Introduction
Fog is defined as the presence of droplets in the vicinity of the Earth's
surface reducing the visibility to below 1 km (American Meteorological
Society, 2017). Reduced visibility associated with fog is a major concern
for traffic safety, in particular for airports, where delays caused by low-visibility
procedures cause significant financial losses (Gultepe et al.,
2009). In spite of significant advances in the skills of numerical weather
forecast models in recent decades, the timing of the appearance and
dissipation of fog is poorly forecasted (Bergot et al., 2007; Steeneveld et
al., 2015). Fog is difficult to model with numerical weather forecast models
because of its local nature and the subtle balance between the physical
processes that govern its life cycle, which must be parameterised in the
models (Steeneveld et al., 2015). Detailed ground-based observations of a
fog condition in real time therefore have a potential for capturing
information which is missed by the models and which could help estimate
whether the fog will dissipate or persist in the near future.
Continental fog often forms by radiative cooling of the surface under clear
skies (radiation fog) or by the lowering of the base of a pre-existing low
stratus cloud to ground level (Gultepe et al., 2007; Haeffelin et al.,
2010). Once the fog has formed, its evolution depends on the physical
processes that impact the liquid water. A delicate balance between radiative
cooling, turbulent mixing and droplet sedimentation has been found in
observational and modelling studies of radiation fog (Brown and Roach, 1976;
Zhou and Ferrier, 2008; Price et al., 2015). While radiative cooling
produces liquid water by supersaturation, turbulent mixing usually is a loss
mechanism for liquid water through the mixing of the fog with drier air or
turbulent deposition of liquid water on the surface (Gultepe et al., 2007).
Schematic overview of the methodology.
Three radiative processes affect the evolution of the fog by cooling or
heating it. Firstly, the cooling from the emission of thermal (longwave, LW)
radiation at the fog top produces liquid water by condensation, which
maintains the fog against the processes that deplete the liquid water. The
advection of a cloud layer above existing fog will shelter the fog from
this radiative cooling and can therefore be an efficient dissipation
mechanism (Brown and Roach, 1976). Secondly, solar (shortwave, SW) radiation
will be absorbed by the fog droplets, mainly in the near-infrared spectrum
(Ackerman and Stephens, 1987), which causes heating and subsequent
evaporation and loss of liquid water. Finally, heating of the ground by
absorption of SW radiation can cause a sensible heat transfer to the fog,
causing the fog to evaporate from below (Brown and Roach, 1976). Fog
therefore often forms during the night, when thermal cooling dominates, and
dissipates a few hours after sunrise due to the increasing heating from
solar radiation (Tardif and Rasmussen, 2007; Haeffelin et al., 2010).
The radiative cooling of fog not only drives condensation, but also
turbulent processes. Once a fog contains a sufficient amount of liquid
water, it becomes optically thick to LW radiation. It will then cool
strongly at its top, while the lower part of the fog is shielded from
cooling (Haeffelin et al., 2013). This cooling from above (and possibly
heating from below) destabilises the fog layer and gives rise to convective
motions; the cold air sinks and the warm air rises. The fog layer will
therefore be turbulent, since convection constitutes a buoyant production of
turbulent kinetic energy (e.g. Nakanishi, 2000). Entrainment of warmer,
unsaturated air from above the fog is therefore enabled, which will cause
evaporation as it mixes with the fog (Gultepe et al., 2007). At the same
time, turbulent eddies near the surface can deposit droplets onto the
vegetation (Katata, 2014), and droplets transported downwards can evaporate
when approaching the warmer surface (Nakanishi, 2000). In addition to
vertical destabilisation, the wind shear can contribute significantly to the
generation of turbulence in fog (Mason, 1982; Nakanishi, 2000; Bergot,
2013).
In this study, we focus on the radiative aspect of this dynamical fog
system. We aim to quantify the cooling (or heating) of the fog layer induced
by the each of the three radiative processes introduced above, based on
continuous observations of the atmospheric column from ground-based remote
sensing instruments. From the cooling rate, we can estimate the condensation
(or evaporation) rate that must occur in response for the fog to stay at
saturation. Even though these condensation rates will be modified by the
dynamical processes inside the fog, they still indicate how strongly the
radiative processes influence the fog liquid water budget. We search answers
to the following questions. How large is the rate of condensation or
evaporation induced by each of the three radiative processes? How much does
this vary from one case to another, and which atmospheric parameters
are responsible for this variability? How can the magnitude of these impacts
be quantified using ground-based remote sensing, and how large are the
uncertainties?
In Sect. 2, we define the quantitative parameters used to describe the three
radiative processes and how they are calculated, and we present the
instruments, the radiative transfer code and the fog events studied. Section 3 provides a detailed description of how the observations are used to
provide input to the radiative transfer code. In Sect. 4, we present the
results when applying the methodology to the observed fog events. In Sect. 5, we discuss the uncertainties of the methodology and explore how sensitive
the radiative processes are to different aspects of the atmospheric
conditions. We also discuss the implications of our findings for the
dissipation of fog. Finally, our conclusions are given in Sect. 6.
Data and methodology
Overview of the approach
Each of the three radiative processes in the fog is studied using a
quantitative parameter. For the process of cooling due to LW emission, we
calculate the rate of condensation in the whole of the fog (in g m-2 h-1) that would occur due to this radiative cooling if no other
processes occurred, and we call it CLW for short. Similarly, we
calculate the evaporation rate due to SW heating inside the fog (in g m-2 h-1) and call it ESW. The third process is the radiative
heating of the surface, which will stimulate a sensible heat flux from the
surface to the overlying fog when the surface becomes warmer than the fog.
With this process in mind, our third parameter is the net radiative flux
(SW+LW) absorbed at the surface (in W m-2), Rnet,s for short.
The relationship between Rnet,s and the sensible heat flux is also
studied (Sect. 4.2).
Figure 1 shows schematically how the three parameters are calculated.
Measurements from several in situ and remote sensing instruments (presented
in Sect. 2.2) are used to estimate the input data of a radiative transfer
model (presented in Sect. 2.3). The input data involve vertical profiles of
clouds, temperature and humidity. The details of how we go from measurements
to input data are presented in Sect. 3. The radiative transfer model
calculates the profile of radiative fluxes and heating rates. The computed
fluxes can be compared to measured fluxes at 10 m above ground level for
validation. From the radiative heating rates, we can calculate the rates of
condensation or evaporation in g m-2 h-1 (explained in Sect. 2.4).
Vertical and temporal resolution of the observations used in this
study. All instruments are located at the SIRTA observatory main facility,
apart from the radiosondes which are launched at Trappes (15 km west of the
site) at approximately 11:15 and 23:15 UTC. The measurements by the cloud
radar, ceilometer and microwave radiometer are obtained from remote sensing,
while the other instruments measure in situ.
Instrument
Measured quantity
Vertical range and resolution
Temporal resolution
Cloud radar BASTA
Reflectivity (dBZ)
RA 0–6 km, RE 12.5 m
12 s
RA 0–12 km, RE 25 m
RA 0–12 km, RE 100 m
RA 0–12 km, RE 200 m
Microwave radiometer
Liquid water path (g m-2)
Integrated
60 s
Temperature profiles (K)
RA 0–10 km, 4–5 degrees of freedom
≈5 min
Humidity profile (g m-3)
RA 0–10 km, 2 degrees of freedom
≈ 5 min
Ceilometer CL31
Attenuated backscatter
RA 0–7.6 km, RE 15 m
30 s
Visibility metres
Horizontal visibility (m)
At 4 m, 20 m
60 s
Thermometers on 30 m mast
Air temperature (K)
At 1, 2, 5, 10, 20, 30 m
60 s
Thermometer (unsheltered)
Surface skin temperature (K)
At ground level
60 s
Cup anemometer
Wind speed (m s-1)
At 10 m
60 s
CSAT-3 sonic anemometer and LI-7500 infrared gas analyser
Sensible heat flux and latent heat flux (W m-2)
At 2 m
10 min
Radiosondes
Temperature (K) and humidity (g m-3) profiles
RA 0–30 km, RE ≈ 5 m
12 h
Pyranometers
Down- & upwelling irradiance in the solar spectrum (W m-2)
At 10 m
60 s
Pyrgeometers
Down- & upwelling irradiance in the terrestrial spectrum (W m-2)
At 10 m
60 s
Observational site and instrumentation
The multi-instrumental atmospheric observatory SIRTA in Palaiseau, 20 km
south of Paris (France), provides routine measurements of a large number of
meteorological variables since 2002 (Haeffelin et al., 2005). In situ and
remote sensing observations taken at this site have been used to study the fog
life cycle since 2006 in the framework of the ParisFog project (Haeffelin et
al., 2010). An advantage of SIRTA is the continuous measurements by several
ground-based remote sensing instruments. Such instruments have been proven
useful for the study of the fog life cycle: the attenuated backscatter from a
ceilometer can detect the growth of aerosols preceding fog formation
(Haeffelin et al., 2016), while a cloud radar can provide information about
the fog vertical development and properties once it has formed (Teshiba et
al., 2004; Boers et al., 2012; Dupont et al., 2012). In this study, we use
the observations from several instruments of SIRTA (Table 1) to analyse
periods when fog occurred. The observatory is located in a suburban area,
with surroundings characterised by small-scale heterogeneities including an
open field, a lake and a small forest.
