In this paper we study the influence of the cloud microphysical
parameterization, namely the effect of different methods for calculating the
supersaturation and aerosol activation, on the structure and life cycle of
radiation fog in large-eddy simulations. For this purpose we investigate a
well-documented deep fog case as observed at Cabauw (the Netherlands) using
high-resolution large-eddy simulations with a comprehensive bulk cloud
microphysics scheme. By comparing saturation adjustment with a diagnostic and
a prognostic method for calculating supersaturation (while neglecting the
activation process), we find that, even though assumptions for saturation
adjustment are violated, the expected overestimation of the liquid water
mixing ratio is negligible. By additionally considering activation, however,
our results indicate that saturation adjustment, due to approximating the
underlying supersaturation, leads to a higher droplet concentration and hence
significantly higher liquid water content in the fog layer, while diagnostic
and prognostic methods yield comparable results. Furthermore, the effect of
different droplet number concentrations is investigated, induced by using
different common activation schemes. We find, in line with previous studies,
a positive feedback between the droplet number concentration (as a
consequence of the applied activation schemes) and strength of the fog layer
(defined by its vertical extent and amount of liquid water). Furthermore, we
perform an explicit analysis of the budgets of condensation, evaporation,
sedimentation and advection in order to assess the height-dependent
contribution of the individual processes on the development phases.
Introduction
The prediction of fog is an important part of the estimation of hazards and
efficiency in traffic and economy . The annual damage
caused by fog events is estimated to be the same as the amount caused by
winter storms . Despite improvements in numerical
weather prediction (NWP) models, the quality of fog forecasts is still
unsatisfactory. The explanation for this is obvious: fog is a meteorological
phenomenon influenced by a multitude of complex physical processes. Namely,
these processes are radiation, turbulent mixing, atmosphere–surface
interactions and cloud microphysics (hereafter referred to as microphysics),
which interact on different scales
e.g.,. The key issue for
improving fog prediction in NWP models is to resolve the relevant processes
and scales explicitly or – if that is not possible – to parameterize them
in an appropriate way.
In recent years, various studies focused on the influence of microphysics on
fog. In particular, the activation of aerosols (hereafter simply referred to
as activation), which determines how many aerosols at a certain
supersaturation get activated and hence can grow into cloud drops, is a key
process and thus of special interest
e.g.,.
investigated and compared the influence of
aerosols on the life cycle of a radiation fog event while using the
one-dimensional (1-D) mode of the MESO-NH model with a two-moment warm
microphysics scheme, after and
, and included an activation parameterization
after . In other fog studies, using single-column
models, different activation schemes such as the simple Twomey power law
activation in and the scheme of
see were
applied. Furthermore, also more advanced methods such as sectional models
have been used for an appropriate activation representation.
used the Sectional Aerosol module for Large Scale
Applications SALSA; in two-dimensional (2-D)
studies for a size-resolved activation. conducted,
similar to , simulations for the ParisFog
Experiment with the MESO-NH model for more information to the MESO-NH model,
see, but using the three-dimensional (3-D) large-eddy
simulation (LES) mode and focusing on the drag effect of vegetation on
droplet deposition. For the fog microphysics, they used the activation
parameterizations after in connection with
saturation adjustment. As outlined above, several different activation
parameterizations have been employed for simulating radiation fog. This
raises the question how different methods affect the structure and life cycle
of radiation fog. Furthermore, schemes that parameterize activation based on
updrafts (typically done in NWP models) might fail for fog. Such schemes
derive supersaturation as a function of vertical velocity, which is valid for
convective clouds that are forced by surface heating but not for radiation
fog, which is mainly driven by longwave radiative cooling in its development
and mature phase .
Although great progress has been made to understand different microphysical
processes in radiation fog based on numerical experiments, turbulence as a
key process has been either fully parameterized (single-column models) or
oversimplified (2-D LES). Since turbulence is a fundamentally 3-D process,
the full complexity of all relevant mechanisms can only be reproduced with
3-D LESs .
Moreover, a disadvantage of most former studies is the use of saturation
adjustment, which implies that supersaturations are immediately removed
within one time step. This approach is only valid when the timescale for
diffusion of water vapor (on the order of 2–5 s) is much smaller than the
model time step. This is the case in large-scale models where time steps are
on the order of 1 min, but in LES of radiation fog, time steps easily go
down to split seconds so that the assumption made for saturation adjustment
is violated and might lead to excessive condensation
e.g.,. As a follow-up to these
studies, which investigated the influence of different supersaturation
calculations for deep convective cloud and stratocumulus, the present work
investigates the effect of saturation adjustment on radiation fog.
As and stated that both
LES and NWP models tend to overestimate the liquid water content and the
droplet number concentration for radiation fog, the following questions are
derived from these shortcomings:
Is saturation adjustment appropriate as it crucially violates
the assumption of equilibrium? How large is the effect of different methods
to calculate supersaturation on diffusional growth of fog droplets?
As the number of activated fog droplets is essentially determined
by the supersaturation, how large is the effect of different supersaturation
modeling approaches on aerosol activation and thus on the strength and
life cycle of radiation fog see?
What is the impact of different activation schemes on the fog life
cycle for a given aerosol environment?
In the present paper we will address the above research questions by
employing idealized high-resolution LESs with atmospheric conditions based on
an observed typical deep fog event with continental aerosol conditions at
Cabauw (the Netherlands).
The paper is organized as follows: Sect. 2 outlines the methods used, that
is, the LES modeling framework and the microphysics parameterizations used.
Section 3 provides an overview of the simulated cases and model setup, while
results are presented in Sect. 4. Conclusions are given in Sect. 5.
Methods
This section will outline the used LES model and the treatment of radiation
and land–surface interactions, followed by a more detailed description of the
bulk microphysics implemented in the Parallelized Large-Eddy Simulation Model
(PALM) and the extensions made in the scope of the present study.
LES model with embedded radiation and land surface model
In this study the LES PALM (; revision
2675 and 3622) was used with additional extensions in the microphysics
parameterizations. PALM has been successfully applied to simulate the stable
boundary layer (BL) e.g., during the first intercomparison of LES for
stable BL – GABLS; as well as radiation fog
. The model is based on the incompressible
Boussinesq-approximated Navier–Stokes equations and prognostic equations for
total water mixing ratio, potential temperature and subgrid-scale turbulent
kinetic energy (TKE). PALM is discretized in space using finite differences on a
Cartesian grid. For the non-resolved eddies, a 1.5-order flux–gradient subgrid
closure scheme after is applied, which
includes the solution of an additional prognostic equation for the
subgrid-scale TKE. Moreover, the discretization for space and time is done by
a fifth-order advection scheme after and a third-order
Runge–Kutta time-step scheme , respectively. The
interested reader is referred to for a
detailed description of the PALM.
