# On the Use of CALIPSO Land Surface Returns to Retrieve Aerosol and Cloud Optical Depths

D. Josset, Jacques Pelon, N. Pascal, Y. Hu, W. Hou

► To cite this version:

D. Josset, Jacques Pelon, N. Pascal, Y. Hu, W. Hou. On the Use of CALIPSO Land Surface Returns to Retrieve Aerosol and Cloud Optical Depths. IEEE Transactions on Geoscience and Remote Sensing, 2018, 56 (6), pp.3256 - 3264. 10.1109/TGRS.2018.2796850. insu-01852539

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# On the Use of CALIPSO Land Surface Returns to Retrieve Aerosol and Cloud Optical Depths

D. Josset<sup>D</sup>, J. Pelon, N. Pascal, Y. Hu, and W. Hou

**Abstract**—The quantification of aerosol and cloud radiative properties, optical depth (OD), and phase function is of high importance to quantify the human impact on climate. Several approaches now exist based on both active (lidar) and passive (spectroradiometers) sensors. However, passive space observations over land are hindered by the important contribution of the surface to the total reflectance. Retrievals of OD from backscatter lidars do not face this issue but are usually based on the use of an a priori value of the so-called lidar ratio, which may lead to a significant uncertainty. The objective of this paper is to analyze a possible path for the space borne backscatter lidar onboard the Cloud Aerosol Lidar Pathfinder Observations satellite to overcome those issues. We will discuss the space-borne retrievals of ODs based on the land surface returns, either in combination with the Moderate Resolution Imaging Spectroradiometer or as a stand-alone lidar method. Analyses will be presented for a few cases on different surface types. The different error sources are discussed and further solutions to reduce them are explored. We show that the surface types have different polarization and multispectral properties, which can open new research areas based on space lidars. Using such an approach, we show that a retrieval technique based on the use of lidar land surface returns can be used to directly retrieve OD of aerosols and semitransparent cloud.

**Index Terms**—Aerosols, laser radar, radiometry, surface reflectance.

## I. INTRODUCTION

THE last International Panel on Climate Change [1] mentioned that the “uncertainties in aerosol forcing remain the dominant contributor to the overall uncertainty in net anthropogenic forcing.” Accurate observations of the aerosol radiative properties over ocean, land, and clouds are, therefore, an important step to better understand the associated processes. In previous analyses, we have shown how the lidar of the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations’ (CALIPSO) mission [2], [3] could be used to

Manuscript received March 16, 2017; revised September 8, 2017; accepted December 8, 2017. The work of D. Josset was supported by the NRL Karles Fellowship. (Corresponding author: D. Josset.)

D. Josset and W. Hou are with the U.S. Naval Research Laboratory Stennis Space Center, Stennis Space Center, MS 39529 USA (e-mail: damien.josset@nrlssc.navy.mil; weilin.hou@nrlssc.navy.mil).

J. Pelon is with Université Pierre et Marie Curie/LATMOS/IPSL/CNRS, 75252 Paris, France (e-mail: jacques.pelon@aero.jussieu.fr).

N. Pascal is with the HYGEOS AERIS/ICARE Data and Services Center, 59658 Lille, France (e-mail: nicolas.pascal@icare.univ-lille1.fr).

Y. Hu is with the NASA Langley Research Center, Hampton, VA 23681 USA (e-mail: yongxiang.hu-1@nasa.gov).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2018.2796850

infer accurate aerosol optical depth (AOD) and clouds OD as well as lidar ratio over clouds [4] or over the ocean [5]–[7]. In this paper, we explore complementary promising ways to retrieve OD over land using the land surface reflectance as obtained by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), and with the Moderate Resolution Imaging Spectroradiometer (MODIS) observations. CALIOP version 4 data are of much better quality than version 2 and it allows us to go beyond the preliminary work we conducted on the topic [8], [9]. The first approach consists in taking advantage of the orbital characteristics of the A-Train to infer the AOD difference between two collocated tracks. The second approach relies on the use of the CALIOP visible (0.5 µm) and MODIS visible (0.5 µm) or infrared (2.13 µm) channels to obtain a nonattenuated reference for the lidar (0.5 µm) surface signal. The third approach we present is based on the lidar vertical information, which is used to determine clear air pixels and create a lidar land surface reflectance map. Comparisons with the MODIS AOD retrievals at 550 nm are presented for several case studies. Even if further work is needed to reach an operational implementation, this paper shows that AOD and cloud OD retrieval using the land surface returns from a space lidar should be seriously considered. This has important applications to better determine aerosol and clouds’ radiative properties [5], [6] as well as the vertical profiles of extinction and heating rates, even for high latitudes and nighttime observations.