In situ measurements of (horizontal) visibility, air temperature, wind
speed, surface skin temperature and SW and LW radiative fluxes are
continuously recorded in the surface layer at the observatory. Radiosondes
measuring the temperature and humidity profiles between ground level and 30 km are launched twice a day from the Météo-France Trappes station,
located 15 km west of SIRTA. Measurements of sensible heat flux taken at 2 m
using the eddy correlation method based on CSAT-3 sonic anemometer are
applied to study the relationship between surface radiation budget and
surface sensible heat flux.
A Vaisala CL31 ceilometer operating at 905 nm provides the profile of
(attenuated) light backscatter at 15 m vertical resolution (Kotthaus et al.,
2016), from which the cloud-base height can be determined (see Sect. 3.1).
The 95 GHz cloud radar BASTA is a newly developed cloud radar, the first
prototype of which has been successfully operating at SIRTA since 2010 (Delanoë
et al., 2016), observing the vertical profile of clouds in zenith direction.
Unlike traditional radars, which emit short, powerful pulses of radiation,
BASTA instead uses the frequency-modulated continuous wave technique, which
makes it much less expensive than traditional radars (Delanoë et al., 2016, http://basta.projet.latmos.ipsl.fr/). Unlike the
ceilometer pulse, the signal of the radar is only weakly attenuated by
clouds and can therefore observe thick and multilevel cloud layers. However,
the signal weakens with the distance to the target, which limits the ability
of the radar to detect clouds with small droplets. BASTA therefore operates
at four different modes, with vertical resolutions of 12.5, 25, 100 and
200 m. The radar switches systematically between the four
modes so that each of them produces a measurement every 12 s based on
3 s of integration time. Better vertical resolution comes at the cost
of sensitivity. The BASTA prototype used in this study can detect clouds at
1 km range (i.e. altitude) with reflectivities (see Sect. 3.2) above -27.5,
-32, -38 and -41 dBZ with the 12.5, 25, 100 and 200 m modes, respectively.
This lower limit for detection increases approximately with the square of
the range, i.e. with 6 dBZ when the range increases by a factor of two.
However, a new prototype that has recently been developed has improved the
sensitivity with about 12 dBZ relative to the first prototype on all levels.
The lowest ≈ 3 altitude levels in the radar data cannot be used
because of coupling (direct interaction between the transmitter and
receiver), which corresponds to the first ≈ 40 m when we use the
12.5 m mode to study the fog layers.
The multi-wavelength microwave radiometer (MWR) HATPRO (Rose et al., 2005)
is a passive remote sensing instrument that measures the downwelling
radiation at 14 different microwave wavelengths at the surface. These
radiances are inverted using an artificial neural network algorithm to
estimate the vertical profiles of temperature and humidity of the atmosphere
in the range 0–10 km and the total amount of liquid water in the
atmospheric column (liquid water path, LWP, g m-2). As the profiles are
based on passive measurements, the vertical resolution is limited; however,
in the boundary layer the measurements at different elevation angles enhance
the resolution of the temperature profile, giving 4–5 degrees of freedom
for the full temperature profile. The humidity profile only has about 2
degrees of freedom (Löhnert et al., 2009). The integrated water vapour
(IWV) is more reliable with an uncertainty of ±0.2 kg m-2, while
the estimate of LWP in general has an uncertainty of ±20 g m-2,
according to the manufacturer. However, for small LWP (< 50 g m-2), investigations by Marke et al. (2016) indicate that the absolute
uncertainties are smaller, with a root mean square (rms) error of 6.5 g m-2. Moreover, much of the uncertainty in retrieving LWP is due to
uncertainties in atmospheric conditions, such as cloud temperature and
humidity profile (e.g. Gaussiat et al., 2007), which usually will not change
dramatically during one fog event. In the absence of higher liquid clouds, the
detection limit of changes in fog LWP should therefore be smaller, probably
of the order of 5 g m-2 (Bernhard Pospichal, personal communication).
To reduce the constant bias in MWR LWP, we subtract the mean LWP retrieved
during the 1 h period of clear sky that is nearest in time to the fog
event of interest. For the three fog events in 2014 studied in this paper
(see Sect. 2.5), the imposed corrections are 1.1, 5.2 and 23.9 g m-2.
An improvement of the instrument algorithm provided by the
manufacturer in 2015 reduced this clear-sky bias to less than 1 g m-2
for the rest of the fog events. An approximate evaluation of the LWP
uncertainty using LW radiation measurements suggests an rms error in LWP of
about 5–10 g m-2 during fog with LWP < 40 g m-2
(Appendix A).
Radiation code ARTDECO
The radiative transfer is calculated using ARTDECO (Atmospheric Radiative
Transfer Database for Earth Climate Observation), a numerical tool developed
at LOA (Lille University) which gathers several methods to solve the
radiative transfer equation and data sets (atmospheric profiles, optical
properties for clouds and aerosols, etc.) for the modelling of radiances and
radiative fluxes in the Earth's atmosphere under the plane-parallel
assumption. Data and a user guide are available on the AERIS/ICARE Data and
Services Center website at http://www.icare.univ-lille1.fr/projects/artdeco. In this paper, the
radiative transfer equation is solved using the discrete-ordinates method DISORT
(Stamnes et al., 1988) in the solar spectrum (0.25–4 µm) and the
thermal spectrum (4–100 µm). The spectral resolution is 400 cm-1
in 0.25–0.69 µm, 100 cm-1 in 0.69–4 µm and 20 cm-1
in 4–100 µm, which gives 303 wavelength bands in total. Gaseous
absorption by H2O, CO2 and O3 is taken into account and
represented by the correlated k-distributions (Dubuisson et al., 2005;
Kratz, 1995). In ARTDECO, the coefficients of the k-distribution are
calculated using a line-by-line code (Dubuisson et al., 2006) from the
HITRAN 2012 spectroscopic database (Rothman et al., 2013). The use of
correlated k-distribution makes it possible to accurately account for
the interaction between gaseous absorption and multiple scattering with
manageable computational time. In addition, the impact of the absorption
continua is modelled using the MT_CKD model (Mlawer et al.,
2012). Optical properties of water clouds are calculated for a given droplet
size distribution (DSD) using Mie calculations. In this study, the DSD is
parameterised using a modified gamma distribution, applying parameter values
presented by Hess et al. (1998) for fog and continental stratus. The
effective radius is 10.7 µm for fog and 7.3 µm for stratus, but we
modify the effective radius in the fog according to the radar reflectivity
(see Sect. 3.2). Ice clouds are represented by the Baum and Co ice cloud
parameterisation implemented in the ARTDECO code (Baum et al., 2014), using
an ice crystal effective diameter of 40 µm.
Radiative fluxes are calculated on 66 vertical levels spanning 0–70 km, 28
of which are located in the lowest 500 m in order to resolve fog layers
well. A Lambertian surface albedo in the SW is applied, with a spectral
signature representative of vegetated surfaces. However, as we observed that
this albedo parameterisation generally overestimates the observed albedo by
≈ 25 %, we downscale the albedo at all wavelengths to better fit
the median albedo of 0.221 of October 2014–March 2015 observed at SIRTA. In
the LW, a constant emissivity of 0.97 is used.
Calculation of radiation-driven liquid water condensation and
evaporation
The radiation-driven condensation (or evaporation) rate is calculated
assuming the air remains at saturation while cooling or warming from SW or
LW radiation only, neglecting all adiabatic motions or mixing, but taking
into account the latent heat of condensation. The derivations below are
based on the thermodynamics of a saturated air parcel, which are described by
e.g. Wallace and Hobbs (2006).
For N model levels at height hj (j=1,…,N), ARTDECO calculates the
radiative heating rate in each of the N-1 layers between these levels,
dTdtrad,j (j=1,…N-1). We assume
that if the jth layer contains cloud, its water vapour content will
always be at saturation with respect to liquid water. To satisfy this, the
condensation rate Crad due to the radiation must be as follows:
Crad,j=-dρsdTdTdtj,
where ρs is the saturation vapour concentration (g m-3) and
dρsdT its change with temperature. dTdtj is the total air temperature tendency, which under the above
assumptions equals the radiative heating rate plus the latent heat of
condensation:
dTdtj=dTdtrad,j+LvρacpCrad,j,
where Lv is the specific latent heat of condensation, ρa the
air density and cp the specific heat capacity of air at constant
pressure. We estimate dρsdT by combining the ideal gas
equation for water vapour (es=ρsRvT) and
the Clausius–Clapeyron equation
(desdT=LvesRvT2), which yields
dρsdT=esRvT2LvRvT-1,
where Rv is the specific gas constant of water vapour, and es is
the saturation vapour pressure, which we estimate from the formula presented
by Bolton (1980):
esT=611.2exp17.67(T-273.15)T-29.65,
with T in K and es is Pa. Combining Eqs. (1) and (2), we get an
expression for the radiation-driven condensation rate:
Crad,j=-dρsdT1+LvρacpdρsdTdTdtrad,j.
