This is the first paper to investigate the relationship
between the shape of the scattering phase function of cirrus and the
relative humidity with respect to ice (RH
Cirrus or pure ice crystal cloud usually forms at temperatures of less than
about
The role of ice supersaturation in forming complex ice crystals has most
recently been studied by Bailey and Hallett (2009), Pfalzgraff et al. (2010), Ulanowski et al. (2013) and Magee et al. (2014). In the cloud
chamber study by Pfalzgraff et al. (2010), it was reported that surface
roughness was at its greatest when supersaturations were near zero.
Moreover, Walden et al. (2003) observed surface roughness on precipitating
ice crystals under conditions of near-zero supersaturation at the South
Pole. Other laboratory studies by Bacon et al. (2003), Malkin et al. (2012)
and Ulanowski et al. (2013) show that ice crystals, under ice-supersaturated
conditions, can become surface-roughened through the development of
prismatic grooves or dislocations on the ice crystal surface. However, as
pointed out by Bacon et al. (2003) and others, the temperature and RH
Theoretical light-scattering studies by (Schmitt and Heymsfield 2010; Macke
et al., 1996a; Macke et al., 1996b; Yang and Liou, 1998; Yang et al., 2008;
van Diedenhoven, 2014b) have shown that the processes of surface roughness and
air inclusions within ice crystals can profoundly alter their scattering
phase functions. As surface roughness increases, the 22 and 46
Radiometric angle-dependent observations of the transmitted and reflected
intensities from cirrus tend to suggest that featureless phase functions
best represent those measurements obtained from below and/or above the cloud
(Foot, 1988; Baran et al., 1999, 2001; Doutriaux-Boucher et al., 2000; Jourdan et al., 2003; Baran, 2012; Cole et al., 2013; Cole et al.,
2014; and references contained therein). Aircraft-based instruments such as
the Polar Nephelometer (PN), which is described by Gayet et al. (1997), have
been used to measure the angular scattered intensity of naturally occurring
single ice crystals at scattering angles between about 15 and
162
The relationship between the scattering properties of atmospheric ice and the physical state in which the ice resides is important to explore, as this may lead to an improvement in the parameterisation of ice optical properties in climate models. Such an improvement can only come about through a deeper understanding of how the growth of ice crystal complexity is related to the atmospheric state. This relationship could then be used to predict appropriate ice-scattering properties for some given atmospheric state, rather than assuming the same scattering properties for all states that are found in a climate model,which is what is generally done in present-day studies. The most recent report of the Intergovernmental Panel on Climate Change (IPCC, 2013) stated that the coupling between clouds and the atmosphere was one of the largest uncertainties in predicting climate change. This uncertainty may well be reduced if appropriate parameterisations could be found between ice crystal scattering properties and the atmospheric state.
In this paper, for one case of mid-latitude cirrus, the relationship between
the scattering phase function and RH
A high-resolution composite MODIS image of the
semi-transparent cirrus case that occurred on 25 January 2010
located over north-east Scotland. The latitude and longitude grid is
superimposed on the image showing latitude 58 to 60
The conditions required for this paper are that the cirrus should be sufficiently optically thick to allow for discrimination between various randomisations of the ensemble model using PARASOL retrievals, the aircraft and satellite should be coincident, and there should be no underlying cloud or broken cloud fields. It is practically very difficult to obtain all these necessary conditions at the same time. The cirrus case occurred on 25 January 2010 off the north-east coast of Scotland, which is shown in Fig. 1. The figure shows a high-resolution MODerate Imaging Spectroradiometer (MODIS) composite image (Platnick et al., 2003) of semi-transparent cirrus obtained at 13:30 UTC. The semi-transparent cirrus can be clearly seen around the north-east coast of Scotland, whilst further to the east, lower level water cloud underlying the cirrus can be seen. At about the same time as the image shown in Fig. 1 was taken, the FAAM (Facility for Airborne Atmospheric Measurements) BAe-146 aircraft was measuring the same high-cloud field.
The FAAM aircraft is an atmospheric research facility which is jointly owned by the Met Office and the National Environment Research Council (NERC). The cirrus case shown in Fig. 1 was sampled by the aircraft as part of the “Constrain” field programme (Cotton et al., 2013). In this paper, one case from the Constrain field programme is presented. There were several other Constrain cirrus cases, but these did not meet the conditions necessary for this paper. This is because the other cases were either optically too thick, there was no coincidence between PARASOL and the aircraft, or there was substantial underlying cloud.
