New evidence from collocated measurements, with support from theory and numerical simulations, that multidirectional measurements in the oxygen A band from the third Polarization and Directionality of the Earth’s Reflectances (POLDER-3) instrument on the Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL) satellite platform within the “A-Train” can help to characterize the vertical structure of clouds is presented. In the case of monolayered clouds, the standard POLDER cloud oxygen pressure product PO2 is shown to be sensitive to the cloud geometrical thickness H in two complementary ways: 1) PO2 is, on average, close to the pressure at the geometrical middle of the cloud layer (MCP) and methods are proposed for reducing the pressure difference PO2 − MCP and 2) the angular standard deviation of PO2 and the cloud geometrical thickness H are tightly correlated for liquid clouds. Accounting for cloud phase, there is thus the potential to obtain a statistically reasonable estimate of H. Such derivation from passive measurements, as compared with or supplementing other observations, is expected to be of interest in a broad range of applications for which it is important to define better the macrophysical cloud parameters in a practical way.
Satellite missions and atmospheric research have for a long time focused on cloud cover to assess its role and characteristics [e.g., the International Satellite Cloud Climatology Project (ISCCP) and the Clouds and the Earth’s Radiant Energy System (CERES) instruments]. Clouds are indeed a key component in the climate system and are a place where important and complex phenomena occur: energy transfer and water transformation. Cloud forcing and feedbacks on the climate system are important and depend on the nature of clouds and their evolution (Soden and Held 2006). Not only do clouds control the incoming radiative energy in the atmospheric system by reflecting part of the solar radiation, but cloud structures also determine the vertical profile of heating rate in the atmosphere. To get these energetic quantities, cloud microphysical parameters (water phase, particle size, and density) as well as macrophysical parameters (optical thickness, altitude, layer thickness, and multilayer character) are necessary. With the emergence of new sensor capabilities as well as the necessary improvement of atmospheric modeling, there is a growing interest in better describing and accounting for cloud structures, for example, to estimate correctly their radiative properties.
Nowadays, satellites and the instruments on them that perform cloud observations are diverse (in their spectral characteristics and spatial resolution), passive [e.g., the Moderate Resolution Imaging Spectroradiometer (MODIS), the Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL), and the Multiangle Imaging Spectroradiometer (MISR)], or active [the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and CloudSat platforms]. The strength of active sensors is their inherent ability to provide information about the vertical profile of the atmosphere with the weakness of small spatial coverage but with a high-spatial-resolution track size, whereas passive sensors measure and provide column-integrated quantities with large spatial coverage though sometimes at low spatial resolution. The synergy of these instruments is looked for (Stephens et al. 2002), and their measurements, while different in nature, should allow at least cross validation of cloud products. The study presented here is twofold. It first uses a combination of active observations to assess the quality of cloud products derived from passive instruments. From there, we derived statistically meaningful relations based on the third Polarization and Directionality of the Earth’s Reflectances (POLDER-3) instrument’s cloud apparent pressure measurements to derive cloud cover parameters from passive instruments only.
Estimation of cloud-top pressure or temperature, or altitude, has been an objective of many spatial measurements dedicated to cloud study (ISCCP and MODIS), meteorology (Geostationary Operational Environmental Satellite, or GOES), or atmospheric gases [the Global Ozone Monitoring Experiment (GOME), the Ozone Monitoring Instrument (OMI), and the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY)]. Techniques for the retrieval of the cloud-top pressure are based on different concepts and capabilities, with active methods (Clothiaux et al. 1998; Berthier et al. 2008), and a number of passive methods. Among this second group, some use information contained in thermal infrared measurements [infrared brightness–temperature technique and carbon dioxide (CO2)-slicing method (Rossow and Schiffer 1991; Smith and Frey 1990; King et al. 1992)], or use the polarimetry of reflected light (Knibbe et al. 2000; Goloub et al. 1994), or use stereoscopy (Hasler et al. 1991; Prata and Turner 1997; Moroney et al. 2002), or use measurements of differential absorption in molecular oxygen bands. Cloud-top pressure might indeed be inferred in principle from measurements of the absorption of reflected sunlight by a well-mixed gas above the cloud. Yamamoto and Wark (1961) first suggested the use of the A band of molecular oxygen (O2) absorption. At different wavelengths in the oxygen A band (between 759 and 771 nm), cloud properties do not change, whereas the absorption of radiation by O2 varies in a considerable way, as the result of rotational transitions produced by the strong magnetic dipole moment of oxygen. This cloud invariance and that known absorption variability allow one in principle to extract, from the ratio of spectral backscattered measurements, information about atmospheric scattering material (van de Hulst 1980; Fisher and Grassl 1991; Stephens and Heidinger 2000). The depth of O2 absorption depends on the amount of absorber above the cloud; hence, the cloud-top pressure can be retrieved, with the main uncertainty, as recognized very early on (Yamamoto and Wark 1961; Saiedy et al. 1965), being due to the account or neglect of radiation’s absorption along its path inside the cloud layer (Wu 1985; Fisher et al. 1991; Koelemeijer and Stammes 1999). Some theoretical studies have shown the potential of high-resolution measurements in the A band to provide not only the cloud-top pressure, but also the mean photon pathlength of photons within the cloud (O’Brien and Mitchell 1992), and even what affects the distribution of photon pathlengths within the cloud (Heidinger and Stephens 2000, 2002): namely, cloud structure characteristics. Although the POLDER sensor does not provide enough spectral resolution, new developments presented here show the potential of the multiangular character of POLDER measurements in the oxygen A band to provide information about the structure of cloudy atmospheres and to address the question of O2 absorption within clouds.
