Fog prediction at Lisbon Airport using a one

Meteorol. Appl. 8, 497–505 (2001)
Fog prediction at Lisbon Airport using a
one-dimensional boundary layer model
João Teixeira1 and Pedro M A Miranda, Centro de Geofisica and Department of Physics,
University of Lisbon, Portugal
1 Present affiliation: UCAR Visiting Scientist at the Naval Research Laboratory, Monterey,
California, USA
Fog is the most important physical process that reduces surface visibility, having a major negative impact on air
traffic. In this study, a one-dimensional boundary layer model was developed in order to predict the occurrence
and intensity of fog. The model uses a selection of parameterisations, suggested by different authors, and uses the
finite element method for the vertical discretisation of the equations. The 1977 Cabauw fog event is used to
validate the model and eight fog events at Lisbon Airport are simulated. The validation shows that the model is
able to predict realistically the fog’s onset, growth and dissipation. The fog forecasts at Lisbon Airport are, in
general, quite reasonable, and a simple simulation of a fog event, where advection played a fundamental role, also
gives realistic results.
1. Introduction
Reduced visibility at and near the surface has always
been one of the main concerns in aeronautical meteorology. This problem seriously affects the taking-off
and landing of aircraft. Reduced visibility at airports
means that flights have to be delayed or diverted, which
can result in heavy financial losses for the aviation
industry.
Among the different atmospheric processes that reduce
visibility at the surface, fog is probably the most important. According to WMO (1966), fog is a suspension of
water droplets or ice in the atmosphere that reduces
horizontal visibility at the surface to less than 1 km.
From a physical point of view, the reduction of visibility associated with fog is the result of the dispersion of
visible radiation by water droplets or crystals and
depends not only on the total amount of condensed
water per volume, but also on the detailed distribution
of drop sizes.
Fog forecasting is usually performed by means of
empirical rules or statistical methods (e.g. Tremant,
1989). Although new cloud schemes in global (Tiedtke,
1993) or regional (Zhao & Carr, 1997) Numerical
Weather Prediction (NWP) models allow the existence
of fog, these models are not yet able to forecast fog
with a reasonable degree of accuracy, mainly due a lack
of resolution (horizontal and vertical) and adequate
parameterisations. Some new studies (Teixeira, 1999),
however, seem to indicate the possibility of improvements in this respect.
Reiff (1987) presents a review of operational models to
forecast fog, and a review on numerical fog studies in
general can be found in Bergot & Guedalia (1994).
Most numerical studies of fog have used one-dimensional (1D) or two-dimensional (2D) boundary layer
models, initially with a relatively simplified physics
(Zdunkowksi & Barr, 1972; Brown & Roach, 1976),
but with more elaborate physics in recent years
(Musson-Genon, 1987; Turton & Brown, 1987; Bott et
al., 1990). While there are new developments in threedimensional (3D) mesoscale studies of boundary layer
clouds and fog (e.g. Golding, 1993; Ballard et al., 1991),
1D models – and in particular one-column versions of
climate or NWP models – have been increasingly used
to develop and validate fog and stratus parameterisations (e.g. Bretherton et al., 1999; Duynkerke et al.,
1999; Teixeira, 1999). As with other boundary layer
processes, which are generally assumed to be driven by
the large-scale flow and thermodynamics, fog is an
obvious candidate for parameterisation. Another good
reason for the continuing interest in these simple
models is the fact that the ‘physical packages’ of
global models are essentially 1D, making the development and validation of one-column models an important step in the improvement of weather and climate
simulations.
At Lisbon Airport fog is a relatively common and
important event, with an average of 28 days per year of
reported fog. According to the local forecasters, it
tends to occur not only as pure radiation fog but also
associated with particular advection patterns, justifying
the hypothesis that, in some cases, it is generated over
the Tagus estuary and then advected to the airport area.
In order to better understand and predict this type of
event, the Portuguese Institute of Meteorology
installed two automatic weather stations for fog detection in 1992. These stations were positioned between
497
J Teixeira and P M A Miranda
the Tagus estuary and the airport and were kept in continuous operation between June 1992 and December
1993. Some of those data are analysed in this paper.
Prior to this work, the problem of forecasting fog at
Lisbon Airport had already been tried with statistical
methods. It was the main purpose of this work to
develop and apply a 1D boundary layer model to simulate and study fog at Lisbon Airport. A version of this
model has already been used as the atmospheric boundary layer component of a wind-wave prediction system
(Teixeira et al., 1995). In section 2 the model is
described. A simple validation of the model is presented in section 3. The results from the simulation of
some fog events at the Lisbon Airport are presented in
section 4. In section 5 a simulation with a simple advection pattern is presented in order to try to simulate a
fog event that was generated over the Tagus estuary
and then advected to the airport area.
