Introduction
Despite a long-standing interest in understanding fog processes, uncertainties
still exist in the physical mechanisms driving fog variability. Forecasting
fog remains a challenge because of the diversity of mechanisms involved
during the fog life cycle and their interactions: local flow, turbulence,
radiation, microphysics, aerosols and surface effects. Several field
experiments have been carried out since the 1970s and have contributed to the
important progress made in understanding fog processes. Noteworthy studies
include campaigns at Cardington in the UK
; Fog-82 in Albany, New York
; Lille 91 in France ; a
campaign in the Po valley in Italy and ParisFog in
France .
Many important features of fog have also been characterized using
one-dimensional (1-D) modelling
.
However, to study some aspects of the characteristics of a fog layer, it
has become necessary to explicitly simulate turbulent motion in 3-D as shown
by , who was the first to use a large eddy simulation
(LES) for fog. LES is a turbulence modelling technique in which most of the
energy-containing eddies are explicitly resolved while eddies smaller than
a certain cutoff size, usually taken equal to the grid spacing, are
parameterized by a turbulence scheme. Since then, have
explored the static stability in a fog layer, and has shown
the various organized structures occurring
in a fog layer, which cannot be resolved in 1-D. Thanks to these studies, the
dynamical characteristics of radiation fog are more clearly identified during
the three stages of the fog life cycle defined by :
the onset, development and dissipation phases. During the formation phase,
small banded structures, identified by as
Kelvin–Helmholtz (KH) billows, occur in the middle of the fog layer in
dynamical and thermodynamical fields. They are sometimes associated with a
burst of turbulent kinetic energy (TKE)
but this is not always the case
. During the development phase, the main dynamical
processes relocate to the top of the fog layer and are associated with the
maximum of TKE and horizontal rolls . During the
dissipation phase, coupled processes between the ground and the top of the
fog layer explain the spatial variability in fog but
the link between dynamics and microphysics has not
been explored specifically in these
LES studies.
The quality of the LES depends on the horizontal and vertical resolutions.
demonstrate that simulations in stable conditions
converge at a 2 m horizontal resolution. Very high vertical resolution is also
essential for representing the divergence of the radiative fluxes in the
first few metres above the surface and therefore to produce the radiative
cooling necessary for the formation of fog
.
So far, most fog LES studies have considered homogeneous canopies. Only
have accounted for the effect of surface
heterogeneities, such as buildings, on radiation fog. Other studies, such as
those by or , have
considered the impact of forests on turbulence structures but not for fog
situations. In this study, we will explore an LES of a fog case that was
observed during ParisFog and was strongly influenced by trees.
Few fog LES studies are based on sophisticated 2-moment microphysical
schemes, which allow the impact of aerosols on the radiation fog life cycle to be
represented. studied the effects of aerosols on
radiation fog with an LES but in a 2-D configuration that could present some
limitations for the dynamical patterns of the fog layer. Additionally, most
of the studies using 1- or 2-moment microphysical schemes fail to
reproduce realistic liquid water contents (LWC) as they tend to overestimate values
near the ground. For instance, simulated
Nc=800cm-3 and LWC =0.4gm-3, and
simulated Nc=250cm-3
and LWC =0.34gm-3 near the surface, both a in 1-D
configuration.
These values are outside the range found by for the same site.
So the question of a possible missing mechanism arises, the inclusion of
which might improve the modelling of microphysical fields. Some aspect of
deposition that relates to the interaction with the ground surface is
important as already shown by with measurements
and or with 1-D
simulations.
The goal of this study is to better understand the physical processes
dominating the fog life cycle at a complex site. LES modelling at very high
resolution (1 m vertically and 5 m horizontally) is used with surface
heterogeneities (barrier of trees) and a 2-moment microphysical scheme. In
order to establish the main ingredients driving the fog life cycle, and to
evaluate how dynamics affects the evolution of fog, sensitivity simulations
are conducted. To our knowledge, this is the first time that an LES study of
radiation fog has been performed at such high-resolution with a sophisticated
microphysical parameterization scheme while considering the effect of
heterogeneities such as forests on the fog dynamics.
Section 2 presents the measurement set-up and the observed case and
describes the numerical model. The reference simulation is analysed in
Sect. 3, and Sect. 4 is devoted to sensitivity tests. Finally, some
conclusions are drawn and perspectives suggested in Sect. 5.
Experimental design and model description
Measurements set-up
The selected fog event was observed on 15 November 2011 during the ParisFog
field campaign at the SIRTA (Site Instrumental
de Recherche par Télédétection Atmosphérique) observatory
(48.713∘ N, 2.208∘ E). The objective of the ParisFog
campaign during three winters from 2010 to 2013 was to better understand the
radiative, thermodynamic, dynamic and microphysical processes occurring
during the fog life cycle. The site where the instrument platform was
installed was a semi-urban area with mixed land cover including forest, lake,
meadows and shrubs next to a built-up area. As shown in Fig. a,
the instrumented zone was located near a forest area.
demonstrated the impact of the tree barrier on the
observed flow when the wind was blowing from the barrier of trees over the
instrument location, as in our case study. This fog case has previously been
studied by using a 1-D model.
View of the measurement site (a) and modelling
domain (b) with the tree barrier. All the simulated averaged results
were taken in the blue contour area.
Temperature and humidity sensors were located at heights between 1 and 30 m
on an instrumented mast, with uncertainties of 0.2 K in temperature and
2 % in relative humidity (RH). Wind speed was measured by two ultrasonic
anemometers at 10 and 30 m a.g.l. (above ground level) on the same mast.
Radiative fluxes were measured at a height of 10 m with 5 and
4Wm-2 uncertainties for downward and upward fluxes,
respectively. Additionally, radiosondes were launched by Météo-France
twice a day from Trappes (48.7∘ N, 2∘ E), situated 15 km
to the northwest of SIRTA.
Aerosol particle measurements were performed using a scanning mobility
particle sizer (SMPS) measuring dry aerosol diameters between 10.6 and
496 nm every 5 min, and by a CCN (cloud condensation nuclei) chamber that gave the CCN number
concentration at different supersaturations from 0.1 to
0.5 % . An RPG-HATPRO water vapour and
oxygen multi-channel microwave profiler was used to measure the liquid water
path (LWP) with an error of up to 20gm-2
. Measurements of dewfall and fog-droplet
deposition were not taken.