In order to account for radiative effects on fog and the Earth's surface
energy balance, the radiation code RRTMG has been recently
coupled to PALM, running as an independent single-column model for each
vertical column of the LES domain. RRTMG calculates the radiative fluxes
(shortwave and longwave) for each grid volume while considering profiles of
pressure, temperature, humidity, liquid water, the droplet number
concentration (nc) and the effective droplet radius
(reff). Compared to the precursor study of ,
improvements in the microphysics parameterization introduced in the scope of
the present study allow a more realistic calculation of the fog's radiation
budget, as nc is now represented as a prognostic quantity instead
of the previously fixed value specified by the user. This involves an
improved calculation of reff, entering RRTMG, which is given as
reff=3qlρ4πncρl13explog(σg)2,
where ql is the liquid water mixing ratio, ρ is the density of
air, ρl is the density of water and σg=1.3
is the geometric standard deviation of the droplet distribution. The
effective droplet radius is the main interface between the optical properties
of the cloud and the radiation model RRTMG. Note that 3-D radiation effects
of the cloud are not implemented in this approach, which, however, could
affect the fog development at the lateral edges during formation and
dissipation phases when no homogeneous fog layer is present. As radiation
calculations traditionally require enormous computational time, the radiation
code is called at fixed intervals on the order of 1 min.
Moreover, PALM's land surface model (LSM) is used to calculate the surface
fluxes of sensible and latent heat. The LSM consists of a multi-layer soil
model, predicting soil temperature and soil moisture, as well as a solver for
the energy balance of the Earth's surface using a resistance
parameterization. The implementation is based on the ECMWF-IFS land surface
parameterization (H-TESSEL) and its adaptation in the DALES model
. A description of the LSM and a validation of the
model system for radiation fog are given in .
Bulk microphysics
As a part of this study, the two-moment microphysics scheme of
and implemented in PALM,
basically only predicting the rain droplet number concentration
(nr) and cloud water mixing (qr), was extended by
prognostic equations for nc and the cloud water mixing ratio
(qc). The scheme of
and is based on the separation of
the cloud and rain droplet scale by using a radius threshold of
40 µm. This separation is mainly used for parameterizing
coagulation processes by assuming different distribution functions for cloud
and rain droplets. However, as collision and coalescence are weak in fog due
to small average droplet radii, the production of rain droplets is
negligible. Consequently, only the number concentration and mixing ratio of
droplets (containing all liquid water and thus abbreviated with
ql here) are considered in the following. The budgets of the
cloud water mixing ratio and number concentration are given by
2∂ql∂t=-∂uiql∂xi+∂ql∂tactiv+∂ql∂tcond-∂ql∂tauto-∂ql∂taccr-∂ql∂tsedi,3∂nc∂t=-∂uinc∂xi+∂nc∂tactiv-∂nc∂tevap-∂nc∂tauto-∂nc∂taccr-∂nc∂tsedi.
The terms on the right-hand side represent the decrease or increase by
advection, activation, diffusional growth, autoconversion, accretion and
sedimentation (from left to right). Following ,
cloud water sedimentation is parameterized, assuming that droplets have
a log-normal distribution and follow a Stokes regime. This results in
a sedimentation flux of
Fql=kF43πρlnc-23(ρql)53exp(5ln2σg),
with the parameter kF=1.2×108 m-1 s-1. The main focus of this paper is to study the
effect of different microphysical parameterizations of activation and
condensation processes on microphysical and macroscopic properties of
radiation fog. Those different activation and supersaturation
parameterizations will be discussed in the following.
Activation
It is well known that the aerosol distribution and the activation process are
of great importance for the life cycle of fog e.g.,.
The amount of activated aerosols determines the number concentration of
droplets within the fog, which, in turn, has a significant influence on
radiation through optical thickness as well as on sedimentation and
consequently affects macroscopic properties of the fog, like, for instance, its
vertical extent. For these reasons, a sophisticated treatment of the
activation process is an essential prerequisite for the simulation of
radiation fog. Several activation parameterizations for bulk microphysics
models have been proposed in literature. In this work, three of these
activation schemes were compared with each other in order to quantify their
effect on the development of a radiation fog event. The schemes considered in
this scope are the activation scheme of , which was
used, for example, by to simulate radiation fog, the scheme of
(used by, for example, ), and the one by
. The latter two represent an empirical and
analytical extension of Twomey's scheme, respectively. Consequently, these
parameterizations are frequently termed Twomey-type parameterizations that
have the following form:
NCCN(s)=N0sk,
where NCCN values are the number of activated cloud condensation nuclei
(CCN), N0 and k are parameters depending on the aerosol distribution,
and s is the supersaturation. The three parameterizations considered in the
present study are variations of Eq. () differing in
mathematical complexity:
. The power law expression (Eq. )
is well known and has been used for decades to estimate the number of
activated aerosols for a given air mass in dependence of the supersaturation.
A weakness of this approach is that the parameters N0 and k are usually
assumed to be constant and are not directly linked to the microphysical
properties. Furthermore, this relationship creates an unbounded number of CCN
at high supersaturations.
. This extended Twomey's power law expression
by using a more realistic four-parameter CCN activation spectrum as shaped by
the physiochemical properties of the accumulation mode. Although an extension
to the multi-modal representation of an aerosol spectrum would be possible,
all relevant aerosols that are activated in typical supersaturations within
clouds and especially fog are represented in the accumulation mode
. Following
and , the activated
CCN number concentration is expressed byNCCN(s)=Csk⋅Fμ,k2,k2+1;βs2,where C is proportional to the total number concentration of CCN that is
activated when supersaturation s tends to infinity. Beside k, the
parameters μ and β are adjustable shape parameters associated with
the characteristics of the aerosol size spectrum such as the geometric mean
radius and the geometric standard deviation as well as with chemical
composition and solubility of the aerosols. Thus, in contrast to the original
Twomey approach, the effect of physiochemical properties on the aerosol
spectrum are taken into account.
