Statistics of cloud optical thickness

Ž . Ž . Fig. 4. Peak values of optical thickness during legs 2 black dots and 3 white dots of the ARAT versus the cloud geometrical thickness derived from the POLDER stereo analysis at the same location. The solid line is the 5r3 slope; the dotted line is the 1r1 slope. which was aligned with POLDER on the ARAT. The three comparisons converge in demonstrating that the cloud optical thickness is rather proportional to H 5r3 than to H.

4. Statistics of cloud optical thickness

The parameterization of optical thickness based on the adiabatic profile of microphys- ical parameters is valid only in the core of a convective cloud cell. However, a stratocumulus is made of a patchwork of convective cells separated by regions of lower optical thickness related to downdrafts and even patches of clear air. In the downdraft regions, the profile of the microphysics deviates significantly from adiabaticity. The radiative parameter of interest in climate studies is the mean cloud albedo and several authors have shown that this mean value is quite sensitive to the horizontal distribution Ž . of optical thickness in a nonlinear way Cahalan et al., 1995 . A parameterization of the mean cloud albedo thus requires a relationship between cloud microphysics and cloud Ž . geometrical thickness such as that given by Eq. 1 , but also a relationship between the spatial inhomogeneity of the cloud properties and its mean albedo. In this section, the cloud layer observed during mission 206 will be divided into samples of different morphological characteristics and the statistics of optical thickness will be documented. Ž . They are fitted to lognormal distributions as was done by Barker et al., 1996 because of the nonlinear relationship between optical thickness and cloud albedo. The optical thickness corresponding to the logarithmic mean is referred to hereafter as the effective lnt optical thickness: t s e . e 4.1. Frequency distributions of optical thickness From the observations shown in Fig. 1, the leg M–A has been arbitrarily divided into Ž . three sections 0–40, 40–80 and 80–120 km . Such samples are sufficiently large for providing significant statistics and short enough for discriminating the different cloud morphologies. Fig. 6 shows the time evolution of the frequency distributions of optical Fig. 5. Comparison of the optical thickness derived from the ARAT POLDER with the adiabatic model Ž . Ž . prediction. a Horizontal map of the ARAT POLDER optical thickness. b Variations along the second Ž . ARAT leg of the POLDER optical thickness at the middle of the POLDER field of view solid line: t polder and of the value calculated with the adiabatic model and the cloud geometrical thickness derived from Ž . Ž LEANDRE cloud top altitude measurements dotted line: t . The values of droplet concentration 400 leandre y3 . Ž . Ž . cm and cloud base altitude 650 m for the adiabatic prediction are selected from the M-IV in situ data. c Ž . Comparison of the estimates defined in b : t versus t . polder leandre thickness for the three sections and for each of the ARAT legs. For each distribution, t e and the log standard deviation s have been reported. This figure reflects the spacertime variations discussed in Section 2. The figure also confirms that the optical thickness distributions are correctly represented by lognormal distributions. The most interesting feature, however, in this figure is the fact that the regions of deep clouds, such as in the H. Pawlowska et al. r Atmospheric Research 55 2000 85 – 102 94 Fig. 6. Frequency distributions of the POLDER optical thickness for the seven ARAT legs. The leg M–A has been divided into three sections from 0 to 40, 40 to 80 Ž . and 80 to 120 km. The values indicated in each distribution are the log of the effective optical thickness ln t and its standard deviation s . The corresponding e lognormal distributions are plotted with dashed lines. southern part of the leg and at the beginning of the flight, are characterized by narrow distributions compared to regions of thinner clouds, such as in the northern part. Fig. 7 summarizes the above analysis with t versus s , as derived from the e distributions measured with the ARAT POLDER, DLR-F20 POLDER, and DLR-F20 OVID. It illustrates clearly the inverse relationship between the mean and the width of the distributions. 4.2. Comparison with the adiabatic estimate The feature discussed above has significant consequences for the parameterization of optical thickness in stratocumulus. A scheme based on droplet concentration and cloud geometrical thickness provides an estimate of the optical thickness at the top of the convective cores. However, the mean cloud albedo is dependent upon the frequency distribution of optical thickness in the cloud layer, which includes regions of downdraft and clear air regions. More precisely, it depends upon the effective optical thickness. The adiabatic estimate thus overestimates t . Depending on how the cloud geometrical e thickness is defined, either corresponding to the maximum cloud top altitude or the mean cloud top altitude, the adiabatic estimate will correspond to the maximum optical thickness or a value slightly below the maximum. If the frequency distribution of optical thickness gets broader, it is likely that the difference between the adiabatic estimate and the effective optical thickness increases. Fig. 7. Effective optical thickness t versus the standard deviation of the distributions s , for the ARAT e POLDER, DLR-F20 POLDER and OVID measurements. The frequency distributions have been calculated over the same sections as in