ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-4043-2016Chemical and physical influences on aerosol activation in liquid clouds: a study based on observations from the Jungfraujoch, SwitzerlandHoyleChristopher R.christopher.hoyle@psi.chhttps://orcid.org/0000-0002-1369-9143WebsterClare S.RiederHarald E.NenesAthanasioshttps://orcid.org/0000-0003-3873-9970HammerEmanuelHerrmannErikGyselMartinhttps://orcid.org/0000-0002-7453-1264BukowieckiNicolashttps://orcid.org/0000-0002-2925-8553WeingartnerErnesthttps://orcid.org/0000-0002-2427-4634SteinbacherMartinhttps://orcid.org/0000-0002-7195-8115BaltenspergerUrsLaboratory of Atmospheric Chemistry, Paul Scherrer Institute, Villigen, SwitzerlandWSL Institute for Snow and Avalanche Research SLF Davos, SwitzerlandWegener Center for Climate and Global Change and IGAM/Department of Physics, University of Graz, AustriaAustrian Polar Research Institute, Vienna, AustriaSchool of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332, USASchool of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USAInstitute of Chemical Engineering Sciences, Foundation for Research and Technology, Hellas, 26504 Patras, GreeceInstitute for Environmental Research and Sustainable Development, National Observatory of Athens, 15236 Palea Penteli, GreeceLaboratory for Air Pollution/Environmental Technology, Empa – Swiss Federal Laboratories for Materials Science and Technology, Ueberlandstrasse 129, 8600 Duebendorf, Switzerlandnow at: Department of Geography, Faculty of Engineering and Environment, Northumbria University, Newcastle Upon Tyne, UKnow at: Grolimund and Partner – Environmental Engineering, Thunstrasse 101a, 3006 Bern, Switzerlandnow at: Institute of Aerosol and Sensor Technology, University of Applied Sciences Northwestern Switzerland, Windisch, SwitzerlandChristopher R. Hoyle (christopher.hoyle@psi.ch)29March2016166404340611May20159June201511March201614March2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/4043/2016/acp-16-4043-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/4043/2016/acp-16-4043-2016.pdf
A simple statistical model to predict the number of aerosols which
activate to form cloud droplets in warm clouds has been established, based on
regression analysis of data from four summertime Cloud and Aerosol
Characterisation Experiments (CLACE) at the high-altitude site Jungfraujoch
(JFJ). It is shown that 79 % of the observed variance in droplet
numbers can be represented by a model accounting only for the number of
potential cloud condensation nuclei (defined as number of particles larger than 80 nm in
diameter), while the mean errors in the model representation may be reduced
by the addition of further explanatory variables, such as the mixing ratios
of O3, CO, and the height of the measurements above cloud base. The
statistical model has a similar ability to represent the observed droplet
numbers in each of the individual years, as well as for the two predominant
local wind directions at the JFJ (northwest and southeast). Given the central
European location of the JFJ, with air masses in summer being representative
of the free troposphere with regular boundary layer in-mixing via convection,
we expect that this statistical model is generally applicable to warm clouds under
conditions where droplet formation is aerosol limited (i.e. at relatively
high updraught velocities and/or relatively low aerosol number
concentrations). A comparison between the statistical model and an
established microphysical parametrization shows good agreement between the
two and supports the conclusion that cloud droplet formation at the JFJ is
predominantly controlled by the number concentration of aerosol particles.
Introduction
Aerosols have a well-documented and pronounced influence on the microphysical
and therefore radiative properties of clouds
e.g.. The properties
of atmospheric aerosol particles thus have a strong potential to affect local
and regional climates. However, the influence of aerosols on clouds remains
the single largest uncertainty hampering the calculation of future climate
scenarios . To reduce this uncertainty, an improved
understanding of the aerosol properties and environmental conditions that
allow parts of the aerosol population to act as cloud condensation nuclei
(CCN) and form cloud droplets is required.
Previous ground-based studies have investigated statistical relationships
between cloud droplet or CCN number concentration, aerosol properties, and
environmental variables e.g.. Based on around 22 days of
data from the Taunus Observatory in central Germany,
determined that the concentration of CCN (as measured at different
supersaturations in a CCN counter) is largely dependent on the measured
particle size distribution, with the CCN concentration increasing with
increasing particle diameter and chemical composition of the aerosol playing
a secondary role.
Various studies have investigated the mechanisms through which the chemical
composition of aerosol influences its water uptake and activation and how
this can be accounted for e.g.. In addition, surface active compounds may influence surface
tension and thus the activation of aerosol particles to form cloud droplets
. Recently, it has been suggested
that this may lead to a temperature influence on aerosol activation
. Nevertheless, the works of, for example,
and suggest that the
relatively small variations in chemical composition of aerosol in areas away
from sources may play a smaller role in determining CCN activity of the
aerosol than variations in the size distribution.
Examining 1 month of data from a remote site in northern Finland,
determined that the highest correlations with activated
aerosol number occur with the number of available CCN, which was defined as
the total number of particles greater than 100 nm in diameter, and
that the number of droplets formed did not strongly depend on updraught
velocity. A set of regimes where the number of cloud droplets formed depends
on updraught velocities (at low ratios of updraught to aerosol number), and
where the number of cloud droplets depends more on the number of aerosol (at
high ratios of updraught to aerosol number), were described by
, based on cloud parcel model studies. At the Jungfraujoch
site, determined that aerosol particles larger than 100 nm
in diameter were typically activated to form cloud droplets in clouds with liquid water
content (LWC) above 0.15 gm-3.
investigated relationships between environmental
variables and activated fraction, defined as the fraction of total particles,
larger than 100 nm in diameter, that have been activated to form
cloud droplets. The latter study based its analysis on one summer and two
winter campaigns, and found that the activated fraction increased with
increasing LWC and decreased with decreasing temperature
below 0 ∘C, as clouds began to glaciate. Also using data from
the Jungfraujoch site, found that with
knowledge of the average chemical composition of aerosol, a very high degree
of correlation could be found between the number of activated aerosol
predicted by the κ-Köhler approach and the
observed number of activated particles measured at different supersaturations
in a CCN counter.