The use of the A band of oxygen to infer cloud properties was operationally applied to the satellite measurements of GOME (Koelemeijer et al. 2002), POLDER (Deschamps et al. 1994), and, more recently, the Medium Resolution Imaging Spectrometer (MERIS; Lindstrot et al. 2006) and Modular Optoelectronical Scanner (MOS; Preusker et al. 2007). From POLDER A-band measurements, cloud apparent pressure Papp and cloud oxygen pressure PO2 have been obtained (Vanbauce et al. 1998, 2003): from the first POLDER/Advanced Earth Observing Satellite (ADEOS) missions (from 1996 to 1997 and in 2003) to the current POLDER-3 sensor on the PARASOL platform in the so-called A-Train (from 2005; PARASOL unfortunately left the A-Train in December 2009). As expected, POLDER oxygen pressure overestimates cloud-top pressure because of photon penetration inside cloud before back-reflection into space. POLDER PO2 was shown for some data intercomparisons to be close to the middle-of-cloud pressure (Vanbauce et al. 2003; Sneep et al. 2008).
In addition to cloud-top pressure, complementary information about cloud geometrical thickness would be very valuable for numerous applications. For example, correct estimation of the surface radiation budget calls for this macroscopic cloud parameter. Assimilation of cloud retrievals into cloud-process and climate models, as well as in weather forecasting, is another example. It would thus be desirable to get, at synoptic scale, both cloud-top altitude and cloud geometrical thickness, and different studies have had these ambitions from passive measurements (Hayasaka et al. 1995; Kuji and Nakajima 2002; Rozanov and Kokhanovsky 2004). The study presented here demonstrates that POLDER A-band measurements can better characterize the geometry of cloud structures: we shall see that, knowing the cloud phase and optical thickness, POLDER oxygen pressure PO2 can be made close to the pressure in the middle of monolayer clouds and that their cloud geometrical thickness may be inferred. This paper is organized as follows. First, the reader is reminded about the parameterization that defines POLDER cloud oxygen pressure and, from simulation of photon pathlength within cloud, simulation of POLDER signal in oxygen A-band channels, and study of POLDER PO2 sensitivity to cloud parameters, expectations are given regarding the significance and sensitivities of POLDER oxygen products. Second, we present the data that have been exploited and confirm in large part the expectations. Third, we make conclusions about this new exploitation of POLDER measurements and present new remote sensing strategies following this advance.
2. Significance and sensitivity of POLDER cloud oxygen pressure: Expectations
a. POLDER PO2 parameterization and first implications
POLDER cloud oxygen pressure is inferred from multidirectional (up to 14) measurements in two channels located in the oxygen A band, at around 763 and 765 nm, whose full widths at half maximum are, respectively, 10 and 40 nm. Figure 1 illustrates the spectral variability of the oxygen absorption coefficient in this domain as well as the POLDER response filters for the two channels.
The POLDER parameterization is as follows [see Buriez et al. (1997) for more details]: It is assumed that, after correction for the weak absorption of gases other than oxygen, 1) the reflectance I765 at 765 nm is a weighted sum of the reflectance I763 at 763 nm and the cloud reflectance I* and 2) the reflectance at 763 nm is equal to I* times the oxygen transmission TO2 of the atmosphere above it. The implicit assumption is thus that the cloud albedo is equal to unity. For each viewing direction, I* and TO2 are obtained from the ratio of I763 and I765, and from TO2—given the air mass—the cloud apparent pressure Papp. Cloud oxygen pressure PO2 is obtained from Papp after correction of the surface effect and when the cloud spherical albedo is higher than 0.3. In the following, the two terms “apparent” and “oxygen” pressures will have the same meaning and will be used interchangeably.
As a direct consequence of the definition of POLDER cloud oxygen pressure PO2, the extinction of photons along their path inside the cloud layer before they eventually escape through the cloud-top boundary is not accounted for: PO2 is thus expected to be larger than the actual cloud-top pressure (CTP). This bias depends on the photon penetration within the cloud. In the case of optically very thick and geometrically very thin clouds, the discrepancy is small because we are closer to the case of an ideal solid reflector.