Presentation of the observed case
Radiation fog formed at 02:00 UTC on 15 November 2011 and dissipated at the
ground around 10:00 UTC on the following morning. Conditions favouring fog
were due to a ridge at 500 hPa centred over the North Sea and anticyclonic
conditions near the surface. One of the features of this event was the
initial formation of a cloud layer at 150 m a.g.l., followed 30 min later
by fog occurring at the surface. As underlined by
, this characteristic is very common at SIRTA and
88 % of the radiation fog events during the field experiment followed a
similar pattern. However, these events are not classified as stratus lowering
as they were followed rapidly by formation of fog at the surface. A delay of
30 min between the formation at 150 m height and at the ground seems too
short to be a stratus lowering, which is mainly driven by the evaporation of
slowly falling droplets that cool the sub-cloud layer
. This suggests that this type of radiation fog
could be linked with, and specific to, the configuration of the SIRTA site.
The fog case is presented following the three phases of the fog life cycle
defined by . Before the fog onset, between 22:00
and 02:00 UTC, the surface boundary layer was stable and a near-surface
cooling was observed, inducing an increase in RH
(Fig. ). Between 00:00 and 01:30 UTC, the RH near the ground
remained nearly constant around 97 %. Wind at 10 m
height was light (speed around 1.8ms-1) as was TKE, with
small variability (Fig. ). At 02:00 UTC, the attenuated
backscatter coefficient measured by the lidar increased significantly at
150 m a.g.l. (not shown), revealing the formation of liquid water at this
height, while the RH at the surface remained at 97 %. The cloud base
height progressively subsided over the next 30 min, at which point it
reached the ground. During this time, the near-surface temperature decreased
by about 1 K in a stable stratification layer. At 02:30 UTC, the appearance
of fog at the ground was associated with a temperature homogenization in the
first 30 m, called temperature convergence by and
corresponding to a neutral stratification. The downwelling longwave (LWD)
radiation flux increased progressively to 325Wm-2 during the
development of the fog layer (Fig. ).
Observed (solid lines) and simulated (dashed lines) temporal
evolution of temperature (a and b) and relative humidity (RH)
(c and d) at 1, 5 and 30 m for the REF (a
and c) and the NTR (without trees) (b and d)
simulations. Simulated fields are averaged over the horizontal area located
downstream of the tree barrier (blue contour area of Fig. b). The grey
shaded areas represent the error for the observational curves.
During the fog development and mature phases, between 02:00 and 07:00 UTC,
the near-surface layer remained quasi-neutral and potential temperature at
the different levels remained constant. The temporal variability in the 10 m
wind speed and TKE was greater from this period. Around 04:00 UTC, TKE at
10 m height increased significantly, from 0.4 to
0.7m2s-2, and then presented some variability around this
value. The vertical gradient of TKE between 30 and 10 m remained positive.
The sodar indicated that the fog-top height reached a maximum of
300 m a.g.l. during the mature phase
.
At the beginning of the dissipation phase, starting at 07:00 UTC, the
surface temperature increased slowly (less than 0.5 K in 2 h) and then more
rapidly after 09:00 UTC. At 10:00 UTC, the downward shortwave (SW) fluxes exceeded
100Wm-2, while near-surface temperature had increased by
1 K compared to the pre-sunrise values. TKE at 30 m decreased during 08:00
to 10:00 UTC, while at 10 m TKE remained approximately constant.
The LWP value measured by the profiler was maximum around 07:30 UTC, at
the beginning of the fog dissipation phase, with 70gm-2
(Fig. ). The non-zero values (5gm-2) before
the fog onset were within the error range of the measurement.
Model description
Presentation of the model
The non-hydrostatic anelastic research model Meso-NH (see
http://mesonh.aero.obs-mip.fr) is used here in an LES configuration.
The LES is based on a 3-D turbulent scheme with a prognostic TKE and a Deardorff mixing
length .
The atmospheric model is coupled with the ISBA surface scheme
Interaction between Soil Biosphere and
Atmosphere; through the SURFEX model
. This scheme simulates the exchanges of energy and
water between the land surface (soil, vegetation and snow) and the atmosphere
above it. It uses five prognostic equations for deep temperature, deep soil
water content, surface temperature, surface soil water content and water
interception storage by vegetation.
In order to consider the impact of trees at the measurement site, we used
the drag approach developed by for a vegetation
canopy. Both this study and have shown that the
drag approach gives better results than the classical roughness law when
reproducing the turbulence downstream of a forest area. The drag approach
consists of introducing an additional term into the momentum and TKE
equations as follows:
∂α∂tDRAG=-CdAf(z)αu2+v2,
with α=u,v or TKE, where u and v are the horizontal wind
components; Cd is the drag coefficient, set to 0.2; and
Af(z) is the canopy area density, representing the surface area
of the trees facing the flow per unit volume of canopy. Af(z) is
the product of the fraction of vegetation in the grid cell by the leaf area
index (LAI) and by a weighting function representing the shape of the trees,
as presented in . The trees introduced in the
simulation domain for the land surface scheme correspond to Atlantic coast
broad leaved trees.
The model includes a 2-moment bulk warm microphysical scheme
, that considers droplet
concentration Nc and mixing ratio rc as prognostic
variables for the fog. An additional prognostic variable Nccn is
used to account for already activated CCN, following the activation scheme of
. The aerosols are assumed to be
lognormally distributed and the activation spectrum is prescribed as the following:
Nccn=CSmaxkFμ,k/2,k/2+1,-βSmax2,
where Nccn is the concentration of activated aerosol,
F(a,b;c;x) is the hypergeometric function, C (m-3) is the
concentration of aerosols, and k, μ and β are adjustable shape
parameters associated with the characteristics of the aerosol size spectrum
such as the geometric mean radius (r‾) and the geometric standard
deviation (σ), as well as solubility of the aerosols (εm)
and temperature (T) (see below for the values in our case study).