Although both and
found that, with a known aerosol size distribution, one can obtain good
correlations between the predicted and observed number of droplets at
a particular supersaturation in a CCN counter, the peak supersaturation
reached in an air parcel is not generally a known quantity. It is also not
possible to say how well the number of droplets predicted in this way
corresponds with the number of droplets in a cloud which has formed some time
ago. Although several studies exist in which a good degree of closure was
achieved between predicted and observed cloud droplet numbers of the
order of 20 % difference between calculated and observed droplet numbers;
e.g., a simple method of
predicting cloud droplet numbers based on easily quantifiable parameters
would be useful.
It has long been recognized that the number and the size of aerosol particles
strongly influences the number of CCN and that, at higher aerosol number
concentrations, clouds will be composed of a greater number of droplets
. Several simple
parametrizations of the number of cloud droplets as a function of the aerosol
diameter and total aerosol number have been suggested for both continental
and maritime locations, ,
mainly for stratus and stratocumulus clouds.
Subsequently, more advanced parametrizations were developed, allowing for the
influence of the aerosol size distribution, updraught velocity, and the
chemical composition and mixing state of the aerosol to be accounted for when
calculating aerosol water uptake and activation to form cloud droplets
e.g.. A parametrization was also developed by
which predicts the number of cloud droplets using four parameters: the total
sub-micron aerosol volume concentration, the number-to-volume aerosol
concentration ratio, the soluble fraction of the particle volume, and the air
updraught velocity. Good agreement was found between the number of droplets
predicted by this parametrization and observed droplet numbers in northern
Finland.
In this study, data from four summer measurement campaigns carried out at the
Jungfraujoch between 2002 and 2011 are used to develop simple statistical
models of the relationship between the number of observed cloud droplets and
various environmental factors, as well as the aerosol number size
distribution, in liquid clouds. Using such an extensive data set collected
over a period of nearly 10 years allows the construction of relationships
which are applicable to a wide range of conditions, although the statistical
model developed here is only valid for liquid clouds. The results from the
statistical models are compared to simulations using an established cloud
droplet formation parametrization for use in climate model simulations of the
aerosol indirect effect.
Measurement site
The Jungfraujoch (JFJ) high-alpine measurement site is located at
3580 ma.s.l., atop an exposed crest in the Bernese Alps,
Switzerland, and is accessible by train throughout the year. The site is
engulfed in cloud approximately 40 % of the time
and local emissions are minimal with the
exception of occasional construction activities. Aerosol measurements have
been carried out at the JFJ since the early 1970s ,
with continuous measurements since 1986
, and the site has been part of the
Global Atmosphere Watch (GAW) programme since 1995. A review of the aerosol
observations at the JFJ is provided by . The location
of the station makes it suitable for continuous monitoring of the remote
continental troposphere. The topography around the measurement site defines
two predominant local wind directions, southeast or northwest. To the
southeast, the Aletsch Glacier gradually slopes away from the JFJ at an
approximate angle of 15∘. In contrast, the northwestern side
drops steeply at an average slope of approximately 46∘. This
difference in topography causes updraught velocities to be higher in air
masses approaching the station from the northwest than from the southeast,
with median peak supersaturations of around 0.41 % (representative
of cumulus or orographic clouds) and 0.22 % (representative of
shallow layer or stratiform clouds) being reached for the respective wind
directions . Therefore, depending on
conditions and wind direction, data gathered at the JFJ can be representative
of convective or of stratiform-type clouds.
The unique topography surrounding the JFJ site and the long-term measurements
performed there provide substantial opportunity for investigating not only
how relationships between environmental variables change between years but
also what effect the differing topography to the north and south has, through
its influence on the vertical wind velocity. Furthermore, the composition of
aerosols in air coming from the south is influenced by different source
regions than air coming from the north. Peak supersaturation values,
updraught velocity, aerosol hygroscopicity, and cloud droplet number
concentration were studied by , who found that all
these quantities showed statistically significant differences between the two
wind sectors. This work was extended by , who
quantified the influence of updraught velocity and particle composition and
concentration on peak supersaturation.
While measurements made at the JFJ often sample the free troposphere, in
summer the air masses are mostly influenced by injections of boundary layer
air due to convective events and frontal
systems . On average during summer, a boundary layer
influence is detected at the JFJ around 80 % of the time, dropping to
around 60 % in spring or autumn or lower than 40 % in January
. The latter study also showed that the large degree of
boundary layer influence is partly due to the effect of the alpine topography
on air flow.
The JFJ observatory is also one of 16 stations of the Swiss National Air
Pollution Monitoring Network. As part of this operation, continuous in situ
observations of about 70 different trace gases are performed by Empa, the
Swiss Federal Laboratories for Materials Science and Technology.
Data collection
Data used in this study were collected as part of the Cloud and Aerosol
Characterisation Experiments (CLACE). The CLACE measurements have been
conducted at the JFJ since 2000. They are a series of intensive winter and
summer campaigns designed to investigate the chemical, physical, and optical
properties of aerosols as well as their interaction with clouds
.
The present study utilizes data collected during four summer campaigns, in
2002, 2004, 2010, and 2011 (Table ).
The following description refers to the basic experimental set-up during all
CLACE campaigns. The particles and hydrometeors were sampled via a total and
an interstitial inlet which were installed through the roof of the laboratory
. The total inlet sampled all the particles that had
a diameter of less than 40 µm, including the hydrometeors, at
wind speeds up to 20 ms-1. The condensed
water of the particles and hydrometeors was evaporated by heating up the top
part of the inlet to approximately 25 ∘C so that all
particles were dried (and therefore residual aerosol particles contained in cloud droplets were set free) while reaching the instruments in the
laboratory. The interstitial inlet only sampled particles smaller than 1 and
2 µm diameter using a size discriminator of PM1 (during
CLACE2002) and PM2 (during CLACE2004, CLACE2010, and CLACE2011)
respectively. Thus, only non-activated particles (i.e. particles that did not
act as CCN and were thus not contained in cloud droplets) passed this inlet.
The transition to laboratory temperatures (typically 20 to
30 ∘C) resulted in the drying of the particles at a relative
humidity less than 10 %. The difference between the number of
aerosol sampled through the total inlet and the number sampled through the
interstitial inlet gives the number of aerosol which were activated to form
cloud droplets, nact. It has been shown by ,
in a comparison with forward scattering spectrometer probe (FSSP) droplet
measurements, that this value can be used as a proxy for the number of cloud
droplets. Therefore this is the approach that we adopt in the present study.