2. Model description
The 1D boundary layer model used in the present
study has prognostic equations for the following mean
variables: horizontal wind components, liquid water
potential temperature and total specific humidity. A
prognostic equation for the turbulent kinetic energy is
also used for the turbulence closure. Some 1D studies
of fog (e.g. Musson-Genon, 1987) use models with
rather elaborate short-wave radiation schemes. One of
the main objectives of this work is to show that a simpler parameterisation of the effects of solar radiation
can be used with a good degree of accuracy. The interaction between fog droplets and solar radiation is, in
the present case, parameterised using flux profiles of a
simple prescribed shape proposed by Hanson & Derr
(1987). The other main difference between the present
model and other published material is the use of linear
finite elements for the vertical discretisation of the
prognostic equations.
2.1. Model equations
For a moist atmosphere it is convenient to use thermodynamic variables that are conserved during phase
transitions, such as the liquid water potential temperature (θ1) and the total specific water content (qt) given
by:


L
θ1 = θ1 − v q1 
c pT 

qt = q + ql
where Lv is the latent heat of vaporization, cp is the specific heat of air at constant pressure, T is the temperature, q is the specific humidity and ql is the liquid water
498
content. The reader is referred to Betts (1973) and
Deardorff (1976) for details.
Under horizontally homogeneous conditions, and
assuming incompressibility, the momentum, water
conservation and thermodynamic equations can be
written in the standard form:
( )
∂u
∂
=−
w′u′ + f ( v − Vg )
∂t
∂z
( )
∂v
∂
=−
w′ v′ − f (u − Ug )
∂t
∂z
(
)
(
)
∂G
∂
∂qt
+ Aqt
=−
w ′q t ′ +
∂z
∂z
∂t
∂G 
∂ θ1
∂
θ  1 ∂F
+L
=−
w′θ 1 ′ −

 + Aθ1
∂z 
∂z
∂t
T c p  ρ ∂z
where the bar denotes mean quantities and the prime
refers to the fluctuations in the quantities, u and v are
the horizontal wind components, w is the vertical wind
component, Ug and Vg are the geostrophic wind components, f is the Coriolis parameter, F is the radiation
flux and G is the drop settling flux. For convenience, let
ψ stand for any of the prognostic variables (u, v, qt or
——
θ1), then (w′ ψ′ ) is the vertical component of the turbulent flux of property ψ, and Aψ is the horizontal advection of property ψ.
As can be noted in the previous equation set, horizontal homogeneity is only strictly assumed for all turbulent terms and for the advective terms in the momentum equations. A horizontal pressure gradient is
implicit in the geostrophic wind terms and some room
is given for horizontal advection of temperature and
humidity, although those terms must be given, or computed from the known variables. As a consequence, 1D
models can only deal with either radiation fogs or with
very simple advection fogs, where the advective terms
can be parameterised.
The model includes a fifth prognostic equation for the
mean turbulent kinetic energy (TKE), which is written
as (e.g. Stull, 1989):
∂e
∂ 
w ′ p′ 
∂u
∂v g
w′θ ′v − ε
= −  w ′e ′ +
− w′ v′
+
 − w′u′
∂t
∂z 
ρo 
∂z
∂z To
where θ′v is the fluctuation of the virtual potential temperature, p is the pressure and ε represents the TKE
dissipation.
Fog prediction using a one-dimensional boundary layer model
2.2. Parameterisation schemes
(a) Turbulence
The model follows the K-diffusion approach to relate
the sub-grid turbulent fluxes and the dissipation ε with
the mean variables of the model. The crucial point in
the closure scheme is the establishment of a relationship between the diffusivity coefficient and the TKE, in
what is sometimes referred as a 1.5 order closure (e.g.
Therry & Lacarrère, 1983).
The mixing length and the dissipation length are computed using the diagnostic relations proposed by
Therry & Lacarrère (1983), as used in Musson-Genon
(1987). The height of the boundary layer is considered
to be the level where the value of TKE is 0.01 m2 s–2.
