Stratocumulus, characterized by higher radiance values are seen to extend over the Ž
. English Channel, eastern England and over western Brittany France . Flights were
Ž .
performed by the ARAT on a leg AM about 100 km long, northwest of Brittany above Ž
. this cloud deck see Fig. 1 in Brenguier and Fouquart, 2000 . AVHRR radiances
revealed that the stratocumulus deck was breaking west of point A and did not extend very far beyond this point. The track was flown eight times between these two points.
Ž .
Once between 9:15 and 9:40 UTC, at a level of 300 m further referred to as AM1 to Ž
. document cloud properties from below cloud base height and extinction , and seven
times at a level of 4500 m between 9:58 and 12:18 UTC to retrieve cloud top height and Ž
extinction coefficient as would be obtained from a space-borne system Table 1 in .
Brenguier and Fouquart, 2000 . In this study, we focus on the second AM and MA legs Ž
. flown by the ARAT further referred to as AM2 and MA2 between 10:34 and 10:54
Ž .
UTC, and 10:57 and 11:17 UTC Table 1 in Brenguier and Fouquart, 2000 . The vertical potential temperature and humidity profiles measured during ARAT
ascent and descent near points M and A, at 9:40 and 12:10 UTC, respectively, are reported on Fig. 1. They show a significant evolution in the vertical structure along the
leg defined by these two points, and during the mission, as the temperature inversion height decreases from about 1000 to 800 m going from M to A. The values of water
vapor mixing ratio in the upper mixed boundary layer are comparable at both points, about 4.1 and 4.3 g kg
y1
in A and M, respectively. A 1.2-K increase in temperature is Ž
. observed between A and M. The lifting condensation level LCL calculated from these
values corresponds to an altitude of about 600 m. These observations are in agreement Ž
with those obtained by the Merlin IV see Pawlowska et al., 2000a, which is further .
Ž referred to as PBB . The visible image obtained from AVHRR see Fouilloux et al.,
. 2000 showed that the radiance values were much larger near M, emphasizing the
increased reflectance and optical depth of the cloud deck closer to the coast.
3. Lidar data analysis
The ARAT was embarking the backscatter lidar LEANDRE 1. This airborne system Ž
. uses a pulsed Nd–Yag laser source, emitting in the visible spectral domain 532 nm
after frequency doubling. A specific channel is also used for the detection of the signal Ž
. at the fundamental wavelength 1.06 mm . This airborne lidar has been used to retrieve
atmospheric aerosol, boundary layer characteristics and cloud scattering properties Ž
during previous campaigns Flamant and Pelon, 1996; Valentin et al., 1994; Flamant et .
Ž .
al., 1998 . In standard analysis procedures, the lidar signal S z, t , obtained as a function of distance z and time t, is first processed to derive the attenuated backscatter
Ž . coefficient b z defined as the product of the real atmospheric backscatter coefficient
a 2
Ž . b z with the two-way transmission T
z between the aircraft and the particles
Ž scattering the lidar beam at a given time or distance z see Spinhirne et al., 1989 for
. more details . The cloud top and base altitudes can be obtained from the so-processed
signals. The optical properties can then be derived provided the characteristics of the systems are accounted for, as we will show in the following subsections.
3.1. Cloud boundary analysis Lidar signal is normalized to atmospheric scattering at an altitude close to the aircraft,
Ž .
using onboard nephelometer measurements Flamant et al., 1998 . Fig. 2 shows two attenuated backscatter profiles obtained in nadir and zenith viewing mode. Larger b
a
values correspond to cloud scattering. Zenith measurements were taken as the aircraft was flying at 300 m above sea level. These vertical profiles have been obtained with a
vertical resolution of 15 m and a horizontal resolution of 100 m, corresponding to an Ž
. acquisition time of 1 s 12 laser shots . During the low-level leg, the overlap between
emitted and received beams prevented from getting valid information below 450 m. Attenuated backscatter profiles obtained in nadir viewing show that the lidar signal is
Ž .
rapidly decreasing as the beam penetrates into the cloud Fig. 2 . Therefore, the
Ž maximum value of attenuated backscatter is found slightly under the cloud top which is
. identified by the sudden increase of backscattered signal . The same is applicable to
cloud base for zenith measurements. Ž
. Most of the time, the true cloud base top cannot be observed from such nadir
Ž .
zenith measurements due to the high extinction of the lidar beam caused by scattering
Fig. 2. Examples of attenuated backscatter coefficient obtained as a function of altitude in zenith and nadir viewing.
J. Pelon
et al.
r Atmospheric
Research 55
2000 47
– 64
52
Ž .
Ž .
Ž .
Fig. 3. Retrievals of cloud base altitude triangle from zenith measurements and of cloud top square and apparent cloud base lower limit of the grey area altitudes from nadir lidar measurements along the leg MA. The distance is measured from point M. The cloud base altitude retrieved in zenith viewing is lower than the
apparent cloud base in nadir viewing due to in-cloud beam attenuation.
