^{2}Deutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany^{3}School of Chemistry, University of Leeds, Leeds, LS2 9JT, UK^{4}Department of Nuclear Engineering, Kyoto University, Kyoto 615-8540, Japan^{5}Meteorologisches Institut München, Ludwig-Maximilians-Universität München, Munich, Germany^{6}Institute of Environmental Physics, University of Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany

**Correspondence**: Mario Nachbar (mario.nachbar@kit.edu)

**Correspondence**: Mario Nachbar (mario.nachbar@kit.edu)

Abstract

Back to toptop
Mean temperatures in the polar summer mesopause can drop to 130 K. The low
temperatures in combination with water vapor mixing ratios of a few parts per
million give rise to the formation of ice particles. These ice particles may
be observed as polar mesospheric clouds. Mesospheric ice cloud formation is
believed to initiate heterogeneously on small aerosol particles (*r*<2 nm) composed of recondensed meteoric material, so-called meteoric
smoke particles (MSPs). Recently, we investigated the ice activation and
growth behavior of MSP analogues under realistic mesopause conditions. Based
on these measurements we presented a new activation model which largely
reduced the uncertainties in describing ice particle formation. However, this
activation model neglected the possibility that MSPs heat up in the
low-density mesopause due to absorption of solar and terrestrial irradiation.
Radiative heating of the particles may severely reduce their ice formation
ability. In this study we expose MSP analogues (Fe_{2}O_{3} and
Fe_{x}Si_{1−x}O_{3}) to realistic mesopause
temperatures and water vapor concentrations and investigate particle warming
under the influence of variable intensities of visible light (405, 488, and
660 nm). We show that Mie theory calculations using refractive indices of
bulk material from the literature combined with an equilibrium temperature
model presented in this work predict the particle warming very well.
Additionally, we confirm that the absorption efficiency increases with the
iron content of the MSP material. We apply our findings to mesopause
conditions and conclude that the impact of solar and terrestrial radiation on
ice particle formation is significantly lower than previously assumed.

Download & links

How to cite

Back to top
top
How to cite.

Nachbar, M., Wilms, H., Duft, D., Aylett, T., Kitajima, K., Majima, T., Plane, J. M. C., Rapp, M., and Leisner, T.: The impact of solar radiation on polar mesospheric ice particle formation, Atmos. Chem. Phys., 19, 4311–4322, https://doi.org/10.5194/acp-19-4311-2019, 2019.

1 Introduction

Back to toptop
The lowest temperatures in the terrestrial atmosphere are encountered in the
polar summer mesopause, where mean daily temperatures at high latitudes can
fall to below 130 K (e.g., Lübken, 1999; Lübken et al., 2009). These
low temperatures in combination with H_{2}O concentrations of a few
parts per million (Hervig et al., 2009; Seele and Hartogh, 1999) lead to
highly supersaturated conditions which allow for the formation of ice
particles (e.g., Lübken et al., 2009; Rapp and Thomas, 2006). When the ice
particle radii reach about 30 nm and their concentration is of the order of
100 cm^{−3} they become optically visible and may be observed as polar
mesospheric clouds (PMCs) (e.g., Rapp and Thomas, 2006). When observed from
the ground, these clouds are often referred to as noctilucent clouds (NLCs).
Because of their particular wavy appearance and their high elevation of about
83 km, PMCs have received much attention since their first reported
observation in 1885 (Leslie, 1885). The current scientific interest in these
extraordinary clouds is substantiated in their potential role as tracer for
the dynamical structure of the summer mesopause (e.g., Demissie et al., 2014;
Kaifler et al., 2013; Rong et al., 2015; Witt, 1962) or for long-term trends
of temperature and H_{2}O concentration caused by anthropogenic
emissions of CO_{2} and CH_{4} (e.g., Hervig et al., 2016;
Thomas and Olivero, 2001; Thomas et al., 1989). However, in order to use
observation of PMCs as a tracer, an in-depth understanding of the processes
involved in PMC formation is necessary.

Wilms et al. (2016) found that in addition to dynamical processes the description of
the initial formation of the ice particles significantly affects modeled PMC
properties. Ice particle formation is believed to initiate heterogeneously on
nanometer-sized recondensed meteoric material, so-called meteoric smoke
particles (MSPs) (e.g., Gumbel and Megner, 2009; Keesee, 1989; Rapp and
Thomas, 2006; Turco et al., 1982). This conjecture is strongly supported by
satellite and rocket-borne observations showing that MSPs are included in PMC
ice particles (Antonsen et al., 2017; Havnes et al., 2014; Hervig et al.,
2012). The initial ice particle formation has been described in two different
ways. Either activation-barrier-free growth is assumed to set in for
saturations in excess of the equilibrium saturation over the curved particle
surface (e.g., Berger and Lübken, 2015; Schmidt et al., 2018) or ice
particle formation is described using classical nucleation theory (e.g., Asmus
et al., 2014; Bardeen et al., 2010; Rapp and Thomas, 2006; Wilms et al.,
2016). Both approaches assume the formation of hexagonal ice and the latter
typically requires much higher critical saturations to initiate ice particle
growth. In order to reduce the large uncertainties in describing the initial
formation of PMC ice particles, we designed a laboratory experiment to study
ice particle formation under realistic mesopause conditions (Duft et al.,
2015). Recently, we investigated the ice activation and growth behavior on
SiO_{2}, Fe_{2}O_{3}, and mixed iron silicate nanoparticles
which serve as analogues for MSPs. We found that the primary ice phase
forming on the MSP analogues under the conditions of the summer mesopause is
amorphous solid water (ASW) (Nachbar et al., 2018b, c). Additionally, we
showed that MSPs adsorb up to several layers of water until ice growth
activates as soon as the saturation exceeds the saturation vapor pressure of
ASW including the Kelvin effect for the ice-covered or “wet” particle
radius and considering the collision radius of water molecules (Duft et al.,
2019).

Asmus et al. (2014) pointed out that MSPs may heat up in the low-density
atmosphere of the mesopause by absorbing solar and terrestrial irradiation.
The extent of this effect depends on the MSP composition and has been
proposed to increase with increasing iron content. Interestingly, satellite
and rocket-borne investigations indicate that MSPs are most likely composed of
iron-rich materials such as magnetite (Fe_{3}O_{4}), wüstite
(FeO), magnesiowüstite (Mg_{x}Fe_{1−x}O,
*x*=0–0.6), and iron-rich olivine
(Mg_{2x}Fe_{2−2x}SiO_{4}, *x*=0.4–0.5) (Hervig et
al., 2017; Rapp et al., 2012). Using nucleation theory, Asmus et al. (2014)
concluded that the warming for such MSP materials significantly impacts the
ice-forming ability of the particles, thus rendering them ineffective nuclei.
However, up until now this conclusion has not been confirmed experimentally.
To this end, we extended our experimental setup with a laser system, which
allows MSP analogues to be exposed to a known intensity of visible light at
three wavelengths (405, 488, and 660 nm). We studied the number of adsorbed
H_{2}O molecules on Fe_{2}O_{3} and
Fe_{x}Si_{1−x}O_{3} nanoparticles under the influence
of the laser light at controlled gas-phase H_{2}O concentration and
background pressure. In this way, we could determine the offset of the
particle temperature from the ambient temperature. The experimental method is
described in more detail in Sect. 2. From the experimentally determined
temperature offsets we then deduce absorption efficiencies using a light
absorption model, which is introduced in Sect. 3. In Sect. 4, we present our
results on the absorption efficiencies and compare them to Mie theory
calculations using literature values of the refractive indices. We estimate
the maximum temperature offset for MSPs in the summer mesopause and discuss
the consequences on ice particle formation. Finally, we summarize our main
conclusions in Sect. 5.

