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<2nm) 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 (Fe2O3 and
FexSi1-xO3) 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.
Introduction
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 H2O 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 H2O concentration caused by anthropogenic
emissions of CO2 and CH4 (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
SiO2, Fe2O3, 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 (Fe3O4), wüstite
(FeO), magnesiowüstite (MgxFe1-xO,
x=0–0.6), and iron-rich olivine
(Mg2xFe2-2xSiO4, 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
H2O molecules on Fe2O3 and
FexSi1-xO3 nanoparticles under the influence
of the laser light at controlled gas-phase H2O 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.
Experimental method
We produce spherical, singly charged Fe2O3, SiO2, or
FexSi1-xO3 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 (Δm/m≤7%) with an electrostatic quadrupole
deflector (DF1) 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 1-5×10-3 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 H2O 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 107
particles in about 1 s, followed by storing of the particles for up to
several hours. Depending on the conditions applied in MICE, H2O
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.
Illustration of the experimental setup. The insert shows a camera
image of the laser beam profile (λ=488 nm) taken at the exit of
MICE. Vertical and horizontal cross sections of the laser beam profile are
shown above and right of the image, overlaid with fitted Gaussian curves. The
red dashed lines indicate the radial extent of the levitated nanoparticle
cloud. See the text for more details.
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 (2×104Da-50×104 Da; 1 Da ≜1 atomic
mass unit =1.6605×10-27 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 H2O molecules until an equilibrium state
between adsorbing H2O 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 Fe2O3
particles with a dry particle radius rdry=3m0/4πρp1/3=2.9 nm
(ρp=5.2 g cm-3), a H2O gas-phase
concentration nH2O=1.1×1016 m-3, and a
temperature of the environment surrounding the particles
Tenv=148.8 K. The black squares show the adsorption curve
without light irradiation for which Tenv equals the particle
temperature Tp. If the particles are heated by light irradiation
(Tp>Tenv), the water molecule flux
desorbing from a particle increases, which causes a reduction in the number
of adsorbed H2O 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 ΔT, which were determined by analyzing the steady-state mass
of adsorbed water molecules. The method for deriving ΔT is presented
below.
(a) Mean particle mass as a function of residence time in
MICE for six different mean light intensities (λ=488 nm,
rdry=2.9 nm (Fe2O3), Tenv=148.8 K,
nH2O=1.1×1016 m-3). The solid curves represent
fits of Eq. (2) to the data. (b) Particle temperature offsets
ΔT (Eq. 4) as a function of the mean light intensities.
We analyze the adsorption data with a parameterization which was originally
used to describe the equilibrium concentration of adsorbed water molecules
cH2O 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 jads
must equal the flux density desorbing from the particle jdes :
nH2O⋅vth4︸jads=cH2O⋅f⋅exp-Edes0RTp+2σvRTprdry︸jdes.
The flux density in the molecular flow regime (left-hand side of Eq. 1)
depends on gas-phase properties, namely the concentration nH2O and
the mean thermal velocity vth=8kTenv/πmH2O of gas-phase H2O 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 cH2O, the vibrational
frequency of a water molecule on the particle surface f=1013 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 Tp, and the mean desorption energy of a
H2O molecule for a planar surface of the particle material
Edes0. 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=6.022×1023⋅mH2O/ρice is the volume of 1 mol of H2O 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 ρicegcm-3=0.9167-1.75×10-4⋅Tp∘C-5×10-7⋅Tp∘C2 for crystalline ice (Pruppacher and Klett, 2010). For
the surface tension of ASW we use σmNm-1=114.81-0.144⋅TK, which is based on
an extrapolation of experimental data for supercooled water (Nachbar et al.,
2018c). The equilibrium concentration of adsorbed water molecules
cH2O is the adsorbed mass of H2O molecules in
equilibrium mads divided by the surface area of a dry
nanoparticle Ap=4πrdry2 and the mass of a water
molecule mH2O (cH2O=mads/Ap/mH2O). We derive the adsorbed mass of H2O
molecules in equilibrium mads from the experimental data with an
exponential fit (represented by the solid curves in Fig. 2a) of the following
form:
mt=m0+mads⋅1-exp-tresτ.
The radius of the wet particle is indicated by the right ordinate in Fig. 2a
and follows from the measured particle mass according to
rwet=rdry3+34πmadsρice1/3.