. This found an analytical solution
to express the activation spectrum using Köhler theory. Therein, it is
assumed that the dry aerosol spectrum follows a log-normal size distribution
of aerosol fd:fd=dNadrd=Nt2πlnσdrdexp-ln2(rd/rd0)2ln2σd.Here, rd is the dry aerosol radius, Nt is the total
number of aerosols, σd is the dispersion of the dry aerosol spectrum
and rd0 is the mean radius of the dry particles. The number of
activated CCN as a function of supersaturation s is then given byNCCN(s)=Nt2[1-erf(u)];u=ln(s0/s)2lnσs,where erf is the Gaussian error function, ands0=rd0-(1+β)4AK327b1/2,σs=σd1+β.In this case, AK is the Kelvin parameter and b and β
depend on the chemical composition and physical properties of the soluble
part of the dry aerosol.
Since prognostic equations were neither considered for the aerosols nor for their
sources and sinks, a fixed aerosol background concentration was prescribed by
setting parameters N0, C and Nt for the three activation
schemes. The different nomenclature of the aerosol background concentration
is based on the nomenclature used in the original literature.
The activation rate is then calculated as
∂nc∂tactiv=maxNCCN-ncΔt,0,
where nc is the number of previously activated aerosols that are
assumed to be equal to the number of pre-existing droplets and Δt is
the length of the model time step. Note that this method does not take into
account reduction of CCN. However, this error can be neglected, since
processes like aerosol washout and dry deposition are of minor importance for
radiation fog. For all activation schemes it is assumed that every activated
CCN becomes a droplet with an initial radius of 1 µm. This results
in a change of liquid water, which is considered by the condensation scheme
and is described in the next section. Furthermore, we performed a sensitivity
study with initial radii of 0.5 to 2 µm, which showed that the
choice of the initial radius had no impact on the results (not shown). This
is consistent with the findings of and
.
Condensation and supersaturation calculation
The representation of diffusional growth, evaporation and calculating the
underlying supersaturation (which is the main driver for activation) is one
of the fundamental tasks of cloud physics. Three different methods have been
evaluated and widely discussed in the scientific community. Namely, these are
the saturation adjustment scheme, the diagnostic scheme, where the
supersaturation is diagnosed by the prognostic fields of temperature and
water vapor, and a prognostic method for calculating the supersaturation
following, for example, , , and .
Basically, the supersaturation is given by s=qv/qs-1, while
the absolute supersaturation (or water vapor surplus) is defined as δ=qv-qs, where qv is the water vapor mixing ratio
and qs is the saturation mixing ratio. In the following, these
three methods are briefly reviewed.
Saturation adjustment.
In many microphysical models, a saturation adjustment scheme is applied. The
basic idea of this scheme is that all supersaturation is removed within one
model time step and supersaturations are thus neglected. Saturation
adjustment thus potentially leads to excessive condensation. Despite the many
years of application of this scheme, its impact on microphysical processes is
discussed controversially e.g.,. Saturation adjustment might hence
especially be a source of error in fog simulations, where very small time
steps are used due to small grid spacings, as already discussed. Using the
saturation adjustment scheme, ql represents a diagnostic value
calculated by means ofql=max(0,q-qr-qs),where q is the total water mixing ratio. The saturation mixing ratio, which
is a function of temperature, is approximated in a first step byqs(Tl)=RdRves(Tl)p-es(Tl),where Tl is the liquid water temperature and p is pressure.
Rd and Rv are the specific gas constants for dry air and
water vapor, respectively. For the saturation vapor pressure (es)
an empirical relationship of is used. In a
second step, qs is corrected using a first-order Taylor series
expansion of qs:qs(T)=qs(Tl)1+γq1+γqs(Tl),withγ=LvRvcpTl2,where cp is the specific heat of dry air at constant pressure and
Lv is the latent heat of vaporization. As previously mentioned, in each
model time step, all supersaturation is converted into liquid water or, in
subsaturated regions, the liquid water is reduced until saturation. In order
to use this scheme with aerosol activation parameterizations, it is necessary
to estimate the supersaturation (see Eq. 5). This can be achieved for the
activation scheme of following, for example, , and
,
directly translating into a droplet number concentration by15sk+2⋅Fμ,k/2,k/2+1,-βs=ϕ1w+ϕ3dTdt|rad322kCπρlϕ2Bk2,32,where ϕ1, ϕ2 and ϕ3 are functions of temperature and
pressure and are given in and
. w is the vertical velocity and B is the beta
function.
Diagnostic supersaturation calculation.
Supersaturation is calculated diagnostically from qv and
temperature T (from which qs can be derived). However, since it
is assumed that the supersaturation is kept constant during one model time
step, the diagnostic approach requires a very small model time step ofΔt≤2τ,due to stability reasons . Here, τ is the
supersaturation relaxation time which is approximated byτ≈(4πDncr‾)-1,where r‾ is the average droplet radius, and D is the diffusivity
of water vapor in air. Due to the low dynamic time step in the present study
imposed by the Courant–Friedrichs–Lewy criterion (on the order of 0.1 s),
however, the condensation time criterion is fulfilled, and no additional time-step decrease is needed. The rate of cloud water change due to condensation
or evaporation is given by18∂ql∂tcond=4πG(T,p)ρwρas∫0∞rf(r)dr19=4πG(T,p)ρwρasrc,where rc is the integral radius and G=1FK+FD included the thermal conduction and the diffusion of water
vapor . The density ratio of liquid water and the
solute is given by ρw/ρa.
Prognostic supersaturation.
The prognostic approach, which was first introduced by
, includes an additional prognostic equation for
the absolute supersaturation. Even though this requires solving one more
prognostic equation, it mitigates the problem of spurious cloud-edge
supersaturations and prevents inaccurate supersaturation caused by small
errors in the advection of heat and moisture
.
The temporal change of δ is given by∂δ∂t-1ρ∇⋅(uρδ)=A-δτ,with A being described byA=-qsρgwp-es-dqsdT⋅gwcp+dTdtrad,with g being gravitational acceleration. The supersaturation relaxation
time is given in Eq. (). The second term on the left-hand side of
Eq. () describes the change of the absolute supersaturation
due to advection, while the right-hand side considers changes of δ due
to changes in pressure, adiabatic compression and expansion, and radiative
effects (from left to right). By doing so, the predicted supersaturation is
used for determining the number of activated droplets as well as the
condensation and evaporation processes. Note that here the absolute
supersaturation is taken, as using s would involve more terms and is more
complex to solve .
Case description and model setup
The simulations performed in the present study are based on an observed deep
fog event during the night from 22 to 23 March 2011 at the Cabauw
Experimental Site for Atmospheric Research (CESAR). The fog case is described
in detail in and was used as a validation case for PALM
by . The CESAR site is dominated by rural grassland
landscape and, although it is relatively close to the sea, continental
aerosol conditions are commonly observed and are characterized by
agricultural processes .