2 Experimental method

Back to toptop
We produce spherical, singly charged Fe_{2}O_{3}, SiO_{2}, or
Fe_{x}Si_{1−x}O_{3} particles with radii smaller than
4 nm in a nonthermal low-pressure microwave plasma particle source (Nachbar
et al., 2018a). The particles are transferred online into the vacuum system
of the experiment (illustrated in Fig. 1), which has been described in detail
elsewhere (Duft et al., 2015; Meinen et al., 2010; Nachbar et al., 2016,
2018b). In brief, singly charged nanometer-sized particles enter the vacuum
chamber through an aerodynamic lens and a skimmer. After the skimmer, the
particles enter an rf octupole serving as an ion guide. The particles are
mass selected ($\mathrm{\Delta}m/m\le \phantom{\rule{0.125em}{0ex}}\mathrm{7}\phantom{\rule{0.125em}{0ex}}\mathit{\%}$) with an electrostatic quadrupole
deflector (DF_{1}) and subsequently enter into the molecular flow ice cell
(MICE). MICE is a modified quadrupole ion trap. A temperature-controlled He
environment at a pressure of $\left(\mathrm{1}-\mathrm{5}\right)\times {\mathrm{10}}^{-\mathrm{3}}$ mbar
thermalizes the particles under molecular flow conditions. The helium
pressure is adjusted with a leak valve attached to a helium cylinder
(99.999 % purity) and the pressure is measured and corrected (Yasumoto,
1980) using a pressure sensor (Ionivac ITR 90). In MICE, the particles also
interact with a well-calibrated (Nachbar et al., 2018b) concentration of
gas-phase H_{2}O molecules, which is maintained by
temperature-controlled sublimation of water vapor from ice-covered surfaces
(Duft et al., 2015). For a typical experiment, MICE is filled with 10^{7}
particles in about 1 s, followed by storing of the particles for up to
several hours. Depending on the conditions applied in MICE, H_{2}O
molecules adsorb on the particles until an equilibrium state is reached or
ice growth initiates on the particles. These processes are monitored by
periodically extracting a small portion of the trapped particle population
from MICE. After extraction, the particles are accelerated orthogonally into
a time-of-flight (TOF) spectrometer for mass measurement.

The setup has been extended with a laser system equipped with three lasers of
different wavelengths, *λ*=405 nm (Obis LX 405), *λ*=488 nm
(Obis LX 488), and *λ*=660 nm (Obis LX 660). A combination of a laser
beam expander (Edmund Optics 10X VIS broadband beam expander), mirrors, and a
quartz glass window guides the expanded laser beam horizontally through the
center of MICE pointing onto a beam dump. The light intensity in MICE was
calibrated by measuring the power and the beam profile in MICE with a
power-meter (Coherent PM USB PS19Q) and a CCD camera (Thorlabs 4070M-GE-TE).
A typical beam profile of the expanded 488 nm laser beam is shown in the
insert of Fig. 1. The red dashed lines indicate the maximum ion cloud
diameter *d*=2 mm calculated for the combinations of particle mass ($\mathrm{2}\times {\mathrm{10}}^{\mathrm{4}}\phantom{\rule{0.125em}{0ex}}\mathrm{Da}-\mathrm{50}\times {\mathrm{10}}^{\mathrm{4}}$ Da; 1 Da *≜*1 atomic
mass unit $=\mathrm{1.6605}\times {\mathrm{10}}^{-\mathrm{27}}$ kg), radio frequency (30–1000 kHz),
and amplitude (200–1000 V) applied in the present study (Majima et al.,
2012). Allowing for a misalignment of the laser beam of up to 0.5 mm from
the ion trap center, we conclude that the particles are located within a
diameter of 3 mm from the center of the expanded laser beam. We use the mean
of the intensity values at *d*=3 mm and the center of the laser beam to
describe the light intensity irradiating from the particles. The uncertainty
is defined by the difference between the intensity value at the center of the
laser beam and the mean value.

In this work, we apply conditions with saturations below the threshold for
ice growth, i.e., where only adsorption occurs. Each experiment begins by
filling MICE with a fresh charge of nanoparticles. The initially dry
nanoparticles adsorb H_{2}O molecules until an equilibrium state
between adsorbing H_{2}O flux and desorbing flux is reached. The
process of reaching the equilibrium state is illustrated in Fig. 2a, which
shows the time evolution of the particle mass for Fe_{2}O_{3}
particles with a dry particle radius ${r}_{\mathrm{dry}}={\left(\mathrm{3}{m}_{\mathrm{0}}/\mathrm{4}\mathit{\pi}{\mathit{\rho}}_{\mathrm{p}}\right)}^{\mathrm{1}/\mathrm{3}}=\mathrm{2.9}$ nm
(*ρ*_{p}=5.2 g cm^{−3}), a H_{2}O gas-phase
concentration ${n}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}=\mathrm{1.1}\times {\mathrm{10}}^{\mathrm{16}}$ m^{−3}, and a
temperature of the environment surrounding the particles
*T*_{env}=148.8 K. The black squares show the adsorption curve
without light irradiation for which *T*_{env} equals the particle
temperature *T*_{p}. If the particles are heated by light irradiation
(*T*_{p}*>**T*_{env}), the water molecule flux
desorbing from a particle increases, which causes a reduction in the number
of adsorbed H_{2}O molecules in equilibrium. This effect is shown by
the colored data for illumination with the 488 nm laser at various mean
light intensities. Figure 2b shows the corresponding particle temperature
offsets Δ*T*, which were determined by analyzing the steady-state mass
of adsorbed water molecules. The method for deriving Δ*T* is presented
below.

We analyze the adsorption data with a parameterization which was originally
used to describe the equilibrium concentration of adsorbed water molecules
${c}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ on a planar surface with sub-monolayer coverage (Pruppacher
and Klett, 2010). In our previous work we have modified this parameterization
to account for the curvature of the nanometer-sized particles and have proven
its functionality for coverages of more than one monolayer (Duft et al.,
2019). The parameterization is derived from the assumption that each water
molecule which collides with a particle adsorbs on it. In equilibrium, the
flux density of water molecules colliding with a particle *j*_{ads}
must equal the flux density desorbing from the particle *j*_{des} :

$$\begin{array}{}\text{(1)}& \underset{{j}_{\mathrm{ads}}}{\underbrace{{\displaystyle \frac{{n}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\cdot {v}_{\mathrm{th}}}{\mathrm{4}}}}}=\underset{{j}_{\mathrm{des}}}{\underbrace{{c}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\cdot f\cdot \mathrm{exp}\left(-{\displaystyle \frac{{E}_{\mathrm{des}}^{\mathrm{0}}}{R{T}_{\mathrm{p}}}}+{\displaystyle \frac{\mathrm{2}\mathit{\sigma}v}{R{T}_{\mathrm{p}}{r}_{\mathrm{dry}}}}\right)}}.\end{array}$$