We also expect some angular variability of PO2, because the photon pathlength or equivalent penetration within the cloud varies with the viewing angle. Thus, both the difference PO2 − CTP and the angular standard deviation σPO2 can be seen as measures of the “distance” between the actual cloud layer of finite thickness and the reference model of an ideally thin reflector. But to what are these quantities sensitive? What is the information content of PO2 − CTP and σPO2? Spectroscopic O2 observations depend on cloud optical thickness, scattering phase function, cloud altitude, and cloud geometrical thickness because all of these parameters affect the length of the photon paths inside the cloud layer (Stephens and Heidinger 2000) and also, as we show here, their angular variability. The remote sensing value of the angular variability of PO2 − CTP and of σPO2 is not obvious, because little theoretical background exists for exploiting them. In the following, we tackle these questions with Monte Carlo calculations of photon penetration within the cloud layer and with estimates of POLDER PO2 from simulation of POLDER’s A-band radiances. In all cases, clouds were modeled as horizontally and vertically homogeneous.
b. Angular variability and dependence of photon penetration within the cloud layer
Photon pathlength enhancement due to multiple scattering within cloud has been studied extensively for transmitted light since the late 1990s, both theoretically (Davis and Marshak 1997, 2002; Mayer et al. 1998; Davis 2006; Scholl et al. 2006) and observationally (Mayer et al. 1998; Pfeilsticker et al. 1998; Pfeilsticker 1999; Min and Harrison 1999; Portmann et al. 2001; Min et al. 2001, 2004; Min and Clothiaux 2003; Scholl et al. 2006). In the preceding years, pathlength enhancement in reflected light received more attention. See O’Brien and Mitchell (1992) for a review of early Russian publications; for example, Dianov-Klokov and Krasnokutskaya (1972) found that effective photon pathlength attained a maximum value equivalent to ∼1.5 times the layer thickness at an optical thickness of about 30 and remained quasi constant thereafter. Interest in pathlengths for light reflected by clouds has regained considerable interest in the past decade, driven by the prospect of space-based O2 A-band observations at high spectral and spatial resolutions (Stephens and Heidinger 2000; Heidinger and Stephens 2000, 2002). A parallel development with, at its core, the same path dependence of reflected light is multiple-scattering/wide-field-of-view lidar as a new way of probing dense clouds using active optical technology from the ground, aircraft, or space (Flesia and Schwendimann 1995; Eloranta 1998; Miller and Stephens 1999; Davis et al. 1999; Cahalan et al. 2005; Polonsky et al. 2005; Hogan and Battaglia 2008; Davis 2008).
The literature is scant with regard to the angular variability of in-cloud pathlength distributions for photons eventually reflected by a cloud layer in different directions. This might be due to the fact that satellite measurements in gas absorbing bands are rarely multidirectional. Some results based on asymptotic models and approximations may guide our search. Van de Hulst (1980) derived the following expression in the asymptotic regime (i.e., large cloud optical thickness τ):
independent of τ, with μ and μ0 being the cosines of the viewing and sun zenith angles (θ and θsun, respectively), 〈L〉 being the mean geometrical path of photons reflected in different upwelling directions, and H being the cloud geometrical thickness. Note that Eq. (1) conforms to the reciprocity principle. Diffusion theory also applies to optically thick clouds but predicts only outgoing fluxes. The associated mean geometrical path 〈L〉 within cloud of reflected photons varies again linearly with H, and, to be more specific, one finds 〈L〉/H ≈ ⅔ + μ0 plus relatively small preasymptotic corrections that are dependent on μ0, τ, and (the asymmetry factor g of) the scattering phase function (Davis et al. 2009). Does 〈L〉 for upward radiances indeed depend only weakly on τ and linearly on H for different and realistic radiative regimes?
We computed photon penetration into uniform plane-parallel clouds from Monte Carlo simulations. We adapted the Monte Carlo code of Cornet et al. (2010) to store the distribution of photon pathlengths within cloud from their entrance to their escape through the cloud-top boundary on a regularly spaced angular bin. For each simulation, 107 Monte Carlo particle histories were computed. Simulations were not exhaustive, but 〈L〉 was obtained for different solar geometries, upward viewing directions, and cloud optical and geometrical thicknesses τ and H. We now focus our attention on what we call the photon vertical penetration length 〈Z〉 within cloud, defined as the mean pathlength 〈L〉 divided by the air mass factor (μ0−1 + μ−1). Length 〈Z〉 can be considered to be the mean “equivalent” vertical penetration of photons in the sense of single scattering: the mean vertical distance between the backscatter material and the cloud top is precisely equal to 〈Z〉 in the case of single scattering. Examples of computed photon penetrations are plotted in Fig. 2 as a function of the viewing zenith angle in the case of liquid clouds with different optical thicknesses 10, 20, and 40 and geometrical thicknesses 2 and 4 km and for θsun = 0°. A standard “C1” scattering phase function for cloud droplets was used (Deirmendjian 1969). To add more realism to the above-mentioned asymptotic studies, the cloud was embedded in a Rayleigh scattering atmosphere stratified with a scale height of 8 km over an absorbing surface (above-cloud Rayleigh scattering was neglected). Cloud base was fixed at 1-km altitude.
Figure 2 highlights two important dependencies: 1) the equivalent vertical penetration 〈Z〉 depends weakly on τ but predominantly on H: 〈Z〉 increases with H and 2) the amplitude of the angular variability of 〈Z〉 also depends strongly on H: 〈Z〉 is highest (lowest) for low (high) viewing zenith angles. These results are close to the asymptotic ones obtained for fluxes and radiances: pathlengths depend mainly on H and are proportional to it, and the predicted weak dependence on τ is confirmed. Moreover, following van de Hulst’s relation [Eq. (1)], we obtain
This dependency in μ and H is close to the ones shown in Fig. 2 (where μ0 = 1) for various choices of H and τ. Quantities PO2 − CTP and σPO2 are both sensitive to the equivalent vertical penetration of photons inside the cloud layer. We can therefore expect both of them to carry information about H that we will exploit further on.