Smax is the maximum of supersaturation for that grid box at a
time step corresponding to dSdt=0. The evolution
of the supersaturation S includes three terms accounting for the effects of
a convective ascent of vertical velocity w, the growth of droplets by
condensation for the newly activated droplets, and radiative cooling, as in
:
dSdt=ϕ1w-ϕ2drcdt+ϕ3dTdt|RAD,
where ϕ1(T), ϕ2(T,P) and ϕ3(T) are functions of temperature
and pressure. Following and after
simplification, Smax can be diagnosed by
Smaxk+2⋅Fμ,k/2,k/2+1,-βSmax2=ϕ1w+ϕ3dTdt|RAD3/22kcπρwϕ23/2B(k/2,3/2),
with B the beta function and ρw the density of water. Thus,
the aerosols potentially activated are exactly
those with a critical supersaturation lower than Smax. The number of
aerosols actually activated in a time step is the difference
between the number of potentially activated aerosols and the
number of aerosols previously activated during the simulation.
The condensation/evaporation rate is derived using the
saturation adjustment scheme. Cloud droplet
sedimentation is computed by assuming Stokes law for the cloud droplet
sedimentation velocity and assuming that the cloud droplet size distribution
nc(D) fits a generalized gamma law:
nc(D)=NcαΓ(ν)λανDαν-1exp-(λD)α,
where λ is the slope parameter, depending on the prognostic variables
rc and Nc:
λ=π6ρwΓ(ν+3/α)Γ(ν)Ncρarc1/3,
α and ν are the parameters of the gamma law, and ρa is the density of dry air.
They were adjusted using droplet spectra measurements from the FM-100 database of our case
study and were set at α=1 and ν=8. These parameters are also used for the radiative transfer.
In addition to droplet sedimentation, fog deposition is also introduced to
represent direct droplet interception by the plant canopies. In the real
world, it results from the turbulent exchange of fog water between the air and
the surface below, leading to collection . In
numerical weather prediction models (NWPs), this process is not usually
included, e.g. in the French NWP model AROME , the
physics of which comes from Meso-NH. As fog deposition is a newly introduced
process, only a simple formulation is considered here as a first step
in order to perform a sensitivity study.
The fog deposition flux FDEP is predicted at the first level of the atmospheric
model (50 cm height) for grassy areas, and over the 15 m height for trees, in a
simplistic way following :
FDEP=ρaχVDEP,
where χ=rc or Nc, and VDEP is the
deposition velocity. In a review based on measurements and parameterization,
showed that VDEP values ranged from
2.1 to 8.0 cm s-1 for short vegetation. Here
VDEP is assumed to be constant, equal to 2 cm s-1.
A test of sensitivity to this value is presented below. Water sedimentation
and deposition amounts are input to the humidity storage of the surface
model. A more complete approach in a further study would include a dependence
of VDEP on momentum transport as in
and also on LAI.
The radiative transfer is computed with the ECMWF radiation code, using the
Rapid Radiative Transfer Model (RRTM; ) for
longwave (LW) radiation and for
shortwave radiation. Cloud optical properties for LW and SW radiation take account of
the cloud droplet concentration in addition to the cloud mixing ratio. For SW
radiation, the effective radius of cloud particles is calculated from the
2-moment microphysical scheme, the optical thickness is parameterized
according to , the asymmetry factor is from
and the single scattering albedo from
. For LW radiation, cloud water optical properties refer
to .
Simulation set-up
For the reference simulation (denoted as REF), the horizontal resolution is
5 m over a domain of 1 km × 1 km and 126 vertical levels are used
between the ground and the top of the model at 1500 m. The vertical
resolution is 1 m for the first 50 m and increases slightly above this
height. Momentum is advected with a 4th order centred scheme (denoted as
CEN4TH), whereas scalar variables are advected with the PPM (piecewise
parabolic method) scheme . The time step is
0.1 s. The domain of simulation is presented in Fig. b. It has a
tree barrier 15 m high and 100 m wide perpendicular to the wind direction
and the rest of the domain surface is composed of grass. The lateral boundary
conditions are cyclic. The radiation scheme is called every second.
The simulation begins at 23:20 UTC on 14 November 2011 before any fog has
formed and it lasted for 12 h. Temperature, humidity and wind speed vertical
profiles were initialized with data from the radiosonde launched from
Trappes. Meteorological conditions at Trappes can differ slightly from those
at the SIRTA site. Therefore wind, temperature and humidity were modified in
the nocturnal boundary layer up to 400 m a.g.l. to fit the data recorded at
the 30 m meteorological mast at the SIRTA site, as illustrated in Fig. A1.
The soil temperature and moisture were given by the soil measurements,
corresponding to a surface temperature of 276 K and a soil moisture of
70 %. Following the profiles from soundings, a geostrophic wind of
8 m s-1 was prescribed, without any other forcing. To generate
turbulence, a white noise of 0.5 K was applied in the first 100 m.
It was also necessary to characterize the aerosol size spectrum for
Eq. (). The supersaturations reached in fog were lower than
0.1 % meaning that the CCNC (cloud condensation nuclei counter) measurements were not directly usable, as
shown by and . However, by using
the kappa-Köhler theory and the SMPS observations, the aerosol
concentrations at supersaturations under 0.1 % can be retrieved if the
aerosol hygroscopicity (κ) at these supersaturations is known. This
method, proposed by , was applied to our case study in the
hour before fog onset. Thus, above 0.1 % supersaturation, the activation
spectrum was found from observations and below 0.1 % it was computed.
This computed activation spectrum is fit according to Eq. ()
(Fig. A2a), which corresponds to the size distribution of aerosol particles
(C=2017cm-3, σ=0.424, r‾=0.1,
εm=1) in red in Fig. A2b. This does not match the measured
distribution (in black) or the lognormal distribution fit on the
accumulation mode (in blue) because the
formulation was not developed for fog with low supersaturation. Deducing the
activation spectrum from measurements provides the exact solution.
The reference simulation
The performance of the REF simulation will first be examined, based on a
comparison with observed values of thermohygrometric, dynamic and radiative
parameters near the ground and LWP. Considering that the REF simulation
reaches good agreement with observations, the vertical evolution and
horizontal variability in the simulated fog will be characterized during the
different phases of the fog life cycle. It should be emphasized that
observations localized at one point will be compared to simulated fields
averaged over a horizontal area located downstream of the tree barrier (blue
contour area of Fig. b), which is representative of the
measurement area. We will see that the simulation domain is divided into
four parts with significant differences among them but with similar
characteristics within each one.