(b) Radiation
The broad band flux emissivity method (Stephens,
1984) is followed for the parameterisation of long-wave
radiation. Inside the fog the emissivity includes contributions from water vapour and liquid water droplets.
For the liquid water emissivity a relation proposed by
Stephens (1978) is used.
As mentioned before, we follow a simple procedure
suggested by Stull (1989) to parameterise the interaction between fog droplets and solar radiation, in contrast with other models that use more detailed schemes.
The solar radiation flux profile inside the fog is prescribed, following Hanson & Derr (1987), as a combination of exponential functions. This profile is ultimately based on the values of the cloud albedo, cloud
absorption and the downward solar flux at the top of
the fog. We follow the relations suggested by Manton
(1980) between the cloud albedo, absorption and the
liquid water path.
(c) Drop settling
In spite of the fact that fog droplets rarely exceed 20
µm, Brown & Roach (1976) found that drop settling
can play a significant role in the evolution of fog. This
is due to the small updraft vertical velocity inside radiation fog. In order to represent drop settling, the parameterisation used by Brown & Roach (1976) is followed; the flux G is parameterised as G = Wg ql where
Wg is the mean settling vertical velocity that is linearly
related to the liquid water.
(d) Sub-grid scale condensation
The model uses a statistical sub-grid scale condensation
scheme based on ideas initially developed by Sommeria
& Deardorff (1977) and Mellor (1977). The cloud cover
and the liquid water are diagnosed from the mean values of the conserved variables total water and liquid
water potential temperature, the variance of these vari-
ables and a distribution function. The distribution
function used is the one proposed by Bougeault (1981).
This distribution function has already been used successfully by Musson-Genon (1987) in a 1D boundary
layer model of fog.
2.3. Boundary conditions and numerical schemes
At the model’s lower boundary, the mean variables and
the TKE are imposed at z0. At the upper boundary (z =
2 km) the fluxes of the mean variables and of TKE are
set to zero, except for liquid water potential temperature, for which a vertical gradient of 0.0035 K m–1 is
imposed, a typical stratification above the boundary
layer.
It is important to note that in this study the surface
boundary conditions are not predicted. It is clear that
to produce operational fog forecasts, the surface conditions must be predicted as well. In any case, as a first
approach to the problem, we think that isolating the
atmospheric modelling problem from the surface and
soil, by imposing the observed values of surface parameters in our simulations, is an adequate way to pursue
this study of fog.
The spatial discretisation of the equations uses a finite
elements method, with linear base functions. This
method has shown good results in previous studies
with 1D boundary layer models (e.g. Mailhot & Benoit,
1982). The finite elements method presents some general advantages, when compared with the finite differences method (for a review, see Temperton, 1991). Two
sets of base functions are used in a staggered grid. The
first set includes the mean variables and the forcing
functions (geostrophic wind, advection), whereas the
second set includes the turbulent fluxes and the TKE.
In all experiments shown, both grids are regularly
spaced in the vertical. The time discretisation of the
equations is done implicitly, following Richtmeyer &
Morton (1967).
3. Validation experiment
In order to validate the model, a fog event that occurred
at Cabauw in the Netherlands, on 3 August 1977, was
simulated. This particular fog situation has already
been studied using 1D boundary layer models developed by Grandin (1983) and Musson-Genon (1987)
(hereafter referred to as G83 and M87, respectively).
All the data used in this validation study was taken
from G83 and M87.
The data is described in G83 and M87, and consists of
the following:
•
vertical profiles of the mean variables, taken as initial conditions at 00.00 UTC, 3 August 1977;
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J Teixeira and P M A Miranda
•
•
hourly series of surface values of the mean thermodynamic variables; and
hourly series of the surface geostrophic wind and
hourly series of the temperature wind in the layer
0–200 m.
The initialisation of TKE is done using a ‘spin-up’ procedure (e.g. Burk & Thompson, 1982). The geostrophic
wind in the layer 0–200 m is calculated using the thermal wind relations and, above this layer, the
geostrophic wind is considered constant. The temperature advection is also determined, for the layer 0–200
m, using the thermal wind values.
The observed temperature at 0.45 m height is taken as
the model surface temperature. It starts with a value of
about 15 °C at 00.00 UTC, decreasing to a minimum
value of about 11 °C just after 03.00 UTC. After that,
the surface temperature, increases almost linearly to
just over 16 °C at 09.00 UTC. The simulation uses a
time step of 60 s and a vertical grid spacing of 20 m. To
relate the simulated liquid water content with visibility,
a diagnostic relation suggested by Kunkel (1984) is
used:
VIS = −
ln (0.02)
β
where VIS is the visibility and β = 144.7(ρq–-1)0.88.