Downstream of the inlets, a scanning mobility particle sizer (SMPS) was used
to measure the total and interstitial aerosol size distribution
respectively. The SMPS measured particles in the size range of 16 to
600 nm. One scan required 6 min. During CLACE2002 and
CLACE2004, the SMPS was installed behind a pinch valve to switch between the
two inlets after each scan (i.e. 6 min). The data in 2002 and 2004
are
therefore at 12 min resolution. For CLACE2010 and CLACE2011, two SMPS
measured simultaneously behind each inlet so that a higher time resolution
(approximately 6 min) could be achieved. Each SMPS consisted of
a differential mobility analyser (DMA), a bipolar charger to obtain charge
equilibrium (krypton source, 85Kr), and a condensation particle counter
(CPC) . During cloud-free periods, the interstitial
and the total SMPS should measure the same aerosol number size distribution.
For the campaigns where two SMPS measured simultaneously, the out-of-cloud
particle size distribution showed differences of up to 10 % for
particles with diameters between 20 and 600 nm. This is within the typical uncertainty for this type
of measurements . To account for these differences
between the two units, the interstitial number size distributions (for each
campaign specific instrument) were corrected towards the total aerosol size
distribution. A size- and time-dependent correction factor was determined by
comparing the total and interstitial number size distributions during all
cloud-free periods .
To monitor the cloud presence, the LWC was measured
using a particle volume monitor PVM-100;, which
measures the LWC by forward light scattering.
A measurement of the horizontal wind speed and direction was provided by the
Rosemount Pitot tube anemometer, which is mounted on a 10 m mast as
part of the SwissMetNet network of MeteoSwiss. Likewise, temperature measured
at the site as part of the SwissMetNet network was used.
In recent years, outdoor tourism activities around the JFJ have increased,
resulting in more frequent local pollution events. Data that are likely
affected by construction activities, snow groomer operation, and other local
anthropogenic influences (mainly cigarette smoke; )
have been removed from the data sets. As the JFJ is characterized as a
background site, sudden, short-lived fluctuations in the aerosol size
distribution can be interpreted as local pollution .
Therefore the affected data were identified by visual inspection of the
aerosol size distribution spectra.
In situ trace gas measurements of O3 and CO were conducted as part of
the Swiss National Air Pollution Monitoring Network (NABEL). Measurements
were recorded at 10 min intervals throughout all study periods, using
a UV absorption technique for O3 (Thermo Environmental Instrument,
TEI49C) and non-dispersive IR absorption photometry (NDIR) for CO (Horiba
APMA360, APMA370) .
Data analysisData processing
For years where two SMPSs were operating simultaneously (CLACE2010,
CLACE2011), nact, as a function of dry particle diameter, could
be calculated directly from the difference between the total and the
interstitial particle number size distributions. For the remaining 2 years
(CLACE2002 and CLACE2004), the SMPS was switched between the total and the
interstitial inlet. For these 2 years, the total measurement was taken to
be the first measurement, with the interstitial measurement immediately
following it used to calculate nact. The two scans inside this
12 min period were assumed to represent the same atmospheric
conditions.
In order to exclude cloud periods that were influenced by the entrainment of
dry air, as well as to exclude mixed-phase clouds, the fraction of activated
particles was analysed as a function of particle diameter. Without
entrainment, in theory all particles above a particular size will be
activated during cloud formation if the aerosol is internally mixed (as is
generally the case at remote sites such as the JFJ). This size is known as the
activation diameter and depends on the peak supersaturation reached within
the air parcel. The activation diameter of the aerosol was calculated for
each measurement time, following . In atmospheric
measurements, the fraction of activated particles increases between
approximately 0 and 1 over a small range of diameters, rather than making a
sharp transition at a particular diameter. Therefore the activation diameter
is defined as that at which half the particles are activated and half are
unactivated.
As described below, for the aged aerosol found at the JFJ, the critical
diameter lies around 80–100 nm. Entrainment and mixing of air into
the cloud will lead to non-activated particles larger than the activation
diameter co-existing with activated particles and therefore the maximum
activated fraction above the activation diameter will be less than 1.
Similarly, the lower water vapour pressure over ice particles in mixed-phase
clouds will lead to evaporation of droplets and deactivation of aerosol,
reducing the activated fraction above the activation diameter. A threshold of
0.9 was defined, and all measurements with maximum activated fractions of
less than this threshold were assumed to be influenced by entrainment or
partial glaciation of the cloud and thus excluded from the analysis.
The data were also filtered to remove any data points that were measured
outside of clouds, in patchy cloud, or on the edges of clouds. This was
achieved based on the measured LWC. For the campaigns that had two SMPS
scanners operating simultaneously (CLACE2010 and CLACE2011), the criterion
follows , where cloud was defined to be present when
the 30th percentile of the 10 s LWC values' distribution during one
6 min scan period was higher than 5 mgm-3. For the
other campaigns which had only one SMPS system operating (CLACE2002 and
CLACE2004), creating a 12 min resolution data set, the criterion used
was that of and , which defined cloudy
conditions if the LWC was higher than 20 mgm-3 for more than
85 % of an hourly period. This more stringent criterion was used to
avoid the inclusion of cloud-free periods in the longer (12 min) SMPS
scanning time. In contrast, using the criterion of
, which was found to be adequate for excluding
cloud-free periods during the 6 min scan time, allowed the inclusion of
more data from the 2010 and 2011 campaigns.
Total water content (TWC) was calculated by adding measured LWC to calculated
gas-phase water (GPW), except during CLACE2010 where it could be determined
directly from a dew point measurement in air sampled through the total inlet.
In campaigns other than CLACE2010, such dew point measurements were not
available and the GPW was calculated, using the ambient temperature, under
the assumption that the in-cloud relative humidity was 100 %.
Data were classified according to wind direction (north and south), in order
to determine whether different factors influence the CCN quality depending on the
origin of the aerosol particles.