Comparison to measurements
Figure a and c show the time series of near-surface observed
and simulated temperature and RH. At the initialization of the simulation,
near-surface temperatures are in agreement with the observations while RH is
very slightly underestimated. During the cooling before fog onset, the model
develops a layer that is too stable, especially in the first 5 m, between
00:00 and 01:00 UTC. The convergence of temperature is simulated with a
30 min delay with respect to the observations.
Based on RH near the surface, the fog starts to appear around 02:00 UTC.
Between 04:30 and 09:00 UTC, simulated and observed temperature are in
fairly good agreement, with a quasi-neutral near-surface layer. The fog
starts to dissipate from the ground at 09:00 UTC, approximately 1 h ahead
of the local observation. This time discrepancy induces a slight
overestimation of near-surface temperature, which is less than 0.5 K at
11:00 UTC. Nevertheless, the negative temperature gradient near the surface
representative of the development of the convective boundary layer is quite
well reproduced after the beginning of the dissipation.
Dynamical fields at 10 and 30 m are fairly well reproduced by the model
(Fig. in red): the 10 m wind speed (Fig. a) is in
good agreement with observation throughout the simulation. Until 03:00 UTC,
a quasi-linear increase in TKE is produced by the model with a higher TKE at
10 m a.g.l. than at 30 m contrary to observations (Fig. b).
Around 03:00 UTC, a more sudden increase in TKE occurs, as in the
observations but 30 min before and with a lower magnitude. Then the
simulated TKE remains almost constant around 0.7m2s-2 from
04:00 UTC onwards, with a slightly higher variability than before. The model
develops similar TKE values at 10 and 30 m, while observed values are higher
at 30 m.
Observed (continuous lines) and simulated temporal
evolution of 10 m wind speed (a), 10 m TKE (black line) and 30 m
TKE (blue line) (b) for the REF (dotted line) and the NTR (without
trees) (dashed line) simulations. Simulated fields are averaged over the
horizontal area located downstream of the tree barrier (blue contour area of
Fig. b). The grey shaded areas represent the error for the
observational curves.
Observed (solid lines) and simulated (dotted lines, with the REF
simulation) temporal evolution of downward and upward (at 1 m)
shortwave (a) and longwave (b) radiation fluxes (in
W m2). Simulated fields are averaged over the horizontal area located
downstream of the tree barrier (blue contour area of Fig. b). The grey
shaded areas represent the error for the observational curves.
Considering the radiative fluxes (Fig. ), the increase in the LWD
flux associated with fog onset is simulated with a delay of 30 min, meaning
that there is a delay in the simulated formation of fog at elevated levels.
This delay is corroborated by the LWP evolution (Fig. ). After
that, the LWD flux of 325Wm-2 is correctly reproduced,
indicating that the temperature and the optical thickness of the fog are
fairly well simulated. Observations develop a difference of
8Wm-2 between longwave upwelling (LWU) and LWD during the fog life cycle, but the
model fails to reproduce this difference, leading to a slight underestimation
of LWU. If the measurements do not contain any errors, this probably means
that the radiative properties of the simulated surface are not perfectly
represented. A test on the emissivity of the surface (1 instead of 0.96)
had no impact on the radiative fluxes, suggesting that the soil temperature
was probably underestimated. The simulated LWP presents a maximum of the same
magnitude than the observation, but occurring 2 h before. After sunrise
(06:59 UTC), the downward and upward SW fluxes are overestimated by up to
15Wm-2. LWD is slightly underestimated in a similar way due
to the advanced dissipation time, as well as the LWP.
The comparison between the REF simulation and observation for the set of
parameters shows fairly good agreement, even though there are a few
discrepancies. The main discrepancies concern the fog life cycle with an
underestimation of the effect of elevated fog formation, and an advance of
1 h in the dissipation time. These elements are probably partly due to the
semi-idealized representation of the SIRTA surface in the simulation, and
also to the comparisons with point observations, given the horizontal
variability that we will see below. They are felt to be acceptable and we can
therefore consider that the REF simulation can be used to explore the
processes driving the fog life cycle and to conduct sensitivity tests.
Time series of LWP (in g m-2) observed (solid line) and
simulated by REF (dashed line). Simulated fields are averaged over the
horizontal area located downstream of the tree barrier (blue contour area of
Fig. b). The grey shaded area represents the error for the
observational curve.
Vertical evolution
First the vertical evolution of the fog is analysed. Figure
represents the time variations in vertical profiles of rc and
Nc, the radiative cooling rate and the vertical velocity in the
updraughts. The vertical and temporal variations in simulated Nc
can be studied as the LWP is realistic, but values of Nc must be
carefully considered as a first comparison to near-surface measurements
clearly shows an overestimation of simulated values. Figure a, c and d
represent the time variation for total TKE (resolved plus subgrid) and dynamical and thermal
production of TKE for the REF simulation, all averaged over the horizontal
area downstream of the tree barrier. A first feature is that subgrid kinetic
energy is 1 order of magnitude lower than resolved kinetic energy (not
shown). This means that the 5 m horizontal resolution allows an LES approach
as most of the eddies are resolved.
Temporal evolution of simulated vertical profiles of cloud mixing
ratio (a, in g kg-1), droplet concentration (b, in
cm-3), radiative tendency (c, in Kh-1)
and updraught vertical velocity (d, in ms-1) for the
REF simulation. Fields are averaged over the horizontal area located
downstream of the tree barrier (blue contour area of Fig. b). The
three phases of the fog life cycle are delimited by dotted lines.
The evolution of rc serves as a basis for decomposing the fog
life cycle into the three phases: formation, between 02:00 and 03:00 UTC,
until the fog becomes optically thick; development, between 03:20 and
08:20 UTC, until rc at upper levels of the fog layer begins to
decrease, and dissipation from 08:20 UTC (Fig. a).
Before the fog onset and during the formation phase, the TKE is small and
spread over a 30 m layer that deepens slowly because of the tree barrier
(Fig. a). TKE mainly occurs by dynamical production, which
presents maxima at two levels: near the surface and at 15 m height due to
the trees (Fig. c). Thermal production is negative because of the
thermal stratification (Fig. d). Radiative cooling near the
ground (Fig. c) and mixing by the tree drag effect are the
ingredients that allow fog to appear at the same time over a 30 m deep layer
(Fig. a). Then the mixing by the tree barrier causes the fog
layer to develop vertically at greater heights (Fig. a). Hence,
the effect of elevated formation is reproduced, even though the height of fog
onset is underestimated (150 m given by the ceilometer and 30 m in the
simulation), and the fog subsides to reach the ground almost instantly.