For the case presented in this paper, the aircraft sampled the cirrus
between the latitudes of about 58 and 59
The nadir-pointing lidar operates at 0.355
The ARIES instrument is fully described in Wilson et al. (1999), but,
briefly, it is a modified Bomem MR200 interferometer that measures infrared radiances
between the wave numbers of 3030.303 and 500 cm
The RH
The model is non-hydrostatic and employs the semi-Lagrangian advection scheme.
In terms of model physics, the model is broadly comparable to the version of
the Met Office operational UKV forecasting system that was used
operationally until the autumn of 2011 (Lean et al., 2008). However, in an
attempt to represent the simulated cloud system as well as possible, the
following changes were made to the ice cloud microphysics. Firstly, the ice
particle size distribution (PSD) parameterisation was changed so as to be
consistent with the PARASOL radiative retrievals (see Sect. 3 for
details). Secondly, the mass–diameter relation of the ice crystals was taken
directly from the Constrain in situ measurements (Cotton et al., 2013), and
is therefore a “best estimate” of this property for the simulated cloud
system. For this paper, the NWP model was initialised at midnight on
25 January 2010, and the RH
At about the same time as the NWP model RH
The ensemble model as a function of ice crystal maximum
dimension,
The model of ice crystals used in this study was developed by Baran and
Labonnote (2007), and it is referred to as the ensemble model of cirrus ice
crystals. The model has previously been fully described by Baran and
Labonnote (2007), but a brief description is given here, and the model is
shown in Fig. 2. The model consists of six elements. The first element is
the hexagonal ice column of aspect ratio unity, and the second element is
the six-branched bullet rosette. Thereafter, hexagonal monomers are
arbitrarily attached as a function of ice crystal maximum dimension,
forming 3-, 5-, 8- and 10-monomer polycrystals. The ensemble model
has previously been shown to predict the volume extinction coefficient, ice
water content (IWC), and column-integrated IWC, as well as the optical depth
of mid-latitude and tropical cirrus to within current experimental
uncertainties (Baran et al., 2009, 2011a, 2013).
Moreover, the model also replicated 1 day of PARASOL cirrus observations
of total reflectance, between the scattering angles of about 60 and
180
The ensemble model area ratio, A
To demonstrate why the ensemble model can replicate in situ estimates of the
volume extinction coefficient to within current experimental uncertainties,
here the model predictions of the area ratio are compared against in situ
estimates of naturally occurring area ratios. The area ratio, A
To compare members of the ensemble model against the in situ-derived
estimates of A
In this study, the PSD assumed is the moment estimation parameterisation of
the PSD developed by Field et al. (2007), hereinafter referred to as F07.
The F07 parameterisation relates the second moment (i.e. IWC) to any
other moment via a polynomial fit to the in-cloud temperature. The
parameterisation is based on 10 000 in situ measurements of the PSD, and the
measurements were filtered using the method of Field et al. (2006) to reduce
artefacts of ice crystal shattering at the inlet of the microphysical probes
(Korolev et al., 2011), and the PSD was truncated at an ice crystal maximum
dimension of 100
Incident unpolarised sunlight is assumed to irradiate a collection of randomly oriented non-spherical particles, each of which possesses a plane of symmetry. The single-scattering properties that are applied to the PARASOL measurements are calculated using the Monte Carlo ray-tracing method, which was developed and made generally available by Macke et al. (1996a). Each member of the ensemble is randomised, using the method of distortion, and maximum randomisations are achieved using distortion and embedding within the volume of the ice crystals spherical air bubbles (Shcherbakov et al., 2006). The method of distortion involves randomly tilting the normal vector to the surface of the ice crystal (by assuming a uniform probability distribution; see Macke et al., 1996a, for further details) at the ice–air interface with respect to its original direction. In this way, at each refraction–reflection event, the directions of the ray paths are changed with respect to their original direction, with the result that featureless scattering matrix elements are predicted. The values of distortion can be between 0 and 1, where 0 represents unperturbed scattering matrix elements, and these retain scattering features such as halo and ice bows. As the distortion is increased to higher values, the optical features are removed in order to produce featureless scattering matrix elements. The distortion method attempts to replicate the complex processes that may occur on and within ice crystals, which could lead to featureless phase functions. Other authors refer to distortion as “microscale surface roughness”. However, this description of surface roughness may not be accurate, as surface roughness can take on different forms (Mason 1971; Pfalzgraff et al., 2010; Bacon et al., 2003; Malkin et al., 2012). For instance, a theoretical electromagnetic study by Liu et al. (2013) has shown that the method of distortion does not accurately reproduce the scattering phase function at high values of idealised surface roughness. In this study, the method of distortion is merely used to randomise the ice crystal so that featureless scattering phase functions are produced.