The particle temperature offset ΔT is determined by a set of two
measurement runs, one without and one with light illumination. The mean
desorption energy for a H2O molecule is determined from the
measurement without light illumination (Tp=Tenv) by
solving Eq. (1) for Edes0. For the data shown in Fig. 2, this
procedure results in Edes0=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 H2O 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 H2O
coverage or the particle temperature on the values of Edes0
determined in our previous study (Duft et al., 2019). Therefore, we can
determine the particle temperature under light illumination assuming a
constant Edes0 value. Rearranging Eq. (1) yields
Tp=Tenv+ΔT=Edes0-2σvrdry4/R⋅lnmadsTp⋅fmH2OπnH2Ovthrdry2.
Since σ and ρice are dependent on the particle
temperature, Eq. (4) should be solved numerically. However, a sensitivity
analysis has shown that calculating ΔT analytically using constant
σTenv and ρiceTenv deviates less than 1 % from the numerical
solution. We therefore analyzed our data using σTenv and ρiceTenv. The determined
temperature offset ΔT can be used with an equilibrium temperature
model to calculate the light absorption efficiency of the particles
Qabs. The equilibrium temperature model is introduced in the next
section.
Equilibrium temperature model
The equilibrium temperature of particles levitated in MICE is described by a
balance between power sources and sinks. Sources are absorption of laser
light Pλa and of infrared radiation emitted by the
environment Penva. Sinks are cooling due to collisions
with the He background gas Pcol and blackbody radiation of the
particle in the infrared Prade. Note that in
equilibrium, the heat from sublimation and condensation cancels. The balance
equation is
Pλa+Penva=Prade+Pcol.
The absorption of laser light with intensity I depends on the material and
wavelength-dependent absorption efficiency of the particles Qabs.
The absorption efficiency is defined as the absorption cross section divided
by the geometrical cross section Ageo=πrdry2. We
assume the layer of adsorbed water molecules to be entirely transparent to
visible light so that Pλa is the power absorbed by the
MSP alone:
Pλa=I⋅Qabsλ,rdry⋅Ageo.
For the cooling due to collisions with the He gas we use the description
presented in Asmus et al. (2014):
Pcol=Acol⋅α⋅p4kTenvvth⋅kγ+12γ-1⋅ΔT.
For particles in the nanometer regime, the collision surface area
Acol must include the radius of the colliding He atom
(rHe=0.14 nm, Bondi, 1964), so that Acol=4πrwet+rHe2. The helium pressure in MICE is
represented by p, vth=8kTenv/πmHe
is the mean thermal velocity of He atoms, γ is the heat capacity
ratio, ΔT=Tp-Tenv 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 αair=1 (Fung and Tang,
1988; Ganta et al., 2011).
For the conditions applied in MICE, Prade and
Penva are several orders of magnitude smaller than
Pλa andPcol 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 Qabsλ,rdry yields
Qabsλ,rdry=AcolI⋅Ageoαpvthγ+18Tenvγ-1ΔT.
Results and discussionAbsorption efficiencies
H2O adsorption measurements similar to those presented in Fig. 2
were recorded for Fe2O3 particles with dry particle radii
between 1.3 and 3.2 nm. Particle temperature offsets ΔT 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 Qabs values derived
from literature data of the complex refractive index m=n+i⋅k,
Qabs was calculated from the extinction efficiency
Qext and from the scattering efficiency Qscat using
Mie theory (Bohren and Huffmann, 2007) according to
Qabsλ,rdry,m=Qextλ,rdry,m-Qscatλ,rdry,m.
Note that the size parameter x=2πrdry/λ 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 Qabs is
proportional to rdry.
Absorption efficiencies as a function of dry particle radius
for Fe2O3 nanoparticles at λ=405, λ=488, and
λ=660 nm. The dotted and dashed curves represent Mie theory
calculations using refractive indices from literature with the colors
indicating the wavelength.
Large differences exist throughout the literature for the imaginary part of
the refractive index for hematite (Fe2O3) 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 Fe2O3 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
Qabs 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
Fe2O3 and iron silicate particles
FexSi1-xO3 (0<x<1)
(rdry=2 nm) of varying iron content. The results are shown in
Fig. 4 together with Mie theory calculations using the refractive indices for
MgxFe1-xSiO3 (Dorschner et al., 1995), FeO
(Henning et al., 1995), FeOOH (Bedidi and Cervelle, 1993), and the mean value
for Fe2O3 from Fig. 3. The data support the assumption that
Qabs 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.