We calculate this condensation rate for all layers within the fog and
finally integrate it into the vertical to obtain the total condensation rate in
the whole of the fog (in g m-2 h-1), thus obtaining CLW and
-ESW. It is worth noting that the gradient dρsdT
increases strongly with temperature. This implies that a warmer fog
condensates more liquid water than a cold fog given the same radiative
cooling rate. In fact, the condensed water per radiative heat loss increases
almost linearly from 0.55 to 0.90 g m-2 h-1 per W m-2 when the
fog temperature increases from -2 to 15 ∘C (not shown).
Thus, the vertical integral of Eq. (5) allows the immediate effect of
radiation on the fog LWP budget to be calculated from the output of the
radiative transfer model. This is possible because we have neglected all air
motion. In reality, negative buoyancy induced by the radiative cooling will
lead to downdraughts and turbulence, which favours entrainment, droplet
deposition and other LWP sink processes, as described in Sect. 1. These
indirect effects of radiation on the LWP budget are not studied in this
paper, as a dynamical model taking into account forcings such as the wind
and surface properties would be required in order to quantify them. When
interpreting the results of this paper, it is important to keep in mind that
the condensation rates CLW and -ESW are not the actual
condensation rates that occur in the fog, but rather the immediate
condensational tendency to stay at saturation induced by the radiative
temperature tendency, which could rapidly be modified by either drying or
warming through mixing processes. Nonetheless, CLW and ESW are
good indicators for how strongly the radiation impacts the fog LWP.
To improve the calculation of condensation rates, we could have taken into
account that fog is often vertically well mixed due to destabilisation
(Nakanishi, 2000), so that the whole of the fog layer cools at the same rate.
However, we found that CLW and ESW only change marginally
(< 2 %) if we apply the fog-layer vertical average radiative
heating rate in Eq. (5) (not shown), which would not significantly affect
our results.
Overview of the analysed fog cases
We calculate the radiation at 15 min intervals in seven fog events that
occurred at SIRTA during the winter seasons 2014–2015 and 2015–2016. An
overview of the atmospheric conditions during each of these fog events is
given in Table 2. The fog events were chosen to cover an important range of
variability in atmospheric conditions such as 2 m temperature and IWV, as
well as fog properties such as geometric thickness and LWP, and we have
included one fog event where cloud layers above the fog were observed.
Considering all fog events at SIRTA in the winter seasons 2012–2016 with
reliable LWP measurements from the MWR (e.g. excluding cases with liquid
clouds above), in total 53 events, the 10th, 25th, 50th,
75th and 90th percentiles of the LWP distribution are 6.6, 16.4,
40.2, 68.0 and 91.2 g m-2, respectively (not shown). The chosen fog
events thus cover the typical range of fog LWP. Fog types can be defined by
the mechanism of formation (Tardif and Rasmussen, 2007). At SIRTA, radiation
fog and stratus-lowering fog occur with about the same frequency, while
other fog types are less common (Haeffelin et al., 2010; Dupont et al.,
2016). Fog during rain occasionally occurs, but such cases have been avoided
in this study because rain or drizzle drops generate very large radar
reflectivities, yielding cloud property retrievals highly uncertain (Fox and
Illingworth, 1997), and because of the wetting bias in the MWR retrievals in
rain (Rose et al., 2005).
Main characteristics of each fog event studied in this paper.
Dissipation time is relative to sunrise (- is before, + is after). The fog
events are classified as radiation fog (RAD) or stratus-lowering fog (STL),
as defined by Tardif and Rasmussen (2007). Pressure is measured at 2 m and
is indicated for the time of formation, while the bracketed value indicates
how much higher (+) or lower (-) the pressure is 24 h
later.
No
Time of formation
Duration
Diss. time rel.
Fog
Pressure
Higher
Min. visibility (m)
Median (max)
Max thickness
2 m temp.
IWV range
(UTC)
(hh:mm)
to sunrise (h)
type
(hPa)
clouds (y/n)
at 4 m
LWP (g m-2)
(m)
range (∘C)
(kg m-2)
1
27 Oct 2014, 04:30
4:20
+2.3
RAD
1006(-5)
n
135
6 (22)
110
7.2–9.4
≈9–13
2
28 Oct 2014, 00:50
8:20
+2.5
RAD
1001(-3)
n
145
130 (209)
450
7.0–9.8
≈7–9.5
3
14 Dec 2014, 06:00
17:10*
-8.6
RAD
999(+0)
n
103
18 (56)
210
(-1.1)–2.5
≈6–9
4
2 Nov 2015, 05:00
9:20
+7.6
RAD
1007(-8)
n
74
62 (105)
275
5.1–8.5
≈9–11
5
8 Nov 2015, 05:50
4:00
+2.9
RAD
1009(-1)
n
128
40 (61)
210
13.7–14.4
≈22–28
6
13 Dec 2015, 06:20
29:20*
+3.9
STL
1003(-3)
n
72
69 (135)
360
2.8–5.7
≈10–14
7
1 Jan 2016, 07:00
5:20
+4.5
RAD
1006(-17)
y
125
67 (154)
410
4.6–5.9
≈12–15
* The cloud base lifted to a few tens of metres on 14 December 2014 during
13:40–15:10 and on 13 December 2015 during 12:20–15:00.
Fog presence is defined by the 10 min average visibility at 4 m being below 1 km (American Meteorological Society, 2017). For a 10 min block to be part of
a fog event, the visibility should be below 1 km for at least 30 min of the
surrounding 50 min period, based on the method proposed by Tardif and
Rasmussen (2007), thus defining the fog formation and dissipation time of
each event. From this definition, fog event numbers 3 and 6 should each be
separated into two events; however, we have chosen to regard them as single
events because the cloud base lifts only a few tens of metres for 2–3 h
before lowering again.
Retrieval of geophysical properties
This section describes how the measurements at SIRTA are used to prepare the
input data to the radiative transfer code: profiles of cloud properties,
temperature and humidity. Before they are used, the data from all the
instruments, except the temperature and humidity profiles from the
radiosonde and MWR, are averaged in a 10 min block around the time of
interest.
Fog and cloud boundaries
The fog or low stratus is searched for in the lowest 500 m of the
atmosphere. Its cloud-base height is found using a threshold value in the
attenuated backscatter from the ceilometer of 2×10-4 m-1 sr-1, following Haeffelin et al. (2016). The cloud-base height is set
to 0 m if the horizontal visibility at 4 m is below 1 km. The cloud-top
height is set to the altitude where the 12.5 m resolution radar data no
longer detect a signal above noise levels. If the visibility at 4 m is below 1 km but the visibility at 20 m is above 1 km, the cloud-top height is set to 10 m.
The presence and vertical extent of higher cloud layers is determined from
the radar. The clouds are assumed to extend over the gates where a signal is
detected above the background noise.
Fog microphysical properties
We assume that the fog contains only liquid droplets and no ice, which is a
reasonable assumption as the screen temperature during the fog events
studied here is a minimum of -1 ∘C (Table 2) and ice crystals in fog
rarely occur at temperatures above -10 ∘C (Gultepe et al., 2007).
The optical properties of the fog then depend only on the liquid water
content (LWC) and the DSD. Only the extinction coefficient at 550 nm is
required as model input in addition to the DSD, since ARTDECO can determine
the optical properties at all 303 wavelengths by Mie calculations from this
information (Sect. 2.3). The extinction coefficient of cloud droplets at
visible wavelengths (including 550 nm) is well approximated by
αext,visible=3LWC2ϱlreff,
with LWC in g m-3, reff the effective radius in µm and
ϱl the density of liquid water in g cm-3 (Hu and
Stamnes, 1993). The optical depth at visible wavelengths (OD) is obtained by
integrating αext,visible in the vertical.
The 12.5 m resolution mode of the radar is used to estimate LWC and reff
at each level in the fog. For liquid droplets, the backscattered radar
signal is proportional to the sixth moment of the DSD, a quantity known as
radar reflectivity Z:
Z=∫0∞D6n(D)dD,
where D=2r is the droplet diameter and n(D)dD is the number
concentration of droplets with diameter between D and D+dD. Z has
units mm6 m-3, but is usually expressed in units of dBZ, defined
by dBZ =10⋅log10(Z). We have chosen to apply the empirical
relationships of Fox and Illingworth (1997) relating the radar reflectivity
Z (dBZ) to LWC (g m-3) and reff (µm):
LWC=9.27⋅100.0641Zreff=23.4⋅100.0177Z
These relationships were derived from aircraft measurements of the droplet
spectrum in stratocumulus clouds, covering the range -40 to -20 dBZ. The
relationships are not valid in the presence of drizzle, which strongly
increases Z as droplets grow larger. Drizzle presence typically occurs when Z>-20 dBZ (e.g. Matrosov et al., 2004). We therefore use the
value of LWC and reff obtained at Z=-20 dBZ for higher Z. The
relationships are plotted in Fig. 2.
Empirical relationships between radar reflectivity (Z) and LWC and
effective radius used in this study, based on Fox and Illingworth
(1997).