c. Simulation of POLDER cloud oxygen pressure PO2
We performed simulations of POLDER apparent cloud pressure for a large number of cases: solar zenith angle between 0° and 60°, τ between 0 and 100, liquid and ice clouds, H between 50 m and 6 km, and cloud-top altitudes between 4 and 10 km. To get cloud pressures, reflectances in the two POLDER oxygen channels were first generated using a standard radiative transfer code, accounting for Rayleigh scattering and the instrument response, and using a k-distribution approach (Lacis and Oinas 1991) with 10 subbands per channel while assuming a dark surface. Then, the POLDER algorithm was applied to get PO2. Figure 3 illustrates the variability of PO2 obtained for θsun = 0° and θ = 60° in the case of liquid clouds having in common the same cloud-top altitude at 4 km but different cloud geometrical and optical thicknesses H and τ. In Fig. 3a, the difference PO2 − MCP, with MCP being the pressure of the geometrical middle of the cloud layer, is plotted as a function of τ, with each curve corresponding to a value of H between 0.05 and 3 km. In Fig. 3b, isocontours of PO2 − MCP are given in the τ ; H plane. These two panels show that PO2 is close to the actual MCP (±30 hPa); the bias is small when 20 ≤ τ ≤ 40 and is almost independent of H. These results mean that the equivalent vertical photon penetration 〈Z〉 is close to one-half of the cloud geometrical thickness for a broad range of cases. Penetration goes beyond MCP for lower τ and does not reach it for higher τ, which makes intuitive sense.
For the same θsun but more vertical viewing directions, the minimum bias between PO2 and MCP would correspond to higher values of τ. Equivalently, for 20 ≤ τ ≤ 40, PO2 would be higher than MCP. For a different solar geometry, photon penetration would be different, but the rule would be the same: maximum penetration for near-zenith viewing angles and, for a certain set of parameters (viewing geometry and optical thickness), 〈Z〉 close to H/2 and PO2 ≃ MCP for any value of H. As an illustration of this principle, the two curves in Fig. 4 give PO2(θ) for θsun at 0° and 60°, for a cloud extending between 2 and 4 km with τ = 30. The result confirms that equivalent photon penetration is higher for viewing directions close to zenith, as was already observed in Fig. 2. Geometries for which PO2 ≈ MCP or, equivalent, 〈Z〉 ≈ H/2 follow the asymptotic expression derived earlier: μ0μH = H/2 for θsun = 0° and θ = 60° or, by reciprocity, θsun = 60° and θ = 0°, which would occur more frequently in actual satellite observations.
When the cloud optical thickness is low (τ ≤ 5), we analyzed that the angular variability of PO2—quantified by its angular standard deviation σPO2—is significantly affected by cloud microphysics. The relative contribution to the measurements of the cloudy layers versus the Rayleigh-scattering atmosphere varies indeed angularly—all the more so since the range of the cloud’s scattering phase function is important. On the contrary, σPO2 is only and highly correlated with the cloud macrophysical parameter H when τ is large enough. This is illustrated in Fig. 5 for the same liquid cloud cases (common cloud-top altitude = 4 km) and θsun = 0°: when τ ≥ 20, isocontours of σPO2 in the τ, H plane (Fig. 5a) are almost parallel to the vertical axis, indicating a nearly one-to-one relation between σPO2 and H. Their correlation is excellent (R2 = 0.996), as shown in Fig. 5b, where each circle represents a value of optical thickness and the solid linear regression line fits the data. The positive linear relation between σPO2 and H (slope ∼ 5.5 hPa km−1) signifies that the angular difference in the equivalent vertical penetration of photons within clouds gets larger as H increases.
Other simulations that we performed highlight the importance of the cloud thermodynamic phase on PO2 angular variability and on the slope of the linear regression between σPO2 and H. An example of our results is given in Fig. 5b (see times signs and the dashed linear regression line) for ice clouds at the same altitudes, composed of inhomogeneous hexagonal monocrystals as described in C.-Labonnote et al. (2000): the figure shows that the correlation is still high in the case of ice clouds, with here a higher linear regression slope (∼6.5 hPa km−1). An immediate consequence of time-dependent diffusion theory (e.g., Davis et al. 2009) is that the ability of light to penetrate clouds depends on the scaled cloud optical thickness (1 − g)τ, with g being the asymmetry factor, that is, the mean cosine of the scattering angle for the given phase function.1 Thus, we logically expect materials with different asymmetry factors, like liquid and ice hydrometeors, to come with different relations. Anticipating the difference in the linear regression’s slope for different hydrometeors is not straightforward, because the slope depends on the zenithal viewing angle θsun, as Eq. (1) suggests and as Fig. 6 shows. In Fig. 6, the variations of the slope for ice and liquid clouds as θsun increases go inversely, which demonstrates the importance of the cloud thermodynamic phase in the relation σPO2–H.