Here the distortion parameter is assumed to have the values of 0, 0.15, 0.25
and 0.4. The distortion value of 0.4 is also combined with embedding the ice
crystal with spherical air bubbles in order to achieve the maximum randomisation of
the ice crystals so as to produce featureless phase functions. The upper
distortion value of 0.4 was chosen as this was found to best fit 1 day of
global POLDER-2 retrievals of directional spherical albedo and measurements
of the linearly polarised reflectance (Baran and Labonnote, 2006). For the
most randomised case of assuming a distortion value of 0.4 and embedding the
ice crystal with spherical air bubbles, the phase functions are calculated
using the modifications by Shcherbakov et al. (2006) applied to the ray-tracing code of Macke et al. (1996a). The statistics describing the tilt
angles were shown by Shcherbakov et al. (2006) to be best represented by
using Weibull statistics, where the Weibull distribution is defined by the
scale (i.e. the distortion as described above) and shape parameters. This
finding was based on cloud chamber measurements of the angular scattered
intensity from a collection of ice crystals at a visible wavelength, and
comparisons between measurements and ray-tracing results showed that the
Weibull statistics were the better match to the measurements. Moreover, the
choice of Weibull statistics is consistent with independent cloud chamber
results found by Neshyba et al. (2013). For the most randomised case
considered in this paper, the Weibull statistics are assumed to have the
following scale and shape parameter values of 0.4 and 0.85, respectively,
and for the spherical air bubble inclusions, a mean free path of 200
To interpret the PARASOL measurements, the scattering phase function is
required. The bulk-averaged scattering phase function, < P
The bulk-averaged asymmetry parameter,
The bulk-averaged volume extinction coefficient,
The bulk values of <
Figure 4a shows the bulk-averaged ensemble-model-predicted scattering
phase functions, calculated at the wavelength of 0.865
The scattering coefficient per particle (m
Of course, the phase functions derived from the ensemble model shown in Fig. 4 may not cover the entire range of possible cirrus phase functions as there are many possible cirrus habits that might occur at particular environmental temperatures (see, for example, Baran, 2012, and references therein). However, in the case of aggregates of hexagonal plates or hexagonal columns, it was shown by Baran (2009), using the ice aggregation model of Westbrook et al. (2004), that after three monomers were attached to the ice aggregate, the asymmetry parameters and phase functions asymptote to their limiting values. This asymptote occurs because the ice aggregation model predicts that the ice monomers making up the ice aggregate are well separated from each other. This separation is sufficient to reduce the effects of multiple scattering on the phase function, resulting in only slight modifications to the scattering angle positions of optical features (see, for example, Fig. 5 and Fig. 6 of Baran, 2009). This aggregation process is fundamental, and the same behaviour would be observed independent of the shape of the initial monomer (Westbrook et al., 2004). Therefore, in the case of pristine aggregates, the position of optical features on the phase functions would not be expected to be fundamentally different to those shown in Fig. 4a. If, on the other hand, the monomers that make up the ice crystal aggregate are sufficiently close to each other, then multiple scattering between monomers becomes important, as the scattered energy is increased and therefore also the phase function. However, the positions of the optical features exhibited by the ice aggregate phase functions do not significantly change position with respect to their scattering angles as these are principally determined by the hexagonal geometry (Um and McFarquhar 2007, 2009). As discussed in the introduction to this paper, the observational evidence indicates that pristine ice crystals are a rarity in nature; therefore the phase functions of highly complex ice crystals exhibiting inclusions, cavities and surface roughness will produce featureless phase functions and the featureless nature of the phase function is invariant with respect to ice crystal habit.
To retrieve the spectral spherical albedo using PARASOL, a radiative
transfer model is required; here the model developed by de Haan et al. (1986)
is used and its application to PARASOL has been fully described by
Labonnote et al. (2001). The radiative transfer model assumes a
plane-parallel cloud, but it is fully inclusive of multiple scattering. Also
taken into account are layers of aerosol below the cloud and Rayleigh
scattering above and below the cloud is also taken into account. The aerosol
model assumed in the PARASOL retrieval has been previously described by
Buriez et al. (2005), and so a description will not be repeated here.