LWC and reff are estimated in each radar gate from cloud base to cloud
top using these relationships, assuming no attenuation of the radar signal. For the lowest
altitudes, where the radar data cannot be used, we apply the reflectivity of
the lowest usable gate (usually at ≈ 50 m). The LWP of the MWR is
then applied as a scaling factor to improve the estimate of LWC. This
scaling is not performed if the MWR LWP is less than 10 g m-2. If a
higher cloud that may contain liquid is detected, the LWP should be
partitioned between the fog and this cloud (see Sect. 4.3). Having obtained
LWC and reff, the profile of αext,visible can thus be
determined using Eq. (6). Below 30 m, we instead use the visibility
measurements, which relate to visible extinction through Koschmieder's
formula (e.g. Hautiére et al., 2006):
αext,visible=-ln0.05Vis≈3.0Vis.
Examples of the profiles of Z, LWC, reff and αext,visible
are shown in Appendix B. Uncertainties in the retrievals of microphysical
properties are also discussed in Appendix B. To reduce the computational
cost, only four different DSDs are given to the radiative transfer code,
with effective radii of 4.0, 5.5, 8.0 and 10.7 µm. In
one model run, the same DSD is used at all altitudes, and it is selected by
applying Eq. (9) on the vertical median of Z.
Profiles of temperature and gases
The radiation code requires the vertical profiles of temperature and the
concentrations of the gaseous species (H2O, CO2, O3) as
input. For CO2, a vertically uniform mixing ratio of 400 ppmv is used,
while for O3 we use the AFGL midlatitude winter standard atmospheric
profile (Anderson et al., 1986) which is provided in ARTDECO. This standard
atmosphere is also used for temperature and humidity (i.e. H2O) above
20 km. Below 10 km, the temperature and humidity from the MWR is applied,
while the previous radiosonde at Trappes is used in 10–20 km. The measured
surface skin temperature is used for surface emission temperature, while the
in situ measured air temperature is used in the 0–30 m layer. When there is
no cloud base below 50 m, the MWR temperature profile is modified in the
lowest 200 m of the atmosphere to gradually approach the temperature
measured at 30 m.
Due to fog top radiative cooling and subsequent vertical mixing, the
temperature profile is often characterised by a saturated adiabatic lapse
rate inside the fog, capped by a strong inversion above the fog top
(Nakanishi, 2000; Price et al., 2015). This vertical structure was also
observed by the majority of the 12 radiosondes launched during four fog
events in the ParisFog field campaign of 2006–2007 (not shown). If a cloud
base is present below 50 m, we therefore let the temperature decrease
adiabatically with height from the measured value at the top of the mast
and then impose an inversion of 5 K per 100 m from the fog top until the
temperature profile of the MWR is encountered. This inversion strength
corresponds to what was typically observed by the aforementioned
radiosondes. When a cloud base is present below 50 m, we also increase the
humidity within the whole of the fog layer to saturation and decrease the humidity
in the atmosphere above with the same integrated amount, thus improving the
estimate of the humidity column above the fog top.
Results
We will now present the results obtained by applying the methodology
described above to the seven fog events in Table 2. We first describe two contrasting fog events in
some detail (Sect. 4.1), then we study the
statistics of the radiative properties in all six fog events without clouds
above (Sect. 4.2), and finally we study the impacts of the clouds appearing
above the last fog event (Sect. 4.3).
Quantitative analysis of two contrasting fog events
Figure 3 shows the time series of several observed and calculated quantities
during the fog event on 27 October 2014. The visibility and LWP time series
(Fig. 3a) reveal that this fog has two distinct stages. From 02 to 06 UTC, intermittent patches of very thin fog exist, seen from the fluctuating
4 m visibility and the 20 m visibility remaining well above the fog threshold.
After 06 UTC, the fog develops in the vertical, causing the visibility at 20 m to drop. The fog grows to a thickness of about 100 m, as can be seen by
the radar (Fig. 3b), reaching a maximum LWP of about 20 g m-2 just
after sunrise, at 07 UTC. A minimum visibility at 4 m (155 m) and at 20 m
(87 m) is also reached at 07 UTC. After sunrise, the visibility steadily
improves, fog dissipating at the surface at 08:50 UTC and nearly 1 h
later at 20 m.
The fog event on 27 October 2014. (a–d) Time series of observed
variables: (a) LWP from MWR (g m-2) and visibility (m) at 4 and 20 m; (b) profile of radar reflectivity (dBZ), and estimated cloud-base height
(CBH) and cloud-top height (CTH); (c) temperature (∘C) at 2, 10 and 20 m, and wind speed (m s-1) at 10 m; (d) net downwelling SW
and LW radiative flux (W m-2) at 10 m. (e–h) Time series of
calculated variables: (e) fog optical depth at 550 nm; (f) downwelling SW
flux (W m-2) at 10 m, comparing model runs including the fog, model
runs not including the fog (clear sky) and the measurement; (g) as (f), but
for the downwelling LW flux; (h) the vertically integrated condensation
rates (g m-2 h-1) due to LW and SW radiation (CLW and
ESW, defined in Sect. 2.1).
Figure 3c–d shows the time series of temperature, wind speed and the net SW
and LW downward radiation observed at 10 m. Before fog formation, the ground
undergoes radiative cooling of ≈ 60 W m-2, which gives rise
to the observed strong temperature inversion in the first 20 m of the
atmosphere. The surface radiation budget stays unchanged during the period
of intermittent fog, indicating that the fog is restricted to below the 10 m
level where the flux is measured. Once the fog starts developing in the
vertical, however, the 10 m net LW radiation increases and becomes close to
zero at the fog peak time at 07 UTC, indicating that the fog is nearly
opaque to LW radiation at this time. In the same period, from 06 to 07 UTC,
the stable temperature profile evolves into a near-isotherm layer. After
sunrise, strong SW absorption at the surface (reaching > 100 W m-2) is associated with a sharp rise in temperature, which likely
explains the dissipation of the fog.
Figure 3e–h shows quantities that are calculated using our methodology.
Until 06 UTC, the fog OD is based on the observed 4 m extinction and an
assumed thickness of 10 m, resulting in a very low fog OD. The estimated fog
OD increases strongly from 06 to 07 UTC, reaching 4 at 07 UTC. This is
associated with a distinct increase in downwelling LW at 10 m, which is qualitatively
consistent with the observations (Fig. 3g). As the LW emissivity of the fog
increases, the radiative cooling is transferred from the surface to the fog,
causing an increase in the calculated CLW, which reaches a maximum of
50 g m-2 h-1 (Fig. 3h). The magnitude of this parameter indicates
that the radiative cooling process can produce the observed maximum in fog
LWP is less than 1 h, which is consistent with the observed increase in
LWP. The underestimation of the downwelling LW at 10 m after 06 UTC can
indicate that the calculated LW emissivity of the fog is slightly
underestimated, and thus also CLW. The calculation also underestimates
the LW flux by about 15 W m-2 before 06 UTC, which is probably due to
uncertainties in the vertical profile of temperature and humidity (see Sect. 5.3).
ESW is small, at only ≈ 2 g m-2 h-1 (Fig. 3h). The
heating of the fog via surface absorption is probably much more important
for evaporating the fog.
Same as Fig. 3 but for the fog event on 13 December 2015.
Figure 4 shows the same quantities as Fig. 3, but for the fog event on 13 December 2015. In contrast to the fog on 27 October 2014, this fog forms from the
gradual lowering of the cloud-base of a pre-existing low stratus, which is
already much thicker than the fog on 27 October 2014. During the whole day, this
fog has an LWP of 50–100 g m-2 and a thickness of 250–300 m and
thus remains optically thick. A transition from fog to low stratus occurs at
12:20 UTC, but the cloud base rises only to ≈ 20 m before descending
again to form fog at 15 UTC (not shown). As the fog is opaque to LW, the
good agreement between the modelled and observed downwelling LW at 10 m
(Fig. 4g) only reflects the temperature of the fog. More interesting is the
good agreement between the modelled and observed downwelling SW radiation at
10 m (Fig. 4f), which indicates that the estimated fog OD is rather precise.
CLW is around 50 g m-2 h-1 with little variability. The ratio
of the fog LWP and CLW has units of time, and it can be interpreted as
a characteristic timescale for the renewal of the fog by radiative cooling;
it is the time in which CLW could produce the same amount of liquid
water that is currently in the fog. This timescale is 1–2 h in this
fog event. ESW reaches 9 g m-2 h-1 around midday and is thus
of less importance. This thicker fog also reflects more SW radiation than
the fog 27 October 2014 so that less SW reaches the surface (Fig. 4f), which
probably helps the fog to persist, although the LWP decreases during the
day.