Ž .
into the cloud the transmission rapidly decreases to zero . This is emphasized in Fig. 3, Ž
. Ž
which shows the retrievals of cloud top square and apparent cloud base lower limit of .
Ž .
the grey area altitudes from nadir measurements, and of cloud base altitude triangle from zenith measurements, as a function of the position of the aircraft along the leg MA.
A AthresholdB algorithm based on the detection of the lidar signal gradient change was Ž
. used to derive cloud base and top heights Trouillet, 1997 from nadir and zenith
measurements. The cloud top altitude can be precisely derived from nadir viewing due to the large signal gradient observed near the cloud top and the lack of attenuation
above. Due to attenuation, the cloud base altitude derived from zenith measurements is fairly different from the apparent base defined with the same threshold from nadir
Ž .
measurements 650 m instead of 900 m, Fig. 2 . Only close to point A is the apparent cloud base deduced from nadir measurements close to the one obtained from zenith. In
this area, COD is decreasing, and clear air areas are even observed in downdrafts, as shown from increased attenuated backscatter coefficients from below the cloud base.
Ž Surface returns are also detected near point A i.e. the beam is not completely attenuated
. in the cloud . The surface echo also gives an absolute altitude reference to within 10 m.
The cloud base altitude is seen to correspond to 650 m. This is in good agreement Ž
. with the altitude determined from in situ measurements see PBB , and is very close to
the LCL height obtained from the soundings. The cloud top height analyzed on this leg Ž
. Fig. 3 is seen to decrease from values larger than 1100 m to less than 800 m from M to
A. It exhibits a larger variability than expected from the temperature soundings given in Ž
Fig. 1. Small-scale variability is also important with variations of the cloud top height .
greater than 100 m over a 5-km horizontal distance and reveals intense convective Ž
motions into the cloud at this scale. The cloud base height z varies slightly between
b
. 620 and 680 m , and was taken to be equal to 650 m in the rest of the study. The cloud
geometrical depth is further referred to this value. 3.2. Analysis of cloud optical properties
In moderately dense clouds, optical properties can be analyzed from the attenuated Ž
backscatter coefficient while accounting for multiple scattering Carnuth and Reiter, .
1986; Spinhirne et al., 1989; Flamant et al., 1996 . In dense clouds, however, the detection bandwidth may significantly contribute to the signal amplitude limitation, and
this effect needs to be corrected for in the case of rapidly varying signals. In direct detection, the detected lidar signal is proportional to the optical power backscattered by
the atmosphere. It can be written as the double convolution of the laser pulse power
Ž . P t
emitted as a function of time t, with the impulse response of the atmosphere
e
Ž .
2
Ž . b z rz as a function of altitude z, and the detection response D t
a
b
a
S z ,t s K z m P t q P
t m D t q S
t , 1
Ž .
Ž . Ž .
Ž . Ž .
Ž . Ž .
s e
b b
2
z where P
and S are additive optical and electrical noises, respectively. K
is the
b b
s
overall detection efficiency of the lidar system. The value of this efficiency factor is determined during upper level flights with reference to molecular and particular extinc-
Ž tion measured onboard the ARAT with a transmission nephelometer Flamant et al.,
. 1998 .
The duration of the pulse emitted by the LEANDRE 1 laser source being very short when compared to the signal sampling time constant, only the second convolution in Eq.
Ž . 1 needs to be considered. This convolution can be calculated using a simple formalism,
which requires the knowledge of the detection bandwidth and of the multiple scattering contribution. The latter can be estimated from the attenuated backscatter coefficient
Ž . Ž
b z , integrated over the cloud depth following previous analysis Platt, 1973; Spin-
a
. hirne et al., 1989 , and accounting for the detection filtering. However, a cloud
scattering model must be defined for this purpose. We have chosen to represent the cloud edge by a steep increase in the scattering and extinction coefficients. The
transition zone at cloud edge thus corresponds to a time propagation of light much smaller than the equivalent time constant of the detection system. The backscatter and
Ž .
extinction coefficients and consequently, their ratio k are kept constant in the first tens of meters below the cloud top. Under such hypotheses and assuming a first order
frequency response of the detection system, the in-cloud attenuated backscatter coeffi- Ž
. cient is given as a function of altitude z
above cloud base z s z y z as
b
b z
b z s
exp y2ha z y exp y
, 2
Ž .
Ž .
Ž .
a
1 y 2ha z z
Ž .
S S
where z is the equivalent height scale of the detection system corresponding to the
S
Ž .
electronic bandwidth. Using the formalism proposed by Platt 1973 , multiple scattering in cloud can be represented as a reduction in the real cloud extinction coefficient a by a
Ž .
Ž . factor 1rh h - 1 . The first term in Eq. 2 corresponds to the two-way atmospheric
transmission. Ž
. Calculation of the integrated attenuated backscatter coefficient IAB has been made
as a function of the normalized penetration distance into the cloud z s z
rz
ˆ
S
Ž .
assuming the same time–distance equivalence as without multiple scattering . The Ž .
theoretical expression of IAB obtained from Eq. 2 is given by k
a
IAB z s
1 y X q Xexp y z y exp y Xz ,
3
Ž .