Fig. 6. The determination of an adiabatic reference of optical thickness for each of the samples analyzed in Section 4.1 is a difficult task. In situ measurements provide accurate estimates of the droplet concentration and of the cloud base and top, for deriving cloud geometrical thickness. However, they are local estimates that do not represent correctly the actual distribution of cloud geometrical thickness within each sample of 7 = 40 km. In addition, in situ measurements during EUCREX mission 206 were not synchronized with remote sensing measurements so that the comparison Ž . between the two is possible only after spacertime interpolation Section 3.1 . Remote Ž sensing measurements provide two independent estimates of the cloud top altitude from . POLDER stereo analysis and from LEANDRE , but the altitude of the cloud base is not documented with these instruments and it must be derived from in situ measurements. Fig. 8 combines these various estimates. It shows the ratio of the effective optical thickness within each sample to the adiabatic reference t , as a function of the ad corresponding standard deviation within the sample. As in Section 3, the adiabatic reference is calculated by three different ways: with in situ measurements of H and N Ž . vertical bars , and with measurements of cloud top altitude derived from POLDER and LEANDRE. Only seven of the samples defined in Section 4.1 can be documented with in situ measurements. For each of those seven samples, however, more than one ascent or descent through the cloud layer are available, providing various values of the adiabatic reference. The vertical bar in Fig. 8 reflects the range of variability of the adiabatic estimates in each of the seven samples. The values of cloud top altitude Fig. 8. Ratio of the effective optical thickness t to the adiabatic prediction versus the standard deviation of e the optical thickness frequency log distribution s . The vertical bars correspond to the range of variability of the adiabatic predictions derived from in situ measurements of cloud geometrical thickness. The white dots correspond to values derived from the POLDER stereo analysis and the black dots correspond to the estimates derived from the LEANDRE measurements of cloud top altitude. Ž . Ž . derived from POLDER stereo analysis Section 3.2 and from LEANDRE Section 3.3 have been averaged over each sample. Values of the adiabatic reference of optical thickness have been derived from the values of mean cloud top altitude by assuming the cloud base is at 650 m and the droplet concentration is 400 cm y3 . The corresponding Ž . Ž . values of the ratio t rt are represented by white POLDER and black LEANDRE e ad dots. Fig. 8 confirms that the adiabatic estimate provides a good diagnostic of the effective optical thickness when the frequency distribution of optical thickness is narrow. When the distribution is broad, the ratio depends significantly upon the value selected for the cloud geometrical thickness in the estimate of the adiabatic reference. There is a significant scatter in the relationship between t rt and the width of the optical e ad thickness distribution because the sampling strategy was not optimum for the estimate of the cloud geometrical thickness. However, this analysis demonstrates that the effective optical thickness can be as small as 40 of the value derived from the adiabatic model when the width of the optical thickness distribution is larger than 0.8. 4.3. Comparison with satellite measurements At the scale of a GCM grid, that is at a scale of about 100 km, the question is to what extent the mean radiative properties of the cloud system can be predicted from its mean dynamical and microphysical properties, and how the inhomogeneity of the cloud structure affects the prediction. OVID and LEANDRE measurements characterize a thin line along the DLR-F20 and Ž ARAT flight tracks, respectively. POLDER measurements on board the ARAT seven . Ž . legs and the DLR-F20 five legs provide better statistics of the horizontal field of Ž . optical thickness with their larger field of view of about 7-km width Section 2 . Finally, satellite measurements with AVHRR, described in FB cover the whole area, but the image was taken 1.5 h before the beginning of the ARAT flight. The frequency distributions of optical thickness derived from these instruments are compared in Fig. 9a. OVID and LEANDRE measurements have a spatial resolution of 220 and 100 m, respectively. POLDER measurements on board the ARAT have been processed at a resolution of 230 m. The spatial resolution of POLDER on board the DLR-F20 depends on the aircraft altitude but it is comparable to the resolution of the ARAT POLDER. AVHRR measurements however have been processed with a coarser spatial resolution of 1.1 km and then averaged over 5 = 5 pixels. The image has been taken at 08:30 UTC. For the comparison, it is assumed that the cloud system is stationary in time and that it y1 Ž . moves uniformly at a wind speed of 10 m s from a direction of 508 Fig. 3 in PBB . The leg M–A in the satellite image is thus translated by 54 km, in the direction of 508, Ž . corresponding to the delay between the image and the beginning of the flight 1.5 h . It is then translated by an additional 84 km distance corresponding to 2 h 20 min of flight duration. The area between these two boundaries is assumed to represent the part of the cloud system that crosses the leg M–A between 10:00 and 12:20 UTC. The frequency distribution of the optical thickness derived from the AVHRR measurements is then calculated within this area for comparison with aircraft measurements. The five