The fog initially formed at midnight (as a thin near-surface layer), induced
by radiative cooling, which also produced a strong inversion with a
temperature gradient of 6 K between the surface and the 200 m tower level.
In the following, the fog layer began to develop: at 03:00 UTC the fog had a
vertical extension of less than 20 m then deepened rapidly to 80 m,
reaching 140 m depth at 06:00 UTC. At 03:00 UTC, the visibility had also
reduced to less than 100 m. After sunset (around 05:45 UTC) a further
invigoration close to the ground was suppressed, and after 08:00 UTC the fog
started to quickly evaporate due to direct solar heating of the surface. For
details, see .
Profiles of potential temperature and relative humidity at different
times, as observed at Cabauw.
The model was initialized as described in the precursor study of
. Profiles of temperature and humidity (see
Fig. ) were derived from the CESAR 200 m tower and used as
initial profiles in PALM. A geostrophic wind of 5.5 m s-1 was
prescribed based on the observed value at Cabauw at 00:00 UTC.
The land surface model was initialized with short grassland as surface type
and four soil model layers at the depths of 0.07, 0.28, 1.0 and 2.89 m. The
measured surface layer temperatures were interpolated to the respective
levels, resulting in temperatures of 279.54, 279.60, 279.16 and 279.16 K
for soil layers one to four, respectively. Furthermore, the initial soil
moisture was set to the value at field capacity (0.491 m3 m-3),
which reflects the very wet soil and low water table in the Cabauw area.
Moreover, the roughness length for momentum was prescribed to 0.15 m. Note
that discussed that this value appears to be a little
high given the season and wind direction. This does not play an important
role in the present study, however, as we will not focus on direct
comparison against observational data from Cabauw.
All simulations start at 00:00 UTC, before fog formation, and end at
10:15 UTC on the next morning after the fog layer has fully dissipated.
Precursor runs are conducted for an additional 25 min using the initial state
at 00:00 UTC, but without radiation scheme and LSM in order to allow the
development of turbulence in the model without introducing feedback during that
time see.
Based on sensitivity studies of , a grid spacing of
Δ=1 m was adopted for all simulations, with a model domain size of
768×768×384 grid points in x, y and z direction,
respectively. Cyclic conditions were used at the lateral boundaries. A sponge
layer was used starting at a height of 344 m in order to prevent gravity
waves from being reflected at the top boundary of the model.
Table gives an overview of the simulation cases. All cases
were initialized with (identical) continental aerosol conditions. Case SAT
represents a reference run with no activation scheme and thus a prescribed
constant value of nc=150 cm-3 (estimated from simulations
of ). This case represents the same setup to the one
described in except for modifications concerning the
aerosol environment as outlined below. Condensation processes were
treated here with the saturation adjustment scheme .
In order to evaluate the influence of saturation adjustment in a one-moment
microphysics scheme on the development of radiation fog, identical
assumptions were made in case DIA and PRG, except that diffusional growth was
calculated with the diagnostic and prognostic method, respectively (see
Sect. ).
Activation spectrum for three different activation schemes of
, , and
for a typical continental aerosol
environment.
Moreover, as small differences in supersaturation can affect the number of
activated droplets significantly, the impact of different methods for
calculating supersaturation on CCN activation is investigated in a two-moment
microphysics approach (see Sect. ). Therefore, the
simulations N2SAT, N2DIA and N2PRG were compared to each other. In all three
cases the activation scheme of is used and
initialized as described below.
Furthermore, cases N1DIA–N3DIA used the activation schemes described in
Sect. . To ensure comparability between the different
schemes, all of them were initialized with a continental aerosol background
described in , which is characterized by an
aerosol with the chemical composition of ammonium sulfate
[(NH4)2SO4], a background aerosol concentration of 842 cm-3,
a mean dry aerosol radius of rd0=0.0218µm and a
dispersion parameter of the dry aerosol spectrum of σd=3.19. For the Twomey activation scheme this results in N0=842 cm-3 and k=0.8, which is a typical value for the exponent for
continental air masses e.g.,p. 289 et
seq.. The Twomey activation scheme does not
allow for taking aerosol properties into account. In contrast, the activation
scheme of requires the parameters C, k,
β and μ to be derived from the aerosol properties. Here, values of
C=2.1986×106 cm-3, k=3.251, β=621.689 and μ=2.589 were used as described in . Finally,
the activation scheme of can directly
consider the aerosol properties, which are prescribed as previously mentioned.
Using those different parameterizations resulted in different activation
spectra, which are shown in Fig. . One can see that especially
the CCN concentration is changed by using these different methods, such that
this part of the study is equivalent to a sensitivity study of different CCN
concentration but is realized by using different coexisting parameterizations.
ResultsGeneral fog life cycle and macrostructure
The reference case SAT is conducted with a constant droplet number
concentration of nc=150 cm-3. The deepening of the
fog layer can be seen in Fig. , which shows the profiles of the
potential temperature, relative humidity and liquid water mixing ratio at
different times.
The fog onset is at 00:55 UTC, defined by a visibility below 1000 m and a
relative humidity of 100 %. In the following the fog layer deepens and
extends to a top of approximately 20 m at 02:00 UTC. However, at this point
the stratification of the layer is still stable with a temperature gradient
of 6 K between the surface and the fog top. The persistent radiative cooling
of the surface and the fog layer leads to a further vertical development of
the fog, which is accompanied with a regime transition from stable to
convective conditions within the fog layer (see Fig. a). This
starts as soon as the fog layer begins to become optically thick (at
03:30 UTC), and when radiative cooling at the fog top becomes the dominant
process, creating a top-down convective boundary layer. The highest liquid
water mixing ratio of ql=0.41 g kg-1 is achieved at
06:00 UTC at a height of 60 m (see Fig. c), while the fog
layer in total reaches the maximum 1 h later at 07:00 UTC. The lifting
of the fog, which is defined by a non-cloudy near-surface layer
(ql≤0.01 g kg-1), occurs at 08:45 UTC. At 11:30 UTC
the fog is completely dissipated.
Profiles of potential temperature (a), relative
humidity (b) and liquid water mixing ratio (c) at different
times for the reference case REF.
Influence of different supersaturation calculation
In this section we discuss the influence of three different method
considering supersaturation. Namely these are (as previously mentioned) saturation
adjustment, a diagnostic supersaturation calculation and a prognostic method.