The flux density in the molecular flow regime (left-hand side of Eq. 1)
depends on gas-phase properties, namely the concentration ${n}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ and
the mean thermal velocity ${v}_{\mathrm{th}}=\sqrt{\mathrm{8}k{T}_{\mathrm{env}}/\mathit{\pi}{m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}$ of gas-phase H_{2}O molecules. The desorbing flux
density (right-hand side of Eq. 1), however, depends on properties of the
particle. The desorbing flux density is the product of the concentration of
adsorbed water molecules in equilibrium ${c}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$, the vibrational
frequency of a water molecule on the particle surface *f* = 10^{13} Hz, and
an exponential function which describes the probability that an adsorbed
molecule desorbs. This probability depends on the ideal gas constant *R*, the
particle temperature *T*_{p}, and the mean desorption energy of a
H_{2}O molecule for a planar surface of the particle material
${E}_{\mathrm{des}}^{\mathrm{0}}$. The second term in the exponential function of Eq. (1)
describes the curvature dependence of the desorption energy, which can be
calculated using the properties of amorphous solid water (ASW) (Duft et al.,
2019). Here, $v=\mathrm{6.022}\times {\mathrm{10}}^{\mathrm{23}}\cdot {m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}/{\mathit{\rho}}_{\mathrm{ice}}$ is the volume of 1 mol of H_{2}O molecules in ASW.
The densities of ASW and crystalline ice are very similar at the temperatures
under investigation (Brown et al., 1996; Loerting et al., 2011). We use the
parameterization ${\mathit{\rho}}_{\mathrm{ice}}\left[{\mathrm{g}\phantom{\rule{0.125em}{0ex}}\mathrm{cm}}^{-\mathrm{3}}\right]=\mathrm{0.9167}-\mathrm{1.75}\times {\mathrm{10}}^{-\mathrm{4}}\cdot {T}_{\mathrm{p}}\left[{}^{\circ}\mathrm{C}\right]-\mathrm{5}\times {\mathrm{10}}^{-\mathrm{7}}\cdot {\left({T}_{\mathrm{p}}\left[{}^{\circ}\mathrm{C}\right]\right)}^{\mathrm{2}}$ for crystalline ice (Pruppacher and Klett, 2010). For
the surface tension of ASW we use $\mathit{\sigma}\left[{\mathrm{mN}\phantom{\rule{0.125em}{0ex}}\mathrm{m}}^{-\mathrm{1}}\right]=\left(\mathrm{114.81}-\mathrm{0.144}\cdot T\left[K\right]\right)$, which is based on
an extrapolation of experimental data for supercooled water (Nachbar et al.,
2018c). The equilibrium concentration of adsorbed water molecules
${c}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ is the adsorbed mass of H_{2}O molecules in
equilibrium *m*_{ads} divided by the surface area of a dry
nanoparticle ${A}_{\mathrm{p}}=\mathrm{4}\mathit{\pi}{r}_{\mathrm{dry}}^{\mathrm{2}}$ and the mass of a water
molecule ${m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ (${c}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}={m}_{\mathrm{ads}}/{A}_{\mathrm{p}}/{m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$). We derive the adsorbed mass of H_{2}O
molecules in equilibrium *m*_{ads} from the experimental data with an
exponential fit (represented by the solid curves in Fig. 2a) of the following
form:

$$\begin{array}{}\text{(2)}& m\left(t\right)={m}_{\mathrm{0}}+{m}_{\mathrm{ads}}\cdot \left(\mathrm{1}-\mathrm{exp}\left({\displaystyle \frac{-{t}_{\mathrm{res}}}{\mathit{\tau}}}\right)\right).\end{array}$$

The radius of the wet particle is indicated by the right ordinate in Fig. 2a and follows from the measured particle mass according to

$$\begin{array}{}\text{(3)}& {r}_{\mathrm{wet}}={\left({r}_{\mathrm{dry}}^{\mathrm{3}}+{\displaystyle \frac{\mathrm{3}}{\mathrm{4}\mathit{\pi}}}{\displaystyle \frac{{m}_{\mathrm{ads}}}{{\mathit{\rho}}_{\mathrm{ice}}}}\right)}^{\mathrm{1}/\mathrm{3}}.\end{array}$$

The particle temperature offset Δ*T* is determined by a set of two
measurement runs, one without and one with light illumination. The mean
desorption energy for a H_{2}O molecule is determined from the
measurement without light illumination (*T*_{p}=*T*_{env}) by
solving Eq. (1) for ${E}_{\mathrm{des}}^{\mathrm{0}}$. For the data shown in Fig. 2, this
procedure results in ${E}_{\mathrm{des}}^{\mathrm{0}}=\mathrm{42.52}$ kJ mol^{−1}. We
only analyze data with coverages above 1 monolayer for which the desorption
energy is expected to depend only weakly on H_{2}O coverage (Mazeina
and Navrotsky, 2007; Navrotsky et al., 2008; Sneh et al., 1996). For such
coverages we did not observe any significant influence of the H_{2}O
coverage or the particle temperature on the values of ${E}_{\mathrm{des}}^{\mathrm{0}}$
determined in our previous study (Duft et al., 2019). Therefore, we can
determine the particle temperature under light illumination assuming a
constant ${E}_{\mathrm{des}}^{\mathrm{0}}$ value. Rearranging Eq. (1) yields

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{T}_{\mathrm{p}}={T}_{\mathrm{env}}+\mathrm{\Delta}T=\phantom{\rule{0.125em}{0ex}}\left({E}_{\mathrm{des}}^{\mathrm{0}}-{\displaystyle \frac{\mathrm{2}\mathit{\sigma}v}{{r}_{\mathrm{dry}}}}\right)\\ \text{(4)}& {\displaystyle}& {\displaystyle}\phantom{\rule{1em}{0ex}}/\left(R\cdot \mathrm{ln}\left({\displaystyle \frac{{m}_{\mathrm{ads}}\left({T}_{\mathrm{p}}\right)\cdot f}{{m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\mathit{\pi}{n}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}{v}_{\mathrm{th}}{r}_{\mathrm{dry}}^{\mathrm{2}}}}\right)\phantom{\rule{0.125em}{0ex}}\right).\end{array}$$

Since *σ* and *ρ*_{ice} are dependent on the particle
temperature, Eq. (4) should be solved numerically. However, a sensitivity
analysis has shown that calculating Δ*T* analytically using constant
*σ*(*T*_{env}) and *ρ*_{ice}(*T*_{env}) deviates less than 1 % from the numerical
solution. We therefore analyzed our data using *σ*(*T*_{env}) and *ρ*_{ice}(*T*_{env}). The determined
temperature offset Δ*T* can be used with an equilibrium temperature
model to calculate the light absorption efficiency of the particles
*Q*_{abs}. The equilibrium temperature model is introduced in the next
section.

3 Equilibrium temperature model

Back to toptop
The equilibrium temperature of particles levitated in MICE is described by a
balance between power sources and sinks. Sources are absorption of laser
light ${P}_{\mathit{\lambda}}^{\mathrm{a}}$ and of infrared radiation emitted by the
environment ${P}_{\mathrm{env}}^{\mathrm{a}}$. Sinks are cooling due to collisions
with the He background gas *P*_{col} and blackbody radiation of the
particle in the infrared ${P}_{\mathrm{rad}}^{\mathrm{e}}$. Note that in
equilibrium, the heat from sublimation and condensation cancels. The balance
equation is

$$\begin{array}{}\text{(5)}& {P}_{\mathit{\lambda}}^{\mathrm{a}}+{P}_{\mathrm{env}}^{\mathrm{a}}={P}_{\mathrm{rad}}^{\mathrm{e}}+{P}_{\mathrm{col}}.\end{array}$$

The absorption of laser light with intensity *I* depends on the material and
wavelength-dependent absorption efficiency of the particles *Q*_{abs}.
The absorption efficiency is defined as the absorption cross section divided
by the geometrical cross section ${A}_{\mathrm{geo}}=\mathit{\pi}{r}_{\mathrm{dry}}^{\mathrm{2}}$. We
assume the layer of adsorbed water molecules to be entirely transparent to
visible light so that ${P}_{\mathit{\lambda}}^{\mathrm{a}}$ is the power absorbed by the
MSP alone:

$$\begin{array}{}\text{(6)}& {P}_{\mathit{\lambda}}^{\mathrm{a}}=I\cdot {Q}_{\mathrm{abs}}\left(\mathit{\lambda},{r}_{\mathrm{dry}}\right)\cdot {A}_{\mathrm{geo}}.\end{array}$$