We observed also (not shown here) an effect of the cloud-top pressure on the difference PO2 − MCP and on the relation σPO2–H. As CTP decreases, PO2 − MCP tends to increase slightly, and the slope of the linear regression decreases. These two effects can be understood as 1) O2 absorption decreasing with altitude: photon penetration within cloud effectively increases and 2) the vertical gradient of pressure decreasing with altitude: an equal difference in vertical penetrations within cloud leads to a lower difference in cloud apparent pressures at higher altitude. We indeed observed lower angular contrast between simulated apparent oxygen pressures for liquid and ice clouds as the cloud altitude increases and, thus, lower slopes. In the case of liquid clouds and for the performed simulations, the slope of the linear regression ranges from 7.2 (for low clouds) down to 2.9 (for high clouds) hPa km−1.
Thus, we expect from simulation that POLDER PO2 might be close to MCP, with a significant dependence on cloud optical thickness (COT) and a slight dependence on CTP, and that H might possibly be retrieved from σPO2 with some required information about the cloud thermodynamic phase and also about the vertical location of the cloud layers. The analysis of measurements given below will confirm this expectation.
3. Significance and sensitivity of POLDER cloud oxygen pressure: Evidence from comparative measurements
From modeling, we expect POLDER’s oxygen-based cloud pressure level PO2, and its angular variability, to be sensitive to the geometrical thickness H of the cloud layer. We further expect PO2 to be close to the pressure at the geometrical middle of monolayer cloud, though with a τ dependence that would vary with the cloud thermodynamical phase, and σPO2, the angular standard deviation of PO2, to be well correlated with H. The richness of existing space-based measurements provided by the A-Train satellite constellation makes it possible for us to check our hypotheses at the global scale and over a long time period. Indeed, some of the POLDER-3/PARASOL data are collocated and quasi simultaneous with measurements of active sensors that are also part of the A-train constellation of satellites: the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) on board the CALIPSO platform and the Cloud Profiling Radar (CPR) on board CloudSat. These sensors have complementary sensitivities to detect thin and thick scattering layers and provide direct information about the vertical profile of the atmosphere, from which one can extract for each transmitted pulse the number of cloud layers and their vertical locations at high spatial resolution. We present below the data that we intercompared and the correlation between cloud parameters that we obtained from these data.
a. Data used in intercomparison studies
For the whole year of 2008, we examined the POLDER cloud oxygen pressure products for which available vertical information about cloud layers was available (i.e., under CALIPSO and CloudSat tracks). The level-2 POLDER cloud oxygen pressure product consists of 1) the cloud oxygen pressure PO2 obtained when cloud optical thickness is not too low [higher than 2 (3) for liquid (ice) clouds], after angularly averaging directional apparent pressures and spatially averaging 3 × 3 POLDER pixels, accounting for cloud fraction and with surface correction above land, and 2) the angular standard deviation σPO2 of cloud oxygen pressure PO2. The level-2 POLDER, CALIOP, and CloudSat data are at different horizontal resolutions: respectively 18 × 21 km2 [(3 × 6 km) × (3 × 7 km)], 0.3 × 1.0 km2, and 1.4 × 2.5 km2. CALIPSO and CloudSat vertical resolutions are respectively 60 and 500 m. Because of these differences in sensor spatial resolutions, data were retained every 5 km. Moreover, both POLDER and MODIS cloud thermodynamic phase information was analyzed, and other MODIS collection-5 products (e.g., cloud-top pressure) were also collected for the same pixels. Thus, cloud optical thickness came from POLDER and cloud thermodynamic phase came from POLDER and MODIS. These data are available through the Cloud–Aerosol–Water–Radiation Interactions (ICARE) Thematic Center and are collocated with CALIPSO 5-km pixels through the “MULTI_SENSOR/CALTRACK_UNIT” project (see the ICARE Internet site at http://www.icare.univ-lille1.fr). For the geometrical thickness and vertical location of the cloud layers, we used the combined CloudSat/CALIPSO “2B-GEOPROF-Lidar” product (available online at http://cloudsat.atmos.colostate.edu/data) that provides location information about a maximum of five cloud layers in the atmosphere. We present here in detail the results for 2008 and for cloud layers that are structurally close to plane-parallel slabs, that is, monolayer horizontally and vertically near-homogeneous clouds (monolayer as classified by CloudSat/CALIPSO, and near–horizontally homogeneous as the cloud fraction estimated by POLDER at 18 × 21 km2 is higher than 0.95). It is, however, obvious that monolayer clouds that have a large vertical extension (several kilometers) will be farther from the plane-parallel reference because of their inhomogeneities. Clouds were classified as liquid or ice when the POLDER and MODIS classifications agree. For 2008, this comparison leads to a total of 1 486 354 data points; among them 754 637 (487 892) are liquid (ice) cases—that is, 83.5% of the points were successfully sorted. For the remaining 16.5%, the thermodynamic phases are classified differently by the two sensors or are deemed to be mixed and, at any rate, have not been considered here.
b. Difference between POLDER PO2 and MCP
1) Histograms and dependence
Figure 7 shows, for 2008, histograms of the difference PO2 − MCP between PO2 and the midcloud pressure MCP for monolayer cloud cases for which data were available under the CloudSat/CALIPSO track. MCP is the pressure at the average cloud altitude computed from the cloud-layer top and base 2B-GEOPROF-Lidar altitudes. For liquid clouds (gray curve), the histogram of PO2 − MCP is quasi symmetric and almost centered: PO2 − MCP = 20 hPa with a standard deviation (SD) = 75 hPa. In the case of ice clouds (black curve), the peak is wider and significantly off center: PO2 − MCP = 54 hPa, with SD = 99 hPa. This spread, plus the fact that ice cases are less numerous, makes the number of samples per class smaller. This result seems to be logical, because ice clouds are vertically more extended and internally variable. The bias between PO2 and MCP for ice clouds can be partly explained by the sensitivity of PO2 − MCP to COT. The histogram for ice clouds with τ ≥ 10, given by the black plot with circle markers in Fig. 7, is indeed less biased. The sensitivity in τ for liquid clouds (not shown here) is weaker.