During this first phase, mean updraught vertical velocities are small, up to
0.15ms-1 (Fig. d), in agreement with
, who observed a vertical velocity of
0.1-0.2ms-1 in a fog layer between 40 and 220 m deep in
China. Considering Eq. () for supersaturation evolution with the
two source terms depending on vertical velocity and radiative cooling,
activation of fog droplets during the fog formation is mainly produced by
radiative cooling at the top of the fog layer (Fig. b and c).
Temporal evolution of mean vertical profiles of total
(resolved+subgrid) turbulent kinetic energy (TKE; in m2 s-2) for
REF (a) and NTR (b) simulations, and
dynamical (c) and thermal (d) production of total TKE
(in m2 s-3) for the REF simulation. Fields are
averaged over the horizontal area located downstream of the tree barrier
(blue contour area of Fig. b). The three phases of the fog life
cycle are delimited by dotted lines.
REF simulation at
02:10 UTC: (a), (b) and (c): horizontal
cross section at 10 m height of wind speed (a, in m s-1),
potential temperature (b, in K) and cloud mixing ratio (c,
in g kg-1). (d) Vertical cross section at Y=500 m of cloud
mixing ratio (in g kg-1) with area of TKE higher than
0.1m2s-2 shaded. The barrier of trees is marked with a
dashed rectangle.
Vertical cross section at Y=500 m at 06:20 UTC for the REF
simulation: (a) cloud mixing ratio (in
g kg-1), (b) droplet concentration (in
cm-3), (c) radiative tendency (in
K h-1), (d) vertical velocity (in m s-1)
and (e) maximum of supersaturation (in %) with the isoline of
rc=0.01 g kg-1 superimposed.
At the beginning of the development phase (around 03:00 UTC), when the fog
depth reaches approximately 80 m, it becomes optically thick to LW
radiation. At that time, TKE increases significantly by dynamical production
(Fig. a and c), in agreement with the findings of ,
which indicates a dynamical change. The optical thickness of the
fog layer causes strong radiative cooling at the top of the layer (greater
than 5.5Kh-1 in absolute value; Fig. c), and
rc values increase in the upper part of the fog layer. Hence, the
fog top becomes the location of the dominant processes. Radiative cooling
induces small downdraughts and buoyancy reversal. In addition to the vertical
velocity of the updraughts, now higher than 0.2ms-1 throughout
the fog layer, a second maximum of droplet concentration of 1100 cm-3
occurs in the upper part of the fog layer around 03:20 UTC. The sudden
optical thickening corresponds to the increase in surface LWD to
320Wm-2 (Fig. ) and to maximum cooling at the
ground (Fig. a). At the same time, temperatures converge in the
vertical levels near the ground, showing the effect of fog on the
stratification as analysed by .
During the development phase, the top of the fog layer is characterized by
vertical wind shear inducing positive dynamical production of TKE, while
small values of positive thermal production appear at the top due to buoyancy
reversal. In the lowest 40 m of the fog layer, the drag effect of the trees
induces values of kinetic energy higher than 0.6m2s-2. The
maximum of rc continues to increase in the upper part of the fog
layer until 05:00 UTC, reaching 0.37 g kg-1 at 120 m
(Fig. a). At the same time, LWD surface fluxes remain constant
while the fog layer continues to deepen and the LWP continues to increase
until 05:00 UTC (Fig. ).
Around 05:00 UTC, a change occurs in the development of the fog layer: it
continues to thicken but at a slower rate, while the LWP begins to decrease
in the simulation. This change of growth at the top of the fog layer is
associated with a warming in the fog layer (not shown) and a decrease in the
maximum radiative cooling near the top which spreads over a greater depth
(Fig. c). This also corresponds to an increased number of
resolved updraughts and downdraughts near the top (Fig. d). The
variability in the fog depth also becomes stronger, in connection with
fog-top waves as we will see below. This change of growth seems to be linked
to the fact that the fog layer reaches the top of the nocturnal boundary
layer, meeting stronger temperature, humidity and wind gradients. This
increases the top entrainment process, limiting the deepening of the fog
layer. With the decrease in top radiative cooling, cloud droplet
concentration becomes more homogeneous in the fog layer, except near the
ground where it decreases by deposition. The cloud mixing ratio also begins
to decrease near the ground (Fig. b).
The beginning of the dissipation phase in the simulation (around 08:20 UTC)
is preceded by the beginning of solar radiation, and a divergence between
surface LWU, which starts to increase, and surface LWD, which starts to
decrease (Fig. ). The dissipation of the fog begins at the
surface, and the fog lifts into a stratus layer. The radiative heating of the
surface induces the convective structure of the fog as vertical velocity in
the updraughts increases (Fig. c and d) and thermal production of
TKE becomes significantly positive (Fig. d). Additionally, after
sunset, downdraughts at the top of the fog layer increase the amount of solar
radiation reaching the ground and this feeds the heating at the base of the fog
layer. Hence, near the ground, both thermal and dynamical effects contribute
to the production of TKE, and to a deepening of the TKE layer to 60 m. The
height of the fog top continues to increase as it is driven by radiative and
evaporative cooling, which induces vertical motions and top entrainment.
Although the mixing ratio decreases at all levels, droplet concentration
increases sharply when the fog layer lifts from the surface
(Fig. b). As the cloud evolves into a stratus layer, droplet
activation is no longer induced by radiative cooling at the top of the fog
layer but by updraught vertical velocity at all cloud depths, and especially
near the stratus base. The stronger vertical velocity activates more droplets
for the same water content. Droplets become smaller and more numerous,
preventing the droplet sedimentation process and limiting the decrease in
LWP. Moreover, the deposition process is no longer active as there are no
cloud droplets at the surface. We will now consider the horizontal
heterogeneity of the fog layer.
Horizontal variability
To better characterize turbulent structures and the impact of trees on the
fog layer, the horizontal variability in the fog layer is examined.