For the cooling due to collisions with the He gas we use the description presented in Asmus et al. (2014):

$$\begin{array}{}\text{(7)}& {P}_{\mathrm{col}}={A}_{\mathrm{col}}\cdot {\displaystyle \frac{\mathit{\alpha}\cdot p}{\mathrm{4}k{T}_{\mathrm{env}}}}{v}_{\mathrm{th}}\cdot k{\displaystyle \frac{\mathit{\gamma}+\mathrm{1}}{\mathrm{2}\left(\mathit{\gamma}-\mathrm{1}\right)}}\cdot \mathrm{\Delta}T.\end{array}$$

For particles in the nanometer regime, the collision surface area
*A*_{col} must include the radius of the colliding He atom
(*r*_{He}=0.14 nm, Bondi, 1964), so that ${A}_{\mathrm{col}}=\mathrm{4}\mathit{\pi}{\left({r}_{\mathrm{wet}}+{r}_{\mathrm{He}}\right)}^{\mathrm{2}}$. The helium pressure in MICE is
represented by *p*, ${v}_{\mathrm{th}}=\sqrt{\mathrm{8}k{T}_{\mathrm{env}}/\mathit{\pi}{m}_{\mathrm{He}}}$
is the mean thermal velocity of He atoms, *γ* is the heat capacity
ratio, $\mathrm{\Delta}T={T}_{\mathrm{p}}-{T}_{\mathrm{env}}$ is the temperature difference
between the particle and the environment, and *α* is the thermal
accommodation coefficient. The particles investigated in this work are
water-covered metal oxides. The thermal accommodation coefficient of He on
comparable surfaces has been measured to be 0.525±0.125 (Fung and Tang,
1988; Ganta et al., 2011). Note that when applying the equilibrium
temperature model to the summer mesopause in Sect. 4.2 we use the thermal
accommodation coefficient of air *α*_{air}=1 (Fung and Tang,
1988; Ganta et al., 2011).

For the conditions applied in MICE, ${P}_{\mathrm{rad}}^{\mathrm{e}}$ and
${P}_{\mathrm{env}}^{\mathrm{a}}$ are several orders of magnitude smaller than
${P}_{\mathit{\lambda}}^{\mathrm{a}}$ and*P*_{col} and can be neglected in the
analysis of the experimental results. For mesospheric conditions, these two
terms may be calculated as presented in Asmus et al. (2014). Substituting
Eqs. (6) and (7) in Eq. (5) and solving for the absorption efficiency *Q*_{abs}(*λ*,*r*_{dry}) yields

$$\begin{array}{}\text{(8)}& {Q}_{\mathrm{abs}}\left(\mathit{\lambda},{r}_{\mathrm{dry}}\right)={\displaystyle \frac{{A}_{\mathrm{col}}}{I\cdot {A}_{\mathrm{geo}}}}\mathit{\alpha}p{v}_{\mathrm{th}}{\displaystyle \frac{\left(\mathit{\gamma}+\mathrm{1}\right)}{\mathrm{8}{T}_{\mathrm{env}}\left(\mathit{\gamma}-\mathrm{1}\right)}}\mathrm{\Delta}T.\end{array}$$

4 Results and discussion

Back to toptop
H_{2}O adsorption measurements similar to those presented in Fig. 2
were recorded for Fe_{2}O_{3} particles with dry particle radii
between 1.3 and 3.2 nm. Particle temperature offsets Δ*T* were
determined from the equilibrium adsorption measurements according to Eq. (4)
and converted to absorption efficiencies for each light intensity according
to Eq. (8). The absorption efficiencies for each set of experiments with the
same dry particle radius were averaged. The results are shown in Fig. 3 as a
function of dry particle radius on a double logarithmic scale. The main
measurement uncertainties originate from the inhomogeneous intensity profile
of the expanded laser beam and the uncertainty of the thermal accommodation
coefficient *α*, which are systematic error sources. The error bars
shown for the particle radius represent the width of the particle size
distribution. In order to compare our data to *Q*_{abs} values derived
from literature data of the complex refractive index $m=n+i\cdot k$,
*Q*_{abs} was calculated from the extinction efficiency
*Q*_{ext} and from the scattering efficiency *Q*_{scat} using
Mie theory (Bohren and Huffmann, 2007) according to

$$\begin{array}{}\text{(9)}& {Q}_{\mathrm{abs}}\left(\mathit{\lambda},{r}_{\mathrm{dry}},m\right)={Q}_{\mathrm{ext}}\left(\mathit{\lambda},{r}_{\mathrm{dry}},m\right)-{Q}_{\mathrm{scat}}\left(\mathit{\lambda},{r}_{\mathrm{dry}},m\right).\end{array}$$

Note that the size parameter $x=\mathrm{2}\mathit{\pi}{r}_{\mathrm{dry}}/\mathit{\lambda}$ is much
smaller than 1 (Rayleigh regime) for all particle sizes investigated in the
present study and that the absorption cross section for such size parameters
is proportional to the volume of the particle and thus *Q*_{abs} is
proportional to *r*_{dry}.

Large differences exist throughout the literature for the imaginary part of
the refractive index for hematite (Fe_{2}O_{3}) in the visible and
near-infrared ranges (Zhang et al., 2015). These differences increase with
increasing wavelength and reach a factor of 40 at *λ*=660 nm. In
order to compare our results with literature data, we collated all works
which determined the real part *n* and the imaginary part *k* of the
refractive index for Fe_{2}O_{3} between 400 and 700 nm (Bedidi and
Cervelle, 1993; Hsu and Matijević, 1985; Longtin et al., 1988; Querry,
1985). Note that the data reported in Longtin et al. (1988) are based on
measurements from Kerker et al. (1979). We calculated the absorption
efficiencies for all sets of refractive indices as a function of the particle
radius. The results are shown by the dashed and dotted curves in Fig. 3 with
the colors indicating the wavelength. The solid lines are mean values of the
absorption efficiencies calculated from literature data. Note that the data
obtained with the refractive indices from Bedidi and Cervelle (1993) and
Longtin et al. (1988) are identical at 488 nm. Our data at *λ*=405 nm agree well with the Mie theory calculations using the literature
refractive indices, except for Bedidi and Cervelle (1993). Our data for
488 nm are also in good agreement with literature, except for the
calculations using the refractive indices from Querry (1985). At 660 nm our
experimental results lie within the large scatter of the literature values.
The absorption efficiencies deduced from the refractive indices of Hsu and
Matijević (1985) and Longtin et al. (1988) are smaller than our results,
whereas the values deduced from Querry (1985) and Bedidi and Cervelle (1993)
are larger. The latter is supported by the work of Meland et al. (2011), who
concluded from angle-resolved light scattering experiments using hematite
particles that the values of the imaginary part *k* of the refractive index
of Querry (1985) and Bedidi and Cervelle (1993) are too high.

Overall, the experimentally determined absorption efficiencies show a linear
trend with particle radius (compare to Mie theory calculations) and are
within the spread of Mie theory calculations using the literature refractive
indices. We therefore conclude that our method of determining
*Q*_{abs} from the equilibrium temperature of nanoparticles via the
amount of adsorbed water is validated. Furthermore, we conclude that the
equilibrium temperature model presented in this work can be used with
literature values of bulk refractive indices of potential MSP materials to
estimate the equilibrium temperature of MSPs in the mesopause.