In the first part, we will describe the methods used and the expected error sources. We will then illustrate the results obtained on the AOD using the three retrieval methods on a few case studies. We will end with different perspectives associated with this paper.

## II. GENERAL PRINCIPLE

The lidar equation links the power received by the telescope to the backscattered coefficient $\beta_{AL}$ (m$^{-1}$ · sr$^{-1}$) at altitude $z(m)$ and the atmospheric transmittance $T_{AL}$, subscript A for atmosphere, and L for lidar. After the calibration procedure, the attenuated backscattered coefficient $\beta_{att}$ (m$^{-1}$ · sr$^{-1}$) is the quantity directly measured by a backscatter lidar

$$ \beta_{att}(z) = \beta_{AL}(z)T_{AL}^2(z). \quad (1) $$

The integration of this quantity at the surface level relates directly to the surface bidirectional reflectance distribution function $\rho_{BRDF}$ [10], [11]. The lidar integrated attenuated
backscatter coefficient $\gamma$ (sr$^{-1}$) is equal to

$$ \gamma = \frac{\rho_{\text{BRDF}}(\theta, x, y, t)}{\pi} \cos(\theta) T_{\text{AL}}^2. \quad (2) $$

The off-zenith angle is noted $\theta$ (radians). The cosine term is close to 1 for nadir observation and will be further neglected. $\rho_{\text{BRDF}}$ considers directionality effects. It is constant for a Lambertian surface, but in general, for land surface and a monostatic lidar system, it will show the opposition effect as for any instrument with a similar geometry [12]. The opposition effect is the large surge in the brightness of the surface in the backscatter direction. It is not only a function of geometry but also a function of longitude $x$, latitude $y$, and time $t$, as it will vary with the roughness of the surface.

This effect was first described in terms of shadowing [13]–[15]. More recent theoretical works suggest that coherent scattering is a possible explanation of this effect [16], [17] even if shielding of particles by each other still has to be considered for a complete solution [18].

For this paper, the lidar integrated attenuated backscatter at the surface level will be noted $\gamma_{\text{SL}}$ (in sr$^{-1}$, with subscript S for surface and L for lidar)

$$ \gamma_{\text{SL}} = F_L(x, y, t) \rho_{\text{BRDF}}^* (\theta, x, y, t) T_{\text{AL}}^2 (\theta, x, y, t). \quad (3) $$

The term $F_L$ considers the instrumental and algorithm imperfections. It includes errors due to lidar calibration and surface signal saturation. $\rho_{\text{BRDF}}^*$ is defined as equal to $\rho_{\text{BRDF}}/\pi$. Both surface reflectance and aerosol atmospheric content are considered a function of time. Aerosol load varies with the anthropogenic emissions and transport. Land surface reflectance is affected by the growth of vegetation, surface erosion, and deposition. This variability impacts the lidar signal.

From (3), usable at all lidar wavelengths, and the knowledge of the surface reflectance, one can derive the aerosol OD as

$$ \tau_{\text{AL}} = -\frac{1}{2} \ln \left[ \gamma_{\text{SL}} / \left( F_L \cdot \rho_{\text{BRDF}}^* \right) \right] \quad (4) $$

and when the correlation coefficients between the different terms can be neglected [6], the associated uncertainty can be written as

$$ \delta\tau_{\text{AL}} = \frac{1}{2} \sqrt{ \left( \frac{\delta F_L}{F_L} \right)^2 + \left( \frac{\delta\rho_{\text{BRDF}}}{\rho_{\text{BRDF}}} \right)^2 + \left( \frac{\delta\gamma_{\text{SL}}}{\gamma_{\text{SL}}} \right)^2 } . \quad (5) $$

The two first terms $\delta F_{LR}$ and $\delta\rho_{\text{BRDF}}$ are the relative error on lidar calibration and on the retrieved reflectance, leading typically to biases, whereas the third term contributes more to the random errors in the retrieval. We will now review three different methods to retrieve the land surface $\rho_{\text{BRDF}}$.