In the first subsection a one-moment microphysics scheme is used and the
impact of the different supersaturation methods is limited to the effect of
diffusional growth. In the second part of this study those methods are
applied in a two-moment microphysics scheme, considering the effect of
such different approaches of supersaturation calculations for activation.
Time series of horizontally averaged relative humidity (rh) and supersaturation
at height levels of 2 m (solid) and 20 m (dotted) for different methods in
treating the supersaturation calculation.
One-moment microphysics scheme: impact of supersaturation calculation on diffusional growth
In this section we discuss the error introduced by using saturation
adjustment for simulating radiation fog with a one-moment scheme in a LES.
For this, we compare three simulations with identical setups (cases SAT, DIA,
and PRG), which differ only in the way supersaturation is calculated and
consequently the amount of condensed or evaporated liquid water. To isolate
this effect, activation is neglected in all cases and nc is set
to a constant value of 150 cm-3 (a typical value in fog layers). The
effect on different supersaturations driving the diabatic process of
activation is discussed in Sect. . As mentioned
before the time step is roughly 0.1 s, which is more than 1 order of
magnitude smaller than the allowed values of 2–5 s for assuming saturation
adjustment . The present case hence is an
ideal environment evaluating the error introduced by using saturation
adjustment and by keeping all other parameters fixed.
Figure shows time series of the horizontally averaged
saturation (supersaturation) for cases SAT, DIA and PRG at selected heights
close to the surface. In all cases saturation occurs simultaneously around
01:20 UTC. In case SAT, relative humidity does not exceed 100 % due to
its limitation by saturation adjustment, while in case DIA and PRG, average
supersaturations of 0.05 % are reached at a height of 2 m, which
corresponds to typical values within fog
.
For cases DIA and PRG, starting from 06:15 UTC (in 2 m height) and
07:15 UTC (in 20 m height), supersaturations are removed and the air
becomes subsaturated (on average). This is in contrast with case SAT, where
the saturation adjustment approach keeps the relative humidity at 100 %
as long as liquid water is present (i.e., until the fog has dissipated).
Around 06:00 UTC, which is shortly after sunrise, relative humidity drops
rapidly in PRG and DIA as a direct consequence of direct solar heating of the
surface and the near-surface air, preventing further supersaturation at these
heights. While we cannot clearly identify the lifting of the fog in case DIA
and PRG (due to the limited humidity range displayed), we note that for case
SAT we can identify lifting times as a decrease of relative humidity around
08:45 UTC at 2 m height and around 09:10 UTC at 20 m height.
Besides this inherent difference in relative humidity, the general time marks
formation, lifting and dissipation, defined by of the
fog layer are identical for cases SAT, DIA and PRG.
Time series of liquid water path (LWP) for cases using saturation
adjustment, the diagnostic approach and a prognostic method for the
diffusional growth.
Figure shows the liquid water path (LWP) for all cases.
Differences in the LWP appear between 04:00 and 11:00 UTC and do not exceed
1 % (lower values for cases DIA and PRG), indicating that the choice of
the condensation scheme does not affect the total water content of the
simulated fog layer.
It can be summarized that, although the assumptions of saturation adjustment
are not valid for the simulation of fog when using a very small time step,
the mean liquid water content is not changed by more than 1 % and the
general fog structure is not altered when using a one-moment microphysics and
neglecting supersaturation. This is probably due to the very small
supersaturation that is not strong enough to generate a significant change in
the effective droplet radius and which could possibly lead to stronger
sedimentation or higher radiative cooling rates.
Time series of LWP for simulations using saturation adjustment
(N2SAT in black), the diagnostic scheme (N2DIA in blue) and the prognostic method
(N2PRG in red). All cases use the activation scheme of
.
Profiles for liquid water mixing ratio (a) and droplet
number concentration (b) at 04:00, 06:00 and 08:00 UTC.
Two-moment microphysics scheme: impact of supersaturation calculation on CCN activation
Even though different methods for calculating supersaturation which interacts
with the diffusional growth are not strong enough to generate any noteworthy
differences by using a one-moment microphysics (considering a constant value
for nc), the impact of different methods modeling supersaturation
on CCN activation by using a two-moment microphysics might be significant.
Overview of conducted simulations. The droplet number concentration
nc is only prescribed for simulations without activation scheme.
In the simulations N1DIA–N3DIA, nc is a prognostic quantity and
is thus variable in time and space. The aerosol background concentration is
abbreviated with Na,tot and used to initialize the activation
schemes. Note for the scheme after a conversion
to the parameter C must be applied, while for both other activation schemes
this value is directly used to prescribe N0 and Nt,
respectively.
Figure shows the LWP for simulations applying the activation
scheme of in conjunction with the usage of
saturation adjustment (N2SAT), the diagnostic scheme (N2DIA) and the
prognostic scheme (N2PRG) for calculating supersaturations. It can be seen
that the prognostic and diagnostic methods produce similar LWP values.
However, for case N2SAT the LWP is nearly 70 % higher than for the other
two cases. In Fig. profiles of the liquid water mixing ratio
(left) and droplet number concentration (right) are shown. From that figure
it can be seen that in case of N2SAT, both the fog height as well as the
liquid water mixing ratios within the layer are higher than in N2DIA and
N2PRG, respectively. However, small differences in ql can also be
found between N2DIA and N2PRG (e.g., at 06:00 UTC in the second third of the
fog layer). This is explained by slightly higher values for the number
concentration in case of N2DIA than in N2PRG. However, both are at
approximately 75 cm-3 at 06:00 UTC. In contrast, in simulation N2SAT, a
number concentration of 120 to 150 cm-3 (at the top) is observed, which
is about 60 %–100 % higher in comparison to N2DIA and N2PRG. These
differences can be explained by the different methods for calculating the
supersaturation, since activation is the main process altering the droplet
number concentration. Therefore, we can implicitly derive from the droplet
number concentration that the predicted and diagnosed supersaturations using
the prognostic and diagnostic method are similar. These differences between
N2SAT and N2DIA–N2PRG are, however, in good agreement with values reported
for a stratocumulus case by . Their Fig. 2
shows that the number concentration of the diagnostic and prognostic method
were also similar and the case with saturation adjustment overestimated the
supersaturation and therefore the droplet number concentration. As the fog
droplet number concentration has a crucial feedback on the overall LWP of the
fog layer, the times of lifting and the time of its dissipation, the
reported differences in nc are significant regarding the accurate
modeling and prediction of fog. The reason why the number concentration is
such a critically parameter can be ascribed to their impact on sedimentation
and radiative cooling, which is explained in more detail in
Sect. .
As in Fig. but also for 2 m (dotted–dashed) and 4 m
(dashed).