Asmus et al. (2014) proposed that the temperature increase in MSPs due to
absorption of solar irradiation increases linearly with increasing iron content of the particle material. In order to experimentally test this
hypothesis, we measured the absorption efficiency at *λ*=488 nm (the
laser wavelength closest to the maximum of the solar irradiation) for
Fe_{2}O_{3} and iron silicate particles
Fe_{x}Si_{1−x}O_{3} (0*<**x**<*1)
(*r*_{dry}=2 nm) of varying iron content. The results are shown in
Fig. 4 together with Mie theory calculations using the refractive indices for
Mg_{x}Fe_{1−x}SiO_{3} (Dorschner et al., 1995), FeO
(Henning et al., 1995), FeOOH (Bedidi and Cervelle, 1993), and the mean value
for Fe_{2}O_{3} from Fig. 3. The data support the assumption that
*Q*_{abs} depends linearly on the iron content. Consequently, the
potential MSP material which would heat up the most is FeO with a
stoichiometric iron content of 0.5.

In this section we discuss the impact of solar radiation on the critical
temperature of the environment *T*_{cr,env} needed to activate ice
growth. To this end we combine our previously presented ice growth activation
model (Duft et al., 2019) with the equilibrium temperature model of this
work. A description of the method can be found in Appendices A and B. In
order to estimate the maximum impact of solar radiation, we assume that the
particles are composed of FeO, the potential MSP material with the highest
iron content and which is therefore expected to heat up the most. To
calculate the water coverage on FeO particles we use an energy of desorption
${E}_{\mathrm{des}}^{\mathrm{0}}=\mathrm{42.7}$ kJ mol^{−1}, which was previously determined
for Fe_{2}O_{3} particles (Duft et al., 2019). For the incoming solar
irradiation we use the maximum solar zenith angle of 45.6^{∘} (21 June,
noon) at 69^{∘} N, a typical latitude of MSP observations. In Fig. 5a
we compare calculated critical temperatures as a function of the MSP radius
with and without particle heating by solar irradiation for an altitude of
87 km (0.27 Pa). Here, we assume a constant H_{2}O mixing ratio of
3 ppm which is typical for the polar summer mesopause (Hervig et al., 2009).

The solid blue curve in Fig. 5a shows results obtained when neglecting solar
heating of the particles (*T*_{p}=*T*_{env}), i.e., representing
non-absorbing particles. For comparison, the dashed black curve shows
calculated critical temperatures using the Kelvin effect of hexagonal ice at
the dry particle radius, which represent the highest activation temperatures
currently assumed in mesospheric models (e.g., Berger and Lübken, 2015;
Schmidt et al., 2018). For *r*_{dry}<1.1 nm, the size range of most
MSPs in the polar summer mesopause (Bardeen et al., 2010; Megner et al.,
2008a, b; Plane et al., 2014), the new activation model excluding solar
irradiation predicts ice particle formation at higher temperatures than
currently assumed in models. This is explained by the uptake of water
molecules by the MSPs, which increases the particle size and therefore causes
a reduction of the Kelvin effect. This effect outweighs the vapor pressure
difference between ASW and hexagonal ice for particle radii smaller than
1.1 nm. The horizontal dotted line at *T*=130 K indicates the measured mean
temperatures at 87 km and 69^{∘} N during June and July (Lübken,
1999). This line intersects with the calculations for non-absorbing particles
at a dry particle radius of about 1 nm, which means that at the mean
temperature of 130 K particles larger than *r*_{dry}=1 nm will
activate ice growth. The solid red curve in Fig. 5a shows results obtained
when including solar heating of the particles
(*T*_{p} > *T*_{env}), yielding lower
*T*_{cr,env} values. With solar heating no particles will activate at
the mean particle temperature of 130 K. However, typical temperature
variations in the summer mesopause are on the order of 10 K (Rapp et al.,
2002), which leads us to conclude that the atmospheric temperature of the
summer mesopause frequently falls below the critical temperature of
non-absorbing as well as of absorbing MSPs for particle radii above 0.5 nm.

Figure 5b shows the offset of the particle temperature from the ambient
temperature Δ*T* at critical conditions for particles with the highest
absorption efficiency (FeO). These values are almost identical to the
difference in critical temperatures between the activation model without and
with solar heating. We find that below *r*_{dry}=1.5 nm even the most
absorbing particles warm by less than 4 K at 87 km in altitude. The particle
heating will be much less for other MSP materials and at lower altitudes due
to the higher collisional cooling rate at higher pressures. In general, the
particle temperature offset reported here is about 5 times less than previous
estimates (Asmus et al., 2014) for two main reasons: (1) the uptake of water
molecules increases the particle surface area and therefore the collisional
cooling rate, and (2) the thermal accommodation coefficient of *α*=0.5
used in previous calculations (see also Espy and Jutt, 2002, and Grams and
Fiocco, 1977) is very likely an underestimation. We use a value of 1 based on
recent results of laboratory experiments, which increases the collisional
cooling rate by a factor of 2 (see Appendix B for more details).

5 Summary and conclusions

Back to toptop
We have presented H_{2}O adsorption measurements on MSP analogues
(Fe_{2}O_{3} and Fe_{x}Si_{1−x}O_{3}
nanoparticles) exposed to variable intensities of visible light at 405, 488,
and 660 nm. The experiments were performed at particle temperatures and
H_{2}O concentrations representative for the polar summer mesopause,
and the visible light covers the maximum in the solar irradiance. The
reduction in the number of adsorbed water molecules under irradiation allows
direct determination of the particle temperature increase caused by light
absorption. We used the measured temperature increase in an equilibrium
temperature model to determine the absorption efficiency of the particles.
The results show that the equilibrium temperature model is applicable and it
can be used with literature values of bulk refractive indices to calculate
the temperature increase in MSPs in the polar summer mesopause. Additionally,
we confirmed that the absorption efficiency increases with increasing iron
content of potential MSP materials (Asmus et al., 2014).

We find that the impact of solar radiation on polar mesospheric ice particle
formation is lower than previously assumed. Critical temperatures for ice
growth activation at 69^{∘} N decrease at most by 4 K for typical MSP
particle sizes. However, for assessing the significance of solar heating of
MSPs on PMC properties, the whole life cycle of mesospheric ice particles has
to be considered. Therefore, we propose that the updated ice activation model
(Appendix A and B) is used in future model studies with and without solar
irradiation for various potential MSP materials in order to evaluate if
absorption of solar irradiation alters properties of polar mesospheric
clouds.

Data availability

Back to toptop
Data availability.

All data are available on request from the corresponding author.

Appendix A: Critical temperatures under the influence of solar radiation

Back to toptop
At the conditions of the polar summer mesopause, ice particle formation
proceeds via deposition of compact amorphous solid water (ASW) on MSPs (Duft
et al., 2019; Nachbar et al., 2018c). Ice growth is activated if the
saturation *S*(*T*_{p}) is larger than the critical
saturation *S*_{cr}(*T*_{p}). In the following, we
present a method for calculating the temperature at which this condition is
fulfilled, the so-called critical temperature.

For a given water vapor mixing ratio *MR* and
atmospheric pressure *p*_{atm}, the saturation is determined by

$$\begin{array}{}\text{(A1)}& {\displaystyle}S\left({T}_{\mathrm{p}}\right)={\displaystyle \frac{MR\cdot {p}_{\mathrm{atm}}}{{p}_{\mathrm{s},\mathrm{a}}\left({T}_{\mathrm{p}}\right)}}\cdot \sqrt{{\displaystyle \frac{{T}_{\mathrm{env}}}{{T}_{\mathrm{p}}}}},\end{array}$$

with the saturation vapor pressure of ASW described by (Nachbar et al., 2018c)

$$\begin{array}{}\text{(A2)}& {\displaystyle}{p}_{\mathrm{s},\mathrm{a}}={p}_{\mathrm{s},\mathrm{h}}\cdot \mathrm{exp}\left({\displaystyle \frac{\mathrm{2312}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\left[\mathrm{J}\phantom{\rule{0.125em}{0ex}}{\mathrm{mol}}^{-\mathrm{1}}\right]-\mathrm{1.6}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\left[\mathrm{J}\phantom{\rule{0.125em}{0ex}}{\mathrm{mol}}^{-\mathrm{1}}\phantom{\rule{0.125em}{0ex}}{\mathrm{K}}^{-\mathrm{1}}\right]\cdot T}{RT}}\right).\end{array}$$