In terms of algorithm implementation, a key component is the detection of the surface. In this paper, it is determined by the lidar signal maximum if it is located 300 m above or below the digital elevation model (DEM) altitude. Otherwise, the DEM itself is used. This procedure compensates for small DEM inaccuracies and gets rid of most dense atmospheric layers that could be mistaken as surface return. The boundaries used to obtain the lidar integrated attenuated backscatter coefficient are the lidar signal 60 m above and 240 m below the surface level.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Difference of colocation between two tracks spaced by 16 days near the equator. The data are taken around 1800TU. Black dotted line: August 6, 2006. Red solid line: August 22, 2006.</figcaption></figure>

The data used in this paper are CALIPSO Level 1 version 4, AQUA MODIS collection 5 level 1 data 500 m aggregated on 1-km reflectance (MYD021KM) for bands 4 (0.55 µm) and 7 (2.13 µm) and directly 1 km for band 11 (0.53 µm). We also used MODIS level 2 atmospheric product for the optical thickness (MYD04).

### III. METHODOLOGY DESCRIPTION

The developments of MODIS aerosol algorithm [19] are showing different paths to retrieve the aerosol optical properties over land. The first method consisted in making the difference of collocated observations from two satellite overpasses so the aerosol OD difference can be measured. The second method is based on the radiance at 2130 nm as a reference over land, as this channel is very weakly attenuated by aerosols. The goal of the third method is to find the observations with the lowest aerosol load at a given location in order to determine the reflectance reference value. We applied these three methods to lidar remote sensing.

#### A. First Method: 16-Day Track Difference

CALIPSO is sampling the same track every 16 days. With an identical surface reflectance, the optical thickness change derived from the application of (4) between two tracks can be written as

$$ \Delta\tau_{\text{AL}} = \frac{1}{2} \Delta \ln(\gamma_{\text{SL}}). \quad (6) $$

A long enough data set would allow one to accurately determine the surface reflectance by sampling the clearest conditions.

A source of uncertainty in this methodology is linked to the reflectance variations between the observation and reference tracks due to the nonperfect colocation and/or time variation. We report in Fig. 1 the laser footprint trajectory for two collocated tracks separated by 16 days. One can see that the distance between these two tracks is around 0.006° (around 660 m), which is larger than the footprint size (diameter around 70 m). This distance is not constant and the track of the 8th and 24th August in the same area is spaced by around 0.002° (about 200 m). This spatial distance and
<figure><img src="image_3.png" /><figcaption>Fig. 2. OD difference between the two tracks in Fig. 1 (August 6, 2006 and August 22, 2006) over the Amazonian forest. There is a high correlation between MODIS and CALIPSO data.</figcaption></figure>

the time difference will induce some variability in the surface reflectance on the two tracks, which will limit the accuracy of this method, especially for surfaces with a high level of spatial variability. To overcome this issue, a high level of spatial but also temporal trajectory control of the space platform would be needed, as each laser shots are separated by 330 m.

We reported in Fig. 2 the AOD difference between two collocated tracks as retrieved from CALIPSO surface return and MODIS (5 km average for CALIPSO data). For the data shown in Fig. 2, the average of the difference with MODIS is 0.0085 and the standard deviation is 0.0350. The difference is reasonably low considering the expected accuracy of MODIS [20], [21] and CALIOP [22], but the detailed uncertainty budget of this comparison is difficult to achieve, as four granules based on two very different retrievals are involved. The high correlation (0.85) is promising for such a simple method and the investigation of the other methodologies will provide a deeper insight into the individual sources of uncertainty.

## B. Second Method: MODIS Reflectance Channel as a Reference

Another way suggested by the MODIS aerosol algorithm [19] is to use the radiance at 2130 nm as a reference over land as this channel is very weakly attenuated by aerosols [23], except for those containing large size particles [20]. We expect this statement to hold true for lidar remote sensing as in the presence of aerosols, the lidar backscatter decreases as the wavelength increases [24]. The underlying assumption of this methodology is that once the visible CALIOP reflectance has been normalized to the MODIS infrared radiance, the relative variations of the surface reflectance are partially corrected. The corresponding equation would be

$$-\frac{1}{2} \ln \left( \frac{F_L \rho_{SL}}{R_{\text{MODIS},\lambda}} T_{\text{AL}}^2 \right) = A\tau + B \quad (7)$$

where A and B are assumed to be constant. The difference with MODIS methodology is one would have to calculate the opposition effect associated with CALIOP measurements, which will change depending on the surface type [25]. Another obvious weakness to consider is the refractive index variation