In order to evaluate the possible effect of the grid spacing, in conjunction
with different methods for calculating the supersaturation, on CCN
activation, we repeated each of the cases N2SAT, N2DIA and N2PRG with two
coarser grid spacings of 2 and 4 m. The general effect of the grid spacing
on the temporal development and structure of radiation fog is discussed in
detail in . In this section, we will focus only on
changes in LWP due to different supersaturation calculations at different
spatial model resolutions. For isolating the effect of the grid spacing, all
simulations with a coarser grid spacing were carried out with the same time
step of 0.125 s, which corresponds to the average time step of the
simulations at highest grid spacing of 1 m. In this way, effects of
different time steps induced by different grid spacings could be eliminated.
Figure shows the LWP for all grid sensitivity runs. First of
all, note that for 1 m grid spacing, the results reflect the results shown
in Fig. and discussed above (i.e., significantly higher LWP for
case N2SAT than for cases N2DIA and N2PRG). Moreover, Fig.
reveals that these results are somewhat sensitive to changes in the grid
spacing. For all cases we observe a tendency towards higher LWP values with
increasing grid spacing, at least for cases N2DIA and N2PRG. These difference
are, however, not larger than 4 g m-2 and are thus significantly smaller
than the observed differences found between the different methods to
calculate supersaturation. Note, however, that the relative change in LWP
with grid spacing is higher for case N2DIA than for case N2PRG.
Quantitatively speaking, in case of 1 m grid spacing the relative difference
of the LWP is 2.1 % between N2DIA and N2PRG during the mature phase, while
for the case with a grid spacing of 4 m it reaches 8.1 %. This might be
explained by the fact that the diagnostic scheme is very sensitive to small
errors (e.g., induced by the numerical advection) in the temperature and
humidity fields e.g.,. A coarser spatial resolution here can lead to
larger error introduced by spurious supersaturation. We thus suppose that the
increased differences (see Fig. ) by larger grid spacings are
induced by spurious supersaturation, which affect the CCN activation and
hence influence the LWP of the fog layer.
Furthermore, we note that coarser grid spacings lead to a later fog formation
time, which is in agreement with and can be
ascribed to under-resolved turbulence near the surface at coarse grids.
In summary, we can thus conclude that the sensitivity to changes in the grid
spacing is rather small, but it might imply differences in the LWP of the
simulated fog layer of up to 4 g m-2.
Time series of LWP and nc (as a horizontal and vertical
average of the fog layer) for the reference and N1DIA–N3DIA case.
Two-moment microphysics scheme: comparison of different activation parameterizations
In numerous previous studies, the influence of aerosols and the activation
process on the life cycle of fog was investigated
e.g.,. Although all three activation schemes
outlined in Sect. 2.2.1 are comparable power law parameterizations that are
initialized with identical aerosol spectra, the effect on simulations of
radiation fog is still unknown. Because changes in nc due to
different activation schemes have a considerable effect on the life cycle of
fog, we might consider that even small differences in nc might
alter simulated fog layers significantly. This part of the study can be
regarded as a sensitivity study of different CCN concentrations realized by
applying different activation schemes, which is illustrated also in
Fig. . However, from a model user's perspective, such a
sensitivity is of great importance, as CCN concentrations are usually
difficult (case studies) or even impossible (forecasting) to obtain, and model
results thus might highly depend on the chosen activation parameterization.
Height–time cross sections for the liquid water mixing ratio for
N1DIA–N3DIA.
LWP and <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
Time series of the LWP for the reference run (case SAT) and the three
different cases (N1DIA–N3DIA) are shown in Fig. a. The highest
LWP occurs for case SAT, which also shows the highest nc during
the formation and mature phase in comparison with the other simulations (see
Fig. b). The time series of nc shown in
Fig. b (representing runs with the three different aerosol
activation parameterization schemes; see Table ) reveal
that, depending on the parameterization used, the a shift in nc
towards smaller or larger values is found. The quantitative differences in
the number of activated aerosol by using the different activation schemes is
due to a slightly different activation spectrum (see Fig. ). A
linear relationship between LWP and nc can be found: a higher
nc leads to higher LWP, which is in agreement with other studies,
like , for example. In principle, a similar qualitative
development of nc can be observed. While nc increases
during fog formation (with a local maximum with values between 70 and
140 cm-3), it remains nearly constant during the mature phase of the
fog (values between 65 and 145 cm-3). We will see later see that
activation here happens mostly at the top of the fog, but due to vertical
mixing in the convective fog layer, cloud droplets are evenly distributed
over a large vertical domain. Furthermore, the mixing layer is increasing in
time so that there is no net change of the (averaged) nc in the
fog layer. As soon as the sun rises and the fog layers start to lift and
turn into a stratocumulus cloud, all cases show a strong increase in
nc. This increase can be explained by stronger supersaturations
induced by thermal updrafts in the developing surface-driven convective
boundary layer due to surface heating by solar radiation. Moreover, we note
that while the qualitative course of nc is similar for all cases,
the choice of the activation algorithm has an impact on the number of
activated aerosols and thus on the strength of the fog layer, e.g., illustrated in Fig. via ql. This is due to the
radiation effect of the droplets. The number of droplets to which a certain
amount of liquid water is distributed plays an important role: the larger the
number of droplets, the larger the radiation–effective surface and the
higher also the optical thickness. As a result the cooling rate in fog with
many small droplets is increased, allowing more water vapor to condense and
the fog to grow stronger. By the same token, sedimentation also depends on
the droplet radius and plays a major role in fog development. This will be
further discussed below.
Time series of simulated visibility in 2 m height. Observations
from Cabauw (dashed lines) were added for illustration only.
Visibility
In Fig. the simulated visibility is shown for the cases N1DIA–N3DIA in
2 m height together with the observed values at Cabauw (for illustration
only). Visibility is calculated from the LES data following
as
vis=1002(ncρql)0.6473.
This visibility estimation (with nc and ql given in units of cm-3 and
g m-3, respectively) thus significantly
depends on the droplet number concentration and the liquid water content.
Unlike in the first part of this paper, analyzing visibility estimations from
the simulations might illuminate the capability of LES to predict visibility.