*p*_{s,h} represents the saturation vapor pressure of hexagonal ice (Murphy
and Koop, 2005). The critical saturation *S*_{cr} needed to activate ice
growth depends on the Kelvin effect calculated at the particle radius
*r*_{wet} (including the number of adsorbed H_{2}O molecules)
and considering the collision radius of a water molecule
(${r}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}=\mathrm{0.15}$ nm, Bickes et al., 1975) (Duft et al., 2019):

$$\begin{array}{}\text{(A3)}& {\displaystyle}{S}_{\mathrm{cr}}\left({T}_{\mathrm{p}}\right)={\left({\displaystyle \frac{{r}_{\mathrm{wet}}}{{r}_{\mathrm{wet}}+{r}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}\right)}^{\mathrm{2}}\cdot \mathrm{exp}\left({\displaystyle \frac{\mathrm{2}v\mathit{\sigma}}{R{T}_{\mathrm{p}}{r}_{\mathrm{wet}}}}\right).\end{array}$$

To determine the critical temperature at which ice growth is activated, the
environmental temperature *T*_{env} is decreased until *S*(*T*_{p}) ≥*S*_{cr}(*T*_{p}). A
reasonable starting point for *T*_{env} is the temperature at which
the saturation over a flat surface is 1 (solve for ${p}_{\mathrm{s},\mathrm{a}}\left({T}_{\mathrm{env}}\right)=MR\cdot {p}_{\mathrm{atm}}$). The coupled calculation of
*T*_{p} and *r*_{wet} is described in Appendix B and has to be
repeated every time *T*_{env} is decreased. The environmental temperature
fulfilling *S*(*T*_{p})=*S*_{cr}(*T*_{p}) is the critical temperature needed to activate ice
growth and $\mathrm{\Delta}T={T}_{\mathrm{p}}-{T}_{\mathrm{env}}$ is the increase in the
particle temperature at conditions of ice particle formation.

Appendix B: Equilibrium particle temperature and wet particle radius

Back to toptop
Substituting Eqs. (6) and (7) in Eq. (5) and
solving for the increase in the particle temperature Δ*T* considering
the dependency of the solar spectrum and of *Q*_{abs} on *λ*
yields

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}\mathrm{\Delta}T={T}_{\mathrm{p}}-{T}_{\mathrm{env}}=({A}_{\mathrm{geo}}\cdot {\int}_{\mathrm{0}}^{\mathrm{\infty}}I\left(\mathit{\lambda}\right)\cdot {Q}_{\mathrm{abs}}\left(\mathit{\lambda},{r}_{\mathrm{dry}}\right)\mathrm{d}\mathit{\lambda}\\ \text{(B1)}& {\displaystyle}& {\displaystyle}\phantom{\rule{1em}{0ex}}+{P}_{\mathrm{env}}^{\mathrm{a}}-{P}_{\mathrm{rad}}^{\mathrm{e}})/\left({A}_{\mathrm{col}}\mathit{\alpha}\mathrm{p}{v}_{\mathrm{th}}{\displaystyle \frac{(\mathit{\gamma}+\mathrm{1})}{\mathrm{8}T(\mathit{\gamma}-\mathrm{1})}}\right).\end{array}$$

Here, *I*(λ) (blackbody radiation assuming *T*=5780 K),
${P}_{\mathrm{env}}^{\mathrm{a}}$, and ${P}_{\mathrm{rad}}^{\mathrm{e}}$ were calculated
as presented in Asmus et al. (2014). The thermal accommodation coefficient
*α*, which is typically used in literature to describe the heating of
MSPs or NLC particles, is 0.5 (e.g., Asmus et al., 2014; Espy and Jutt, 2002).
This value seems to originate from the work of Grams and Fiocco (1977) and
was chosen due to a lack of relevant measurements determining *α* at
realistic mesopause conditions. More recently, measurements of *α* for
N_{2} on water droplets and for air on fused silica
which show that *α* is close to unity have become available (Fung and Tang, 1988; Ganta et
al., 2011). We therefore used *α*=1. The collision surface area of a
particle ${A}_{\mathrm{col}}=\mathrm{4}\mathit{\pi}{\left({r}_{\mathrm{wet}}+{r}_{{\mathrm{N}}_{\mathrm{2}}}\right)}^{\mathrm{2}}$ is
described by the collision radius of a nitrogen molecule
${r}_{{\mathrm{N}}_{\mathrm{2}}}=\mathrm{0.19}$ nm (Hirschfelder et al., 1966) and the wet particle
radius *r*_{wet} (Eq. 3). The wet particle radius can be
calculated with the mass of adsorbed water in equilibrium *m*_{ads},
which can be obtained by rearranging Eq. (1):

$$\begin{array}{}\text{(B2)}& {\displaystyle}{m}_{\mathrm{ads}}={A}_{\mathrm{p}}\cdot {m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\cdot {\displaystyle \frac{{n}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\cdot {v}_{\mathrm{th}}}{\mathrm{4}f}}\cdot \mathrm{exp}\left({\displaystyle \frac{{E}_{\mathrm{des}}^{\mathrm{0}}}{R{T}_{\mathrm{p}}}}-{\displaystyle \frac{\mathrm{2}\mathit{\sigma}v}{R{T}_{\mathrm{p}}{r}_{\mathrm{dry}}}}\right).\end{array}$$

Note that *m*_{ads} and ${P}_{\mathrm{rad}}^{\mathrm{e}}$ depend on the
particle temperature. Consequently, Δ*T* (Eq. B1) has to be solved
numerically. In our approach we alternatingly calculate *T*_{p} and
*m*_{ads} until the relative change in Δ*T* is less than
0.01 %.

Author contributions

Back to toptop
Author contributions.

DD, HW, and MN designed the research. KK and MN designed and installed the laser setup. MN, TA, and KK carried out the experiments. MN performed the data analysis. HW performed the calculations of the critical temperature in the mesopause. MN prepared the paper with contributions from all co-authors. DD, TM, JMCP, and MR supervised the activities in each group. TL supervised the project.

Competing interests

Back to toptop
Competing interests.

The authors declare that they have no conflict of interest.

Special issue statement

Back to toptop
Special issue statement.

This article is part of the special issue “Layered phenomena in the mesopause region (ACP/AMT inter-journal SI)”. It is a result of the LPMR workshop 2017 (LPMR-2017), Kühlungsborn, Germany, 18–22 September 2017.

Acknowledgements

Back to toptop
Acknowledgements.

The authors thank the German Federal Ministry of Education and Research
(BMBF, grant numbers 05K13VH3 and 05K16VHB) and the German Research Foundation
(DFG, grant number LE 834/4-1) for financial support of this work. We
acknowledge support by the Deutsche Forschungsgemeinschaft and Open Access
Publishing Fund of Karlsruhe Institute of Technology. TA is supported by a
research studentship from the UK Natural Environment Research Council's
SPHERES doctoral training program.

The
article processing charges for this open-access

publication
were covered by a Research

Centre of the Helmholtz
Association.

Review statement

Back to toptop
Review statement.

This paper was edited by Andreas Engel and reviewed by three anonymous referees.

References

Back to toptop
Antonsen, T., Havnes, O., and Mann, I.: Estimates of the Size Distribution of Meteoric Smoke Particles From Rocket-Borne Impact Probes, J. Geophys. Res.-Atmos., 122, 12353–12365, 2017.

Asmus, H., Wilms, H., Strelnikov, B., and Rapp, M.: On the heterogeneous nucleation of mesospheric ice on meteoric smoke particles: Microphysical modeling, J. Atmos. Sol.-Terr. Phys., 118, 180–189, 2014.