However, the aerosol is principally maritime-based, and so its optical depth
will be much smaller than the cirrus optical depth, and as such it will not
be of any significance for the purposes of this paper. At the wavelength of
0.865
The methodology of retrieving the spectral spherical albedo using PARASOL multi-directional measurements of total reflectance has been previously described by (Doutriaux-Boucher et al., 2000; Buriez et al., 2001; and Labonnote et al., 2001), but a brief description of the retrieval is given here. The total reflectance of the cloud is specified by the vertical volume extinction coefficient, the vertical extent of the cloud and the scattering phase function. The cloud optical depth is therefore given by the integral of the vertical extinction over the vertical depth of the cloud. Since the cloud is essentially over a non-reflecting surface, the only directional information, under the assumption of a plane-parallel homogeneous layer, is provided by the assumed scattering phase function. However, inhomogeneity in the cloud can also affect the directional reflection as shown by Buriez et al. (2001), but this effect is not currently accounted for in the PARASOL retrieval algorithm due to its highly variable nature. It has been previously shown by Doutriaux-Boucher et al. (2000) that there is a one-to-one relationship between the cloud optical depth and the cloud spherical albedo (i.e. integral of the plane albedo over all incoming directions, where the plane albedo is a function of solar zenith angle alone) if the surface below the cloud is black. The cloud optical depth is retrieved by matching the simulated cloud reflectance to the measured cloud reflectance at each scattering angle. If the phase function were a perfect representation of the cloud, then the retrieved cloud optical depth will be the same at each scattering angle. Therefore, the retrieved spherical albedo would also be the same at each scattering angle. If the assumed phase function were a poor representation of the cloud, then this would result in a directional dependence on the spherical albedo, which would be unphysical. This retrieval methodology forms the basis of this paper, and it has been applied by other studies that have utilised PARASOL measurements to test ice cloud scattering phase functions (see, for example, Doutriaux-Boucher et al., 2000; Labonnote et al., 2001; Baran et al., 2001; Knapp et al., 2005; Baran and Labonnote, 2006).
As previously stated, the retrievals of spherical albedo are performed on a
pixel-by-pixel basis, and the data products derived from the PARASOL
observations are only used if the following four conditions are met: (i) for
each 6 km
The averaged spherical albedo,
In the sections that follow, the model phase functions shown in Fig. 4 and
the total optical properties given in Table 1 are applied to the PARASOL
measurements, on a pixel-by-pixel basis, to retrieve the phase function that
best minimises Eq. (5) and satisfies rejection of the Levene null
hypothesis. Results of this analysis are then used to explore possible
relationships between the shape of the scattering phase function and
RH
The UKV-model-predicted field of the water vapour mixing
ratio (
Before exploring the possible relationship between RH
To validate the NWP model prediction of the RH
A comparison between the retrievals, dropsonde measurements,
in situ measurements and NWP model predictions of RH
The NWP model prediction of the vertical profile of RH
Figure 8a and b show that the two in situ RH
The NWP-model-predicted cloud depth is therefore about 3 km, which is also in good agreement with the lidar-derived maximum cloud depth shown in Fig. 7a at approximately 13:33:00 UTC, when the aircraft was above the cloud top.
The PARASOL estimates of ensemble model randomisations
(based on minimised RMSE) and retrievals of optical thickness as a function
of latitude and longitude.
In this section, the methodology described in Sect. 4 is used to estimate
the ensemble model phase function which best minimises the RMSE and rejects
the Levene null hypothesis at the 5 % significance level. The ensemble
model phase functions used here were previously described in Sect. 3.1.1,
and are shown in Fig. 4. The results from the phase function estimates for
each pixel, showing the phase function model that best minimised RMSE, are
shown in Fig. 9a. The total number of retrievals, showing only those
retrievals over the sea, in Fig. 9a is 292. However, 130 of these
retrievals correspond to indeterminate results. The reason for the
indeterminate results at those pixels is because the retrieved spherical
albedo at each of the scattering angles was the same for all ensemble
models. The similarity of retrieved results in the indeterminate cases is
because the retrieval conditions stated in Sect. 4 were not met. These
indeterminate results are shown as black squares in the figure. A comparison
between Figs. 9a and 1 show that the indeterminate results generally
occurred in the presence of multi-layer cloud. Figure 9b shows the
averaged retrieved PARASOL decadal optical thickness (averaged over all
available scattering angles) at each of the pixels shown in Fig. 9a. The
figure shows that the retrieved PARASOL optical thickness ranged between
less than 1 and up to about 250. The largest optical thicknesses retrieved
by PARASOL are associated with the broken frontal cloud shown in Fig. 1
(right-hand side of the figure), and the positions of the broken frontal
cloud fields are also predominantly associated with the positions of the
indeterminate results shown in Fig. 9a. Figure 9a and b show that
even for PARASOL-retrieved optical thicknesses of between about 10 and 30,
discrimination between ensemble models is still possible. The physical
reason for this was recently given by Zhang et al. (2009). In their paper,
it is physically argued that, even if the optical thickness is increased to
large values, the shape of the phase function is still retained at
top of the atmosphere. This is because scattering within the cloud is
dominated by forward scattering, which results from strong diffraction in
the forward direction (Macke et al., 1995), and this single-scattering
information is still retained in the presence of strong multiple scattering.