Figure reveals that visibility follows the same general
temporal developed for all cases, with a rapid decrease at fog formation,
deepening and dissipation, with minimum values at around 100 m (which is close
to the observed values). We also see noteworthy differences, particularly
shortly before 02:00 UTC (before fog deepening) at around 05:45 UTC
(shortly after sunrise). For both time marks, cases N1DIA–N3DIA display
sudden increases in visibility, due to an fast decrease in nc in
2 m height, which are not reproduced by case SAT, as nc is
fixed value in this case. The sudden increase in visibility around 00:45 UTC
in the observations is possibly related to this process. Also, the time marks
of formation and dissipation vary. For cases N1DIA–N3DIA, the formation time
is significantly advanced compared to case SAT, while dissipation time only
shows a small tendency towards earlier times, at least for N1DIA and N3DIA.
Case N2DIA displays a different behavior, with a later fog formation and
higher visibility and accordingly earlier dissipation time. This is in line
with the findings discussed above (i.e., a much weaker fog layer that, as a
direct consequence, can dissipate much faster). Otherwise, all cases display
almost identical visibility as soon as the fog has deepened.
Table of fog's life cycle time marks.
SimulationOnsetMaximumLiftingDissipationN1DIA00:25 UTC05:10 UTC08:10 UTC10:05 UTCN2DIA00:50 UTC04:25 UTC07:55 UTC09:10 UTCN3DIA00:25 UTC05:15 UTC08:10 UTC09:50 UTCTime marks of the fog life cycle
The effect of the different droplet concentration (induced by the usage of
different activation schemes) on the time marks of the fog life cycle is
summarized in Table . While N1DIA and N3DIA have
similar time marks, N2DIA stands out and shows a delayed onset by 25 min,
while the maximum liquid water mixing ratio is reached 45 min earlier than
in the other cases. Also lifting and dissipation are affected and occurred 15
and 40 min (with respect to simulation N3DIA) earlier. This is due to a
lesser absolute liquid water mixing ratio which evaporates faster by the
incoming solar radiation. Therefore, it can be concluded that the use of
different activation schemes (if they change the droplet number
concentration) has an effect on the time marks on the life cycle as well as
on the fog height and the amount of liquid water within the fog layer.
Profiles (instantaneously and horizontally averaged) of liquid water
mixing ratio at 04:00, 06:00 and 08:00 UTC, and profiles of liquid water
budget terms at 06:00 UTC.
Budgets of liquid water and droplet number concentration
In this section we will analyze the budgets of liquid water and droplet
number concentration in physical terms. As in the preceding section, we will
use the cases with different activation parameterizations, since they provide
us a range of different CCN concentrations. Figure a shows the
profiles of the liquid water mixing ratio at 04:00, 06:00 and 08:00 UTC,
i.e at different times during the mature phase of the fog. A detailed
analysis of budgets at other stages of the life cycle of the fog is beyond
the scope of this paper. The maximum ql in the fog layer is
reached at approximately 06:00 UTC at a height of 60 m. Afterwards a
further vertical growth of the fog can be observed, where no further increase
in liquid water takes places as a result of larger vertical extent of the
mixing layer and due to rising temperatures after sunrise. Moreover,
Fig. b and c show the liquid water budget during the mature phase
of the fog at 06:00 UTC, when the fog was fully developed. Almost all three
cases show identical values for condensation rates in the lowest part of the
fog layer, with values being in the same order as the evaporation rates so
that the net gain in this region appears to be small (see
Fig. b). However, the N2DIA case (with the lowest
nc) exhibits a generally lower absolute evaporation rate compared
to both other cases, which can be attributed to the slightly higher mean
values of the relative humidity (not shown) than in N1DIA and N3DIA. In the
upper part of the fog layer, higher values of the condensation rate are
observed (especially for N1DIA and N3DIA) with a concurrent decrease in
evaporation rates, leading to differently strong deepening of the fog layer.
At a height of approximately 80 m, a maximum of the evaporation rates can be
observed, representing the presence of subsaturated regions at this height
and the top of the fog. Larger differences can be observed in the
sedimentation rates. First and foremost the sedimentation is proportional to
the liquid water mixing ratio (see also Eq. ). The strength of
sedimentation also depends on the mean radius of the droplets, which
increases with a decreasing number of activated drops. Here, a lower
nc for a given amount of liquid water leads to a higher mean
radius, compared to a higher nc where the same amount of water is
distributed to more drops, decreasing the mean radius. Integrated over
height,
all three cases exhibit approximately the same sedimentation rates.
Therefore, case N2DIA experiences the strongest loss of liquid water due to
sedimentation (in relative terms). Moreover, Fig. c shows that
sedimentation partially counteracts the gains caused by condensation at the
upper edge of the fog. The net advection transports liquid water from the
second third of the fog layer (position of the maximum) to higher levels. It
can be summarized that all terms contribute significantly to the net change
of the liquid water mixing ratio, illustrating that all microphysical
processes deserve a proper modeling for radiation fog. In the mature phase,
however, sedimentation plays a key role, showing the highest values for the
individual tendencies. As a result liquid water is slowly and constantly
removed from the fog layer. These findings are in good agreement with
previous investigations by .
The sum of all tendencies, which is shown in Fig. d, is the
height-dependent change of the liquid water. Also here it can be seen that in
the lower 50 m the net tendency is negative, while in higher levels we
observe a positive tendency so that the fog continues growing vertically
while the liquid water content within the fog layer decreases.
Figure a additionally shows the profiles of nc. We
note that the profiles of the different cases differ quantitatively but not
qualitatively. The stage of the fog can thus be identified in the profiles
for all cases. At 04:00 UTC, the highest supersaturations occur close to the
ground due to cooling of the surface and near-surface air, leading to high
activation rates and therefore high nc near the surface (not
shown). At 06:00 UTC a well-mixed layer has developed that is driven by the
radiative cooling from the fog top. While the turbulent mixing leads to a
vertical well-mixed nc, we note the maximum at the top, where the
radiative cooling induces immense aerosol activation. This is further
illustrated in the budget of the nc in Fig. b and c,
where instantaneous data at 06:00 UTC are shown. Here, we see clearly that
aerosol activation at the top of the fog layer is the dominant process in the
mature phase of the fog, while activation near the surface is comparably
small. Evaporation of droplets, though small in magnitude, occurs only at the
fog top, reflecting upward motions of foggy air penetrating the subsaturated
air aloft where droplets then evaporate. Also, we see that both advection and
sedimentation rates are much smaller than activation rates so that the net
change in nc is controlled by the activation near the fog top
during the mature phase of the fog.
Profiles (instantaneously and horizontally averaged) of
nc at 04:00, 06:00 and 08:00 UTC, and profiles of nc
budget terms at 06:00 UTC.