Bardeen, C. G., Toon, O. B., Jensen, E. J., Hervig, M. E., Randall, C. E., Benze, S., Marsh, D. R., and Merkel, A.: Numerical simulations of the three-dimensional distribution of polar mesospheric clouds and comparisons with Cloud Imaging and Particle Size (CIPS) experiment and the Solar Occultation For Ice Experiment (SOFIE) observations, J. Geophys. Res.-Atmos., 115, D10204, https://doi.org/10.1029/2009JD012451, 2010.

Bedidi, A. and Cervelle, B.: Light scattering by spherical particles with hematite and goethitelike optical properties: Effect of water impregnation, J. Geophys. Res.-Sol. Ea., 98, 11941–11952, 1993.

Berger, U. and Lübken, F.-J.: Trends in mesospheric ice layers in the Northern Hemisphere during 1961–2013, J. Geophys. Res.-Atmos., 120, 11277–211298, 2015.

Bickes, R. W., Duquette, G., van den Meijdenberg, C. J. N., Rulis, A. M.,
Scoles, G., and Smith, K. M.: Molecular Beam Scattering Experiments with
Polar Molecules: Measurement of Differential Collision Cross Sections for
H_{2}O+H_{2}, He, Ne, Ar, H_{2}O and NH_{3} +H_{2}, He,
NH_{3}, J. Phys. B, 8, 3034–3043, 1975.

Bohren, C. F. and Huffmann, D. R.: Absorption and Scattering of Light by Small Particles, WILEY-VCH Verlag GmbH & Co. KGaA, 530 pp., 2007.

Bondi, A.: van der Waals Volumes and Radii, J. Phys. Chem., 68, 441–451, https://doi.org/10.1021/j100785a001, 1964.

Brown, D. E., George, S. M., Huang, C., Wong, E. K. L., Rider, K. B., Smith,
R. S., and Kay, B. D.: H_{2}O condensation coefficient and refractive
index for vapor-deposited ice from molecular beam and optical interference
measurements, J. Phys. Chem., 100, 4988–4995, 1996.

Demissie, T. D., Espy, P. J., Kleinknecht, N. H., Hatlen, M., Kaifler, N., and Baumgarten, G.: Characteristics and sources of gravity waves observed in noctilucent cloud over Norway, Atmos. Chem. Phys., 14, 12133–12142, https://doi.org/10.5194/acp-14-12133-2014, 2014.

Dorschner, J., Begemann, B., Henning, T., Jäger, C., and Mutschke, H.: Steps toward interstellar silicate mineralogy, II. Study of Mg-Fe-silicate glasses of variable composition, Astron. Astrophys., 300, 503–520, 1995.

Duft, D., Nachbar, M., Eritt, M., and Leisner, T.: A Linear Trap for Studying the Interaction of Nanoparticles with Supersaturated Vapors, Aerosol Sci. Tech., 49, 682–690, 2015.

Duft, D., Nachbar, M., and Leisner, T.: Unravelling the microphysics of polar mesospheric cloud formation, Atmos. Chem. Phys., 19, 2871–2879, https://doi.org/10.5194/acp-19-2871-2019, 2019.

Espy, P. J. and Jutt, H.: Equilibrium temperature of water–ice aerosols in the high-latitude summer mesosphere, J. Atmos. Sol.-Terr. Phys., 64, 1823–1832, 2002.

Fung, K. H. and Tang, I. N.: Thermal-accommodation measurement of helium on a suspended water droplet, Phys. Rev. A, 37, 2557–2561, 1988.

Ganta, D., Dale, E. B., Rezac, J. P., and Rosenberg, A. T.: Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator, J. Chem. Phys., 135, 084313, https://doi.org/10.1063/1.3631342, 2011.

Grams, G. and Fiocco, G.: Equilibrium temperatures of spherical ice particles in the upper atmosphere and implications for noctilucent cloud formation, J. Geophys. Res., 82, 961–966, 1977.

Gumbel, J. and Megner, L.: Charged meteoric smoke as ice nuclei in the mesosphere: Part 1 – A review of basic concepts, J. Atmos. Sol.-Terr. Phys., 71, 1225–1235, 2009.

Havnes, O., Gumbel, J., Antonsen, T., Hedin, J., and La Hoz, C.: On the size distribution of collision fragments of NLC dust particles and their relevance to meteoric smoke particles, J. Atmos. Sol.-Terr. Phys., 118, 190–198, 2014.

Henning, T., Begemann, B., Mutschke, H., and Dorschner, J.: Optical properties of oxide dust grains, Astron. Astrophys., 112, 143–149, 1995.

Hervig, M. E., Stevens, M. H., Gordley, L. L., Deaver, L. E., Russell, J. M., and Bailey, S. M.: Relationships between polar mesospheric clouds, temperature, and water vapor from Solar Occultation for Ice Experiment (SOFIE) observations, J. Geophys. Res.-Atmos., 114, D20203, https://doi.org/10.1029/2009JD012302, 2009.

Hervig, M. E., Deaver, L. E., Bardeen, C. G., Russell, J. M., Bailey, S. M., and Gordley, L. L.: The content and composition of meteoric smoke in mesospheric ice particles from SOFIE observations, J. Atmos. Sol.-Terr. Phys., 84/85, 1–6, 2012.

Hervig, M. E., Berger, U., and Siskind, D. E.: Decadal variability in PMCs and implications for changing temperature and water vapor in the upper mesosphere, J. Geophys. Res.-Atmos., 121, 2383–2392, 2016.

Hervig, M. E., Brooke, J. S. A., Feng, W., Bardeen, C. G., and Plane, J. M. C.: Constraints on Meteoric Smoke Composition and Meteoric Influx Using SOFIE Observations With Models, J. Geophys. Res.-Atmos., 122, 13495–413505, 2017.

Hirschfelder, J., Curtiss, C. F., and Bird, R. B.: Molecular Theory of Gases and Liquids, John Wiley & Sons, 1249 pp., 1966.

Hsu, W. P. and Matijević, E.: Optical properties of monodispersed hematite hydrosols, Appl. Opt., 24, 1623–1630, 1985.

Kaifler, N., Baumgarten, G., Fiedler, J., and Lübken, F.-J.: Quantification of waves in lidar observations of noctilucent clouds at scales from seconds to minutes, Atmos. Chem. Phys., 13, 11757–11768, https://doi.org/10.5194/acp-13-11757-2013, 2013.

Keesee, R. G.: Nucleation and particle formation in the upper atmosphere, J. Geophys. Res.-Atmos., 94, 14683–14692, 1989.

Kerker, M., Scheiner, P., Cooke, D. D., and Kratohvil, J. P.: Absorption index and color of colloidal hematite, J. Colloid Interf. Sci., 71, 176–187, 1979.

Leslie, R. C.: Sky Glows, Nature, 32, p. 245, 1885.

Loerting, T., Bauer, M., Kohl, I., Watschinger, K., Winkel, K., and Mayer, E.: Cryoflotation: Densities of Amorphous and Crystalline Ices, J. Phys. Chem. B, 115, 14167–14175, 2011.

Longtin, D. R., Shettle, E. P., Hummel, J. R., and Pryce, J. D.: A Wind Dependent Desert Aerosol Model: Refractive Properties, Air Force Geophys. Lab., Air Force Syst. Command Hanscom Air Force Base, 115 pp., 1988.

Lübken, F.-J.: Thermal structure of the Arctic summer mesosphere, J. Geophys. Res.-Atmos., 104, 9135–9149, 1999.

Lübken, F. J., Lautenbach, J., Höffner, J., Rapp, M., and Zecha, M.: First continuous temperature measurements within polar mesosphere summer echoes, J. Atmos. Sol.-Terr. Phys., 71, 453–463, 2009.