Radiation-driven condensation and evaporation in six fog events without
clouds above
Figure 5 shows the values of our three radiation parameters calculated every
15 min during the six fog cases without higher clouds (Table 2). CLW
varies significantly, from 0 to 70 g m-2 h-1 (Fig. 5a). Firstly,
when the fog is not opaque to LW radiation, CLW is smaller, because the
fog emits less than a blackbody. The optical depth of a cloud in the LW is
principally determined by its LWP (Platt, 1976). We therefore plot CLW
against the MWR LWP in Fig. 5a, which shows that CLW increases strongly
with LWP when LWP is smaller than 20–30 g m-2. Remember, though, that
the MWR LWP is not used in the input data to the radiation code when it is
less than 10 g m-2 (Sect. 3.2). When the fog is opaque (LWP > ≈ 30 g m-2), the radiative cooling is restricted
to the uppermost 50–100 m of the fog (Appendix B), in agreement with
previous studies (Nakanishi, 2000; Cuxart and Jiménez, 2012). CLW
then is in the range 40–70 g m-2 h-1, varying significantly between fog
events and to a lesser degree (≈ 5–15 g m-2 h-1) within
the same event (Fig. 5a). This variability is not related to LWP since
the LW emissivity is already close to 1 at an LWP of 30 g m-2. We can
interpret from Fig. 5a that the timescale of renewal by LW cooling
(introduced in Sect. 4.1) in opaque fog is in the range 0.5–2 h, being longer
for fog with higher LWP and even reaching 3 h for parts of the fog on 28 October 2014. This is similar to the typical timescale for observed major
changes in the fog LWP (not shown). The magnitude of CLW can be
compared to the results of Nakanishi (2000), who studied the liquid water
budget of fog in a large-eddy simulation. His Fig. 14a shows the
domain-averaged profile of condensation rate in a 100 m thick fog with LWP of
about 15 g m-2 (seen from his Fig. 5b) in the morning. Condensation
occurs in the upper 50 m of the fog, and the integral over these 50 m gives
roughly 30–40 g m-2 h-1, which is similar to our results (Fig. 5a).
CLW (a), ESW (b) and Rnet,s (c) (defined in Sect. 2.1), calculated every 15 min
from formation time to dissipation time for
the six fog events without clouds above in Table 2. (d) Measured 10 min
average sensible heat flux at 2 m vs. measured 10 min average Rnet,s (at 10 m) during the daytime fog hours of all fog events in Table 2,
excluding 28 October 2014 because the measurements are biased.
To investigate possible causes for the observed variability of CLW in
opaque fog, three cases of opaque fog (OD > 10) are
compared in Fig. 6. CLW are 63.4, 47.7 and 61.6 g m-2 h-1 (Fig. 6a). Since the fog is opaque, the budget of LW radiation
at the fog top is the main determining factor for the radiative cooling.
Figure 6b shows the LW fluxes at fog top in the three cases; the length
of the vertical line indicates the net negative LW budget. The net LW budget
is -73 W m-2 both on 2 and 8 November 2015, but the condensation
rate is still higher by 14 g m-2 h-1 on 8 November 2015. This is
explained by the higher temperature of the fog top on the latter date (Fig. 6c), causing a higher condensation rate with the same cooling (see Sect. 2.4).
The fog conditions on 28 October 2014 and 2 November 2015 differ in
condensation rate by 16 g m-2 h-1. These two fog conditions have a
very similar temperature, so the difference is explained by the LW radiative
budget at the fog top, which is -100 W m-2 on 28 October 2014, i.e. 27 W m-2 more negative than on 2 November 2015. This higher LW deficit can be
explained by the lower humidity above the fog (Fig. 6d) and possibly also
the lower temperature in the first 1 km above the fog (Fig. 6c). Thus,
CLW in fog without a cloud above varies significantly both from
differences in fog OD, the fog temperature and the LW emission from the
atmosphere above.
Figure 5b shows ESW, which varies in 0–15 g m-2 h-1.
ESW obviously depends on the amount of incoming SW radiation, so we
plot it against the solar zenith angle. At one given angle, there is a
variability of a factor of 4 between the fog cases. This variability is
explained by the fog OD. Thinner fog, such as on 27 October 2014 and
14 December 2014, will interact less with the SW radiation and therefore absorb less
than thicker fog, such as on 28 October 2014 and 2 November 2015. ESW will also
depend on fog temperature through dρsdT, just like
CLW. All in all, ESW is generally much smaller than CLW, even
for thick fog near (winter) midday, but it still represents a significant
reduction in the net radiation-driven condensation rate in fog in daytime
relative to night-time.
Comparison of three fog events at 07:30 UTC: (a) CLW (defined
in Sect. 2.1); (b) LW fluxes at fog top (cross is downwelling, circle is
upwelling, thus length of vertical line indicates the (negative) LW budget
at fog top). (c) Temperature and (d) humidity profiles estimated with the
method described in Sect. 3.3. The fog top is located at the bottom of the sharp temperature inversion.
Rnet,s varies from 0 to 140 W m-2 during the daytime in the six fog
cases (Fig. 5c). Absorption of SW is the dominant term, and therefore we
highlight the dependency on the solar zenith angle. However, net LW emission
significantly reduces Rnet below non-opaque fog
(27 October and 14 December 2014) with up to -60 W m-2 and also frequently reaches -10 W m-2 in the opaque fog because the ground is warmer than the
fog (not shown). Since thicker fog reflects more SW radiation, the absorbed
SW is smaller below thick fog than thin fog at a given solar zenith angle,
and this gives rise to the case-to-case variability in Rnet,s of a
factor of 3 seen in Fig. 5c, e.g. from 40 W m-2 to 120 W m-2 at a
solar zenith angle of 70∘. To study to what extent this absorbed
heat is transferred to the fog, we compare the measurements of Rnet,s
(at 10 m) with the sensible heat flux measurements at 2 m during fog in
daytime (Fig. 5d). The two parameters are clearly correlated (R=0.56). The
fraction of sensible heat flux to Rnet,s in these data is found to
have a 25 and 75 percentile of 0.20 and 0.40, respectively. Since 1 W m-2 heating of the fog corresponds to an evaporation rate of about 0.7 g m-2 h-1
(Sect. 2.4), the sensible heat flux will cause an
evaporation rate of roughly 0.15–0.30 g m-2 h-1 per W m-2 of
radiation absorbed at the surface. With a surface absorption of 100 W m-2 at
midday below thin fog, this correspond to 15–30 g m-2 h-1 of evaporation, which is almost as large as CLW. Considering
that measurements using the eddy covariance method could underestimate the
turbulent heat fluxes (Foken, 2008), the heating of the fog by Rnet,s
might in reality be even stronger than what we found here.
Radiation-driven condensation and evaporation in a fog with clouds
above
Case study of the fog event on 1 January 2016, when clouds appeared
above the fog. Panels are the same as in Fig. 3, with a few additions. In
(b), there are two panels, the upper one showing the reflectivity from the
200 m mode of the radar and the lower one that of the 12.5 m mode. In (e), the
optical depths of the cloud layers above the fog are also indicated, and in
(f–h) the results obtained when including only the fog (and not the higher
clouds) have been added.
Figure 7 presents the fog event occurring on 1 January 2016, during which the
BASTA cloud radar detects cloud layers appearing above the fog: traces of a
stratus at ≈ 1.6 km from 07:00 to 08:30 UTC, and a higher and thicker
stratus after 11 UTC. During the presence of the second cloud, the fog
evaporates rapidly around 12–13 UTC, leaving only traces of a cloud at
≈ 150 m (Fig. 7b).
The radar mode at 200 m resolution is just sensitive enough to detect the
cloud at ≈ 1.6 km, so its geometrical thickness is uncertain.
However, peaks in the LWP (Fig. 7a) appear at corresponding times when the
cloud is observed by the radar. We therefore model the cloud as a liquid
stratus and partition the LWP between the fog and overlying stratus cloud in
the following way: in the period 06:45 to 07:30 (07:30 to 08:45) UTC, the
first 30 (20) g m-2 is attributed to the fog layer, and the rest to
the stratus. This results in an OD of the stratus of ≈ 10 when it is
present (Fig. 7e). The stratus has a strong impact on CLW (Fig. 7h),
reducing it by 90–100 %, because it increases the downwelling LW
radiation at the fog top (not shown). The presence of the stratus may
therefore explain why the fog does not develop vertically, but instead
decreases its geometric thickness and LWP while the stratus is present (Fig. 7a–b).
A second higher cloud appears at 11 UTC between 4 and 6 km. The cloud
persists and deepens while the fog dissipates. From the radiosounding at
11:35 UTC, we know that the temperature in the 4–6 km layer is -25
to -13 ∘C. Since the LWP drops to zero after the fog cloud
disappears, we choose to model the overlying cloud as a pure ice cloud, even
though it is possible that it also contains liquid water while overlying the
fog, which could explain the peaks in LWP around 12 UTC (Fig. 7a). To get a
rough estimate of the OD of this cloud, we use an ice water content of 0.05 g m-3, which corresponds to the average ice water content found by
Korolev et al. (2003) for glaciated frontal clouds at temperatures of around
-20 ∘C. This results in an OD of ≈ 5 in the beginning,
growing with the observed thickness of the cloud (Fig. 7e). This cloud
reduces CLW by ≈ 70 % (Fig. 7h), which is less than the
effect of the first stratus. This is because the cloud is higher and colder,
thus emitting less LW than the first cloud (Stephan Boltzmann's law).