Absorption efficiencies for rdry=2 nm particles at
λ=488 nm of various particle materials as a function of the
relative stoichiometric iron content. Blue squares and the triangle represent
experimental results for FexSi1-xO3 (0<x<1) and Fe2O3 particles, respectively. The
black circle, square, diamond, and stars represent Mie theory calculations
for FeO, Fe2O3, FeO(OH), and
MgxFe1-xSiO3 particles using refractive
indices from literature (see text).
The impact of solar radiation on ice particle formation
In this section we discuss the impact of solar radiation on the critical
temperature of the environment Tcr,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
Edes0=42.7 kJ mol-1, which was previously determined
for Fe2O3 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 H2O mixing ratio of
3 ppm which is typical for the polar summer mesopause (Hervig et al., 2009).
Critical temperature (a) and particle temperature offset (b) at 87 km in altitude for FeO particles as a function of dry
particle radius. The blue curve represents critical temperatures calculated
with the activation model neglecting solar irradiation, and the red curves
consider solar irradiation. For comparison, we show the equilibrium
saturation calculated using the Kelvin equation for hexagonal ice with the
dry particle radius represented by the dashed black curve.
The solid blue curve in Fig. 5a shows results obtained when neglecting solar
heating of the particles (Tp=Tenv), 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 rdry<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 rdry=1 nm will
activate ice growth. The solid red curve in Fig. 5a shows results obtained
when including solar heating of the particles
(Tp > Tenv), yielding lower
Tcr,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 ΔT 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 rdry=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).
Summary and conclusions
We have presented H2O adsorption measurements on MSP analogues
(Fe2O3 and FexSi1-xO3
nanoparticles) exposed to variable intensities of visible light at 405, 488,
and 660 nm. The experiments were performed at particle temperatures and
H2O 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
All data are available on request from the corresponding
author.
Critical temperatures under the influence of solar radiation
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 STp is larger than the critical
saturation ScrTp. 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 patm, the saturation is determined by
STp=MR⋅patmps,a(Tp)⋅TenvTp,
with the saturation vapor pressure of ASW described by (Nachbar et al.,
2018c)
ps,a=ps,h⋅exp2312Jmol-1-1.6Jmol-1K-1⋅TRT.ps,h represents the saturation vapor pressure of hexagonal ice (Murphy
and Koop, 2005). The critical saturation Scr needed to activate ice
growth depends on the Kelvin effect calculated at the particle radius
rwet (including the number of adsorbed H2O molecules)
and considering the collision radius of a water molecule
(rH2O=0.15 nm, Bickes et al., 1975) (Duft et al., 2019):
ScrTp=rwetrwet+rH2O2⋅exp2vσRTprwet.
To determine the critical temperature at which ice growth is activated, the
environmental temperature Tenv is decreased until STp≥ScrTp. A
reasonable starting point for Tenv is the temperature at which
the saturation over a flat surface is 1 (solve for ps,aTenv=MR⋅patm). The coupled calculation of
Tp and rwet is described in Appendix B and has to be
repeated every time Tenv is decreased. The environmental temperature
fulfilling STp=ScrTp is the critical temperature needed to activate ice
growth and ΔT=Tp-Tenv is the increase in the
particle temperature at conditions of ice particle formation.
Equilibrium particle temperature and wet particle radius
Substituting Eqs. (6) and (7) in Eq. (5) and
solving for the increase in the particle temperature ΔT considering
the dependency of the solar spectrum and of Qabs on λ
yields
ΔT=Tp-Tenv=(Ageo⋅∫0∞Iλ⋅Qabsλ,rdrydλB1+Penva-Prade)/Acolαpvth(γ+1)8T(γ-1).
Here, Iλ (blackbody radiation assuming T=5780 K),
Penva, and Prade 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
N2 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 Acol=4πrwet+rN22 is
described by the collision radius of a nitrogen molecule
rN2=0.19 nm (Hirschfelder et al., 1966) and the wet particle
radius rwet (Eq. 3). The wet particle radius can be
calculated with the mass of adsorbed water in equilibrium mads,
which can be obtained by rearranging Eq. (1):
mads=Ap⋅mH2O⋅nH2O⋅vth4f⋅expEdes0RTp-2σvRTprdry.
Note that mads and Prade depend on the
particle temperature. Consequently, ΔT (Eq. B1) has to be solved
numerically. In our approach we alternatingly calculate Tp and
mads until the relative change in ΔT is less than
0.01 %.
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
The authors declare that they have no conflict of
interest.
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
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
This paper was edited by Andreas Engel and reviewed by three
anonymous referees.
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