For the purposes of this study, an estimate of the updraught velocity
(wact) at cloud base was calculated, similarly to
, from the local topography and the horizontal wind
speed measured at the JFJ (vJFJh) using
wact=tan(α)vJFJh,
where α is the inclination angle of the flow lines at the cloud base.
These values were α=46∘ for the northern terrain and
α=15∘ for the southern terrain for further
details see. This equation is based on the assumptions
that the flow lines of the updraught strictly follow the terrain on either
side of the JFJ research station and that there is neither sideways
convergence nor divergence of the flow lines between the cloud base and the
JFJ.
Selection of predictor variables
Six different predictor variables either measured at the JFJ or calculated
for the cloud base were included in the statistical analysis. These were the
height of the JFJ above cloud base, updraught velocity, number of available
potential CCN particles (hereafter referred to as nCCN, see
definition below), air temperature at the cloud base, CO, and O3.
The height of the JFJ above the cloud base was calculated by using the TWC and temperature measured at the JFJ, assuming a moist adiabatic
temperature lapse rate (6 K km-1) and thus calculating the temperature
(and therefore the distance below the JFJ) at which the partial pressure of
water in the air mass decreased below the saturation vapour pressure. This
approach is described in detail in and implicitly
assumes that a minimal amount of water is lost from the air mass via
precipitation between the cloud base and the JFJ. The height of the JFJ above
the cloud base was included as a predictor variable as it determines the
amount of condensed water at the altitude of the measurements, and it is also
related to the age of the cloud, during which scavenging or coagulation
processes may occur.
The updraught velocity, estimated as described in Sect. ,
was chosen as it is known to influence the peak supersaturation achieved
during cloud formation and, therefore, the activation diameter of the aerosol
and the activated fraction of a particular aerosol size distribution.
The nCCN is estimated from the measured aerosol size
distributions. As described in Sect. , the aerosol number size
distribution is known to play an important role in defining the number of
cloud droplets formed, with larger particles more likely to be activated, and
the smallest particles rarely playing a role in cloud formation. Therefore,
it is necessary to choose a minimum diameter, above which a particle can be
considered a potential CCN (here, a potential CCN is considered to be an
aerosol particle that may act as a CCN when subjected to supersaturation with
respect to liquid water). As described above, at aerosol number
concentrations larger than approximately 100 cm-3,
found that the activation diameter at the JFJ is around
100 nm. Further, reported that there is
a systematic difference in the activation diameter for aerosol in air masses
approaching the JFJ from the north (87 nm) and from the south
(106 nm). Here we have chosen a diameter of 80 nm as the lower size
bound defining potential CCN. The relatively low value was chosen so as not
to exclude potentially important sizes of aerosols.
The air temperature at cloud base (calculated from the temperature at the
JFJ) was chosen to account for any temperature-dependent effects on water
uptake to the aerosols which may influence activation. However, the cloud
base temperature was found not to contribute significantly in the linear
regression models for the years 2010 and 2011 (i.e. the years with most
observational data). It was thus excluded by backward elimination of
explanatory variables for final model selection. Likewise, no significant
relationship between air pressure and nact was found.
Finally, the two chemical tracers CO and O3 were included in the
analysis to account for the history of the air parcels. While CO is a primary
pollutant and O3 is produced photochemically as a secondary pollutant
from precursors such as volatile organic compounds and nitrogen oxides, both
of these can act as tracers of anthropogenic emissions or of biomass burning
events
e.g.,
and therefore in this study they are used as indicators of the degree of
influence of polluted air masses, in an attempt to determine whether this has an
important effect on particle activation at the JFJ. Ozone at the JFJ may be
influenced by stratospheric intrusions, but a modelling study
has suggested that this is the case for less than
20 % of the year, making such events relatively rare.
Statistical analysis
In order to determine if and how environmental and chemical factors can be
related to the number of cloud droplets (i.e. the number of activated
aerosol, nact), we chose a simple multiple linear regression
model for the analysis. Multiple linear regression is a commonly used
statistical method for explanatory and theory-testing purposes, and thus it is
appropriate to use in assessing how the environmental and chemical variables
contribute to the prediction of nact. It is likely that several of the predictor variables
selected for this analysis will be cross-correlated; thus traditional
regression indices (p value, regression coefficients) will fail to
appropriately partition the predictor variables into respective contribution
to the overall R2 of the model . Nevertheless,
active research in the statistical sciences has led to a set of tools for the
assessment of the relative importance of individual covariates in linear
regression models in the presence of correlated explanatory variables.
A widely used approach, first proposed by , hence
referred to as LMG, but better known in the sequential additive version
proposed by , allows assigning shares of “relative
importance” to a set of regressors in a linear model .
Here we use the LMG method, in its implementation in the “relaimpo”
package, developed by and available for the scientific
computing language R , to assess the relative importance of
individual explanatory variables in a simple linear regression model for the
cloud droplet numbers in warm tropospheric clouds.
Below we detail the LMG method and its application to our statistical model
following . Once the set of explanatory
variables/regressors (xi1,…,xip) is defined, as in our analysis
in Eq. (), the multiple linear regression model is fitted and
the regression coefficients for each explanatory variable
(βk,k=0,…,p) included in the model are estimated by minimising
the sum of squared unexplained parts. The coefficient of determination
(R2) can then be expressed using the fitted response values
(yi^) and estimated coefficients (βk^) as the ratio
between the model and total sum of squares (MSS and TSS respectively), i.e.
R2=MSSTSS=∑i=1n(yi-y¯^)2∑i=1n(yi-y¯)2.
The LMG method decomposes the coefficient of determination into non-negative
contributions that sum to the total R2. First sequential (i.e. regressors
are used in listed order, e.g. as given in our model in Eq. )
sums of squares (SSS) are derived via analysis of variance (ANOVA). These
sequential sums of squares, for each regressor, sum to the MSS of the TSS.
Next sequential R2 contributions are derived by dividing SSS by TSS. These
sequential R2 contributions are then utilized in the LMG method. As the
order of the explanatory variables in any regression model is a permutation
of the available regressors x1,…,xp, it can be denoted by
the tuple of indices r=(r1,…,rp). The set of regressors
entered in the model before regressor xk in the order of r can
then be denoted as Sk(r). Thus the portion of R2 allocated to
explanatory variable xk in the order r can be written as
seqR2({xk}|Sk(r))=R2({xk}∪Sk(r))-R2(Sk(r)).