distributions are reported in Fig. 9a. While OVID and POLDER data are available for the whole flight, the LEANDRE data have been processed for optical Ž . Fig. 9. a Frequency distributions of optical thickness over the whole cloud system sampled by the aircraft, Ž . derived from the ARAT POLDER, DLR-F20 POLDER, OVID, AVHRR, and LEANDRE measurements. b Frequency distributions of effective radius derived from the DLR-F20 OVID and AVHRR measurements. The adiabatic predictions of effective radius at cloud top, for four values of cloud geometrical thickness, from 100 to 400 m, are indicated by vertical bars on top of the graph. Table 1 Ž . Ž . Values of effective optical thickness t and standard deviation s for different instruments e Instrument t s e POLDER ARAT 9.27 0.91 DLR-F20 POLDER 10.48 0.90 OVID 7.39 0.73 LEANDRE 6.46 0.75 AVHRR 8.21 0.44 Ž . thickness on only a part of the ARAT third leg Pelon et al., 2000 . Their statistical significance is thus slightly lower. The values of effective optical thickness and standard deviation s measured by the various instruments are summarized in Table 1. Both POLDER measurements have similar distributions, but OVID estimates show almost no values larger than 35, while the maximum values with POLDER are larger than 70. The AVHRR distribution is narrower with no values larger than 15. Three reasons can be explored for explaining such a discrepancy. Ž . i The difference in spatial resolution: the pixels of AVHRR are four to five times larger than POLDER pixels. Smoothing of the optical thickness field obviously reduces the proportion of large values if they are restricted to single pixels. This hypothesis has been tested by averaging the POLDER values over 25 pixel areas before the calculation of the frequency distribution. The difference with the initial distribution is not significant and it can be concluded that spatial resolution is not sufficient to account for the discrepancy. In addition, OVID data show the same feature while their spatial resolution is even smaller than the POLDER one. Ž . ii Stationarity of the cloud system: the AVHRR image analyzed here was taken at 08:30 UTC while aircraft measurements were performed between 10:00 and 12:20 UTC. Ž . Numerical mesoscale simulations Fouilloux and Iaquinta, 1997 have shown that the horizontal inhomogeneity of the cloud system increases during the morning, with a maximum at 12:00 UTC. In addition, the translation used to compensate for the cloud advection between 08:30 and 10:00 to 12:20 UTC is such that part of the analyzed cloud layer is over land while the aircraft measurements were performed over sea. It is also likely that the surface could influence cloud homogeneity, even if the main structures are stationary. Ž . iii The retrieval scheme: both OVID and AVHRR optical thicknesses are derived from monodirectional radiance measurements at two wavelengths. POLDER estimates are derived from measurements of the multidirectional radiances. It is likely that the difference between the distributions reflects the difference in the retrieval methods. In particular, the use of directional radiances with POLDER provides a better description of the variability of the cloud optical thickness and possibly a better estimate of the large values. Fig. 9b shows additional information from AVHRR and OVID with the retrieved values of droplet effective radius. Both instruments, despite their very different spatial resolutions, show similar distributions of droplet radii. However, the comparison with in Ž . situ measurements Fig. 5 in PBB reveals that the droplet radii are overestimated, with values up to 11–14 mm while the maximum values in PBB are smaller than 8 mm. This is confirmed by the comparison with the values of effective radius at the top of an adiabatic cloud that are reported in Fig. 9b, for various values of the cloud geometrical thickness, from 100 to 400 m. The overestimation of the droplet effective radius seems to be inherent to the multiwavelength retrieval methods. It has been reported by many Ž . authors Platnick and Twomey, 1994 and it has been attributed to anomalous absorption Ž . Stephens and Tsay, 1990 . This additional similarity between OVID and AVHRR measurements supports our above conclusion that the difference in the distributions of optical thickness are related to the retrieval techniques rather than to the spatial resolution of the instruments. Ž . The effective optical thickness derived from POLDER 10.6 corresponds to the adiabatic estimate over the smallest observed cloud cells, such as in the northern end of the leg at the beginning of the flight and well below the adiabatic estimate derived with the mean geometrical thickness observed with the M-IV during the cloud traverses, namely 280 m. At 280 m and a droplet concentration of 400 cm y3 , the adiabatic estimate of optical thickness would be 14.9. In other words, to obtain an adiabatic estimate of optical thickness of 10.6, with a geometrical thickness of 280 m, a droplet concentration of 150 cm y3 is required, well below the value of 400 cm y3 measured in situ with the M-IV. The comparison is worst with the effective value derived from Ž . AVHRR 8.8 . These various calculations illustrate the difficulty in assessing experi- mentally the indirect effect because of the low sensitivity to droplet concentration Ž 1r3 . Ž 5r3 . N compared to the high sensitivity to cloud geometrical thickness H . They also reveal that the effect of cloud inhomogeneities on the prediction of optical thickness is significant compared to the accuracy needed in a GCM for the simulation of the indirect effect.

5. Conclusions