<figure><img src="image_4.png" /><figcaption>Fig. 3. (a) CALIPSO quicklook (logarithm of attenuated backscatter coefficient) for August 24, 2006 1800TU showing a smoke layer over the Amazonian forest. (b) MODIS visible image (RGB) at the same time, the solid line is the CALIPSO track. (c) CALIOP AOD as a function of latitude using MODIS bands 4, 7, and 11 as a reference for CALIOP surface reflectance and MODIS MYD04 product (red dots). (d) (Half logarithm) ratio of CALIPSO 532-nm surface return and the MODIS band 11 (526–536 nm) channel (corrected from cosine of zenith angle and divided by $\pi$) as a function of MODIS aerosol OD (MYD04, 550 nm). The 1:1 slope is shown (black solid line) for reference. Larger values retrieved near 17S in (c) are circled in (d).</figcaption></figure>

between infrared and visible. To understand the advantage of the different wavelengths (aerosol contamination versus refractive index change), we used MODIS channels 4, 7, and 11 (respectively, 0.55, 2.13, and 0.53 $\mu$m).

We illustrate the application of this method on a case of biomass burning plume, optically thick enough to almost fully attenuate the surface return, as we can see in Fig. 3(a). It is a daytime granule, August 24, 2006 1800TU during a fire event over the Amazonian forest, as can be seen on the MODIS visible image [see Fig. 3(b)]. Fig. 3(d) represents the half logarithm ratio of the lidar $\gamma_{SL}$ to the MODIS level 1 reflectance $R_{\text{MODIS},\lambda}$ (corrected from cosine of zenith angle and divided by $\pi$) as a function of MODIS 550-nm aerosol optical thickness for this track between 20S and 5S. Fig. 3(c) represents the same quantities as a function of the latitude. Fig. 3(c) and (d) shows that there is a relatively good correlation between the ratio of CALIPSO/MODIS and MODIS AOD at 550 nm equal to 0.73, 0.64, and 0.76 for bands 4, 7, and 11, respectively. However, we find in (7) coefficients A equal to 0.65, 0.67, and 0.63 and B equal to 0.24, 0.39, and 0.23, which is far from the 1:1 slope. The low correlation is because of the AOD values higher for CALIPSO than for MODIS between 15S and 17S.

This difference is related to the DEM inaccuracies shown in Fig. 4 (between 17.5S and 15S), which are not corrected by our method when the error is larger than 300 m. This methodology requires an accurate determination of surface elevation.

An alternative to overcome the inaccuracies of the DEM is to use the maximum of the lidar signal. As we can see in Fig. 5,
<figure><img src="image_5.png" /><figcaption>Fig. 4. Same as Fig. 3(a) but limited to the 20S–15S area. Blue dots: DEM value. Red line: surface return from the lidar. As we can see, there is a large discrepancy between the DEM value and the altitude of the surface return north of 17.5S.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Same as Fig. 3(c) and (d) but using the maximum of the lidar signal instead of the DEM information. The anomalous variations observed in Fig. 3(c) have been eliminated.</figcaption></figure>

this removes the high apparent optical thickness between 15S and 17S. The correlation coefficient increase significantly to 0.87, 0.78, and 0.90 for bands 4, 7, and 11, respectively. The corresponding values are 0.98, 1.06, and 0.93 for A and 0.11, 0.30, and 0.09 for B.

The limitation of this approach is obvious as for high optical thickness, the maximum of the lidar signal will not be on the surface but in the aerosol layer. This explains why the maximum of aerosol OD around 12S is reduced between Figs. 3 and 5.

The difference of reflectance and opposition effect between MODIS and CALIPSO vary with the surface characteristics (chemical composition and roughness). Interestingly, the lower level of correlation occurs when the 2130-nm band is used, which implies that for this case, refractive index difference is a more important error source than aerosol contamination. The high correlation we found with MODIS retrieval [see Fig. 3(d)] seems promising, but we expect that the methodology would have to be calibrated on different surfaces to determine A and B values. A small-scale analysis in the presence of known surface types would allow to better understand the uncertainty associated with this method. This work would probably require dedicated field measurements related to land surface and atmospheric data. Such an effort is far beyond the scope of this paper. However, Section III-C will provide elements of answers concerning the surface properties relevant to a space backscatter lidar.