Using Eq. () the metric LMG can be written as
LMG(xk)=1p!∑permutationseqR2({xk}|r),
which can be further simplified to
LMG(xk)=1p!∑S⊆{x1,…,xp}/{xk}n(S)!(p-n(S)-1)!seqR2({xk}|S),
as orders with the same Sk(r) can be summarized into one summand
.
Time series for several quantities measured directly during the
CLACE2011 campaign or derived from other CLACE2011 data. The number of CCN,
shown in the top panel, refers the number of particles larger than
80 nm in diameter, which are considered potential CCN in constructing
the statistical models (see text). In the bottom panel, the colour of the
points indicates the wind direction, with yellow showing wind classified as
being northwest and red southeast. Data are only plotted for times when the
JFJ was in cloud.
In the following we propose simple linear regression models developed based
on 4 years of observations from the JFJ, Switzerland. Additionally,
the best performing regression model was run for subsets of the data
corresponding to the different years, and wind directions, to identify any
features in the data which were particular to these subsets. The aim of this
analysis was to determine whether a single statistical model can be
constructed which will be generally applicable for the prediction of the
number of cloud droplets for all years and wind directions.
Results
In total, 2399 data points were included in the analysis, with the majority
being from 2010 (1087) and 2011 (896). Data were limited in 2002 (206 points)
and 2004 (210 points) compared to those in 2010 and 2011, since there were more
episodes of entrainment or partially glaciated clouds where data were
excluded from this analysis. The 2002 campaign was relatively short and the
time resolution of the measurement data set was lower in 2004 and 2002 than
in later years, as described above, yielding fewer data points. In
Figs. to , time series of the predictor variables are
shown for each campaign. In these plots, it can be seen that the data sets
include a wide range of conditions with respect to meteorology and air parcel
composition. In the upper panels of the plots, nCCN is plotted
together with nact. In 2011 and 2010 (Figs. and
) there are episodes of relatively high nCCN, during
which not all particles larger than 80 nm are activated, as shown by the
lower nact numbers. Additionally, the fraction of particles that
are activated appears to be lower when the wind is from the southeast (red
symbols in the bottom panel of the plots). In 2004 (Fig. ), however,
nCCN is generally fairly low, with, in a few
cases, larger nact than CCN, indicating that also particles below
the chosen cut-off diameter for potential CCN are being activated. In 2002
(Fig. ), there is a broad range of nCCN values, and
activation appears to be high in almost all cases, regardless of wind
direction or updraught velocity. In all years, the mixing ratios of CO and
O3 (second panel) appear to be fairly well correlated with each
other, except around day 12 of the 2002 campaign (overall R=0.65). There
does not appear to be an appreciable link between wind direction and CO or
O3 mixing ratio. The temperature range is similar for all the data
sets, with temperatures generally between 270 and 280 K. An episode of
warmer temperatures in the first half of the 2010 campaign corresponds with
relatively high CO and O3 values, as well as higher aerosol number
concentrations. The cooling after day 20 is accompanied by a marked reduction
in nCCN, as well as an increase in the fraction of aerosol which
are activated to form cloud droplets. As can be seen in the bottom panel of
each plot, the updraught velocities are generally lower when the wind is from
the southeast than when it is from the northwest, consistent with the
findings of .
As for Fig. but for CLACE2010. Note that the axis
ranges differ from those in Fig. .
As for Fig. but for CLACE2004. Note that the axis
ranges differ from those in Fig. .
Statistical relationships for combined data
The modelled number of cloud droplets is plotted against the observed number
(nact), for a variety of statistical model formulations, in
Fig. (). In panel a, only nCCN is used to predict
the number of cloud droplets. Already here a good relationship is found, with
a correlation (R) of 0.89; however, the intercept in the model leads to an
unphysical cut-off at low modelled numbers. Including the updraught velocity
improves the model slightly, while the R value remains the same, the root
mean squared error (RMSE) reduces slightly from 59.7 to 58.1. Further
improvements are found by including all five selected explanatory variables
(panel c) and, in panel d, by using all variables as well as the log of the
updraught velocity rather than the updraught velocity itself. The latter
statistical model was found to provide the best representation of the
observed number of droplets, with an R value of 0.91, RMSE of 54.2, and
a mean error (ME) of 38.1.
As for Fig. but for CLACE2002. Note that the axis
ranges differ from those in Fig. .
The number of cloud droplets calculated using different statistical
models, plotted against the observed number of residuals. The model used for
(a) included only the nCCN; for (b)nCCN and updraught velocity are included in the model; in
(c) all variables are included. In (d) all
variables are included, but the log of the updraught velocity is used.
The statistical model presented in panel d of Fig. provides
a simple and reasonably accurate way of predicting the number of cloud
droplets formed based on only a few explanatory variables. The number of
activated aerosol (considered equivalent to the number of droplets) predicted
by this model is given by
nact= 0.57nCCN+2.58O3+0.03H-1.02CO+28.48log(ω)-41.28,
where ω is the estimated updraught velocity at cloud base in
ms-1, CO and O3 are mixing ratios in ppb, and H is the
height of the JFJ above the cloud base in metres (H must be greater than
0).
The model considering only the number of CCN, as shown in panel a of
Fig. , is
nact=0.57nCCN+43.27.
The same analysis was performed with changes in the minimum size of
aerosol considered to be CCN to 70, 90, and 100 nm
(Fig. ), but this did not improve the model
skill in relation to the results obtained when counting only aerosol larger
than 80 nm to determine nCCN. In fact, there was little
variation in the model skill when these different size criteria were used in
the definition of potential CCN.
The number of cloud droplets calculated using a statistical model,
based on a regression analysis including only the number of potential CCN,
plotted against the observed number of residuals. Potential CCN
are considered to be all particles with a diameter (a) larger than 70 nm,
(b) 80 nm, (c) 90 nm, and (d) 100 nm.
It should be noted that at very low nCCN, the statistical model
may return negative values for the number of droplets, which is obviously
unphysical. However, this only applies to a very small number of points (16
of the 2399 points presented here) and thus does not compromise the general
applicability of the proposed model.