The time evolution of the simulated visibility profile is
presented in Figure 1(a), which can be compared with
Figure 1(b) showing observed visibilities. The analysis
of the figures shows that the fog’s generation and initial
growth (until around 04.00 UTC) is reasonably well
simulated. However, the minimum of visibility (maximum of liquid water) observed around 04.30 UTC and
the weakening of the fog between 05.00 and 06.00 UTC
are not well simulated, either by the present model or
by M87 and G83. On the other hand, the model predicts local minimum values of visibility (<60 m) a few
metres below the fog’s top, in agreement with observations, but not necessarily at the right time.
There is a slight overestimation of the fog’s depth.
However, this overestimation rarely exceeds 20 m,
which is the value of the model’s vertical resolution. So
we do not consider this to be a serious problem of the
model.
The fog dissipation period is again reasonably well simulated by the model. This result shows that the simplified parameterisation scheme, which was used for the
short-wave radiation effects, is able to generate a realistic simulation of the fog’s dissipation stage. It can be
said that, in general, the model performs reasonably
well in simulating this particular fog event.
It is interesting to note that these results, although far
500
Figure 1. Vertical profile of visibility for the fog event at
Cabauw. (a) Numerical simulation of evolution; contours are
60 and 300 m. (b) Observed evolution; contours are 30, 60 and
300 m. Courtesy of Luc Musson-Genon.
from perfect, seem to compare better with the observations, in terms of fog onset and evolution, than LES
(Large Eddy Simulation) model results from a study of
the same case (Nakanishi, 2000). It is not our intention,
however, to claim that a 1D model can represent the
general properties of fog in a more accurate way than
LES models. But the fact that the 1D model’s visibility
looks more realistic than the LES visibility, shows the
difficulty and complexity of fog simulation and prediction. It also suggests that 1D fog prediction can still be
a very viable option.
In order to assess the role of the different processes on
the fog’s evolution, the temperature tendencies were
analysed. The horizontal advection tendency is constant during the simulation and equal to –0.18 K day–1.
Until the onset of fog the cooling tendencies close to
the surface from radiation and turbulent mixing are
almost constant in time and with values of the same
magnitude of the advection values. After the fog’s
onset, the liquid water increases and as a consequence
the long-wave cooling starts to play a major role, with
large values close to the fog’s top as is typical of stratiform boundary layer clouds. After sunrise, the surface
temperature increases and the solar radiation starts to
penetrate into the cloud, warming the fog. These effects
together with the long-wave cooling at the top produce
a more intense turbulent mixing that contributes to an
intensification of the fog event for a couple of hours,
until it finally dissipates the fog.
Figure 2 shows the evolution of the profiles of temperature and specific humidity. These profiles seem to be
related, as expected, since close to the surface the
atmosphere is in a quasi-saturated state. At 03.00 UTC
Fog prediction using a one-dimensional boundary layer model
a pronounced surface inversion can be seen on the temperature profile, characteristic of the onset of fog. At
06.00 UTC, a 120 m mixed layer, in both T and q, has
been formed. If this is compared with the results shown
in Figure 1 it is possible to identify this mixed layer as
the fog itself. The mixed layer is a characteristic of deep
radiation fog (e.g. Brown, 1987; Stull, 1989). The inversion is now located at the fog’s top, where a strong
radiative cooling process is active. At 09.00 UTC the
temperature profile becomes unstable due to the solar
heating of the surface and the consequent generation of
turbulence. In general, the simulated structure of both
T and q is quite realistic when compared with the
observations.
The overall behaviour of the model in predicting
boundary layer properties and the interaction with the
surface are discussed in Teixeira et al. (1995). The validation result shown here is just an example of what the
model is able to achieve in terms of fog simulation. A
much more detailed validation of the model is discussed in Teixeira & Miranda (2000), where the model’s
sensitivity to the parameterisation of some different
physical processes is also studied.