<figure><img src="image_7.png" /><figcaption>Fig. 6. CALIPSO land surface reflectance mapping (integrated attenuated backscatter coefficient $\gamma_{SL}$ in sr$^{-1}$) at 532 nm using the vertical information to choose clearest profile ($\gamma_{atm} < 0.01$ sr$^{-1}$) for CALIPSO nighttime observations of August 2006. A monthly average allows to map most of the continental surface.</figcaption></figure>

### C. Third Method: Low-Resolution Land Surface Mapping

In the first method, we presented the two tracks that are not exactly collocated. In the second method, the opposition effect, or more generally the difference of geometry between passive and active sensors, has to be considered. An alternative to overcome these issues is to use an average of the lidar surface reflectance at a coarser spatial resolution than the distance between two tracks. The variance of the surface signal along the track provides a metric of the surface reflectance variability (and associated uncertainty). In this methodology, there is a balance to find between spatial scale chosen for the map and spatial surface heterogeneity as well as surface temporal variations. In other words, using a coarser spatial scale allows to reduce the time scale of surface mapping. We can select only the clearest conditions based on CALIOP atmospheric profiles to create a land surface reference to retrieve aerosol optical thickness. The advantages and limitations of this method will be discussed in Section IV.

To map the land surface reflectance, we are using here one month of nighttime CALIPSO observations (August 2006), which can then be used as a reference for daytime retrievals. As the space between two noncollocated tracks is around 170 km at tropical latitudes and we are aiming to use nighttime data as a reference for daytime aerosol retrieval, we are using a 1° × 1° average, as location of daytime observation cannot be more than 85 km away than the closest nighttime observation.

Clearest conditions are determined by a threshold value of atmospheric integrated backscatter coefficient, $\gamma_{atm} < 0.01$ sr$^{-1}$. Both atmospheric profiles used to retrieve clearest conditions and lidar surface returns are averaged on a 5-km resolution grid, prior to the land surface mapping process, to increase the signal-to-noise ratio and lower aerosol contamination. The lidar shots hitting surfaces, which IGBP classifies as water, have been excluded from the mapping process.

Fig. 6 shows the land surface reflectance map at 532 nm (total return) as retrieved by this procedure. Interestingly,
<figure><img src="image_8.png" /><figcaption>Fig. 7. (Top) Ratio of CALIPSO 532-nm perpendicular channel to the total channel (depolarization). (Bottom) Ratio of CALIPSO 1064- and 532-nm channels (color ratio).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8. (Top) Color ratio occurrences for different surface returns as a function of their IGBP classification (five subtypes shown). (Bottom) Same as top but for the depolarization.</figcaption></figure>

the values of the lidar return over land and ocean seem to be similar. The ocean surface return typically ranges between 0.03 and 0.06 sr⁻¹ (see [5, Fig. 1]). However, these values seem to be lower than previous estimations based on radiometry [25]. It would be interesting to investigate this matter and to better understand if this similarity is a real geophysical feature or if F_L (x, y, t) [see (3)] is significantly lower than 1. A possible step forward would be to compare these maps of land surface reflectance, either to global scale measurement of the BRDF based on an instrument like POLDER or to perform dedicated airborne field measurement. The surface spatial and temporal heterogeneity are dependent on the averaging scale selected for the surface mapping. Its variance provides an uncertainty estimate of the calculated AOD. In terms of temporal variations, the median reflectance for the whole map (532 nm) shown in Fig. 6 is 0.041 sr⁻¹ for August 2006 and 2007. The values are between 0.036 and 0.038 sr⁻¹ for August 2008–2013. The difference is expected to come from the change of off-nadir angle in November 2007 (from 0.3° to 3°) and how it relates to the BRDF. Although the change is important enough to be mentioned, we do not expect the change to impact the methods discussed in this paper.

Interestingly, the variances of the reflectance are relatively stable with time. Between 2006 and 2013, analyses for the month of August provide a range of median variances of the reflectance between 8.6 × 10⁻⁴ and 9.7 × 10⁻⁴ sr⁻² after removing the values over Antarctica, where the lidar partial saturation and water/ice transition would require a

dedicated investigation. There is no clear variation after the change of off-nadir angle. MODIS AOD uncertainty is approximately 0.08 for a mean value of 0.2 and a 10 km averaging [20], [21]. Preliminary results [8] were suggesting that the variance of the land surface reflectance leads to an AOD uncertainty lower than this value. Until more research has been conducted to determine the value of F_L (x, y, t), it is difficult to confirm these results and accurately use (5) to derive the AOD uncertainty budget. Additionally, we expect the AOD uncertainty to vary as a function of the place, year, and season as the surface cover changes. An optimal resolution and sampling strategy would have to be explored more thoroughly in order to minimize the AOD uncertainty.

In order to better understand land surface characteristics as seen by the space lidar, we also investigated the land surface mapping of the other channels. The land surface depolarization ratio at 532 nm is shown in Fig. 7 (top) as well as the 1064- to 532-nm lidar surface signal ratio (bottom). These depolarization and color ratios give an indication of the land surface type. For example, as we can see, the Andes mountains show a lower color ratio than any other part of South America. Sahara shows the larger depolarization values for desert areas. As expected larger, color ratios are observed over dense forests.