Comparison with physically based parametrization
To put the results presented in Figs. and
into the context of previous work, a state of the
art cloud droplet formation parametrization was used to calculate the cloud
droplet number for the same data points. Here we apply the sectional form of
the cloud droplet formation model of and
, with the giant CCN correction as described by
. In applying this parametrization, input data are
required, describing the chemical composition, aerosol size distribution,
updraught velocity, pressure, and temperature. For the aerosol, the size
distributions obtained by the SMPS are used (in original bin form), while an
average aerosol hygroscopicity of 0.25 (corresponding to an aerosol mixture
of roughly 42 % ammonium sulfate and 48 % insoluble aerosol) is assumed,
which is similar to the hygroscopicity value found from 17 months of
measurements at the JFJ by , for particles with a critical
dry diameter of around 80–100 nm. The parametrization was also run for the
overall median hygroscopicity value given by of 0.2, as
well as
a value of 0.3, to test the sensitivity of the results to small changes in
assumed hygroscopicity within the bounds of that which has been measured at
the JFJ. Vertical velocity for the parametrization input was calculated using
the method of , multiplied by an estimated correction
factor of 0.25, following the suggestions of .
Pressure and temperature at cloud base are also used, calculated in the same
way as for the statistical model. A comparison of the predicted number of
cloud droplets and the number of observed cloud residuals is shown in
Fig. . The agreement between the modelled and observed
data is excellent, with an R value of 0.86, RMSE of 67.2, and an ME of 42.8.
The errors for Eq. (), in panel d of Fig. , are
only slightly lower than this. The R and error values for the microphysical
parametrization run for the three different hygroscopicity parameters are
shown in Table . There it can be seen that within the range
of likely hygroscopicity values for the JFJ there is little variation in the
R values or errors from the model calculations. A slight decrease in the
RMSE and ME is found when the hygroscopicity value is increased from 0.2 to
0.25 and 0.3.
The number of cloud droplets calculated with the microphysical
parametrization, plotted against the measured number of residuals.
Parameters describing the performance of the microphysical
parametrization in capturing the number of observed cloud droplets, when run
for three different hydroscopicity parameters.
The modelled number of cloud droplets (Eq. ) plotted
against the observed number of residuals. Only data for northwestern wind
conditions are included in (a), while only data for
southeastern wind directions are included in (b).
The number of cloud droplets calculated by the microphysical
parametrization, separated by wind direction, compared to the number of
observed cloud droplet residuals.
Difference between wind directions
It was observed by that the number and properties of
aerosol in air parcels approaching the JFJ from the southeast was different
from those in air approaching from the northwest. Further, they found that
the activation diameter of particles differed considerably between the two
wind directions. Therefore the total data set used here was divided according
to wind direction, and the statistical model given by Eq. ()
was applied to see whether its ability to reproduce the observed number of
droplets differed between the two wind directions. This comparison is shown
in Fig. . The R values for the northwestern wind direction
and the southeastern wind direction are the same (0.9), but the RMSE and ME
are both substantially lower for the northwestern wind direction (RMSE of
49.3 vs. 67.4 and ME of 34.5 vs. 49.4). In the northwesterly case it can be
seen that the model shifts from a slight overestimation of the observed
number of cloud droplets to a slight underestimation, with the crossover
occurring at about 150 dropscm-3. The data in the southeastern
case appear to closely follow the 1:1 line. Therefore there appears to be
no systematic bias introduced by considering both wind directions in the
model together.
The results of the microphysical parametrization simulations, separated by
wind direction, are shown in Fig. . Here it is seen
that the microphysical parametrization is better able to represent the number
of droplets in the northwestern wind case (R of 0.91), while in the
southeastern case the RMSE increases to 107, and the model underestimates
the number of cloud droplets, particularly for numbers of residuals above
about 300 cm-3. This may be due to differences in turbulence and
vertical wind velocity between the northwestern and southeastern wind cases,
which are not resolved by our vertical wind velocity estimation.
Difference between years
To determine how representative the model in Eq. () is for
data from different years, the results were broken up into data for each
year, shown in Fig. . For 2002, 2010, and 2011, the
modelled data are well correlated with the observed number of droplets (R of
between 0.89 and 0.95), but the slope varies between different years.
While the data from 2011 lie along the 1:1 line, the 2010 data seem to be
composed of two different groups of points with different slopes, below and
above approximately 300 dropscm-3. It is not surprising that the
R and error values are better for 2010 and 2011, as these years provide by
far the most data points to which the model was fitted. The R for 2002
(0.95) was the highest of all years, but many of the data points are
below the 1:1 line and the RMSE was higher than for the other years (82.7).
The data collected during 2004 are less well fit by the model (R of 0.76,
RMSE of 47.2). However, as there were so few data points in 2004, and these
were mostly at low droplet numbers, it is difficult to say whether this is due to
the data sampled or the conditions being fundamentally different during
2004.
The modelled droplet numbers (Eq. ) plotted against
the observed number of residuals for each year separately.
Again, the results of the microphysical parametrization are shown, this time
separated by year, in Fig. . The RMSE for the 2002 data
is higher than for the statistical model (124 vs. 82.7), and the
microphysical parametrization was found to generally underestimate the number
of cloud droplets in cases where there were more than approximately 200
residuals cm-3. It is interesting to note that the statistical
model also generally underestimates the observed values for 2002. For 2004,
the microphysical parametrization represents the observational data better
than the statistical model, with an R value of 0.82 compared with the 0.76
of the statistical model and an RMSE of 42.9 compared to 47.2 for the
statistical model. For 2010 and 2011, both the statistical model and the
microphysical parametrization represent the observed data well.
The number of cloud droplets calculated by the microphysical
parametrization, separated by year, compared to the number of observed cloud
droplet residuals.
The differences between the years were also investigated by re-fitting the
statistical model to each individual year of data
(Fig. ). Naturally, this results in higher
values of R and smaller errors. For example, in 2002 a good correlation is
seen, with R of 0.96 and an RMSE of only 53.5. In 2002, it can also be
seen that the model underestimation of points above
500 dropscm-3 seen in previous plots is not due to a saturation
effect, as the observed droplet number can be predicted over the whole range
of nCCN with one set of parameters. The model representation of
2004 is improved when the model is fitted to only 2004 data, but the R
value is still only 0.83, lower than for the other years. This appears to be
related to the overall low range of nCCN observed in 2004. Both
2010 and 2011 are well represented by models fitted specifically to these
data.