However, its effect is still more important than the variability in CLW
found between cases without a higher cloud (Sect. 4.2). The cloud at 4 km
also causes a 50–80 % reduction in ESW and a
15–30 % reduction in the SW that reaches the surface. These effects are
due to reflection and absorption of SW radiation by the overlying cloud, and
they increase with time as the cloud thickens. Thus, in the SW the cloud has
the opposite effect on the fog LWP to that in the LW. However, the LW effect is
more important than the SW effect for the fog LWP budget in this case:
CLW decreases by ≈ 35 g m-2 h-1 due to the cloud
presence, which is much more than the decrease in ESW of ≈ 4 g m-2 h-1
or the ≈ 10 W m-2 reduction in the SW
absorbed at the surface (not shown) which should correspond to less than 5 g m-2 h-1 decrease in evaporation by sensible heat flux (see Sect. 4.2).
The modelled and observed downwelling SW at 10 m are compared in Fig. 7f.
They agree well both when there is only the fog (e.g. at 10 UTC), when both
the fog and the cloud at 4 km are present (e.g. at 12 UTC) and when only the
cloud is present (e.g. at 14 UTC), which provides a validation of the
estimated OD of the fog and the cloud.
Discussion
We link the variability in the radiative parameters found in Sect. 4 to
various properties of the atmospheric conditions, such as fog LWP and the
presence of clouds above the fog. In order to understand better how
each factor impacts the radiation-driven condensation and evaporation,
theoretical sensitivity studies are performed in which each input parameter is varied
separately. Sensitivity to fog microphysical properties,
temperature and humidity is analysed in Sect. 5.1, while impacts of higher
clouds are explored in Sect. 5.2. Finally, a discussion of uncertainties is
presented in Sect. 5.3.
Sensitivity of radiation-driven condensation and evaporation to fog
properties, temperature and humidity
Figure 8 explores the sensitivity of our radiation parameters to the LWP and
droplet sizes of the fog, which together determine its optical properties
(see Sect. 3.2). The model runs use the input of the semi-transparent fog
on 27 October 2014 at 08:30 UTC (Fig. 3), modifying only the fog LWP
and/or the droplet effective radius.
Dependency of CLW (a), ESW (b), Rnet,s (c) (defined
in Sect. 2.1), and the downwelling LW flux at the surface (d) on the fog
LWP and effective radius. All other input data are fixed to the values of 27 October 2014 at
08:30 UTC: the fog is 100 m thick with no above clouds and there is a
solar zenith angle of 73.9∘.
Figure 8a shows that CLW increases fast with fog LWP when LWP is less
than ≈ 30 g m-2. For higher LWP, the increase is much weaker,
and beyond 50 g m-2 it approaches a constant value as the emissivity of
the fog approaches 1. The dependency on reff for a given LWP is weak,
which is due to a near cancellation between decreasing surface area and
increasing absorption efficiency with reff, so that the LW optical
depth of liquid clouds are almost entirely determined by LWP (Platt, 1976).
The LW cooling process is thus sensitive to the fog LWP only if LWP
< ≈ 40 g m-2, and it is not sensitive to droplet sizes
within the range of effective radii studied here. Figure 8d shows that the
downwelling LW flux at the surface increases with LWP in a very similar way
to CLW, which we use to evaluate the uncertainty in CLW due LWP
uncertainty (Appendix A).
Figure 8b shows that ESW also increases with LWP. Compared to CLW,
ESW depends less strongly on LWP for thin fog, but it keeps increasing
with LWP also for opaque fog with LWP well above 50 g m-2. This is due
to the SW radiation being largely diffused in the forward direction, rather
than being absorbed, so that much SW still remains to be absorbed even far
down inside an optically thick cloud. Note also that some absorption occurs
even in when LWP = 0, because of absorption by water vapour inside the cloud
(Davies et al., 1984). ESW is also sensitive to the sizes of the
droplets: for a given LWP, the largest effective radius (10.7 µm)
gives a ≈ 50 % larger evaporation rate than the smallest
effective radius (4 µm), which can appear counterintuitive since the
total surface area of the DSD decreases with reff. This occurs due to
an increase in absorptivity in the near infrared with droplet size (Ackerman
and Stephens, 1987).
The dependency of Rnet,s on fog properties (Fig. 8c) is the sum of LW
and SW cloud effects. The fog reduces the SW reaching the surface by
reflecting SW radiation, and this effect increases with LWP and decreases
with reff (Twomey, 1977). In the LW, radiative cooling of the surface
is reduced as LWP increases, thus increasing
Rnet,s with LWP, because
the cooling is transferred to the fog top. Beyond LWP ≈ 40 g m-2, the sensitivity of Rnet,s to LWP is only due to SW.
Rnet,s is about half as large when LWP is 100 g m-2 than for LWP
of 20 g m-2. In thick fog, the smallest droplets only let through half
as much SW as the biggest droplets, while the dependency on droplet size is
less pronounced for thin fog.
Sensitivity of CLW (defined in Sect. 2.1) to changing the
fog top temperature (a), the temperature in the first 100 m above the fog
(b), the temperature in the first 3 km above the fog (c) and the humidity
above the fog (d). All other input data are kept constant at the values for
13 December 2015 at 10 UTC: the fog is 290 m thick with no clouds above and a
visible optical depth of 16.4. To the right of each result is a plot showing
how the profile of temperature or humidity is modified from the original
profile (thick line).
Sensitivity of CLW (a), ESW (b) and Rnet,s (c) (defined in Sect. 2.1) to the altitude, type and visible optical depth of a
cloud appearing above the fog. All other input data are kept constant at the values
for 13 December 2015 at 10 UTC (the same time as in Fig. 9). Solar zenith angle is 75.7∘.
In Fig. 9, we explore the sensitivity of CLW to the vertical profiles
of temperature and humidity. In these tests, we use the opaque fog on
13 December 2015 at 10 UTC. Figure 9a confirms that an increase in fog top temperature
leads to a higher CLW, by about 3 g m-2 h-1 per ∘C, caused both by higher emission of LW radiation by the fog
(Stephan–Boltzmanns law) and the increase with temperature of the
condensation rate per W m-2 (Sect. 2.4). A temperature change in the
atmosphere above the fog has a weaker impact of about 1.4 g m-2 h-1 per ∘C (Fig. 9c). Figure 9b illustrates that the first
100 m above the fog is in fact responsible for half of this effect, which
is because most of the downwelling LW radiation under a cloud-free sky comes
from the first few tens of metres, as noted by Ohmura (2001). The
sensitivity to temperature above the fog is thus mainly related to the
strength of the inversion at the fog top. The sensitivity of CLW to
increased water vapour above the fog is about 2 g m-2 h-1
per added kg m-2 of IWV (Fig. 9d), which confirms the importance of
the dryness of the atmosphere found in Sect. 4.2.
Impact of radiation-driven condensation and evaporation on fog
dissipation
The evolution of a fog depends on the competition between processes that
produce liquid water and processes that remove it. Radiative cooling from
the emission of LW is found to be capable of producing 40–70 g m-2 of
liquid water per hour in the absence of a higher cloud layer, which is a
significant source for maintaining the fog LWP and capable of renewing the fog
water in 0.5–2 h (see Sect. 4.2). If a fog layer does not increase its
LWP in spite of the LW cooling, it is because the sink processes for liquid
water amount to a similar magnitude. Sink processes can be heating which
counteracts the cooling: either the radiative heating processes studied in
this paper or other sources of heat, such as entrainment at fog top or
adiabatic heating from subsidence. Another sink process is the deposition of
fog droplets at the surface, which has been found to be important for
limiting fog LWP (Mason, 1982; Price et al., 2015). If the LW cooling
decreases while the sink processes do not, it will shift the LWP balance
towards a reduction, eventually leading to fog dissipation. We found that
CLW increases with fog temperature and decreases with the humidity in
the overlying atmosphere; thus, warm fog with a dry overlying atmosphere
will be more resilient to dissipation than colder fog with a more humid
overlying atmosphere. However, these factors cannot be expected to vary very
fast, so they will probably not be an initiating factor for the dissipation
of a fog layer. In contrast, the appearance of a second cloud layer
above the fog can occur very fast by advection and instantly reduce CLW
by several tens of g m-2 h-1 (Sect. 4.3). This should be
sufficient to shift the balance in LWP in the direction of a fast reduction,
leading to the dissipation of the fog.
In Fig. 10, we explore how a higher cloud affects the radiation-driven
condensation and evaporation in an opaque fog as a function of the OD and base
altitude of the cloud. The impact on CLW (Fig. 10a) increases with the
cloud OD, but beyond an OD of 5 this dependency is no longer very strong.
The effect of the cloud weakens with increasing altitude of the cloud base;
an opaque cloud at 10 km reduces CLW by only ≈ 30 %, while
a cloud at 2 km reduces it by ≈ 100 %. This altitude dependency
is due to the decrease of the temperature of the cloud with altitude due to
the atmospheric lapse rate. At a given cloud OD and altitude, the effects of
ice and liquid clouds are very similar. ESW is also reduced by the
presence of a higher cloud (Fig. 10b), since the cloud absorbs and reflects
the SW radiation that would otherwise be absorbed in the fog. It also
decreases with OD of the cloud, while the altitude matters little. The
decrease with cloud OD continues even for opaque clouds. However, beyond an
OD of 5 it has already been more than halved and it decreases less rapidly.