Fig. 8 shows how lidar color and depolarization ratios correlate to IGBP classification. There is definitely a signature that allows to discriminate between different surface types. It is especially true for water body and ice/snow. We can
<figure><img src="image_10.png" /><figcaption>Fig. 9. Aerosol optical thickness retrieval with CALIPSO 532 nm (blue circle) using the land surface mapping as compared with MODIS product at 550 nm (red dots). (Left) North East China, East Russia August 26, 2006 0437TU. (Right) August 27, 2006 1155TU South Africa.</figcaption></figure>

see some secondary maxima in the distributions, which could indicate that the surface type has more the characteristics of another IGBP classification. Although evergreen needleleaf and broadleaf show similar depolarization ratios, they differ significantly in terms of color ratio. It is interesting to see such features and it opens important perspectives of research to classify surface types with a simple backscatter lidar.

Note that what we refer to as IGBP misclassifications could be an intrinsic limitation related to time varying effects (erosion, vegetation growth, decay, and so on) that are not in the fixed IGBP data but that will be in the space lidar surface return. The IGBP surface types reported in the CALIPSO data set are the same as those used in the CERES/SARB surface map, which has a resolution of 10 × 10 (around 18.5 × 18.5 km resolution at the equator). However, we expect that this resolution does not reflect on the space lidar capabilities. Considering that the CALIPSO algorithm can classify atmospheric features at the shot to shot and 5-km scale, we would expect that the improvement of classification of the land surface type by lidar could be achieved at these resolutions as the signal-to-noise ratio is higher.

If we note the map reference reflectance $γ_{SL0} = F_L$. $ρ_{BRDF}$, the total column aerosol optical thickness retrieval $τ_{AL}$ can be simply written as

$$τ_{AL} = \frac{1}{2} \ln(γ_{SL} / γ_{SL0}). \qquad (8)$$

Two examples of AOD retrieval over two different areas are reported in Fig. 9. The first one is over the North East of China/East Russia on August 26, 2006 around 0437 UTC. The second one is over South Africa on August 27, 2006 around 1155 UTC. The integrated values of the surface return $γ_{SL}$ were calculated using daytime CALIPSO L1 data for August 2006. One can see in Fig. 9 that like the other methods, the AOD agreement is relatively good.

The average difference in AOD with respect to MODIS is 0.021 (0.009) for the 26th (27th), which would indicate a relatively good self-calibration of this methodology with an absence of bias but local differences remain. The standard deviation is high 0.16 (0.12) and the correlation is quite variable 0.49 (0.82) in those two cases, which is consistent with a crude handling of surface reflectance variability.

<figure><img src="image_11.png" /><figcaption>Fig. 10. Same as Fig. 6 for the ratio of the MODIS observations at 2.13 and 0.53 µm during daytime on clearest conditions determined by the collocated lidar data ($γ_{atm} < 0.01$ sr$^{-1}$).</figcaption></figure>

## IV. SOURCES OF UNCERTAINTY DISCUSSION

### A. Surface Reflectance (Real and Apparent) Properties

The opposition effect as well as the spatial and temporal land reflectance variations will affect the accuracy of the retrieval. The different methodologies we have presented handle this error source differently.

The use of two collocated tracks considers the opposition effect but poorly deals with track to track and 16-day temporal variability.

The advantage of the second method based on MODIS reflectance data is to overcome issues related to the land surface spatial and temporal variations, as the lidar and radiometer signals are totally collocated. However, to fully estimate the uncertainty of this method, it is needed to have a precise knowledge of the surface bidirectional reflectance to characterize the opposition effect. A direct comparison of MODIS and POLDER would offer some insights even if it would require to analyze a high number of occurrences. It would also have the advantage to provide information about the BRDF linear polarization.

The reflectance variation between 532 and 2130 nm is dependent on the surface type. To characterize this source of uncertainty, we used daytime collocated CALIPSO (shot to shot) and MODIS data to obtain the ratio of MODIS-to-MODIS reflectance ratio at 2130 and 530 nm on clearest conditions determined by the lidar ($γ_{atm} < 0.01$ sr$^{-1}$ using a 5-km average basis). Fig. 10 shows important variations of
such a reflectance ratio within those categories on this map, which seems to be at least qualitatively related to surface types. The ratio over the Australian deserts is much higher than that over the Amazonian rainforest and the ratio on the western part or the United States is much higher than that on the eastern part, which receives much more annual precipitation. A dedicated mesoscale characterization of land surface would be useful to improve the accuracy of the AOD retrievals performed with this method. This may already exist to some extent in current models and this will be subject of future discussions with modelers and a dedicated investigation.