As for Fig. , but the model was re-calculated
to provide the best fit for each year individually.
As a further way to assess the general applicability of the proposed linear
model, we sampled 100 data points at random (without replacement; i.e.
individual data points are allowed to be drawn only once to avoid a sampling
bias as e.g. in) from each year of data, and the R and
error values were calculated with (i) the general model and (ii) the models
fitted to each sampled set of 400 observations (i.e. 100 observations from
each year) separately. To ensure for statistically robust results this
analysis was performed for a set of 1000 random samples, and the results are
summarized in Fig. . Due to the small number of data points in
2004 (210) and 2002 (206), the samples for these years did not differ
greatly. In Fig. , it is apparent that the individually fitted
models for the 1000 subsets perform slightly better than the simultaneously
applied general model (as expected); however, given the small differences in
both R and error values between the individual and general models,
illustrated by the overlap of the inner quartile ranges in both R and error
values, the general model can be considered to be robust for the data set and
applicable over a wide range of observed conditions.
Discussion
The analysis above shows that the number of cloud droplets can be reasonably
well predicted by a single statistical model, containing the
nCCN, the log of the updraught velocity, the height above cloud
base, and the mixing ratios of CO and O3. The contribution of each
variable to the variance explained by Eq. () is shown in
Fig. , along with error bars, denoting the range of the
contributions of each variable in the random sampling analysis described in
the previous section. The range of the parameters included in
Fig. is relatively small, indicating that the
contribution to the explained variance is similar regardless of the sample
taken from the data set.
A box plot of the R2, RMSE and ME values for the application of
the general model (Eq. ) to 1000 random samples of 100 data
points from each year. The red boxes show the range of R2 and error values
when Eq. () is applied to the sampled data, while the blue
boxes show the ranges when the model is refitted individually to the data
sampled in each case.
The contribution of each of the model variables in
Eq. () to the explained variance. The error bars show the
spread of the variation of the contribution values in the random samples from
Fig. .
By far the greatest contribution to the explained variance is from
nCCN, but including additional explanatory variables does
improve the model with respect to absolute biases. The O3 and CO
mixing ratios contributed around 10 and 4 % respectively of
predictive ability to the model, suggesting that for sites such as the JFJ,
which are located relatively far from direct emissions sources, the chemical
history or source region of the air mass is not greatly relevant in
predicting the activation of aerosol to cloud droplets. Previously,
and found that the
hygroscopicity parameter of aerosols observed at the JFJ is not highly
variable. The results presented here also indicate that changes in aerosol
properties, which would generally be correlated with CO or O3
concentrations, are not large enough to substantially influence aerosol
activation. The height above the cloud base, H, contributed a small amount
(around 7 %) to the explained variance. This is likely due to the
height above cloud base being a measure of the total amount of condensible
water in the cloud, with greater condensible water generally leading to more
droplets. The cloud base temperature was not found to be significantly
correlated with the cloud droplet number over the combined data set;
therefore we find no evidence that temperature-dependent influences of
surface active compounds play a significant role in cloud droplet activation.
A previous study carried out at the JFJ, by , found that
when the number of potential CCN with diameter greater than 100 nm
reduced below 100 cm-3, the activation diameter shifted to smaller
sizes, so that significant numbers of aerosol smaller than 100 nm
began to activate. However, the ability of Eq. () to predict
nact does not deteriorate at low particle numbers, possibly
because in this work particles larger than 80 nm are considered
potential CCN.
A linear dependence of the number of cloud droplets on nCCN
implies that there is not a strong competition for water vapour during most
of the activation phase of cloud droplet formation. Whether or not this
occurs depends on the CCN number, the slope of the CCN spectrum, vertical
velocity, the degree of external mixing, the presence of giant CCN (sea salt,
dust), and temperature
e.g.. A good
indicator of linearity is expressed by the partial sensitivity of the droplet
number to the number of aerosol, ∂Nd/∂Na (also known as the aerosol–cloud index, ACI), for a given set of
aerosol and cloud formation conditions. The closer the ACI is to unity, the
less competition effects are present, linearity applies, and vice versa. The
ACI can be calculated either numerically with a parcel model
or with a parametrization adjoint
. The latter is used here to
establish the degree to which linearity holds for the conditions at the JFJ.
The results of this calculation are shown in Fig. . In panel
a, it can be seen that the ACI increases from near zero at low updraught
velocities to around 0.4 at updraught velocities of approximately
1 ms-1 and higher (note that the updraught velocities shown in Fig.
have been corrected by a factor of 0.25, as described in
Sect. ). This suggests that the form of the relationship
between the number of droplets and nCCN does not change at
updraught velocities higher than approximately 1 ms-1. Therefore while
the updraught has only a small influence on the number of cloud droplets
under these conditions, it does slightly influence the relationship between
the number concentration of aerosol and the number of droplets. Panel b of
Fig. shows the sensitivity of the droplet number to
nCCN as a function of nCCN. Here it can be seen that
the sensitivity does not display any obvious trend with increasing
nCCN, supporting our choice of a linear relationship between the
number of droplets and nCCN.
The sensitivity of the modelled droplet number to the updraught
velocity (corrected by a factor of 0.25, following
) (a) and to the number of particles
larger than 80 nm (b).
A comparison of the statistical models developed in this study, and the
microphysical parametrization, with the performance of two existing models by and , which are based only on
nCCN.