A first conclusion from these histograms is that, on average, the difference between POLDER oxygen pressure and MCP is essentially unbiased for liquid clouds as well as for ice clouds with high-enough optical thickness. Although it was shown earlier that simulated PO2 is sensitive to the viewing cosine μ, our empirical finding that PO2 − MCP ≃ 0 may be explained by the asymptotic result from van de Hulst (1980). If photon penetration 〈Z〉 within cloud varies angularly as in Eq. (2), then, on average (for a large number of solar and upwelling directions, assumed to be independent, with zenith angles between 0° and 90°), it will tend to a certain fraction of H in the limit of many samples that will depend on the specific angular sampling.2 POLDER PO2, as defined by the cumulative vertical path of detected photons, appears to deviate from the true CTP by a pressure differential corresponding roughly to H/2. We will therefore use MCP as a new baseline for PO2.
Histograms shown in Fig. 7 give a first insight into the effect of cloud parameters on PO2 − MCP. Figure 8 shows more precisely the effect of COT and CTP on PO2 − MCP, on average. In Fig. 8, each symbol represents the mean of PO2 − MCP obtained for different classes of COT (Fig. 8a) and CTP (Fig. 8b). Error bars represent the confidence width of the mean. Also plotted, in solid lines, are histograms of COT and CTP in arbitrary units. Color codes are as in Fig. 7. Figure 7a shows that the dependence of PO2 − MCP on COT differs with the cloud thermodynamical phase. For ice clouds (black), PO2 − MCP is very sensitive to COT, with very positive values when COT is smaller than approximately 35 and negative values when it is above that value. This means that, for ice clouds, photons penetrate on average much more than the middle of the cloud layer when COT is small, reach it for COT ≃ 35, and do not reach it when COT > 40. This behavior is consistent with what simulations have suggested (see Fig. 3b). For liquid clouds (gray), the difference is less COT dependent and, for each COT class, PO2 − MCP is on average positive and smaller than 30 hPa. Figure 7b shows that PO2 − MCP is on average mostly positive by bin of CTP and is the largest when CTP is low. This result might be related to the variation with altitude of the photon penetration and of the correspondence of oxygen pressure and vertical path as discussed at the end of section 2.
The difference PO2 − MCP depends in a complex way on cloud macrophysics—cloud optical and geometrical thickness—and on cloud-top pressure, and also depends on the angular characteristics of the measurements. However, if cloudy situations are very diverse over the whole year of 2008, the average dependence of PO2 − MCP on COT, H, and CTP is not random. Trends are indeed observable for PO2 − MCP when classes of COT, H, and CTP are considered. This is shown in Figs. 9a and 9b for liquid clouds and Figs. 10a and 10b for ice clouds. The gray shading indicates the sample density. The left (right) panels in Figs. 9 and 10 give isocontours of PO2 − MCP in COT, H (COT, CTP) coordinates. For ice clouds, PO2 − MCP depends mostly on COT and in a way close to what simulations suggest (see again Fig. 3b): PO2 − MCP is negative for high COT (COT > 40) and is positive for low COT (COT < 30). For liquid clouds, however, PO2 − MCP is positive for most of the cases, except for low-level clouds (CTP > 800 hPa). Although the magnitude of |PO2 − MCP| is small for most liquid cloud situations (∼30–40 hPa), which is interesting, this statistical result obtained from measurements is not supported by the simulations we performed. So far, an explanation for this difference is lacking.
2) Improvement of POLDER PO2 product
For monolayer clouds in 2008, the dependence of PO2 − MCP on cloudy structure parameters obtained from measurements suggests a possible phase-dependent correction of PO2 to make it a better estimate of MCP. A technique for a PO2 correction would be to unbias it by the polynomial that fits the function that relies on PO2 − MCP and cloud parameters (as in Fig. 8 for the dependence on COT). In this exercise, the geometrical thickness would not be known. Instead of a two-dimensional fit, we corrected first PO2 from its COT dependence. Figures 9c and 9d for liquid clouds and Figs. 10c and 10d for ice clouds show isocontours of PO2 − MCP after the COT-based correction. It shows that this correction does remove most of the bias between PO2 and MCP where occurrences are numerous, in both the COT, H and COT, CTP planes. The correction, however, does not appear to perform as well for liquid clouds when CTP is higher than 850 hPa and for some cases of ice clouds when COT is smaller than 10.