Land surface mapping error sources are similar to the
difference track methods, but in order to obtain an absolute
calibration of the OD, it relies on a different temporal and
spatial variability. The associated variance has been discussed
in Section III-C. In addition, the reference can be biased if
nonclear air is classified as clear air. The mean aerosol optical
thickness over land is estimated to be around 0.2 [20], and
we would expect this value to represent an upper boundary
of the error that occurs in that case as the CALIOP vertical
profile should mitigate this error source significantly. There
are several ways to reduce this error. The first one would
simply be to reduce the threshold of clear air integrated
backscatter coefficient. Another way is to use several measure-
ments over the same surface and analyze the trend of surface
reflectance with aerosol load estimated from the lidar vertical
information.

B. Lidar Calibration

The lidar calibration uncertainty for each profile impacts
directly the OD retrievals. The lidar calibration error in
CALIPSO versions 1, 2, and 3 data was a slow seasonal
calibration shift [26], [27] function of the relative position
of the sun and satellite orbit. The calibration improvements
related to CALIPSO version 4 data are designed to address
this issue and we do not expect this error source to have a
noticeable impact on the results presented here. This statement
is validated by internal NASA analysis and research papers
presenting these results will be submitted to the peer review
process in the near future.

C. Lidar Saturation

The evidence of saturation of the CALIOP signal has been
suspected for some time over the ocean [5]. Internal analysis
within the CALIPSO team confirmed it to occur on most dense
medium through the analysis of the low-level instrumental
flags. This leads to the addition of a saturation flag into the
version 4 data. However, due to the data averaging process
onboard the platform and the complexity of the saturation
flag algorithm, the data in its current state mostly provide
information about the signal strength within the atmospheric
column. This implies false positives due to liquid water clouds
and a loss of correlation between the low-level instrumental
information and the final flag, which is especially pronounced
for the "possibly saturated" value.

In general, there is a low level of understanding on how
saturation manifests itself in the lidar surface return. For the

specificities of the CALIOP instrument, saturation manifests
itself as a loss of linearity in the surface return. It is quite
different from the saturation of a camera pixel, where all the
information related to the saturated pixel is lost. This loss of
linearity is not quantified as of today.

If the saturation flag is used as a filter of the data analysis
shown in Fig. 2, the correlation coefficient increases slightly
around 0.87 if we remove either “certainly saturated” or both
“certainly and possibly saturated.” If only “certainly saturated”
is removed, it filters out the area where a low number of
MODIS observations exist (around 28S) and the average of
the difference with MODIS is lowered slightly to 0.0066 and
the standard deviation to 0.0305. When we remove both
“certainly and possibly saturated,” then the results are biased
low with respect to MODIS with an average of the difference
of 0.0249 and a standard deviation of 0.0321. Consider-
ing the novelty of the approach we propose, the difference
with MODIS can be considered insignificant (within MODIS
uncertainty), but the shift is qualitatively interesting. It is
counterintuitive, but removing the data classified as saturated
by the flag can have a similar impact as an increase of
saturation. It is because saturation lowers the value of the
surface return (it creates a low bias in the OD) and remov-
ing the highest value of the surface return has a similar
effect.

For the data used to present the second method (see Fig. 3),
removing the data flagged as both “possibly” and “certainly”
saturated (or only “certainly” saturated) improves slightly the
value of the correlation coefficient to 0.78 (0.78), 0.71 (0.70),
and 0.81 (0.80) for bands 4, 7, and 11, respectively. The A/B
coefficients get closer to the 1:1 line (0.72/0.12, 0.78/0.25,
and 0.68/0.12 for the three MODIS bands). For the data
used in Fig. 5, the use of the saturation flag has no effect
within the limit of the significant figures we used. It is
because the number of shots classified as saturated is not
insignificant (8.5% “possibly saturated” and 2% “certainly
saturated”) and they are mostly present over the mountain area,
where the algorithm has difficulties to find the surface level.
Basically, the use of the saturation flag removes areas, where
the algorithm fails to detect the surface level correctly, but the
impact of saturation itself is nonexistent with respect to the
other error sources.