4. Fog events at Lisbon Airport
After the validation, the model is used to simulate eight
cases of fog that occurred at Lisbon Airport, which
correspond to all cases of dense fog observed in the
chosen winter. The data used in these simulations consisted of the following:
•
•
•
vertical profiles of the initial conditions for the
–
–, q–) and initial surface presmean variables (θ, u–, v
sure, p, at 00.00 UTC for each one of the eight
cases, taken from radiosondes launched at Lisbon
Airport;
hourly series of the surface values of the variables
mentioned above; and
geostrophic wind at the surface, 850 hPa and 700
hPa estimated from synoptic charts at 00.00 and
12.00 UTC and linearly interpolated in the vertical
and in time.
The synoptic charts were also used to evaluate the
advection of temperature, using the thermal wind relation.
All simulations use a time step of ∆t = 60 s and a vertical grid spacing of ∆z = 20 m. For each case, three different sets of simulations were performed, in order to
study the sensitivity of the results to (a) the inclusion of
horizontal advection of temperature and (b) to the
lower boundary condition for moisture.
The results are summarized in Table 1. In general, the
results are reasonable. In the default simulations (no
advection of temperature, no surface saturation
Figure 2. Numerical simulation of the Cabauw fog event.
Vertical profiles of (a) temperature and (b) specific humidity at
00.00, 03.00, 06.00 and 09.00 UTC.
imposed) and when the advection of temperature is
included, the model is able to predict four of the eight
cases of observed fog. When the saturation of the surface moisture is imposed, the model is able to predict
seven of the eight cases of fog. The results are not very
sensitive to the imposed temperature advection. It
could be argued that this is the result of the method
used for the evaluation of thermal advection, which disregards mesoscale features, but it is consistent with the
hypothesis that all those cases correspond to events of
radiation fog.
In Figure 3 the evolution of the simulated and observed
visibility are shown for the two best cases, occurring on
21 January and 2 December 1989. The model results are
quite reasonable, when compared with the observations. In Figure 3(a), the evolution of the simulated visibility is quite remarkable, when compared with the
observations. This is true for most of the time, but after
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J Teixeira and P M A Miranda
Table 1. Summary of the results of the fog prediction experiments at Lisbon Airport (see text for details). ‘Yes’
means that fog was predicted by the model in that run.
Case
15 November1989
2 January 1989
4 January 1989
21 January 1989
1 December 1989
2 December 1989
5 January 1989
7 February 1990
Control simulation
Temperature advection
Saturated surface
No
No
Yes
No
Yes
Yes
Yes
No
No
No
No
No
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
that, and during the fog evolution, the model results are
quite realistic. Even the dissipation stage is simulated in
a reasonable way, although with a certain delay. These
good results suggest that, in some situations, the use of
a 1D model might be enough to achieve a good fog
forecast at Lisbon Airport.
A more detailed analysis of all simulations emphasises
the importance of the schemes used to deal with water
and temperature fluxes into the model’s domain. It is
clear that to achieve a good fog forecast, a model to
forecast the surface conditions must be introduced and
that horizontal inhomogeneities must be taken into
account. A simple example is shown in the following
section.
5. Simulation with a simple local advection
pattern
It has been known for some time that the Tagus estuary is a possible ‘source’ for many cases of fog observed
at Lisbon Airport (see Figure 4). In order to study this
situation, and to be able to forecast (nowcast) fog at
Lisbon Airport, the Portuguese Meteorological Institute installed in the winter of 1992/93 a couple of automatic fog detection stations between Lisbon Airport
and the Tagus estuary.
Figure 3. Comparison between observed and simulated visibility values for (a) case 1 (21 January 1989) and (b) case 2 (2
December 1989) of fog at Lisbon Airport.
10.00 UTC the model is not able to simulate the dissipation of fog in a realistic way.
In Figure 3(b) there is a discrepancy between the model
and the observations at 00.00 UTC, because the
observed fog started already before midnight, while
there is no fog in the initial state of the model. After
502
A good example of the output of these stations can be
found in Figure 5; this shows the time evolution of the
measured visibility at both stations between 00.00 UTC
and 06.00 UTC for 9 January 1993. In both stations the
visibility changes rather abruptly and fog is observed at
Station 1 more or less one hour earlier than at Station 2.
Horizontal advection is thus the simpler explanation
for the observed behaviour.
The values measured at the stations provide some helpful information in order to incorporate a simple horizontal advection term for the total water content in the
1D model:
 ∂qt 
∆q
= −C t


∆x
 ∂t  adv
Fog prediction using a one-dimensional boundary layer model
Figure 6. Comparison between observations (smoothed with
a moving average filter) and model results at Station 1 for the
advection fog case (9 January 1993), from 00.00 to 06.00 UTC.