Majima, T., Santambrogio, G., Bartels, C., Terasaki, A., Kondow, T., Meinen, J., and Leisner, T.: Spatial distribution of ions in a linear octopole radio-frequency ion trap in the space-charge limit, Phys. Rev. A, 85, 053414, https://doi.org/10.1103/PhysRevA.85.053414, 2012.

Mazeina, L. and Navrotsky, A.: Enthalpy of Water Adsorption and Surface
Enthalpy of Goethite (*α*-FeOOH) and Hematite (*α*-Fe_{2}O_{3}), Chem.
Mater., 19, 825–833, 2007.

Megner, L., Gumbel, J., Rapp, M., and Siskind, D. E.: Reduced meteoric smoke particle density at the summer pole – Implications for mesospheric ice particle nucleation, Adv. Space Res., 41, 41–49, 2008a.

Megner, L., Siskind, D. E., Rapp, M., and Gumbel, J.: Global and temporal distribution of meteoric smoke: A two-dimensional simulation study, J. Geophys. Res.-Atmos., 113, D03202, https://doi.org/10.1029/2007JD009054, 2008b.

Meinen, J., Khasminskaya, S., Rühl, E., Baumann, W., and Leisner, T.: The TRAPS Apparatus: Enhancing Target Density of Nanoparticle Beams in Vacuum for X-ray and Optical Spectroscopy, Aerosol Sci. Tech., 44, 316–328, 2010.

Meland, B., Kleiber, P. D., Grassian, V. H., and Young, M. A.: Visible light scattering study at 470, 550, and 660 nm of components of mineral dust aerosol: Hematite and goethite, J. Quant. Spectrosc. Ra., 112, 1108–1118, 2011.

Murphy, D. M. and Koop, T.: Review of the vapour pressures of ice and supercooled water for atmospheric applications, Q. J. Roy. Meteor. Soc., 131, 1539–1565, 2005.

Nachbar, M., Duft, D., Mangan, T. P., Martin, J. C. G., Plane, J. M. C., and
Leisner, T.: Laboratory measurements of heterogeneous CO_{2} ice
nucleation on nanoparticles under conditions relevant to the Martian
mesosphere, J. Geophys. Res.-Planet., 121, 753–769, 2016.

Nachbar, M., Duft, D., Kiselev, A., and Leisner, T.: Composition, Mixing State and Water Affinity of Meteoric Smoke Analogue Nanoparticles Produced in a Non-Thermal Microwave Plasma Source, Z. Phys. Chem., 232, 635–648, 2018a.

Nachbar, M., Duft, D., and Leisner, T.: The vapor pressure over nano-crystalline ice, Atmos. Chem. Phys., 18, 3419-3431, 2018b.

Nachbar, M., Duft, D., and Leisner, T.: Volatility of Amorphous Solid Water, J. Phys. Chem. B, 122, 10044–10050, 2018c.

Navrotsky, A., Mazeina, L., and Majzlan, J.: Size-Driven Structural and Thermodynamic Complexity in Iron Oxides, Science, 319, 1635–1638, 2008.

Plane, J. M. C., Saunders, R. W., Hedin, J., Stegman, J., Khaplanov, M., Gumbel, J., Lynch, K. A., Bracikowski, P. J., Gelinas, L. J., Friedrich, M., Blindheim, S., Gausa, M., and Williams, B. P.: A combined rocket-borne and ground-based study of the sodium layer and charged dust in the upper mesosphere, J. Atmos. Sol.-Terr. Phys., 118, 151–160, 2014.

Pruppacher, H. R. and Klett, J. D.: Microphysics of Clouds and Precipitation, Springer, 2010.

Querry, M. R.: Optical Constants, Contractor report, US Army Chemical Research, Delvelopement and Engineering Center (CRDC), Aberdeen Proving Ground, MD, 415 pp., 1985.

Rapp, M. and Thomas, G. E.: Modeling the microphysics of mesospheric ice particles: Assessment of current capabilities and basic sensitivities, J. Atmos. Sol.-Terr. Phys., 68, 715–744, 2006.

Rapp, M., Lübken, F. J., Müllemann, A., Thomas, G. E., and Jensen, E. J.: Small-scale temperature variations in the vicinity of NLC: Experimental and model results, J. Geophys. Res.-Atmos., 107, 11 pp., 2002.

Rapp, M., Plane, J. M. C., Strelnikov, B., Stober, G., Ernst, S., Hedin, J., Friedrich, M., and Hoppe, U.-P.: In situ observations of meteor smoke particles (MSP) during the Geminids 2010: constraints on MSP size, work function and composition, Ann. Geophys., 30, 1661–1673, https://doi.org/10.5194/angeo-30-1661-2012, 2012.

Rong, P. P., Yue, J., Russell, J. M., Lumpe, J. D., Gong, J., Wu, D. L., and Randall, C. E.: Horizontal winds derived from the polar mesospheric cloud images as observed by the CIPS instrument on the AIM satellite, J. Geophys. Res.-Atmos., 120, 5564–5584, 2015.

Schmidt, F., Baumgarten, G., Berger, U., Fiedler, J., and Lübken, F.-J.: Local time dependence of polar mesospheric clouds: a model study, Atmos. Chem. Phys., 18, 8893–8908, https://doi.org/10.5194/acp-18-8893-2018, 2018.

Seele, C. and Hartogh, P.: Water vapor of the polar middle atmosphere: Annual variation and summer mesosphere Conditions as observed by ground-based microwave spectroscopy, Geophys. Res. Lett., 26, 1517–1520, 1999.

Sneh, O., Cameron, M. A., and George, S. M.: Adsorption and desorption
kinetics of H_{2}O on a fully hydroxylated SiO_{2} surface, Surf. Sci.,
364, 61–78, 1996.

Thomas, G. E. and Olivero, J.: Noctilucent clouds as possible indicators of global change in the mesosphere, Adv. Space Res., 28, 937–946, 2001.

Thomas, G. E., Olivero, J. J., Jensen, E. J., Schroeder, W., and Toon, O. B.: Relation between increasing methane and the presence of ice clouds at the mesopause, Nature, 338, 490–492, 1989.

Turco, R. P., Toon, O. B., Whitten, R. C., Keesee, R. G., and Hollenbach, D.: Noctilucent clouds: Simulation studies of their genesis, properties and global influences, Planet. Space Sci., 30, 1147–1181, 1982.

Wilms, H., Rapp, M., and Kirsch, A.: Nucleation of mesospheric cloud particles: Sensitivities and limits, J. Geophys. Res.-Space, 121, 2621–2644, 2016.

Witt, G.: Height, structure and displacement of noctilucent clouds, Tellus, 14, 1–18, 1962.

Yasumoto, I.: Thermal transpiration effects for gases at pressures above 0.1 torr, J. Phys. Chem., 84, 589–593, 1980.

Zhang, X. L., Wu, G. J., Zhang, C. L., Xu, T. L., and Zhou, Q. Q.: What is the real role of iron oxides in the optical properties of dust aerosols?, Atmos. Chem. Phys., 15, 12159–12177, https://doi.org/10.5194/acp-15-12159-2015, 2015.

Short summary

Polar mesospheric clouds (PMC) are water ice clouds forming on nanoparticles in the polar summer mesopause. We investigate the impact of solar radiation on PMC formation in the laboratory. We show that Mie theory calculations combined with an equilibrium temperature model presented in this work predict the warming of the particles very well. Using this model we demonstrate that the impact of solar radiation on ice particle formation is significantly lower than previously assumed.

Polar mesospheric clouds (PMC) are water ice clouds forming on nanoparticles in the polar summer...

Atmospheric Chemistry and Physics

An interactive open-access journal of the European Geosciences Union