Figure presents horizontal and vertical cross sections of wind
speed, cloud mixing ratio, potential temperature and TKE at 02:10 UTC during
the formation phase. The tree barrier tends to block the flow upstream. It
enhances the turbulence by wind shear downstream, accelerating the flow near
the ground and creating longitudinal structures in the direction of the wind.
Ascents occur upstream and small subsidences downstream (up to
2 cm s-1, not shown). The subsidences bring warmer and dryer
air from above to the ground. Therefore, structures of stronger wind near the
ground downstream of the trees coincide with structures of warmer, clear air
as they delay fog formation. The fog forms at the surface upstream of the
trees, and 500 m downstream, while it appears first at elevated levels over
the intermediate area between the trees and downstream
(Fig. d). The fog takes about 1 h to cover the entire domain
at ground level. Thus, heterogeneity of the surface vegetation explains
heterogeneities in fog onset over the SIRTA site, as well as the fog property
of developing first at elevated levels. After the formation phase, the base
of the fog layer is at the ground over the whole domain. These results are in
agreement with the effects of buildings on fog studied by
who found a 1.5 h period of heterogeneity of fog
formation over the airport area.
During the development phase, as shown in the vertical cross sections of
Fig. at 06:20 UTC, horizontal rolls appear at the top of the
fog layer and are associated with dynamical production of TKE by shear. They
are aligned almost perpendicularly to the mean wind direction (not shown).
These structures correspond to KH instability, previously
observed by and modelled by
and . They have depths
corresponding to about one-third of the fog layer height, as in
, and a horizontal wavelength of the order of 500 m.
These horizontal rolls explain the oscillations at the top of the fog layer
visible in Figs. and . They become well marked from
05:00 UTC when the increase in depth of the fog layer begins to slow down,
as the fog layer reaches the top of the nocturnal boundary layer, meeting
stronger wind gradients. The horizontal rolls induce strong horizontal
variability in the cloud mixing ratio near the top of the fog, with larger values
in the ridges of the fog-top rolls, and smaller ones in the troughs
(Fig. a). Local updraughts occur upstream of the crest of the
wave, and downdraughts downstream (both up to 1.2ms-1; Fig. d).
The maximum of droplet concentration occurs near the top
of the fog layer (Fig. b) in the radiative cooling layer
(Fig. c), and preferentially upstream of the crest of the wave
rather than downstream, in the ascent area, where the droplets are
preferentially activated and transported. These extrema of droplet
concentration do not appear in Fig. as they are hidden by the
spatio-temporal average.
Inside the fog layer, the radiative cooling is negligible, while vertical
velocity presents strong spatial heterogeneities. Maxima of supersaturation
appear to be strongly correlated with vertical velocity
(Fig. e), with values up to 0.25 %, which are probably
overestimated, although this cannot be confirmed as measurements of
supersaturation peaks are not available beyond the surface. However, droplet
concentration variations are smooth, and do not show a strong correlation
with the maximum supersaturation, because of the pre-existing droplets. Near
the ground, maximum simulated values of supersaturation lie around 0.1 %
while and reported observed
supersaturation peaks lower than 0.1 %.
During the dissipation phase, heterogeneities remain at the top of the fog
layer, but the signature of KH waves disappears (not shown). The dissipation
of fog at ground level takes about 20 min, and, as noted in
, does not reveal a clear effect of surface
heterogeneity.
Having characterized vertical and horizontal heterogeneities of the fog
during its life cycle, sensitivity tests are now presented to identify the
sources of variability and their impact on the fog life cycle.
Sensitivity study
In order to better characterize the physical processes dominating the fog
life cycle, sensitivity tests were conducted in a second step. The resulting
simulations and their differences relative to the REF simulation are
summarized in Table .
Simulation configurations for sensitivity tests.
Name of simulation
Difference of configuration with REF
NTR
No TRee: homogeneous surface
NDT
No Deposition on Trees
NDG
No Deposition (on Grass or trees)
DE8
Deposition velocity equal to 8 cm s-1
DX2
Horizontal resolution = 2 m
WE3
3rd order WENO advection for momentum
WE5
5th order WENO advection for momentum
WENO: Weighted Non-Oscillatory,
.
Impact of trees
To evaluate the impact of trees on the fog life cycle, a simulation called
NTR is run, in which the tree barrier was replaced by grass. Deposition on
the grass was considered over the whole domain. Figure a shows
that, without trees, the 10 m wind speed is overestimated over the
measurement area. As in REF, but 30 min earlier, the model develops a sudden
increase in TKE around 02:30 UTC at the beginning of the development phase.
This change is linked to the increase in the optical thickness and not to the
turbulence induced by the trees (Figs. b and b). After
this period, TKE is underestimated and remains stronger at 10 m height than
at 30 m, contrary to observation. This means that the drag effect of trees
is responsible for the observed stronger TKE at 30 m height. The fact that
the REF simulation develops very similar TKE at 10 m and 30 m a.g.l.
probably means that the representation of surface heterogeneities is still
underestimated. This can be explained by the broad range of surface covers
present in reality, in addition to the trees (lake, small buildings, etc.)
but not included in the simulation.
Temporal evolution of simulated vertical profiles of cloud mixing
ratio (a, c and e; in gkg-1) and
droplet concentration (b, d and f; in
cm-3) for NTR, NDG and DE8 simulations. Fields are averaged
over the horizontal area located downstream of the tree barrier (blue contour
area of Fig. b).
Vertical cross sections at Y=500 m and 02:20 UTC of potential
temperature (in K) for the REF (a), NTR (b),
WE3 (c) and DX2 (d) simulations, with area of cloud mixing
ratio higher than 0.1 g kg-1 superimposed with dots and the barrier of
trees marked with a dashed rectangle.
Time series of LWP (in gm-2) observed (in black),
and simulated (in colour) for the different simulations. Simulated fields
are averaged over the horizontal area located downstream of the tree barrier
(blue contour area of Fig. b). The grey shaded areas represent the
error for the observational curves.
The main differences in dynamics between NTR and REF appear first on total
TKE, with a thinner layer of TKE values greater than
0.5m2s-2 and smaller maxima (Fig. b). Before
the fog formation, the too thin layer of turbulence near the ground in NTR
limits the supply of warmer air from above. This induces an overestimation of
the vertical temperature gradient before the fog, and emphasizes the cooling
in the low levels of 2 K less than in REF (Fig. b).