However, at the largest retrieved optical thicknesses shown in Fig. 9b,
multiple scattering will be so strong that discrimination between models
will no longer be possible, and some of these largest optical thicknesses
are associated with the indeterminate results. Figure 9c shows the
estimated randomisations at each PARASOL pixel, but with the indeterminate
results removed, again using only the minimised RMSE value to select the
best model phase function. The yellow squares in Fig. 9c correspond to
the most randomised phase function (i.e. distortion
Differences between the directionally averaged (<
The estimated randomisations for two of the pixels shown at the top left of
Fig. 9c are further examined in Fig. 10a and b. The figure shows
the spherical albedo differences plotted as a function of scattering angle
for each of the two pixels, and in each of the figures, the RMSE values are
shown that were derived from the spherical albedo differences assuming the
four models. The first pixel shown in Fig. 10a is located at latitude
59.03
From Fig. 9c it can be seen that using minimised RMSE test, 5 of the
12 pixels are associated with pristine model phase functions
(distortion
The Levene test statistic,
In the case of the five pixels associated with pristine phase functions, it
can be seen from Table 2 that the Levene null hypothesis must be accepted.
Therefore, the variances in the spherical albedo differences determined
using the RMSE best-fit model are not sufficiently different from the
variances obtained using all other phase function models. A similar result
to the above was found for the three pixels, which were associated with the
moderately distorted phase function (distortion
Same definitions as Table 2 but with the Levene test statistic applied to a group of seven pixels, where the fully randomised model phase function was found to best fit spherical albedo differences using minimised RMSE values. The model pair tests are between all other scattering phase function models and the fully randomised scattering phase function model.
The Levene test statistic was also applied to some pixels associated with
the most randomised phase function in order to test whether
Since no one model phase function can be uniquely assigned to any of the
12 pixels, which show small differences in RMSE between models, suggests
that the model phase functions do not correctly describe the backscattering
properties of the cirrus located at those pixels and/or there might be
underlying water cloud affecting the results. To investigate the possibility
that there might be an underlying water cloud beneath the cirrus
contaminating the 12 pixels, the range-corrected lidar images were
further investigated under higher resolution to see whether there was any water
cloud beneath the cirrus. The aircraft passed over the 12 PARASOL pixels at
between about 13:20:00 and 13:30:00 UTC. Between these times, the
high-resolution lidar images showed only reflection from the sea surface
with no evidence of underlying water cloud (results not shown here for
reasons of brevity). It is noted here that the averaged retrieved PARASOL
optical thickness (averaged over the 12 pixels) was found to be 1.81
The space-based remotely sensed cloud products are available from
Since it is unlikely that underlying water cloud affected the results discussed above indicates that there might have been backscattering structure present on the cirrus phase function which is not represented by any of the models. Or more simply, there was insufficient scattering angle information available to distinguish between models. Interestingly, Baran et al. (2012) also found that, for a case of mid-latitude, very high IWC anvil cirrus near to the cloud top, the PN-measured averaged scattering phase function also exhibited unusual backscattering features. Clearly, such findings of optical features on the scattering phase function of naturally occurring ice crystals indicate the need for radiometric or in situ observations to sample the scattered angular intensities over a more complete range of scattering angle than is currently possible. Measuring the forward and backscattering intensities alone is not sufficiently general (Baran et al., 2012). However, the most common retrievals shown in Fig. 9a are representative of the most randomised ice crystals, and these have featureless phase functions. For the purposes of retrieving cirrus properties using global radiometric measurements, it is most likely that featureless phase functions are still generally better at representing cirrus radiative properties than their purely pristine counterparts (Foot, 1988; Baran et al., 1999, 2001; Baran and Labonnote, 2006; Baum et al., 2011; Cole et al., 2013; Ulanowski et al., 2013; Cole et al., 2014).