These results correspond with previous studies. For example,
found the number of cloud droplets to be directly
proportional to the particle number concentration when the ratio of updraught
velocity to particle number concentration was high, but they found that, under low
ratios, the number of cloud droplets formed was only dependent on the
updraught velocity. In that study, the lower limit of the regime where the number of cloud
droplets depends on the number of particles was found to be an updraught to
particle number concentration ratio of 10-3 ms-1 cm3), which,
for a CCN concentration of 800 cm-3, requires a vertical wind speed of
only 0.8 ms-1. Examining Figs. to , it can be
seen that almost all of the northwestern wind cases, and most of the southeastern wind cases, have vertical wind speeds higher than 1 ms-1 (if the
wind speeds in Figs. to were corrected by a factor of
0.25, as was done for the microphysical modelling, 67 % would still be
above 1 ms-1). Therefore, based on the study of , a
direct dependence of the number of droplets on the number of potential CCN
would be expected. The study of showed that under
relatively clean conditions, the details of the aerosol number size
distribution determined the number of cloud droplets; however, when the
accumulation mode particle concentrations were above approximately
1000 cm-3, the chemical composition of the particles played the major
role in determining the number of cloud droplets. also
found that the importance of the particle chemistry increases relatively to
that of the particle sizes at lower updraught velocities. Under conditions
where the aerosol population is externally mixed, the number of cloud
droplets formed may also not be directly dependent on the number of CCN, as
changes in the relative abundance of particles with differing
hygroscopicities will influence the formation of cloud droplets.
Nevertheless,
found that there was little change in the activation
diameter of particles (less than 20 nm) when comparing polluted and background
air masses at a non-urban site. These studies support the idea that for cloud
formation at remote sites such as the JFJ, with updraught velocities above
approximately 1.0 ms-1 and relatively low aerosol number
concentrations, the number of cloud droplets formed should be dependent on
the number and size of the aerosol present.
Finally, the statistical models and the microphysical parametrization
presented in this study are compared with two existing parametrizations,
those of and , both of which used
nCCN to predict the number of cloud droplets which would be
formed. The parametrization is given by
Ndroplets=-2.10×10-4A2+0.568A-27.9,
where A is the number of aerosol in the size range 100 nm–3.0 µm in diameter. We use the version suggested for use in maritime air masses
(their Eq. 12), as the version for continental air masses (their Eq. 13)
produces a very poor representation of the number of observed droplets at the
JFJ (not shown). This is possibly because the maritime parametrization is
more representative for air masses with relatively low aerosol number
concentrations, as encountered at the JFJ. The maritime parametrization is
described as being valid over the range of aerosol number concentrations of
36 to 280 cm-3.
The parametrization is derived from a combination of the
continental and maritime parametrizations of and should
therefore be valid over the range of aerosol number concentrations of 36 to
1500 cm-3. It is given by
Ndroplets=3751-exp-2.5×10-3A.
The modelled cloud droplet number concentration is plotted against the
measured values for Eqs. () and () as well as
against the models of and and the
microphysical parametrization, in Fig. . Comparison of
Eqs. () and () with the other models
considered shows that, although all five models provide a similar degree of
explained variance (between 74 and 83 %), error values are higher for the
and models. The microphysical
parametrization has a slightly lower R value than the other models but has
better error values than the and models.
While all five models show a good correlation between modelled and measured
cloud droplet numbers, the model of has a too shallow
slope, resulting in a general underestimation of the observed values. Both
the and models have included
a saturation effect at higher nCCN which limits the number of
cloud droplets formed, similarly to the effect described by
. No such saturation effect is observed at the JFJ,
but it cannot be ruled out that such an effect may occur at higher
aerosol number concentrations than those presented here.
Conclusions
Using data from four summertime CLACE campaigns performed at the high-altitude research station at the Jungfraujoch, we have shown that the number
of cloud droplets formed in warm clouds can be rather accurately represented
by a simple statistical model (Eq. ), producing a similar
degree of accuracy to that achieved with a microphysical parametrization. The
majority of the variance in the observed droplet numbers is explained by the
number of potential CCN, which is defined in this study as the total number
of particles with a dry diameter greater than 80 nm. Using the number of
potential CCN alone, 79 % of the observed variance is explained
(Eq. ). With the addition of further explanatory variables,
such as CO and O3 mixing ratios, and the height above cloud base, the
RMSE and ME errors can be slightly reduced.
Although tuning the statistical model to each year of data separately
produces slightly improved results, Eq. () represents the
observed droplet numbers from the individual years quite adequately.
Likewise, the model is applicable to data from both of the predominant wind
directions at the JFJ, and although there is more variability in the model's
ability to predict the number of droplets formed during southeasterly wind
conditions, there appears to be no substantial bias.
In contrast to previous studies in which such models were constructed
e.g., no evidence for a saturation effect of
high CCN numbers was observed; instead, the number of droplets formed increased
continually with nCCN. Such a saturation effect is expected to
occur at higher aerosol number concentrations, for example closer to aerosol
sources or in more polluted environments.
It should be noted that the statistical model is based only on data collected
during summer campaigns and that periods with partially or fully glaciated
clouds have been excluded from the data set (as described in
Sect. ). During such periods the number of activated
aerosol is also influenced by water uptake by ice particles, changing the
relationship between the number of CCN and the number of cloud droplets. The
statistical model is thus considered valid only for liquid clouds.
Due to the location of the JFJ station on the alpine divide, with air masses
approaching from both the north and the south, we expect
Eqs. () and () to be broadly applicable to the
remote European continental troposphere but with a boundary layer
influence. Indeed, these equations should be generally applicable to
conditions where droplet activation occurs in the aerosol limited regime.
While such empirically derived relationships have their limitations, and may
not remain valid under substantially perturbed atmospheric conditions, they
provide a simple and computationally efficient way to calculate the number of
cloud droplets in warm clouds, when appropriately applied.
Acknowledgements
C. R. Hoyle was funded by Swiss National Science Foundation (SNSF) grant
number 200021_140663. M. Gysel was supported by the ERC under grant
615922-BLACARAT. EU FP7 project BACCHUS (project number 603445) is
acknowledged for financial support.A. Nenes acknowledges support from a US Department of Energy EaSM proposal, a Georgia Power Faculty Scholar chainr and from a Cullen-Peck Faculty Fellowship. The CLACE experiments were supported by
the Global Atmosphere Watch plus (GAW+) research program through MeteoSwiss. Meteorological
measurements from the SwissMetNet Network were obtained through MeteoSwiss.
The JFJ experimental site is supported by the International Foundation High
Altitude Research Stations Jungfraujoch and Gornergrat (HFSJG). The Swiss
National Air Pollution Monitoring Network is run by Empa in collaboration
with the Swiss Federal Office for the Environment.
Edited by: V.-M. Kerminen
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