Figure a presents the temporal evolution of cloud mixing ratio
vertical profiles during the NTR simulation, to be compared to
Fig. a for REF. Figure a and b show instantaneous
vertical cross sections of potential temperature at the fog formation with
REF and NTR. The stronger cooling in NTR homogenizes the fog formation at the
ground and prevents elevated fog formation. The consequence is that the onset
of fog in NTR occurs almost 2 h earlier than actually observed and than in
the REF simulation (Fig. d).
During the formation and development phases, the fog layer is thinner in NTR
than in REF. This is due to the formation at the ground and the absence of
mixing without trees, thus limiting the vertical development. The maximum of
cloud mixing ratio in NTR is increased compared to REF, due to the absence of
warming by entrainment. It leads to largely overestimated cooling near the
ground in comparison to observations (Fig. b). Inside the fog
layer, despite the increase in rc, the positive temporal
evolution of Nc, called the production of Nc is not
higher than in REF (Fig. b), as smaller vertical velocities and
higher cloud mixing ratio production compensate for the stronger cooling in
the activation process. During the development and the mature phases, the LWP
is also largely overestimated with NTR (Fig. a).
During the development phase, 500 m wavelengths of KH waves are more smooth
and regular without trees and this is noted during the whole phase. This is
shown on kinetic energy spectra applied to vertical velocity over the whole
fog depth, computed according to and presented in
Fig. . The spectra of REF and NTR present two main
differences: firstly the TKE variance is smaller with NTR at wavelengths
shorter than 200 m. This means that the flow presents fewer fine-scale
structures without the tree drag effect. Secondly, the peak of variance at
500 m wavelength, corresponding to the KH waves, is more pronounced in NTR.
To summarize, the absence of the tree barrier produces an unrealistic simulation,
as it causes the fog onset to occur too early (almost 2 h in advance). It
also induces cooling that is too strong in the low levels, and a large
overestimation of the LWP. The absence of trees also modifies the signature
of the KH waves at the top of the fog layer, with a more regular pattern and
fewer small-scale heterogeneities. The impact of the deposition process will
now be examined more precisely.
Impact of deposition
Three simulations were carried out to better characterize the role of the
deposition process, all keeping the tree barrier. The first one, called NDT,
removed only deposition over trees compared to REF. In this case, trees acted
as grass for deposition. This was done by activating deposition only at the
first level of the model. The second one, called NDG, removed deposition
altogether. The third one, noted DE8, considered a deposition velocity
VDEP of 8 cm s-1 over grass and trees, which is
the upper bound given by instead of
2 cm s-1 as in REF.
NDT very slightly increases the LWP during the fog life cycle
(Fig. a). Conversely, removing deposition everywhere with NDG has a
considerable impact. The onset of fog occurs at the surface and not at 30 m height and almost 2 h earlier than in observations and in the REF
simulation (Fig. c). During the development phase, there is no
longer a vertical gradient of rc and Nc
(Fig. c and d).
The fog layer is deeper throughout the life cycle, and therefore the LWP is
largely overestimated with a maximum between 05:00 and 06:00 UTC of about
twice the observed value (Fig. ). Due to the larger amount of cloud
water near the ground, the dissipation at the ground is delayed by more than
1 h.
In contrast, DE8 induces a significant reduction of the LWP, and the onset of
fog near the ground coincides relatively well with observation. The formation
of fog at elevated levels is more pronounced, and rc over the
whole fog depth is reduced during the development phase compared to REF
(Fig. d and e). This means that the deposition process is highly
sensitive to the deposition velocity.
have already shown that including a deposition
term in simulations seems to have some effect on the droplet concentration in
the layer near the ground and consequently on visibility. However, the effect
they found was less pronounced than the one seen here. A possible explanation
is that both u∗, the friction velocity, and the mean volumetric
diameter of droplets used in their parameterization were underestimated. In
our case, the deposition process, even with a simple parameterization, appears
to be essential to correctly simulate the fog life cycle and to approach the
observed LWP. Neglecting this process modifies the fog life cycle in terms of
onset and dissipation times. The elevated fog formation, which is a
climatological characteristic of the SIRTA site, is the result of two
effects: the tree drag effect, which mixes the lowest levels, and the
deposition process, which erodes the near-surface water content. We will now
examine the impact of the horizontal resolution on the simulated fog life
cycle.
Sensitivity to effective resolution
In order to assess the impact of spatial resolution on the fog life cycle, a
2 m horizontal resolution simulation (called DX2) was carried out using the
same momentum advection scheme as in REF (CEN4TH). According to
, kinetic energy (KE) spectra deduced from
simulations allow the effective resolution to be set up as the scale at which
the model starts to depart from the theoretical slope, which is -3 for
vertical velocity spectra applied to stable turbulence. Mean KE spectra
applied to the vertical wind component reveal an effective resolution of the
order of 4–5 Δx for simulations with CEN4TH (DX2 and REF), in
agreement with , namely 8 and 20 m, respectively
(Fig. ).
With DX2, top entrainment is more active as updraughts and downdraughts are
represented at finer resolution, limiting the cooling near the surface
(Fig. d) and the vertical development of the fog.
In two other tests performed on the wind transport scheme, keeping the 5 m
horizontal resolution, the CEN4TH scheme was replaced by the WENO (Weighted
Non-Oscillatory; ) scheme at 3rd order (called WE3)
or 5th order (called WE5). These spatial schemes, associated with an explicit
Runge–Kutta temporal scheme, allow time steps 10 times larger than CEN4TH
associated with a leap-frog temporal scheme, but they were run here with the
same small time step (0.1 s) for comparison. Due to the upstream spatial
discretization, WENO schemes are implicitly diffusive and are therefore
characterized by a coarser effective resolution, especially WE3 because of
its lower order. Figure shows that the effective resolutions
are 35 m (i.e. 7Δx) and 70 m (i.e. 14Δx) for WE5 and WE3, respectively.
Mean kinetic energy (KE) spectra for vertical wind computed over the
whole fog layer and horizontal domain at 06:20 UTC for the REF, WE3, WE5, DX2
and NTR simulations. The dashed line corresponds to the -3
theoretical slope.