Conclusions
The main objective of this work was to investigate the influence of the
choice of the supersaturation calculation and activation parameterizations
used in LES models on the life cycle of simulated nocturnal deep radiation
fog under typical continental aerosol conditions. For this purpose we
performed a series of LES runs based on a typical deep fog event as observed
at Cabauw (the Netherlands).
In the main part of this study we applied a two-moment microphysics scheme
with an activation parameterization of and
investigated the influence of three different (but commonly used)
supersaturation calculation methods, i.e., saturation adjustment, a diagnostic
method, and a prognostic method, on the life cycle and LWP of the simulated
fog event. From the results we found that in the case of saturation adjustment,
nearly 60 % higher droplet number concentrations are produced in
comparison with simulation with the diagnostic or prognostic method. This
results in a more than 70 % higher LWP for the saturation adjustment case
and a later occurrence of lifting and dissipation of the fog layer. An
explanation for such differences between the schemes can be found in the
general assumptions made within the methods. As saturation adjustment assumes
that the complete water vapor surplus is removed within one time step, the
supersaturation used for activation must be parameterized. In agreement with
we found that those values are higher than
in the other cases, which leads to great feedback of the fog layer. Moreover,
we found that the diagnostic method and the prognostic method yield similar
results. However, in a grid spacing sensitivity study we observed that the
relative differences between the prognostic and diagnostic approach increase
as the spatial resolution decreases. We assume that this is due to larger
errors of spurious supersaturations which lead to an overestimation of
activation in the diagnostic case. This in turn affects the sedimentation
velocity as well as the effective radius and hence the radiative cooling,
which results in higher values for the LWP.
In a further test, using a one-moment microphysics scheme, we compared the
possible error introduced by using saturation adjustment in comparison with
an diagnostic and prognostic method for calculating the supersaturation for
diffusional growth, i.e., neglecting activation and prescribing a constant
droplet number concentration. With these assumptions we were able to isolate
the error introduced by saturation adjustment on condensation and
evaporation. However, the results showed that, although the model time step
was inappropriate for the assumptions made during saturation adjustment, the
differences in LWP are at most 1 % and the general life cycle is not
affected. This could be attributed to the fact that the typical
supersaturations in fog are in the range of a few tenths of a percent, and
the resulting absolute differences are too small to induce further
influence on dynamics, microphysics or radiation. This result implies that
saturation adjustment is an acceptable method if no activation
parameterization is available (with simultaneous consideration that the
latter is highly recommended).
In a second part of our study, the effect of different activation schemes of
, , and
on the simulated fog life cycle was
investigated. Even though these parameterizations appear to be rather
similar, our results indicate that the resulting number of activated aerosols
(and consequently the number of droplets), known to be a crucial parameter
for the fog development, can differ significantly. However, it must be
mentioned that these differences are attributed to the fact that the CCN
concentration is different for the investigated schemes. This part of the
study can thus also be understood as a sensitivity study for different CCN
concentrations realized by the usage of different activation schemes.
In order to get a deeper insight into the spatial and temporal development of
deep radiation fog, we performed an additional analysis of budgets
nc and ql during the mature phase of the fog for
simulations with different aerosol activation parameterizations. We found
that gain of liquid water is dominated by condensational growth throughout
the fog layer with a maximum at the top of the fog layer (due to longwave
radiative cooling) and by significant sedimentation of fog droplets from
upper levels towards lower levels, while only little liquid water is lost by
sedimentation (to the ground) and evaporation. The fact that the simulated
cases display significant differences in the fog strength could be traced
back to the differences in the condensational growth at the fog top, induced
by different activation of CCN. For nc, our simulations indeed
indicate that activation is the dominant process, located in a narrow height
level, while all other processes (i.e., evaporation, advection and
sedimentation) were found to be comparably small. The amount of generated
liquid water thus is a direct consequence of the strength of the activation
process and is thus related to the number of CCN and accordingly the
activation parameterization used in the model.
In summary, the present study indicates that the choice of the used
supersaturation calculation can be a key factor for the simulation of
radiation fog. In agreement with we
recommend using the prognostic approach to calculate the supersaturation for
fog layer in case of a two-moment microphysics considering activation.
With this, the effect of spurious cloud-edge supersaturation is mitigated and
activation rates that are too large are omitted. Further, the choice of the chosen
activation scheme has a noticeable impact on the number concentration of CCN
and hence on the LWP and fog layer depth. However, we have no means to give
advice on which activation parameterization performs best. In order to give a
more educated recommendation here, we would need observational data of size
distributions from aerosol and fog droplets.
In order to overcome the remaining limitations of the present study that are
related to microphysical parameterizations, we are currently working on a
follow-up study in which we are revisiting this particular fog case using a
Lagrangian particle-based approach to simulate the microphysics of droplets.
This will allow for explicitly simulating the development of the 3-D droplet
size distribution in the fog layer e.g.,. This
approach will also allow resolving all relevant microphysical processes such
as activation and diffusional growth directly instead of parameterizing
them. As such simulations are computationally very expensive, only a very
limited number of simulations are feasible at the moment, so most future
numerical investigations will – as in the present work – rely on bulk
microphysics parameterizations. Based on the results using the Lagrangian
approach, however, we hope to be able to give an educated recommendation on
the best choice for such bulk parameterizations.
Code availability
The PALM used in this study (revision 2675 and
revision 3622) is publicly available on
http://palm-model.org/trac/browser/palm?rev=2675 (last access: 28 May 2019) (PALM, 2019a) and
http://palm-model.org/trac/browser/palm?rev=3622 (last access: 28 May 2019) (PALM, 2019b), respectively. For analysis, the model has been
extended and additional analysis tools have been developed. The extended
code, as well as the job setups and the PALM source code used, are
publicly available on 10.25835/0067929 (PALM group, 2019c). All questions concerning the
code-extension will be answered from the authors on request.
Author contributions
The numerical experiments were jointly designed by the authors.
JS implemented the microphysics parameterizations, conducted the simulations and
performed the data analysis. Results were jointly discussed. JS prepared the
paper, with significant contributions by BM.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
This work has been funded by the German Research Foundation (DFG) under grant
MA 6383/1-1, which is greatly acknowledged. All simulations have been carried
out on the Cray XC-40 systems of the North-German Supercomputing Alliance
(HLRN; https://www.hlrn.de/, last access: 28 May 2019).
Financial support
This research has been supported by the German Research Foundation (grant no. MA 6383/1-1).The publication of this article was funded by the
open-access fund of Leibniz Universität Hannover.
Review statement
This paper was edited by Barbara Ervens and reviewed by
Thierry Bergot and one anonymous referee.
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