Since the fog in this case is opaque to LW, the cloud affects Rnet,s
(Fig. 10c) mainly through its reflection of SW radiation, and the change is
not dramatic since the fog is already reflecting most of the SW radiation.
However, for thin fog, Rnet,s is more strongly affected by the cloud,
increasing due to the LW emission by the cloud and decreasing due to the SW
reflection, similarly to how it is affected by fog LWP for thin fog in Fig. 8c
(not shown).
The following conceptual comparison of the fog case on 13 December 2015 (Fig. 4)
and the fog case on 1 January 2016 (Fig. 7) illustrates the possible role of
radiation in determining the different evolutions of these two fog events.
Both occur near midwinter at a temperature of about 5 ∘C, and
both are optically thick with LWP ≈ 100 g m-2 around midday (a).
While the fog cloud dissipates completely right after midday on 1 January 2016,
the fog on 13 December 2015 only slightly reduces its LWP during the afternoon,
from ≈ 70 to ≈ 50 g m-2. Based on the radiative
transfer calculations, on 13 December 2015 CLW is ≈ 50 g m-2 h-1 and varies little, while on 1 January 2016 CLW is reduced from
50 g m-2 h-1 to 15 g m-2 h-1 when the higher cloud appears
(h). The production of liquid water by LW cooling is thus 35 g m-2 h-1 higher in the fog on 13 December 2015 than in the fog on 1 January 2016, and
the sink processes for liquid water must be stronger to dissipate the
former. Conversely, the cloud also reduces the SW heating of the fog: at
midday, ESW is ≈ 5 g m-2 h-1 less on 1 January 2016
compared to 13 December 2015, and the SW reaching the surface is ≈ 40 W m-2 less (f) (which means that the evaporation rate from sensible heat
is likely ≈ 10 g m-2 h-1 less, see Sect. 4.2). However,
this is less important than the difference in CLW. Differences in other
processes probably also play a role in the very different developments of
the two fog events. For instance, the higher wind speed on 1 January 2016
(≈ 3 m s-1, against 1–1.5 m s-1 on 13 December 2015)
could indicate that loss of liquid water by turbulent processes is more
significant on 1 January 2016 and also contributes to its dissipation.
Uncertainty analysis
Rough estimates of the relative uncertainty (in % of the
estimated value) of each radiation parameter (defined in Sect. 2.1) due to
various sources of uncertainty, for thin (LWP < ≈ 30 g m-2) and thick (LWP > 30 g m-2) fog. The
last two rows are relevant when an opaque or semi-transparent cloud
overlies the fog. See text for details.
Uncertainty source
CLW
ESW
Rnet,s (day)
Thin
Thick
Thin
Thick
Thin
Thick
Fog LWP
10–50b
< 10
20–40b
10
10
10
Droplet effective radius
< 5
< 5
20
20
20
30
Neglecting absorbing aerosols
–
–
10–30a
10–30a
< 5
< 5
Temperature profile
5
5–10
–
–
–
–
Humidity profile
5–10
5–10
–
–
–
–
OD of semi-transparent cloud above
20–80c
20–80c
50–80
50–80
30
20
OD of opaque cloud above
< 10
< 10
50
50
30
20
a Uncertainty towards higher values only.
b Uncertainty is highest for the thinnest fog.
c Uncertainty is bigger for low clouds than high clouds.
Effect on ESW (defined in Sect. 2.1) by adding aerosols to the
fog layer on 13 December 2015 at 12 UTC. Urban and continental average aerosols
are defined as in Hess et al. (1998). The aerosol optical depth (AOD) is
spread evenly across the 275 m thick fog layer.
Type of aerosol
Aerosol single scattering albedo at
AOD at 550 nm, at
ESW
aerosol
at 550 nm, at 80 % relative humidity
80 % relative humidity
(g m-2 h-1)
No aerosols
–
0
7.9
Urban
0.817
0.05
11.0
0.15
16.5
Continental average
0.925
0.05
8.8
0.15
11.5
Table 3 provides rough estimates of the relative impact of the uncertainties
in different measured and retrieved input data to the calculated values of
CLW, ESW and Rnet,s. We assume that the uncertainties in
these input data are more significant than the uncertainties related to the
physics of the radiation model itself. The quantitative estimates are based
on the results found in the sensitivity studies and on some further
investigations that will be explained below.
Firstly, uncertainty arises from the estimates of fog optical properties.
The uncertainty in fog LWP is found to be of the order of 5–10 g m-2
when LWP < 40 g m-2 (Appendix A). This corresponds to an
uncertainty in CLW of 10–15 g m-2 h-1 (or 50 %) when
LWP < 20 g m-2 and 3–5 g m-2 h-1 (or 10 %) when LWP
is 20–40 g m-2 (Fig. 8a). ESW is affected both by the fog LWP and
reff (Fig. 8b). The estimated uncertainty in reff of 30 %
(Appendix B) indicates an uncertainty of ≈ 20 % in ESW,
while the LWP uncertainty of ≈ 5–10 g m-2 causes a similar
uncertainty for small LWP, but lower for higher LWP (Fig. 8b). These
uncertainties in LWP and reff will also cause uncertainties of the order of 20–30 % in Rnet,s, based on Fig. 8c. The uncertainties in
Rnet,s are also estimated using the observed and modelled downwelling
fluxes at 10 m, finding an rms error of 0.046 in the SW transmissivity
(translating to 20 W m-2 SW absorption at solar zenith angle of
70∘), and an rms error in the LW absorption of 13.8 W m-2
when LWP < 20 g m-2 and 4.8 W m-2 when LWP is in 20–40 g m-2 (Appendix A). Finally, it should be noted that in the presence of a
higher cloud containing liquid, the partitioning of LWP between the fog and
this cloud will increase the uncertainty in the fog LWP.
Neglecting aerosols in the calculations is another source of uncertainty.
While the scattering by aerosols will be small compared to that of the fog,
additional in-fog heating by aerosol absorption of solar radiation can
significantly increase ESW, since multiple scattering by droplets
increases the probability of absorption (Jacobson, 2012) and since the fog
droplets themselves only weakly absorb in the near infrared. Previous
studies (Chýlek et al., 1996; Johnson et al., 2004) have found that this
increase in absorption is limited to ≈ 15 % in stratocumulus
clouds. However, this effect might be enhanced in fog, since the aerosol
concentration can increase because the boundary layer is shallow and the
fog is in direct contact with the surface. We test the impact of aerosols on
ESW by adding two standard aerosol populations described by Hess et al. (1998)
to the fog layer on 13 December 2015, with relatively low (0.05) and
relatively high (0.15) aerosol optical depth at 550 nm (AOD) (Table 4). The
main difference between the two populations is that the urban aerosols
include more black carbon particles than the continental average aerosols.
Black carbon is responsible for most of the absorption, while its
contribution to AOD is only 20 and 6 % in the two populations. The resulting increase in ESW ranges from ≈ 10 % for continental average aerosols of AOD 0.05 to more than 100 % for
urban aerosols with AOD 0.15 (Table 4). Retrievals of AOD at SIRTA from a
sun photometer, which requires direct sunlight and therefore has sparse
temporal coverage, indicate that AOD is closer to 0.05 than 0.15 most of the
time in October–March. Considering this, and that some aerosols will be
located above the fog, the runs where AOD is set to 0.05 are the most
realistic and show that the increase in ESW due to aerosols is probably
not higher than 10–30 %. However, if black carbon optical depth
increases due to a strong pollution event, ESW could be more strongly
enhanced. To investigate the aerosol effect on ESW in more detail,
measurements of the aerosol chemical composition should be used in addition
to the AOD, since the most important parameter to be estimated is the fraction of AOD
represented by absorbing aerosols. Due to the swelling of non-absorbing water
soluble aerosols, this fraction is also impacted by the relative humidity at
which AOD is measured. The interaction of the aerosols with the fog (e.g.
immersion, wet deposition) can also modify their optical properties
(Chýlek et al., 1996).
CLW has uncertainty related to the temperature and humidity profiles.
As the screen temperature is known, fog temperature is more uncertain in
opaque fog than in thin fog through the temperature difference between
screen level and fog top. Since there is observational evidence that fog
temperature profile is near adiabatic (Sect. 3.3), we assume that the
uncertainty of the fog top temperature is less than 1 ∘C even for very thick
fog, which should impact CLW less than 10 % (Fig. 9a). The MWR
temperature profile has an uncertainty of less than 1 ∘C in the
lower atmosphere (Löhnert and Maier, 2012) and even with significant
uncertainty in the shape of the temperature inversion above the fog, the
sensitivity studies indicate that the impact on CLW is well below 10 % (Fig. 9b–c). The IWV of the MWR has an uncertainty of 0.2 kg m-2
(Sect. 2.2), which corresponds to a very small uncertainty in CLW (Fig. 9d). However, as the vertical distribution of humidity is roughly estimated
with only 2 degrees of freedom (Löhnert et al., 2009), sharp decreases
in humidity, e.g. at the top of the boundary layer, will not be correctly
represented. By analysing a case study in which the humidity profiles from the
radiosonde and the MWR disagree strongly due to such a sharp decrease, we
find an induced bias in CLW of less than 10 % (≈ 4 g m-2 h-1).