We considered, then, an additional correction for the dependence of PO2 − MCP on CTP. It was motivated by the idea to do better than a COT-based correction, because this first correction was not “perfect,” and because of CTP effects suggested by simulations and by the observed dependence of PO2 − MCP on CTP (Fig. 7b). If the “true” CTP is directly inferred from CloudSat/CALIOP measurements under their tracks, CTP is estimated elsewhere in the POLDER/MODIS swath with MODIS CTP that is much closer to the actual CTP than POLDER PO2 (Sneep et al. 2008). A second-order MODIS CTP correction that will concern the entire swath would be pertinent. We are, however, aware of the departure of the present MODIS collection-5 CTP from the true one, as discussed in Holz et al. (2008)—in particular, for marine low-level clouds due to low-level temperature inversions. Our own comparisons showed us that MODIS CTP overestimates slightly (less than 40 hPa) the true CTP < 700 hPa, and underestimates it strongly (by ∼100 hPa) when CTP > 800 hPa; that is precisely the cases for which an additional correction would be valuable. For this last reason, we decided—for a MODIS CTP correction of PO2—to wait for the MODIS collection-6 products, in which CTP estimation should improve significantly (Menzel et al. 2008). Instead, we performed a correction of PO2 based on the true CloudSat/CALIOP CTP. Results are given in Figs. 9e and 9f for liquid clouds and Figs. 10e and 10f for ice clouds. It is observable that this CTP correction decreases the bias between PO2 and MCP for liquid low-level clouds. For ice clouds, the improvement is not obvious, especially for optically thick clouds. After these corrections, histograms of PO2 − MCP (shown in Fig. 7) are more centered and sharper than before any correction: for liquid clouds and for ice clouds (red and blue lines, respectively), the respective medians are 3 and 0 hPa and the corresponding SDs are 66 and 82 hPa.
c. Relation between σPO2 and H for monolayer clouds
Simulations suggest a possible strong correlation between the angular standard deviation σPO2 of POLDER cloud oxygen pressure and the geometrical thickness H of monolayer clouds. Study of the significance of PO2 from both simulations and measurements shows also the importance of cloud thermodynamic phase. We thus studied the relation between σPO2 and H under the CALIPSO/CloudSat track, where cloudy atmospheres were flagged as monolayered, while distinguishing the cloud thermodynamic phase. For liquid clouds in 2008, isocontours of the ensemble mean of σPO2 by class of COT and H, as shown in Fig. 11, are very close to those obtained from simulations (Fig. 5a). When τ ≥ 10, the ensemble mean of σPO2 appears thus highly correlated with the cloud macrophysical parameter H.
If we plot, as in Fig. 12 with gray shades for symbols and lines, the average σPO2 for 25 bins of geometrical thickness H for liquid cloud with τ ≥ 10, we find that the one-to-one monotonic relation between σPO2 and H is close to linear, which again is consistent with Eq. (2) from van de Hulst (1980) and simulation results (Fig. 5b). The red dashed line in Fig. 12 fits the relationship well until around 9000 m. The slope of this linear regression is ∼3.2 hPa km−1 (or conversely 311 m hPa−1). This average experimental slope is within the range 2.9–7.2 hPa km−1 obtained from simulations. The slope seems locally higher for low H (1000–4000 m) and lower above (6000–8000 m), which confirms the dependence of the slope on CTP as discussed in section 2.
For ice clouds with τ ≥ 5 (black dots and lines in Fig. 12), the relation is also close to linear for H higher than 6 km and smaller than 13 km with the weakest positive slope. However, for H < 5 km, σPO2 for ice clouds seems to be decreasing as H increases, which describes a novel dependence that simulations did not predict at all. It is a challenge to explain this anticorrelation. We suspect that this strong effect of the cloud thermodynamic phase on the σPO2–H relation is quite fundamental. It may give insight into cloud-ice vertical structures and microphysics.
For liquid clouds, the linearity of the relation σPO2–H appears to be robust. Estimation of H from σPO2 is therefore possible from the fit between the ensemble average of σPO2 and the geometrical thickness. This technique was tested using a cubic fit of the relation σPO2–H for liquid clouds with τ ≥ 10 (as shown by the green dashed curve in Fig. 12), and cloud geometrical thickness was thus inverted for each datum. The resulting ensemble mean bias for 2008 between the inverted geometrical thickness Hinv and H is given in absolute and relative values, respectively, in Figs. 13a and 13b. These figures show that the difference Hinv − H is on average mostly between −200 and +200 m. The relative bias is mostly smaller than 10% for clouds with H ≥ 1500 m.
4. Conclusions about POLDER/PARASOL product improvement and a new remote sensing strategy
We propose here a new and original way to characterize cloud structures from multidirectional measurements in the oxygen A band. It originates from simulations of photon transport within clouds, of POLDER signals in the oxygen A band, and of the POLDER cloud oxygen pressure product. A new and extensive intercomparison of data from A-Train measurements confirmed the potential of this approach. The improved use of POLDER measurements in the A band to characterize cloud structures is based on the following idea: the omission of oxygen absorption along photon pathlength within a cloud layer—a fundamental hypothesis of the POLDER PO2 algorithm—is not a weakness and can be exploited:
For a set of parameters (solar and viewing zenith angle and cloud optical thickness), the vertically equivalent photon pathlength within the cloud layer—called here photon penetration—is close to one-half of the cloud geometrical thickness H; a new piece of information about cloud is thus possibly reachable—that is, POLDER PO2 may provide the pressure at the geometrical middle of a cloud layer (MCP).