Ž . ˆ
ˆ ˆ
2 1 y X
Ž .
Ž .
where X s 2 ah z . Let k be the backscatter to extinction coefficients ratio BER . The
S
apparent BER, k , is then defined as krh. For large values of z and X, the IAB tends
ˆ
a
towards the asymptotic value k r2. Note that this value is the same as the one
a
Ž .
calculated for an infinite detection bandwidth z s 0 and that the corresponding
S
Ž .
expression of the IAB is equivalent to the one obtained by Platt 1973 . However, the value of X is unknown and the assumption that X is large may be
Ž . questionable. According to Eq.
2 , this parameter also depends on the apparent backscatter coefficient. Since there exists an altitude for which the apparent backscatter
coefficient is maximum, the IAB is a function of the maximum of apparent backscatter coefficient. This function does not have to be known because the IAB and the maximum
of apparent backscatter coefficient can be determined independently. In Fig. 4, the IAB
Ž .
obtained for selected lidar profiles non-saturated zenith and nadir measurements is given as a function of the maximum value of the attenuated backscatter obtained into the
Fig. 4. Integrated attenuated backscatter coefficient as a function of maximum attenuated backscatter Ž
. coefficient at 532 nm for legs AM2 and MA2.
cloud. As the cloud top temperature is close to 08C, only water droplets are assumed to be found in the cloud. In this case, the BER in the cloud is constant and equal to 0.057
y1
Ž .
sr , independent of the cloud droplet distribution Pinnick et al., 1983 . It can be
shown that the asymptotic value of the IAB is the same for large X and large attenuated Ž
. backscatter values i.e. k r2 . This allows us to derive the multiple scattering factors, as
a
we now discuss. From Fig. 4, we observe than the IAB tends towards a value of 0.044 sr
y1
. Therefore, the apparent BER is estimated to be k r2 s 0.044 0.006 sr
y1
. The
a
uncertainty is estimated from the fluctuations around the mean value given by the dotted lines in Fig. 4. The corresponding value of the multiple scattering factor is h s 0.62
Ž .
0.10. It is slightly higher than the one determined by Spinhirne et al., 1989 , most likely Ž
because clouds were observed with a different solid angle our lidar observations were .
made closer to the cloud . Ž .
The true extinction coefficient a at cloud top is then retrieved from Eq. 2 , using the Ž
. relationship b s k a and the maximum backscatter coefficient value measured Fig. 4 .
Due to amplitude limitation caused by the finite detection bandwidth, the use of this
inverse relationship leads to large errors for high extinction coefficient values. An 8 statistical error due to noise in the attenuated backscatter coefficient for example results
in a 20 error on a retrieved extinction coefficient of the order of 0.015 m
y1
. The bias is more difficult to estimate. In Fig. 4, it can be seen that for values of b close to 0.8
a y1
y1
Ž .
km sr
, there appears to be a slight difference about 10 in the IAB given by the Ž .
theoretical expression given by Eq. 3 and the experimental points. This may be due to the inadequacy of our simple model to represent cloud extinction, and may lead to an
underestimation of medium range extinction. The extinction coefficient at cloud top a , retrieved as a function of distance along
t
leg MA2 is reported in Fig. 5. To reduce the large variability induced by the inversion Ž
. method, the data have been filtered over five-point total number intervals using a
median filter. Also reported is the altitude of the maximum value of the attenuated
Ž .
Fig. 5. Lidar-derived cloud top extinction coefficient at 532 nm solid line and maximum in-cloud apparent Ž
. backscatter coefficient height dotted line along leg MA2. The retrieval is performed on a 1-s accumulation
Ž .
period corresponding to an horizontal resolution of 100 m . Values are filtered using a 5 point median filter.
Ž .
Fig. 6. Vertical distribution of the cloud top extinction coefficient at 532 nm for legs AM2 and MA2. The Ž
. dotted line represents Eq. 11 . The solid line marks the altitude of the highest cloud observed.
backscatter coefficient. Extinction and altitude simultaneous increases and decreases are indicative of convective cells, already identified in Fig. 3. The correlation coefficient
between these two parameters is 0.92. Small-scale fluctuations appear to be more important on the extinction coefficient than on the cloud top altitude. This results in the
vertical distribution of the cloud top extinction shown in Fig. 6. Data from legs AM2 and MA2 have been included to emphasize vertical fluctuations of the cloud optical
properties caused by the entrainment process at top of the cloud deck. In Fig. 6, 99.9 of the values of the cloud-top height are observed between 1120 and 850 m. The largest
value of cloud-top extinction is about 0.17 m
y1
. Precision in the filtered values of the extinction coefficient is expected to be of the order of 10. This figure is further
discussed in Sections 5 and 6.
4. COD