WE3 significantly reduces the top entrainment and the supply of warmer, dryer
air from above. This emphasizes the cooling near the surface
(Fig. c) as the diffusive contribution of the advection
operator dissipates small updraughts and suppresses part of the resolved
KE variance, in particular that present at the top of the fog
layer. This induces an overestimation of the thermal gradient near the
surface before the fog, and leads to cooling that is too strong by 1 K
during the fog (not shown). The consequences of the increased cooling are
that the LWP is largely overestimated throughout the fog life cycle, and the
dissipation is delayed (Fig. b). Considering the LWP, WE3 tends to
be closer to the NTR simulation, meaning that a diffusive transport scheme
significantly diminishes the tree drag effect.
In contrast, the differences between WE5 and REF are very small: only the LWP
is higher with WE5 during the dissipation phase due to a slightly deeper fog
layer. This underlines the less diffusive behaviour of WE5 and its higher
accuracy compared to WE3.
Thus the jump in the effective resolution with the diffusive WE3 scheme
affects the fog life cycle significantly, while the smaller deviation with
WE5 has almost no impact. Increasing numerical implicit diffusion seems to
have almost the same effect as removing the drag effect of trees. This also
underlines the importance of the numerical schemes for correct handling of
the cloud edge problem .
Conclusion
Large eddy simulations of a radiation fog event observed during the ParisFog
campaign were performed, with the aim of studying the impact of dynamics on
the fog life cycle. In order to study the local structures of the fog depth,
simulations were performed at 5 m resolution on the horizontal scale and
1 m on the vertical scale near the ground, and included a tree barrier
present near the measurement site, taken into account in the model by means
of a drag approach. The model included a 2-moment microphysical scheme, and a
deposition term was added to the droplet sedimentation, representing the
interception of droplets by the plant canopies and acting only at the first
vertical level above grass, and above the height of the trees.
The performance of the reference simulation was satisfactory as it gave
fairly good agreement with the classical near-surface measurements and the
LWP. This good performance allowed the processes driving the fog life cycle
to be explored.
The formation of the fog at elevated levels and the fact that it subsided to
the ground in a very short time, a frequently observed characteristic of
radiation fog events at the SIRTA site, has been explained. It is a
consequence of the tree drag effect when the wind meets this obstacle and the
deposition effect, which reduces the formation of droplets near the surface.
In contrast, the fog formed at the surface first upstream and 500 m
downstream of the trees, leading to a duration of about 1 h for fog
formation at the surface over the whole domain.
At the beginning of the development phase, the fog became optically thick to
LW radiation, inducing a significant increase in KE by
dynamical production, which was also associated with temperature convergence
at low levels. The radiative cooling near the top of the fog layer was the
main source of droplet activation so the droplet concentration was maximum in
the upper levels of the cloud.
During the development phase, the fog layer depth grew more slowly when the
fog reached the top of the nocturnal boundary layer, encountering stronger
thermodynamical gradients and wind shear. Horizontal rolls at the top of the
fog layer, associated with KH instabilities, became prominent.
The cloud droplet concentration became quasi-homogeneous in the fog layer
when averaged over time but extremes of droplet concentration occurred
locally near the top of the fog in the radiative cooling layer, with maxima
preferentially upstream of the crests of the waves rather than downstream in
the ascent area. This indicates that vertical velocity makes up the main
contribution to droplet activation at the top of the fog layer, followed by
the contribution of radiative cooling. Inside the cloud layer, maxima of
supersaturation were directly linked to the local updraughts, while variations
in droplet concentration were smoother.
During the dissipation phase, as the fog evolved into a stratus layer, the
cloud mixing ratio decreased at all levels. However, a sharp increase in the
droplet concentration occurred over the whole depth of the cloud because
droplets were now only activated by the convective ascents.
Various sensitivity tests allowed the main processes affecting the evolution
of fog to be identified. The tree drag effect and the deposition process were
considered as essential to correctly reproduce the main characteristics of
the fog. The absence of the tree barrier produced an unrealistic fog
simulation, with too early an onset, excessively strong cooling and a large
overestimation of the LWP.
Neglecting the deposition process over the whole vegetation canopy exerted
the most significant impact on the fog prediction. It overestimated LWP,
prevented elevated fog formation, modified the fog life cycle and
suppressed vertical and temporal heterogeneities of the microphysical fields.
Conversely, increasing the droplet deposition velocity from 2 to
8 cm s-1 reduced the LWP.
Increasing the horizontal resolution to 2 m did not change the fog
prediction significantly, which means that grid convergence seems to be
achieved at these resolutions. Conversely, increasing the numerical diffusion
with a momentum transport scheme of lower order, involving a coarser
effective resolution, drastically limited the top entrainment, and tended
strongly towards the solution where the tree drag effect was ignored. This
underlined the importance of the properties of numerical schemes in LES,
particularly at cloud edges.
This study demonstrates the feasibility and the interest of LES including
surface heterogeneities to improve our understanding of fog processes. At
these fine resolutions, surface heterogeneities have a strong impact,
explaining part of the variability in the fog layer and making these
simulations very challenging. Therefore, horizontal and vertical
variabilities in the fog layer also need to be more thoroughly explored in
future field experiments. The horizontal variability, especially at the onset
of the fog, also stresses that one point observation may not be very
representative of what happens over a coarser grid box of a numerical weather
prediction model.
One of the main points of this study is that fog water deposition should not
be neglected in 3-D fog forecast models, as still often occurs. It influences
not only near-surface fields but also the whole fog life cycle. In this
study, the deposition term was introduced quite crudely and this would need
some refinement in further studies. It would need to take account of the
wind speed and the turbulence, and it could also consider the hygroscopic
nature of canopies. By analogy with dry deposition, it would also be better
to take droplet diameter into account. Other studies have also shown that fog
water deposition is strongly enhanced at the forest edge, becoming up to
1.5–4 times larger than that in closed forest canopies
, so it could be interesting to simulate the edge
effect of fog water deposition. It is also crucial to perform measurements of
fog water deposition and dewfall during field experiments
.
This study has shown the great importance of some dynamical effects operating
at 1st order for correct predictions of the fog life cycle. Microphysics
near the ground will be further explored in a future study, and the impact of
aerosols on the fog life cycle will be considered.