The differential photon penetration within cloud as a function of zenithal viewing angle leads to information about cloud macrophysics carried by PO2 variability: angular standard deviation σPO2 is potentially very strongly correlated with cloud geometrical thickness.
Validation of the information content of POLDER measurements in the A band has been possible as a result of the collocated and quasi-simultaneous observations from POLDER-3/PARASOL and those from the active sensors CPR/CloudSat and CALIOP/CALIPSO within the A-Train. True cloud altitude and geometrical thickness were obtained from the two active sensors through the combined CloudSat/CALIPSO 2B-GEOPROF-Lidar product. Aqua/MODIS data were also collected to reinforce the POLDER cloud thermodynamic phase detection, which was shown to be fundamental in this study.
Data analysis over the whole year of 2008 confirms that POLDER cloud pressure PO2 is on average close to the pressure at the geometrical middle of monolayer clouds under the CloudSat/CALIPSO track. Deviation PO2 − MCP is mainly caused by a dependence in cloud optical thickness that can be strong for ice clouds. It was demonstrated that, cloud thermodynamic phase function being considered, a correction of this dependence is possible and leads to an improved PO2 product that is statistically closer to MCP. A second-order correction in cloud top was simulated that may improve further the significance of PO2. Use of additional available data like POLDER Rayleigh pressure or the next version of MODIS CTP as a CTP proxy shall be investigated in the future.
We also studied, for the same dataset, the relation between the angular standard deviation σPO2—POLDER level-2 product—and the geometrical thickness H of monolayer clouds. In the case of liquid clouds, we found a statistically significant correlation between σPO2 and H for clouds having τ ≥ 10. A fit of the almost linear relation H = f (σPO2) for these liquid clouds, consistent with simulation results, leads to an estimate Hinv of H from σPO2. The mean differences Hinv − H for 2008 are mostly confined to the range from −200 to +200 m. For monolayer ice clouds in 2008, the relation σPO2 = f (H) does not follow simulation results, and σPO2 decreases on average as H increases when H ≤ 6 km, while a linear behavior is again observable for thicker ice clouds.
There are numerous applications for global cloud-top altitude and cloud geometrical thickness retrievals from a passive technology. Based on an original idea, the study presented here opens the path to numerous developments and certainly new remote sensing strategies that would exploit multidirectional measurements in gas absorption bands. Although we exploited here actual POLDER cloud oxygen pressure level-2 products that might be improved, we obtained for a whole year interesting statistical correlations among the POLDER oxygen pressure products, MCP, and H.
Perspectives for an improved exploitation of POLDER measurements are 1) questioning the choice of the least-biased viewing angle to get cloud apparent pressure against the present angular averaging, 2) accounting for more parameters (CTP, θsun, etc.) to define the relation between σPO2 and H, 3) defining an iterative or cross-validation process for the estimates of CTP, MCP, and H from PO2 and σPO2, with possibly additional data used as a CTP proxy, 4) studying the climatological behavior of σPO2 versus H: accounting for scene geography (land/ocean and latitude) and, more generally, for spatial and temporal variabilities of σPO2 = f (H) may certainly lead to a better estimate of H—from local or conditioned statistics—and its climatological behavior, and 5) understanding the dependence of POLDER PO2 products on cloud parameters for ice clouds.
For this approach to be applied operationally, an important question is the identification of cloud monolayered scenes under the POLDER swath. If every cloud scene is considered to be single layered, an “effective” middle-of-cloud pressure and geometrical thickness might be provided, but the relevance of such an effective product would need to be addressed. Another solution is to find a way to distinguish monolayered versus multilayered cloudy atmosphere. The use of the MODIS multilayer flag product (Wind et al. 2010) could be a good track to follow. POLDER measurements alone could also help. Current research indeed suggests that σPO2 is sensitive to the multilayered features of cloud structures.
This study has been financed through grants from the French research CNRS program Programme National de Télédétection Spatiale (PNTS) and the CNES program Terre, Océan, Surfaces Continentales, Atmosphère (TOSCA). CALIOP-collocated PARASOL and MODIS data were provided in digest form by the ICARE Thematic Center (Université Lille 1; http://www.icare.univ-lille1.fr/) through the MULTI_SENSOR data project. We thank the CloudSat Data Processing Center (Colorado State University Cooperative Institute for Research in the Atmosphere; http://www.cloudsat.cira.colostate.edu/) for providing the CloudSat 2B-GEOPROF-Lidar data.
Corresponding author address: Nicolas Ferlay, Laboratoire d’Optique Atmosphérique, UFR de Physique, Université Lille 1, Sciences et Technologies, Villeneuve d’Ascq, 59655 CEDEX, France. Email: firstname.lastname@example.org
This captures the fact that, after a scattering event on a cloud particle (1–100 μm in size), radiation at ∼0.76 μm tends to propagate farther into the forward hemisphere rather than into the backward one.
Contrary to global solar illumination, the cosine μ0 of the solar zenith angle is in general not sampled uniformly up to unity by sun-synchronous-orbiting satellites (since equator crossing times differ significantly from local noon/midnight), nor will its distribution be symmetric around its mean, which will be somewhat less than ½. At the same time, most imaging sensors will not take the viewing zenith angle all the way to 90°, and its mean will be significantly larger than ½ (cos 60°, which is near or beyond the edge of even the widest swaths).