Here, it is also of interest to note the change in the asymmetry parameter
values shown in Table 1. From the pristine ensemble model phase function to
the most randomised ensemble model phase function, the change in the
asymmetry parameter is about 5 %. A change in the asymmetry parameter of
5 % is radiatively important, as illustrated by the following example.
Given that the instantaneous solar irradiance arriving at the top of Earth's atmosphere is about 1370 Wm
Associating the PARASOL estimations of shape of the
scattering phase function at each pixel to the NWP-model-predicted field of
RH
The PARASOL estimations of the shape of the scattering phase function, based
on applying the minimised RMSE and the Levene tests, are shown in Fig. 11a. In the
figure, the yellow pixels were assigned the most randomised
phase function, the brown pixels are the locations where no one model phase
function could be uniquely assigned. The blue pixels show the locations
where either phase function model, apart from the most randomised phase
function, could be assigned. The results shown in Fig. 11a are now
directly compared against the NWP-model-predicted RH
The NWP results shown in Fig. 11b are at the cloud top. However, the
PARASOL retrievals might be based on reflected solar radiation that comes
from the extent of the cloud and not just from the cloud top. In reality,
solar radiation at 0.865
The percent (%) probability of the penetration depth of
solar radiation at 0.865
To calculate the depth of penetrating radiation at 0.865
Figure 12a and b show that, by a depth of 1 km from the cloud top, the probability of penetration has been more than approximately halved for optical depths greater than 0.3. By 1.5 km from the cloud top, the probability of penetration is generally less than 5 %. The percent probability of penetration shown in Fig. 12a and b is similar. This is because the scattering phase function used in the Monte Carlo calculations, at backscattering angles, is largely invariant with respect to the scattering angle. This is simply because the scattering phase functions representing the most randomised ice crystals are flat and featureless at backscattering angles.
From Fig. 12a and b, it can be concluded that the PARASOL measurements of the total reflectance are biased towards the cloud top, and therefore comparison between the NWP model at the cloud top and PARASOL estimations of the shape of the scattering phase function is acceptable.
This paper has demonstrated the potential of using space-based remote
sensing to investigate relationships between the scattering properties of
ice crystals and atmospheric state parameters. However, one drawback of
current space-based multi-angle measurements is the limited range of
multi-angle samplings: in this paper, only seven measurement angles were
available. In regions where NWP model values of RH
Climate model parameterisations of the asymmetry parameter are currently assumed to be invariant with respect to atmospheric state variables. It is desirable, as argued by Baran et al. (2009, 2014) and Baran (2012), to relate general circulation model prognostic variables directly to ice optical properties, so that the prognostic variables can then be directly related to space-based radiometric measurements. Only through directly relating general circulation model prognostic variables to radiative measurements can the possibility of error cancellation be removed from within climate models.
This paper has explored the relationship between RH
It has also been demonstrated in this paper that the Met Office nested
high-resolution NWP-model-predicted vertical profiles of RH
For this one cirrus case, it is found that featureless phase function
models, representing highly randomised ice crystals, were shown to be
generally associated with NWP model RH
Currently, the ice radiation scheme in climate models does not take into account ice crystal complexity as a function of atmospheric state. Further research in this area will prove or disprove whether this climate model assumption needs to change.
The radiative transfer model assumes a plane-parallel layer with a vertical
extent of 3 km. This cloud depth is consistent with the lidar result shown
in Fig. 7a. The vertical resolution of the cloud layer is assumed to be
0.1 km, and the cloud top is situated at an altitude of 10 km, which is also
consistent with the lidar result shown in Fig. 7a. The relevant
Sun–satellite geometry for this case has been applied to the Monte Carlo
calculations; that is, the solar zenith angle is 75
The BAe-146 aircrew, Direct Flight operations staff, and FAAM and FGAM
instrument operators are thanked for their assistance during the flight. The
Facility for Airborne Atmospheric Measurements is owned by the Met Office
and the Natural Environment Research Council. Richard Cotton and Steven Abel
are thanked for their processing of the aircraft humidity measurements. The
image shown in Fig. 1 is kindly reproduced with permission from the NERC
Satellite Receiving Station, Dundee University, Scotland
(