We finally turn to the uncertainties related to the properties of the higher
clouds. Firstly, as shown in Sect. 4.3, higher clouds may be undetected by
the radar due to their low reflectivity. This is confirmed from non-fog
conditions, when the ceilometer often detects low stratiform clouds that
significantly affect the downwelling LW at 10 m but that are invisible to
the radar (not shown). For the method of this paper to be reliable in cases
where such thin clouds may occur, a more sensitive radar is required.
According to Stephens et al. (2002), low-level liquid clouds frequently have
reflectivity down to -40 dBZ. The radar should therefore preferably have a
sensitivity of -40 dBZ for all altitudes at which liquid clouds occur (≈ 1–6 km), even though it is probably less critical for mid-level clouds,
which often contain some ice, which enhances their reflectivity. At high
altitudes, thin cirrus clouds may also have reflectivity down to -40 dBZ,
but those with reflectivity below -25 dBZ rarely have OD > 1
(Stephens et al., 2002). Since high-level clouds with OD < 1 do not
impact our results dramatically (Fig. 10), a sensitivity of -25 dBZ at high
altitudes is acceptable.
Given that the higher cloud is detected, its altitude and thus temperature
is readily estimated, so the uncertainty in its radiative impact is mainly
related to its emissivity, which based solely on radar observations probably
cannot be less uncertain than a factor of 2. If we are confident that the
cloud is opaque (OD > ≈ 5), the uncertainty in its
impact on CLW is only a few g m-2 h-1, while a less
opaque cloud will cause uncertainty of several tens of g m-2 h-1 (Fig. 10a). The relative uncertainty in ESW and Rnet,s caused by
higher clouds are smaller than for CLW when the cloud is
semi-transparent, but on the other hand it is also important for thick
clouds (Fig. 10b–c). Finally, it should be noted that cases of fractional
cloud cover also will cause uncertainty, since the radar only sees what
appears directly above, while clouds covering only parts of the sky also
affect the radiation, in particular if they block the direct sunlight.
To conclude, the uncertainty in CLW is small (≈ 10 %) when
the fog is opaque (LWP > ≈ 30 g m-2) and there
is either no higher cloud or the higher cloud is opaque and covers the entire
sky, while a non-opaque fog and/or non-opaque overlying cloud will introduce higher
uncertainty. A similar conclusion can be drawn for ESW, although the
uncertainty in the case of opaque fog/cloud remains higher than for
CLW, since the SW radiation penetrates deeper into the clouds than the
LW cooling.
Conclusions
In this study, the magnitude and variability of the radiation-driven
condensation and evaporation rates in continental fog during midlatitude
winter have been quantified from observations of the atmospheric profile. We
used a radiative transfer code to quantify the immediate tendencies in fog
liquid water due to radiative cooling and heating, before they are modified
by turbulent motions. Based on the results of this study, Table 5 summarises
how different atmospheric conditions will impact the susceptibility of a fog
to dissipation by affecting the radiative processes.
Summary of how the susceptibility of fog to dissipation is affected
by variability in atmospheric conditions through radiative processes.
Positive (negative) means that the fog is more (less) likely to
dissipate due to lower (higher) net production of liquid water by the
indicated radiative process (defined in Sect. 2.1) due to the indicated
atmospheric property. See text for details.
Atmospheric
Less LW-driven
More SW-driven
More surface
property
condensation (CLW)
evaporation (ESW)
heating (Rnet,s)
Clouds above fog
strongly positive
negative
negative
Thin fog LWP (< 30 g m-2)
strongly positive
negative
positive
Absorbing aerosols in fog
–
positive
–
Higher fog temperature
negative
weakly positive
weakly positive
More humidity in atmosphere above fog
positive
–
–
Stronger temperature inversion above fog
weakly positive
–
–
Firstly, the cooling of the fog by emission of LW radiation provides an
important source of liquid water. In opaque fog (LWP > ≈ 30 g m-2) without an overlying cloud layer, this cooling seen in
isolation will cause 40–70 g m-2 h-1 of condensation, which means
that the fog typically can renew its liquid water in 0.5–2 h through
this process. Its variability can mainly be explained by fog top temperature
and the humidity above the fog, with warmer fog below a drier atmosphere
producing more liquid water. In thin fog, the condensation is weaker, and
the estimate is more uncertain due to the uncertainty in LWP of the fog.
The solar radiation absorbed by fog droplets causes a radiative heating of
the fog layer during the daytime. This heating decreases with solar zenith angle
and increases with droplet effective radius and fog LWP. At (winter) midday,
the evaporation rate from this heating can reach 15 g m-2 h-1 in
thick fog, while it is weaker for thin fog (0–5 g m-2 h-1), based
on absorption by pure liquid droplets only. The role of absorbing aerosols
in fog is not extensively studied in this paper, but our results indicate
that it increases the absorption of solar radiation by 10–30 % in a
typical air mass at SIRTA. This aerosol absorption effect can be worth
investigating in more detail using observations of aerosol chemical
composition, as it could be stronger during pollution events. The important
parameter is the optical depth of the absorbing aerosols, which might be
only a small fraction of the total aerosol optical depth.
The radiative heating of the surface in daytime is more important in thin
fog than thick fog, and it is found to vary from 40 to 140 W m-2 at a
solar zenith angle of 70∘ from the thickest to the thinnest fog
studied here. In situ observations indicate that at least 20–40 % of
this energy is transferred to the fog as sensible heat. Since 1 W m-2
heating of the fog corresponds to an evaporation rate of ≈ 0.7 g m-2 h-1,
this process can cause an evaporation rate of up to 30 g m-2 h-1 when the sun is high and thus is likely to be very important for
reducing the LWP of the fog. A more detailed investigation of the surface
energy budget during fog could lead to a more precise quantification of the
evaporation of fog by sensible heat.
The appearance of a second cloud layer above the fog strongly reduces the LW
cooling of the fog, especially a low cloud. The LW-induced condensation rate
can be reduced by 100 % if the low cloud is optically thick, and even by
more than 50 % for a semi-transparent cloud of optical depth 1. The
presence of an overlying cloud can therefore be a determining factor for fog
dissipation as the fog will then have much of its production of liquid water
cut off. In cases in which no cloud appears above the fog it is unlikely that
the LW cooling can change fast enough for it to be a determining factor for
the dissipation. The detection of clouds above the fog with the cloud radar
is therefore crucial for analysing the impact of radiative processes on fog
dissipation. To detect all important clouds above the fog, the radar
sensitivity must be sufficient to capture thin water clouds, requiring a
sensitivity of -40 dBZ in the lower troposphere, and optically important
high clouds, requiring a sensitivity of -25 dBZ in the upper troposphere.
The current generation BASTA radars, which have a sensitivity of -40 dBZ up to 4 km and -30 dBZ at 10 km, should be able to detect most of the important
clouds.
The results were obtained from seven observed fog events at the SIRTA
observatory (Table 2) as well as sensitivity studies. Since our methodology
treats radiative processes separately from dynamical processes, these results
should be applicable to all fog occurring in the range of temperature and
integrated water vapour (IWV) of the events in this study, which cover the
range (-1)–14 ∘C and 6–28 kg m-2. Thus it is a significant
sample of midlatitude winter conditions. The same methodology should in
principle be applicable to other climate zones as well, although ice
crystals in fog occurring in very cold conditions would require a different
retrieval method for fog optical properties due to the larger particle sizes
(Gultepe et al., 2015). For pure liquid fog, the methodology should be
generalisable to all fog types, as the radiative processes are not directly
dependent on the fog formation mechanism.
The results of this paper have been obtained from the use of multiple
instruments, in particular cloud radar, ceilometer and microwave radiometer.
If these measurements can be rapidly transferred and processed, the
methodology of this paper could be applied to quantify the radiation-driven
condensation and evaporation rates in the fog in real time to be used to
support short-term fog forecast. In order to be less instrumentally
demanding and thus more applicable to other sites, a simplified method using
only the cloud radar and ceilometer could be envisaged, supplemented by
screen temperature and visibility measurements and IWV from a GPS. Even
though LWP will be less accurately estimated without the microwave
radiometer, this method would still be able to capture the most important
factors: higher cloud presence, fog vertical extent, fog temperature and
IWV. For the efficient application of this methodology, a generalised
retrieval algorithm of the (approximate) SW and LW emissivity of all clouds
above the fog using cloud radar only would be very useful. Such a retrieval
method could be developed by relating cloud altitude, thickness and reflectivity to
satellite products of cloud optical depth.
The methodology of this paper could also be used to verify radiation schemes
in numerical weather prediction models during fog and as a reference when
studying how the presence of multilayer clouds affects the prediction of fog
life cycle by these models.