Figure 4. Location of Lisbon Airport and the Tagus estuary.
In this case, the introduction of a simplified water
advection helps to solve the problem of estimating the
horizontal inhomogeneities of the thermodynamic
variables. It should be noted, however, that this is a
very crude way of estimating the horizontal advection
terms and that it has been used here only as a test.
6. Conclusions
Figure 5. Observed visibility at the two automatic fog stations
near Lisbon Airport in the advection fog case (9 January
1993), from 00.00 to 06.00 UTC.
where ∆x is the distance between the stations, ∆qt =
1g kg–1 and C = ∆x/∆tadv is the ‘advection’ velocity
(with ∆tadv ≈ 1 h, which is the approximate time lag
between the arrival of fog at Station 1 and Station 2).
This advection term was introduced into the 1D model,
in the first 100 m above the surface and until the fog’s
onset, in an experiment that was set up to simulate the
fog evolution at Station 1. In this study a time step of
∆t = 30 s and a grid spacing of ∆z = 4 m were used.
Figure 6 shows the time evolution of the measured and
simulated visibility at Station 1. The patterns of variation of the simulated and measured visibility are
remarkably similar. The most striking feature is the
arrival of fog, almost at the same time, both in the
observations and in the simulations. Also, after the
arrival of fog at the station, the simulated values of visibility are very close to the observed ones. In fact, the
difference between the simulated and measured values
of visibility, after the fog arrival, is typically never
greater than 30 m.
In this study, a 1D boundary layer model was developed, in order to study fog at Lisbon Airport. The 1D
model has prognostic equations for the mean quantities
(horizontal wind components, liquid water potential
temperature and total specific water) and for the mean
turbulent kinetic energy, which is used to parameterise
the turbulent fluxes of the mean variables. The model
uses simple parameterisations of the effects of solar and
long-wave radiation, with a good degree of accuracy.
The equations are discretised using the linear finite elements, in a staggered grid.
The validation study showed that the fog’s onset and
initial growth is reasonably well simulated. The model
predicted minimum values of visibility a few metres
below the fog top in agreement with observations. The
fog dissipation stage was again reasonably well simulated by the model. The main conclusion from the validation is that the use of a simple solar radiation parameterisation scheme is probably good enough for the
forecast of fog dissipation.
The model was used to simulate eight cases of fog that
occurred at Lisbon Airport. The fog forecast results
were reasonable and not very sensitive to the imposed
temperature advection. The analysis of the time evolution of the simulated and observed visibility for the two
best simulations suggests that, in some situations, the
use of a 1D model might be enough to achieve a good
fog forecast.
In order to study fog events that are generated over the
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J Teixeira and P M A Miranda
Tagus estuary and then advected to the airport area, a
further case was analysed, using data from two automatic fog detection stations located between the airport
and the estuary. In both stations the visibility was
found to change abruptly, allowing for the evaluation
of a mean propagation speed of the fog ‘front’, which
was used to incorporate a simple horizontal advection
term for the total water content in the 1D model. An
analysis of these 1D fog simulations at Station 1
showed a remarkable similarity between the simulated
and measured visibility. The methodology followed in
the present study is rather simple and cannot account
for all features of the process of onset and dissipation of
fog. In many cases, namely in the area of Lisbon,
mesoscale processes are dominant in the definition of
the horizontal advection of atmospheric properties and
it would be impossible to address the problem without
a full 3D mesoscale model. While these models are
available, they are still much more difficult to use for
operational boundary layer prediction, both for computational and data initialisation reasons, leaving some
space for the practical use of simpler models, like the
one presented in this paper.
In any case, in order to produce operational fog forecasts with the 1D model presented in this paper, we will
need to be able to predict the surface boundary conditions, by coupling the model with a surface scheme,
and the large scale forcing. This can be achieved by
coupling the 1D model with the output of a global or
limited-area NWP model, much in the same way as
done by Musson-Genon (1989).
Acknowledgements
The authors acknowledge the contribution of the
Portuguese Institute of Meteorology, and in particular
of João Jacinto Ferreira and Fernanda Tavares, for providing the data used in this study and for their support.
We also would like to thank A. Beljaars, H. Wessels
and L. Musson-Genon for providing information concerning the validation fog case. Comments made by
two anonymous referees are also gratefully acknowledged. This study was accomplished with the financial
support of the Portuguese Foundation for Science and
Technology under Grant 3/3.2/EMG/1968/95.
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