The intent of a quality flag is to improve the retrieval,
so it could be more fruitful to use it as a guide to correct
the signal from its partial saturation (i.e., “repair” saturated
shots). Currently, there are a few paths that could be explored
to achieve this goal. As the perpendicular 532-nm channel
saturates much less than the total channel, it could be used
to estimate the attenuation of the perpendicular channel in
a similar way as we have presented in method 3. This will
provide an estimate on how saturation biases the total channel
reference. Alternatively, research conducted by the CALIPSO
team seems to indicate that the transient response of the
detector (tail of the signal) could also be used to recreate
the nonsaturated surface return as the “tail-to-peak ratio” is
a constant in the absence of saturation [28]. Furthermore, an
evaluation is possible using comparisons with MODIS surface
reflectance as presented here in method 2.
## D. Surface Detection

All methods may suffer from an uncertainty related to the surface altitude inaccuracy of the DEM. More generally, the method fails when the surface level is not estimated accurately. This appears clearly in the example shown in method 2 and is likely to contaminate the reference maps of method 3. It is the primary uncertainty driver at this stage of this paper, because it negates the fundamental assumption of these methods, which is that we are using the lidar surface return. Improving this part is a mandatory next step, as it creates an ambiguity that prevents us from discriminating accurately between the different error sources present in method 3. For example, we cannot statistically quantify to which extent the surface detection fails on a saturated surface as we discussed in one of the cases studied in Section III-B. To improve surface characterization, a refined DEM (from the CloudSat team) has been used in CALIPSO V4, and a more sensitive scheme used for lidar return detection. Further improvements can be made. Surface detection has to work when the surface return is extremely weak making it difficult to develop a stand-alone lidar algorithm. There are possibilities based on the high number of observations available, altitude models, and other A-Train platforms. The range resolved, multiwavelength depolarization capacity of CALIPSO should also help to discriminate between the real surface return and a dense atmospheric layer like cloud or aerosol.

Although the case studies we showed work relatively well, it is necessary to address this issue before we can fully assess the influence of the other sources through a statistical analysis.

## V. CONCLUSION

The different ways to directly derive aerosol optical thickness over land have been looked at using CALIPSO V4 data. Preliminary results are promising and the ideas used to develop passive algorithms seem to apply well to active remote sensing. It appears that a simple backscatter lidar like the one onboard CALIPSO has the capability to classify different surface types and to identify IGBP misclassification. It could be directly transposed to the analysis of aerosols and semitransparent cloud optical thickness. More research related to the surface detection is necessary to go further. As a second step, a study of land reflectance and opposition effect variability at high spatial resolution will have to be performed to fully assess and improve the accuracy of these methods. Once this is done, it will be straightforward to include retrieval based on polarization and the 1064-nm channel. A study of the opposition effect variability at high spatial resolution is difficult. An airborne lidar campaign can help to map the land surface properties at a higher resolution than space observations but at a smaller geographical scale and dedicated field missions based on lidar and passive instruments would also be helpful. In terms of perspectives, our finding could lead the path to new lidar missions designed to better characterize aerosol, clouds, and surface radiative properties. Our results show that aerosol optical thickness determination over desert is not an intrinsic limitation contrary to passive retrievals. Performing a land surface mapping at global scale would also allow extending previous research [29], [30], which would be helpful to new

developments in the field of greenhouse gas measurements by integrated path lidar. This paper could also raise the awareness of the need for a specific airborne instrument dedicated to study the opposition effect variability at high spatial resolution. Although such an instrument still has to be conceptualized and developed, it could build on previous research and be based on a recently proposed multistatic space lidar system [31].

## ACKNOWLEDGMENT

The authors would like to thank CNES and NASA for data availability. They acknowledge the fruitful collaboration and discussions related to the Interagency Agreement IAA (NASA LaRC/NRL) - RPO201513. They would like to thank CALIPSO and MODIS project and science teams for data treatment and availability, French (http://www.icare.lille-univ.fr) and U.S. (http://www-calipso.larc.nasa.gov and http://cloudsat.cira.colostate.edu) archive centers for CALIPSO and CloudSat Missions for providing the data used in this paper, the AERIS/ICARE Data and Services Center for the collocation of CALIPSO and MODIS data (CALTRACK product), and the Aeris data infrastructure for the data, processing, and development supports.

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D. Josset, photograph and biography not available at the time of publication.

J. Pelon, photograph and biography not available at the time of publication.

N. Pascal, photograph and biography not available at the time of publication.

Y. Hu, photograph and biography not available at the time of publication.

W. Hou, photograph and biography not available at the time of publication.